STUDIES IN MULTIDISCIPLINARITY
VOLUME 3
Multidisciplinary Approaches to Theory in Medicine
S T U D I E S
I N
M U L T I D I S C I P L I N A R I T Y
SERIES EDITORS
Laura A. McNamara Sandia National Laboratories, Albuquerque, New Mexico, USA Mary A. Meyer Los Alamos National Laboratory, Los Alamos, New Mexico, USA Ray Patony The University of Liverpool, Liverpool, UK
On the cover: Cover image caption: A visualisation of ventricular fibrillation. Depolarisation wavefronts are computed in an anisotropic geometrical model of the canine heart, obtained from diffusion tensor imaging, using the Fenton-Karma (1998) equations: see Chapter 21 of this volume. (Fenton, F. & Karma, A. (1998) Vortex dynamics in three-dimensional continuous myocardium with fibre rotation: Filament instability and fibrillation. Chaos 8 20–47).
STUDIES IN MULTIDISCIPLINARITY
VOLUME 3
Multidisciplinary Approaches to Theory in Medicine EDITED BY
Ray Patony The University of Liverpool Liverpool, UK and Laura A. McNamara Sandia National Laboratories Alburquerque, NM, USA
2006
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Series Dedication Studies in Multidisciplinarity is dedicated to the memory of Ray Paton. Sure, he that made us with such large discourse, Looking before and after, gave us not That capability and god-like reason To fust in us unused. – William Shakespeare, Hamlet
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Foreword Gordon Shepherd Department of Neurobiology Yale University School of Medicine
It is a pleasure to open this volume with a few words of praise for its editor, Ray Paton. We became acquainted a number of years ago when Ray contacted me about joining him in the effort to bring together investigators who were developing methods for applying theoretical approaches to biology and medicine. The present volume is a testimony to his vision and persistence. Although younger investigators may take theory in these fields for granted, it was not always so. The magnitude of Ray’s achievement can be appreciated with a brief perspective on where he started. Traditionally, biology and medicine have been driven by inventions of new experimental instruments and methods, as expressed by the byword of the nineteenth century, ‘‘Teknik ist alles’’. While fundamental insights in physics could be obtained by a combination of mathematics and relatively simple mechanical instrumentation until well into the nineteenth century, biology had to wait for the development of a combination of highly sophisticated technical advances in chemistry, optics, and electromagnetism, among others. No real biology could be done until the cell could be seen, no real understanding of the nervous system was possible until electrical activity could be recorded, as occurred in the middle of the nineteenth century. This focus on technique yielded the birth of biologically based medicine, which continued to build into the twentieth century. It was however significant that, from the start, this new field differed from physics in a crucial aspect. Whereas the rise of physics had been driven by a vii
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combination of experiment and theory, biology lacked the kind of theoretical basis that had been essential for physics, as expressed in the well-known observation, ‘‘You can’t understand a fact without a theory’’. This was largely due to the extraordinary complexity of biological phenomena, a complexity that was only magnified by the need in medicine to account for both normal and pathological phenomena. In the twentieth century, theory in biology at first rested on analytical mathematics, such as the models developed by N. Rashevsky in Chicago and A. V. Hill in London. For all their sophistication, these theories had little impact on experimentalists, who by mid-century were engaged in founding what we call modern biology. The cornerstone of course was the identification of DNA in 1953 by Watson and Crick. The fact that this great achievement involved not only the essential experimental evidence but also a theoretical model – an actual palpable three-dimensional model – was not the least reason for the persuasiveness of this new insight into the fundamental nature of biological matter. Even more persuasive as a harbinger of a new marriage between experiment and theory in biology and medicine was the model of Hodgkin and Huxley for the action potential. This has been the foundation for understanding the structure and function of all membrane channels, which are the ubiquitous carriers of ion fluxes that are essential to the functioning of virtually every cell and organ system in the body. Their medical importance multiplies daily with the evidence for genetic disorders that result in channelopathies that affect these functions throughout the body. The lore of the Hodgkin–Huxley model includes the account of how Huxley cranked out the differential equations underlying the action potential on a hand calculator, illustrating the fact that the development of theory is also methods-limited. These limitations were of course overcome with the introduction of the digital computer. This did not happen overnight. For example, many years were required just to get the H–H model into a digital form that could be widely accessed and used. During this time, the revolution in modelling methods took place with the development of the digital computer. The constraints of oversimplified analytical models were replaced by the arbitrary complexity that could be built into numerical representations of biological phenomena and medical applications. Thus, as in the case of experimental biology and clinical medicine, theory also depended on technical breakthroughs. Some of the first numerical models were developed in the 1950s to analyse the passage of radioactively labelled substances injected into humans through the different body compartments – blood, extracellular space, intracellular space, cerebrospinal fluid, etc. This involved generic representations of compartments in terms of capacities and flux rates
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between them. These in turn could be used as the basis for developing other types of compartmental representations, such as the compartmental modelling of the functional properties of neuronal dendritic trees by Wilfrid Rall. Our work on the functional interactions between dendrites had its origins in the Hodgkin–Huxley model for the action potential, and looked forward to the increasing use of models today for analysing dendritic, neuronal and circuit functions in the brain. This software is now easily accessible at websites for NEURON and GENESIS. Establishing modelling as an essential theoretical component to the interpretation and guidance of experimental studies during this time had to overcome often strong opposition from experimentalists, for several reasons. Most experimentalists are convinced they don’t need theory, although all studies are motivated and interpreted within a theoretical framework, whether explicit or not. Many experimentalists who might be interested in applying theory are critical of available models as too simplistic, or too recondite. Many theories that explain the data do not offer hypotheses that can be tested in the real world. And there are often gulfs of communication and terminology between experimentalists and theorists, as well as between those working in different systems. All of this is relevant to understanding the huge challenges that Ray Paton faced as he began the task of encouraging the application of theory to problems in medicine. One of the cardinal aspects of his approach was to base it broadly on bringing people together from many different fields. Thus, he recognised that biology involves many levels of organisation, from molecules and cells to systems and behaviour. He recognised that it involves many disciplines, from molecular biology through the basic sciences to the clinical disciplines. And he recognised that it required bringing people together with these disparate backgrounds and interests, at meetings and in volumes such as this, in order to begin to put together coherent concepts of how the body functions and how medicine can bring modern technical advances to bear on correcting pathologies of body functions. All these qualities were found in the international meetings that he organised over the past more than a decade, and all are on display in this volume. Readers can find here a rich harvest of articles. Topics covered include practical applications of theory to genotypes and phenotypes of disorders of haemoglobin, T cell activation and beyond, vasopressin and homeostasis, cardiac arrhythmias, angiogenesis, and liver fibrosis in biopsy specimens. They include fundamental biological concepts of molecular evolution and its implications for medicine, modelling stochastic neural systems, physiological modelling, systems biology, and tissue as a network. They include theory behind medical imaging. They include new informatics approaches such as advanced data mining and personalised medicine,
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and data mining applied to studies of hepatitis. They include topics in the theoretical basis of medicine itself, such as the basis of medical decision making, what is a medical theory, expert systems, and reliability of measurements. They include moral issues such as medicine and moral epistemology, and hope and despair in tissue engineering. And they include topics in medical education and educational theory. This volume therefore is an excellent representative of Ray Paton’s concept of theory in medicine. It includes the kinds of theories that he wanted to see developed for all aspects of medicine, across the different biological levels, the different technical disciplines, and the different medical fields. It expresses his steady commitment to an integrated approach, bringing together theory and experiment for the benefit of biology and medicine, just as they had and continue to do for physics and chemistry in the preceding century. It is a testament to a loyal friend, warm colleague, skilled theorist, and a true visionary. Gordon M. Shepherd December 15, 2004
Contributors
Alarcon, Tomas – Bioinformatics Unit, Department of Computer Science, University College London, London WC1E 6BT, UK Arber, Werner – Division of Molecular Microbiology, Biozentrum, University of Basel, CH-4056 Basel, Switzerland Aslanidi, Oleg V. – Cardiovascular Research Institute, University of Leeds, Leeds LS2 9JT, UK Baigent, Stephen – Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK Banaji, Murad – Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT, UK Baranzini, Sergio E. – Department of Neurology, University of California at San Francisco, California, USA Biktashev, Vadim N. – Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 3BX, UK Biktasheva, Irina V. – Department of Computer Science, The University of Liverpool, Liverpool L69 3BX, UK Byrne, Helen – Centre for Mathematical Medicine, Division of Applied Mathematics, University of Nottingham, Nottingham NG7 2RD, UK Callard, Robin E. – Immunobiology Unit, Infection and Immunity, Institute of Child Health, University College London, 30 Guilford St., London WC1N 1EH, UK Chan, Cliburn C.T. – Department of Biostatistics and Bioinformatics, Duke University Laboratory of Computational Inmunology, Centre for Bioinformatics and Computational Biology, 106 North Building, Research Drive, Box 90090, Durham NC 27708, USA Clayton, Richard H. – Department of Computer Science, University of Sheffield, Sheffield S1 4DP, UK
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Cohen, Irun R. – The Department of Immunology, The Weizmann Institute of Science, Rehovot 76100, Israel Detours, Vincent – Institute of Interdisciplinary Research, Free University of Brussels, Campus Erasme (CP602), 808 route de Linnik, B-1070 Brussels, Belgium Dioguardi, Nicola – Scientific Direction, Istituto Clinico Humanitas, IRCCS, Rozzano, Milan, Italy and ‘‘M. Rodriguez’’ Foundation – Scientific Institute for Quantitative Measures in Medicine, Milan, Italy Dixit, Narendra M. – Department of Chemical Engineering, Indian Institute of Science, Bangalore, India Downham, David Y. – Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK Dumont, Jacques E. – Institute of Interdisciplinary Research, Free University of Brussels, Campus Erasme (CP602), 808 route de Linnik, B-1070 Brussels, Belgium Efroni, Sol – National Cancer Institute Center for Bioinformatics, Rockville, MD, USA Fioretti, Guido – Department of Quantitative Social and Cognitive Sciences, University of Modena and Reggio Emilia, Italy Fox, John – Cancer Research UK, Advanced Computation Laboratory, 44 Lincoln’s Inn Fields, London WC2A 3PX, UK Fujie, Hajime – Department of Gastroenterology, University of Tokyo Hospital, Tokyo, Japan Glasspool, David – Cancer Research UK, Advanced Computation Laboratory, 44 Lincoln’s Inn Fields, London WC2A 3PX, UK Greller, Larry D. – Biosystemix, Ltd. (RS, LDG), 1090 Cliffside La RR1PO, Sydenham, Ontario K0H 2T0, Canada Haas, Olivier C.L. – Biomedical Engineering Systems Group, Control Theory and Applications Centre, Coventry University, Priory Street, Coventry CV1 5FB, UK Harel, David – The Department of Applied Mathematics and Computer Science, The Wiezmann Insitute of Science, Rehovot 76100, Israel Holden, Arun V. – Cardiovascular Research Institute, University of Leeds, Leeds LS2 9JT, UK Holmba¨ck, Anna Maria – Department of Physical Therapy, Lund University, Lund, Sweden Leinster, Sam – School of Medicine, Health Policy and Practice, University of East Anglia, Norwich NR4 7TJ, UK Leng, Gareth – Centre for Integrative Physiology, College of Medical and Veterinary Sciences, The University of Edinburgh, George Square, Edinburgh EH8 9XD, Scotland, UK
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Lexell, Jan – Department of Physical Therapy and Department of Rehabilitation, Lund University Hospital, Lund, Sweden and Department of Health Sciences, Lulea˚ University of Technology, 971 87 Lulea˚, Sweden Longtin, Andre – Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada Maenhaut, Carine – Institute of Interdisciplinary Research, Free University of Brussels, Campus Erasme (CP602), 808 route de Linnik, B-1070 Brussels, Belgium Maini, Philip – Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK Matsumura, Naohiro – Faculty of Engineering, The University of Tokyo, Tokyo, Japan McMichael, John P. – Management Science Associates, Tarentum, Pennsylvania, USA Mousavi, Parvin – School of Computing, Queen’s University, Kingston, Ontario K7L 3N6, Canada Ohsawa, Yukio – School of Engineering, The University of Tokyo, Tokyo, Japan Okazaki, Naoaki – Faculty of Engineering, The University of Tokyo, Tokyo, Japan Panovska, Jasmina – Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK Perelson, Alan S. – Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Reeves, Colin R. – Biomedical Engineering Systems Group, Control Theory and Applications Centre, Coventry University, Priory Street, Coventry CV1 5FB, UK Ribeiro, Ruy M. – Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Sabatier, Nancy – Centre for Integrative Physiology, College of Medical and Veterinary Sciences, The University of Edinburgh, George Square, Edinburgh EH8 9XD, Scotland, UK Saiura, Akio – Department of Digestive Surgery, Cancer Institute Hospital, Tokyo, Japan Somogyi, Roland – Biosystemix, Ltd. (RS, LDG), 1090 Cliffside La RR1PO, Sydenham, Ontario K0H 2T0, Canada Tauber, Alfred I. – Center for Philosophy and History of Science, Boston University, Boston, MA 02215, USA Thagard, Paul – Philosophy Department, University of Waterloo, Ontario N2L 3G1, Canada Toh, Cheng Hock – Department of Haematology, The University of Liverpool, Liverpool L69 3BX, UK Vertosick, Jr. Frank T. – The Neurosurgery Group, 8 Old Timber Trail, Pittsburgh, PA 15238-2137, USA
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Weatherall, Sir David J. – Weatherall Institute of Molecular Medicine, University of Oxford, John Radcliffe Hospital, Headington, Oxford OX3 9DS, UK Williams, David F. – UK Centre for Tissue Engineering, Division of Clinical Engineering, The University of Liverpool, Daulby Street, Liverpool L69 3GA, UK Wood, Nigel Bruce – Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7 GAZ, UK Xu, Xiao Yun – Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7 GAZ, UK Yates, Andrew J. – Biology Department, Emory University, 1510 Clifton Road, Atlanta, GA 30322, USA
Biographies
Tomas Alarcon received his degree in Theoretical Physics in 1996 and his PhD in Physics in 2000, both from the University of Barcelona. Later he spent three years as postdoctoral fellow at the Center for Mathematical Biology, Oxford, working under the supervision of Philip K Maini (Oxford) and Helen M Byrne (Nottingham). Currently he is a Research Fellow at the Bioinformatics Unit, Department of Computer Science, University College London. Werner Arber received his Diploma in Natural Sciences from the Swiss Polytechnical School in Zu¨rich and completed his doctorate in Biological Sciences at the University of Geneva. Dr. Arber has spent most of his career teaching and conducting research in molecular biology at the Universities of Geneva and Basel in Switzerland, but he has also held postdoctoral research and Visiting Professor positions at the University of Southern California in Los Angeles, at the University of California in Berkeley, at Stanford University and at the MIT in Cambridge, Massachusetts. Dr. Arber is a past President of the International Council for Science (ICSU) and a past member of the Swiss Science Council. His research interests include microbial genetics, horizontal gene transfer, bacterial restriction and modification systems, mobile genetic elements, site-specific recombination, and the molecular mechanisms of biological evolution. In 1978, he was awarded the Nobel Prize in Medicine and Physiology for the discovery of restriction enzymes and their application to problems of molecular genetics. Oleg V. Aslanidi studied at the Department of Applied Mathematics, Tbilisi State University, Georgia (1990–1993), before moving to the Pushchino State University, Pushchino, Russia, where he received his BS degree in xv
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Biophysics (1996) and the PhD degree (1999). He is a postdoctoral research fellow at the Computational Biology Laboratory in the School of Biomedical Sciences, University of Leeds, since 2001. His research interests are in computational biology, nonlinear phenomena, and parallel computing. Stephen Baigent is a Lecturer in the Mathematics Department at University College London (UCL). He holds BA, MSc, and DPhil degrees in Mathematics from the University of Oxford. For his doctorate he studied geometrical aspects of geophysical fluid mechanics, but upon joining to UCL as a Research Assistant his interests shifted towards biomathematics, and in particular the modelling of cell–cell communication. Before taking up his current post he held a Wellcome Trust Biomathematics Fellowship for five years. He is now involved in a variety of biomathematics projects, including the building of models of brain circulation, arteriovenous malformations, and liver function. Murad Banaji grew up in India and the United Kingdom. He studied physics at King’s College London, then underwent training as a secondary school teacher. After teaching science for a few years in an innercity London school, he returned to the university to do a PhD in mathematics. Since completing his PhD in 2001, he has been working at University College London on constructing a computational model of the cerebral circulation. Dr. Banaji lives in London with his eight-year-old son, Amlan. Sergio E. Baranzini, PhD is an Assistant Professor in the Department of Neurology at the University of California at San Francisco. Dr. Baranzini has a BS/MS in Biochemistry and a PhD in Human Molecular Genetics from the University of Buenos Aires, Argentina. Dr. Baranzini joined the Department of Neurology at UCSF in 1997 as a postdoctoral fellow. His current research focuses on molecular mechanisms of complex diseases with an emphasis on functional genomics and bioinformatics in the neurological disorder, multiple sclerosis. Vadim N. Biktashev received his BScþMSc degree in Biophysics from the Moscow Institute of Physics and Technology, Moscow, Russia, in 1984, and the PhD degree from the same institute in 1989. He is a Reader of Applied Mathematics in the Department of Mathematical Sciences, The University of Liverpool. He has been in Liverpool since 1999. His research interests are in the mathematical theory of autowaves, with applications in mathematical biology, particularly mathematical cardiology.
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Irina V. Biktasheva received her BScþMSc degree in Physics and Technology from Tomsk State University, Russia, in 1985, and then two PhD degrees, from Institute of Theoretical and Experimental Biophysics, Russian Academy of Science in 2000 and from Leeds University in 2001. She is a Lecturer in Biocomputing at the Department of Computer Sciences, The University of Liverpool. She has been in Liverpool since 2002. Her research interests are in computational biology and dynamics of spiral waves, in particular computational cardiology. Helen Byrne has been a member of the School of Mathematical Sciences at the University of Nottingham since 1998, and was promoted to a Chair in applied mathematics in 2003. After training as an applied mathematician at the Universities of Cambridge and Oxford, she now works in the field of mathematical biology, focusing in particular on aspects of solid tumour growth. She currently holds an EPSRC advanced research fellowship which enables her to concentrate full time on her research interests. Through active collaboration with experimentalists and clinicians, she aims to ensure that the mathematical models that researchers develop and analyse can provide genuine insight into problems of medical interest. Robin E. Callard, Professor of Immunology at the Institute of Child Health, University College London, has been an experimental immunologist for 35 years and headed Infection and Immunity at ICH from 1998 to 2004. His research interests in experimental immunology include dendritic cell responses to Neisseria meningitides and interactions with T cells; genetic epidemiology and skin biology in allergic dermatitis; and function of cytokines in human antibody responses. Over the past five years, he has developed a research programme on mathematical modelling of T cell proliferation and differentiation directed at understanding homeostatic control of T cell populations; transcription factor and cytokine control of Th1 and Th2 cell differentiation; and p53 regulation of apoptosis following DNA damage. Along with Professor J Stark, he initiated and set up CoMPLEX (Centre for Mathematics and Physics in the Life Sciences and Experimental Biology) at UCL. He is presently on the CoMPLEX Executive Committee and Co-Director of the CoMPLEX Four Year PhD Programme in Modelling Biological Complexity. His research over the past ten years has been supported by grants from the BBSRC, MRC, EPSRC, Wellcome Trust, Spencer Dayman Meningitis, and National Eczema Society. Cliburn C. T. Chan has a medical degree from the National University of Singapore and a PhD in nonlinear dynamics from the University College
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London. He did a postdoctoral research in the Department of Immunology at Imperial College London, collaborating with experimental immunologists to build models of immune cell regulation and signalling. He is currently with the Department of Biostatistics and Bioinformatics at Duke University, modelling host–pathogen interactions and helping to construct an ontology of the innate immune system. Richard H. Clayton was awarded a BSc degree in Applied Physics and Electronics from the University of Durham (UK) in 1986, and a PhD degree from the University of Newcastle upon Tyne (UK) in 1990. He is currently a Senior Lecturer in Bioinformatics and Computational Biology in the Department of Computer Science at the University of Sheffield. His research interest covers computational biology of the cardiovasular system, and he has a specific interest in cardiac arrhythmias. Irun R. Cohen is the Mauerbeger Professor of Immunology at the Weizmann Institute of Science; Director of the Center for the Study of Emerging Disease; a founder and steering committee member of the Center for Complexity Science, Jerusalem; and Director of the National Institute for Biotechnology in the Negev, Beer Sheva. Cohen does basic research in immunology and has developed novel immune therapies, such as T-cell vaccination for autoimmune diseases and peptide therapy for Type-1 diabetes mellitus, both are in clinical trials now. Cohen studies and models design principles of the immune system behaviour. Vincent Detours has conducted theoretical immunology research at the Los Alamos National Laboratory and at the Santa Fe Institute, both of which are in New Mexico, USA. He is now involved in cancer research and bioinformatics at the Free University of Brussels’ Institute for Interdisciplinary Research. Nicola Dioguardi is currently the Director of Scientific Research at the Istituto Clinico Humanitas in Milan, Italy. Born in Bari, Italy, in 1921, he received his degree in Medicine and Surgery in 1947 from the University of Bologna. He is an internationally recognized medical researcher with more than 400 publications to his credit. Since 1978, his research has focussed on hepatic functioning, with an emphasis on the possibility of expressing this knowledge in both qualitative and quantitative terminologies. More recently, he has worked to develop a mathematical and geometric computational model of liver lesions. In his long career, he has served as Director of the Institute of Medical Semiotics, and the Institute of Medical Pathology at the University of Cagliari, as well as the Institute
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of Clinical Medicine and the Institute of Internal Medicine, both at the University of Milan. Narendra M. Dixit received his PhD in Chemical Engineering in 2002 from the University of Illinois at Urbana-Champaign. He was a postdoctoral researcher at the Los Alamos National Laboratory until 2004, where he worked on viral dynamics. He is particularly interested in understanding the principles of action of different drug agents, the impact of pharmacokinetics on treatment outcome, and modelling virus–cell interactions. He has returned to his home country and since February 2005 is an Assistant Professor in the Department of Chemical Engineering at the Indian Institute of Science in Bangalore. David Y. Downham was Senior Lecturer in Statistics and Head of the Department of Statistics and Computational Mathematics at the University of Liverpool. Since retirement in 1996, he has pursued his research interests in data analysis. He has published over 90 original articles, reviews, and book chapters. Fellow contributor Sam Leinster (see Chapter 6) has unknowingly made an essential contribution to this chapter by successfully operating in 1998 on Dr. Downham’s cancerous growth, for which he is grateful. Jacques E. Dumont holds both the MD and the PhD degrees and is the founding director of the Institute of Interdisciplinary Research at the University of Brussels. His major work focuses on signal transduction, control of the thyroid gland, and thyroid disease. He has had a longstanding interest in the theoretical foundations of signal transduction. Sol Efroni is a postdoctoral fellow at the National Cancer Institute, Center for Bioinformatics, where his work includes computational analyses of cellular molecular pathways over high-throughput experiments. He received a PhD in both immunology and computer science from the Weizmann Institute of Science and developed Reactive Animation during his PhD thesis research. Guido Fioretti holds an MSc in electronic engineering and a PhD in economics, both from the University of Rome ‘‘La Sapienza’’. He is a lecturer of Computational Organization Science at the University of Bologna, School of Science and works on computational models of individual and organisational decision-making. His articles have appeared in Advances in Complex Systems, Economics and Philosophy, Journal of
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Artificial Societies and Social Simulation, Metroeconomica, Computational Economics, and European Journal of Operations Research. John Fox was educated in the UK, but carried out research in artificial intelligence and cognitive science at Carnegie-Mellon and Cornell Universities in the USA before returning home in the late 1970s. He worked with Medical Research Council and, later, the Imperial Cancer Research Fund’s laboratories in London (now Cancer Research UK), where he set up the Advanced Computation Laboratory at Cancer Research UK. In 1996, it was awarded the 20th Anniversary Gold Medal of the European Federation of Medical Informatics for its work on PROforma, a formal language for modelling clinical decisions and care pathways, and associated software for supporting patient care. Fox has published widely in computing, biomedical engineering, and cognitive science. A recent book, ‘‘Safe and Sound: Artificial Intelligence in Hazardous Applications’’ (MIT Press, 2000) deals with many aspects of the use of AI in medicine.His group also maintains OpenClinical, a resource for anyone interested in the role of knowledge management and AI in improving consistency and quality of care (www.openclinical.org). Hajime Fujie is a physician in the Department of Gastroenterology, University of Tokyo Hospital. He has treated cases with liver diseases, especially viral hepatitis, such as hepatitis type B or C, and hepatocellular carcinoma. As most of the hepatocellular carcinoma is related with chronic viral hepatitis in Japan, the subject of his research is hepatocarcinogenesis related with hepatitis virus as well as pathophysiology of chronic viral hepatitis. Recently, he and his colleagues studied glucose and lipid metabolism alteration in chronic hepatitis type C. David Glasspool holds a PhD in Psychology from University College London, an MSc in Cognitive Science from the University of Manchester, and a BSc in Computing with Electronics from the University of Durham. His research centres on cognitive systems – both intelligent computational systems and human cognition – with particular interests in executive control, routine behaviour, and planning in the face of uncertainty. He has worked as a cognitive scientist at the Advanced Computation Laboratory of Cancer Research UK since 1998. Larry D. Greller is Chief Scientific Officer and co-Founding Director (with Dr. Roland Somogyi) of Biosystemix, Ltd. in Kingston, Ontario. Biosystemix specialises in providing advanced data mining, data analysis, and mathematical modelling solutions to biomedical research in the
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pharmaceutical, biotechnology, academic, and public sectors. He has over 15 years of broad industrial applied research experience in nonlinear dynamics, mathematical modelling, and detection of patterns in large-scale biological data. Previously, he held academic positions in applied mathematics, computer science, and simulation at the University of Denver and the University of Missouri-Columbia.His current research interests include computational reverse engineering of gene and protein interaction networks directly from data. Dr. Greller received his PhD in mathematical molecular biology from the University of Pennsylvania, an MS in Computer & Information Science from Penn’s Moore School of Electrical Engineering, and a BS in Physics from the Drexel University. Olivier C.L. Haas graduated in Electrical Engineering from Joseph Fourier University, Grenoble, France and obtained his PhD from Coventry University, UK. He is currently Senior Lecturer in Computing and Control Systems, coordinator of the Biomedical Engineering Systems Group within the Control Theory and Applications Centre at Coventry University, UK, and Honorary Research Fellow at the University Hospitals Coventry and Warwickshire NHS Trust, Coventry, UK. His research interests include systems modelling, optimisation, image processing, and control engineering applied to medical systems and in particular, to the treatment of cancer with radiotherapy. David Harel has been at the Weizmann Institute of Science since 1980. He was Department Head from 1989 to 1995, and was Dean of the Faculty of Mathematics and Computer Science between 1998 and 2004. He is also co-founder of I-Logix, Inc. He received his PhD from MIT in 1978, and has spent time at IBM Yorktown Heights, and at Carnegie-Mellon and Cornell Universities. In the past, he worked mainly in theoretical computer science, and now he works in software and systems engineering, modelling biological systems, and the synthesis and communication of smell. He is the inventor of statecharts and co-inventor of live sequence charts, and co-designed Statemate, Rhapsody, and the Play-Engine. He received the ACM Outstanding Educator Award (1992), and the Israel Prize (2004), and is a Fellow of the ACM and of the IEEE. Arun V. Holden received his BA degree in Animal Physiology from the University of Oxford, Oxford, UK in 1968, and the PhD degree from the University of Alberta, Edmonton, AB, Canada, in 1971. He holds a personal Chair in Computational Biology in the School of Biomedical Sciences, and is in the Cardiovascular Research Institute at Leeds, University of Leeds. He has been based in Leeds since 1971. His research
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interests are focused around integrative computational biology, nonlinear phenomena, and excitable physiological systems. Anna Maria Holmba¨ck is a Senior lecturer in Physiotherapy and Sports Science in the Department of Health Sciences at Lund University. She has more than 20 years of experience in teaching sport physiology, and her main research interests include the structure and function of skeletal muscle and measurements in human performance. Sam Leinster is the founder Dean of the School of Medicine, Health Policy and Practice at the University of East Anglia which is one of the recent medical schools established in response to the perceived need to train more doctors in England. His major interests are curriculum planning and assessment. Prior to taking up his current post in 2001, he was Director of Medical Studies in the University of Liverpool where he was responsible for the introduction of a problem-based, student-centred curriculum in 1996. He has a background in surgical oncology with clinical interests in breast cancer, malignant melanoma, and soft tissue sarcoma. His research has been on the epidemiology and molecular biology of breast cancer and the psychological correlates of breast disease as well as aspects of medical education. He was Chair of the Association for the Study of Medical Education from 1998 to 2004. Gareth Leng gained a first class Honours degree in Mathematics from the University of Warwick before moving into biology for his PhD studies. He was a project leader at the Babraham Institute, Cambridge for 17 years until 1994, when he was appointed as Professor of Experimental Physiology at the University of Edinburgh. His research interests are mainly focused on hypothalamic regulation of the pituitary gland, using experimental and theoretical approaches. Between 1997 and 2004, he was Editor-in-Chief of The Journal of Neuroendocrinology. Jan Lexell is an Associate Professor of Rehabilitation Medicine and Senior lecturer in Geriatrics at Lund University, and Adjunct Professor of Clinical Neuroscience at Lulea˚ University of Technology. He is clinically active as medical director of a post-polio clinic, and pursues research as the director of a neuromuscular research laboratory. His research interests include muscle physiology and morphology, muscle strength and fatigue, and rehabilitation interventions following brain injury, spinal cord injury, and/or chronic neurological disorders. He has published over 100 original articles, reviews, and book chapters.
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Andre Longtin is a Professor in the Department of Physics at the University of Ottawa, where he is also cross-appointed to the Department of Cellular and Molecular Medicine. His main research areas are theoretical neurophysics, as well as nonlinear dynamics and stochastic processes. He graduated with an Honors BSc (1983) and an MSc (1985) in Physics from the University of Montreal. He obtained his PhD in Physics from McGill University in 1989. He was an NSERC Canada postdoctoral fellow in the Complex Systems Group and the Center for Nonlinear Studies at Los Alamos National Laboratory, before taking an assistant professorship in Physics at the University of Ottawa in 1992. He is a Fellow of the American Physical Society. Carine Maenhaut completed a PhD thesis devoted to the identification and characterisation of different G-protein-coupled receptors and now focuses her work on the control of the proliferation and differentiation of normal thyroid cells in vitro. More specifically, she is searching for new genes involved in this process. This work has been extended to thyroid tumours, involving the analysis of gene expression profiles in those tissues using microarray technology. Philip Maini obtained his doctorate in mathematical biology under Professor J.D. Murray, FRS in 1986 at the Centre for Mathematical Biology (CMB), Mathematical Institute, Oxford. After a brief period as a postdoctoral researcher at the CMB, Dr. Maini moved to the University of Utah as an Assistant Professor, then returned to the CMB in 1990. He was appointed Director in 1998 and took up the Chair in Mathematical Biology in 2005. Dr. Maini’s work consists mainly of deterministic mathematical modelling of spatio-temporal phenomena, with particular applications in developmental biology, wound healing, and cancer tumour dynamics. Naohiro Matsumura is an Assistant Professor in the Graduate School of Economics, Osaka University. The topics of his research include communication mining and communication modelling as fundamental analysis of communication data, as well as communication design and communication management as practical application for change discovery. He has established some novel methodologies towards the understanding of the nature of human–human conversational communication. He has been collaborating with researchers and professionals in variety of fields, such as artificial intelligence, information science, medical science, social psychology, cognitive science, and marketing planner to tackle the worthy but complicated problems in our real world.
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John P. McMichael is the president and CEO of Dimensional Dosing Systems Inc. and former Director of Informatics and Visiting Research Assistant Professor of Surgery at the Thomas E. Starzl Medical Transplantation Institute of the University of Pittsburgh. He is also the Chief Medical Informatics Officer of Management Science Associates Inc., a Pittsburgh-based company. He has developed and patented a number of computer applications and systems to assist physicians in treating and caring for patients. He has extensive experience in the fields of artificial intelligence, systems design, and healthcare delivery, and is acknowledged as a world leader in the building of biological and mathematical models that describe the relationships between drug dose and patient response for use in decision support systems. His current work has resulted in revolutionary approaches to drug prescribing paradigms and has resulted in related patient treatment innovations. He has also developed dosing systems and conducted clinical trials for diabetes, immunosuppression, anticoagulation,and antibiotics. Parvin Mousavi is an Assistant Professor in the School of Computing at Queen’s University, Canada. She received her PhD in Electrical and Computer Engineering from the University of British Columbia, Canada and her MSc in Engineering and Physical Sciences in Medicine from the Imperial College of Science, Technology and Medicine, UK. Her current research interests include application of machine learning and pattern recognition in computational biology, medical image analysis, and computer-aided diagnostics. Yukio Ohsawa is an Associate Professor in the Graduate School of Business Sciences, University of Tsukuba. He defined a ‘‘chance’’ as an event significant for making a decision, and has organised international meetings on Chance Discovery – for example, the Fall Symposium of the American Association of Artificial Intelligence in 2001. He co-edited the first book on Chance Discovery published by Springer-Verlag and relevant specialised journals of crisis management, information science, fuzzy logic, and others. Since 2003, the Chance Discovery Consortium has enabled researchers in cognitive sciences, information sciences, and business sciences, and business workers to exchange and develop methods for real-world Chance Discovery. Naoaki Okazaki obtained his Master of Engineering in 2003 at the Graduate School of Information Science and Technology, The University of Tokyo. His research topics include text mining such as automatic text summarisation, term recognition, question/answering, information
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visualisation, etc. He is currently a research fellow at the University of Salford, UK and working for the National Centre for Text Mining, which initially focused on text mining applications in the biological and medical domains, in cooperation with the University of Manchester and the University of Liverpool. Jasmina Panovska is currently a postdoctoral researcher in Heriot-Watt University in Edinburgh. She graduated from Oxford University with a BA in June 1999 and a MMath Degree in June 2000. In April 2005, she went on to study a DPhil Degree at Oxford University under the supervision of Professor P K Maini from Oxford University and Prof H M Byrne from Nottingham University. Her doctoral research is in mathematical modelling of tumour growth and expansion as well as potential therapeutic protocols. During the course of her research she is interested in studying various biological systems such as tumour growth, wound healing or cellular communications using mathematical techniques and numerical simulations and finding ways to verify them experimentally. Alan S. Perelson is a senior fellow at Los Alamos National Laboratory in New Mexico. He received BS degrees in Life Science and Electrical Engineering from MIT, and a PhD in Biophysics from UC Berkeley. He was Assistant Professor, Division of Medical Physics, Berkeley, Assistant Professor of Medical Sciences at Brown University in Rhode Island, and has been a staff member, group leader, fellow, and now senior fellow at Los Alamos National Laboratory. He is one of the founders in the field of Theoretical Immunology and his research on modelling HIV and HCV infections helped found the field of viral dynamics. He led the programme in Theoretical Immunology at the Santa Fe Institute, and his group at Los Alamos National Laboratory has been involved in developing models and analysing immunological phenomena since 1974. Colin R. Reeves is a Professor of Operational Research in the School of Mathematical and Information Sciences at Coventry University. His main research interests are broadly in the area of natural computation, covering topics such as artificial neural networks and the development of heuristic methods for optimisation. Most recently, his work has centred around the methodology and applications of evolutionary algorithms, on which subject he has published widely, with more than 80 articles on related topics. He edited and co-authored the well-regarded book ‘‘Modern Heuristic Techniques for Combinatorial Problems’’ (McGraw-Hill), and his latest book, ‘‘Genetic Algorithms: Principles and Perspectives’’
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(co-authored with Jon Rowe) has recently been published by Kluwer. He is a member of the editorial board of 5 major journals in the area of natural computation. Ruy M. Ribeiro got his PhD in 1999 from the University of Oxford, UK and then moved to Los Alamos National Laboratory, New Mexico, first as a Postdoctoral Research Associate and subsequently became a staff member in the Theoretical Biology and Biophysics Group. His research interests focus on the modelling of immune system and viral infection dynamics, with special emphasis on analyses of data from experiments in those fields. He loves the sunny, blue skies of New Mexico. Nancy Sabatier completed her PhD in Neuroscience in 1999 at The University of Montpellier, France. During her doctoral research, she investigated the cellular mechanisms involved in the calcium response induced by vasopressin in the neuroendocrine vasopressin cells of the supraoptic nucleus. She currently holds a postdoctoral position with Gareth Leng at The University of Edinburgh. Her present research focuses on the underlying mechanisms and the physiological consequences of dendritic release of oxytocin in the supraoptic nucleus in vivo. Akio Saiura is a staff surgeon in the Cancer Institute Hospital in Tokyo, Japan. He specialised in hepato-biliary-pancreatic surgery and transplant immunology. He reported that the circulating progenitor cells contributed to the transplant in arteriosclerosis in the Journal of Nature Medicine in 2001. Currently, he performs surgery of more than 150 hepato-biliarypancreatic malignancies per year. He introduced co-authors Ohsawa and Fujie, who had both been his swimming mates, twenty years ago when the three were 18 years old. Since then, the three colleagues have been exchanging interdisciplinary ideas. Gordon M. Shepherd is a Professor of Neuroscience at Yale University School of Medicine. He trained with Wilfrid Rall in compartmental modelling of neurons, leading to the identification of dendrodendritic microcircuits. He has also modelled logic operations in dendritic spine interactions, and ligand–receptor interactions in the olfactory system. He has been the editor of Journal of Neurophysiology and Journal of Neuroscience, and has authored and edited ‘‘The Synaptic Organisation of the Brain’’, now in its fifth edition. He is currently involved in developing neuroinformatics databases at senseLab.med.yale.edu as part of the Human Brain Project and the Neuroscience Database Gateway.
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Roland Somogyi is President and co-Founding Director (with Dr. Larry Greller) of Biosystemix, Ltd. Biosystemix applies its advanced computational methods and biomedical domain expertise for the data-driven discovery of predictive clinical models and molecular function. These predictive solutions are provided to industrial and public sector partners for cutting-edge efforts in novel target discovery, more efficient screening and toxicological assays, and the enabling of personalised medicine. Dr. Somogyi has twenty years of experience in academia, government, and industry, in the areas of genomics, computational biology, and the biophysics of cell signalling. Previously, he was Chief Scientific Officer at Molecular Mining Corporation (Kingston, Ontario), and has held positions at Incyte Genomics (Palo Alto, California), the National Institutes of Health (NIH; Bethesda, Maryland), and the Pharmacological Institute at the University of Bern (Bern, Switzerland). As PI at NIH, his group pioneered methods for high-fidelity, high-throughput gene expression measurements, exploratory data mining and visualisation, and network reverse engineering. Dr. Somogyi is frequently called upon as an invited speaker at international meetings in computational biology and genomics, and has organised a number of conference symposia. In addition, high-level government committees in both North America and Europe have sought his expertise as an advisor on genomics, bioinformatics, and systems biology. Dr. Somogyi holds an MSc in Biology and a PhD in Biophysics and Physiology (Summa cum Laude) from the University of Konstanz (Konstanz, Germany). Alfred I. Tauber, Zoltan Kohn Professor of Medicine and Professor of Philosophy, is Director of the Center for Philosophy and History of Science at Boston University. While primarily teaching and writing in the philosophy of science, he originally trained as a biochemist and haematologist. His most recent publications include ‘‘The Immune Self ’’, ‘‘Theory or Metaphor?’’ (Cambridge, 1994), ‘‘Confessions of a Medicine Man’’ (MIT, 1999), ‘‘Henry David Thoreau and the Moral Agency of Knowing’’ (California, 2001), and ‘‘Patient Autonomy and the Ethics of Responsibility’’ (MIT, 2005). Paul Thagard is a Professor of Philosophy, with cross-appointment to Psychology and Computer Science, and Director of the Cognitive Science Program, at the University of Waterloo. He is the author of ‘‘Coherence in Thought and Action’’ (MIT Press, 2000), ‘‘How Scientists Explain Disease’’ (Princeton University Press, 1999), ‘‘Mind: Introduction to Cognitive Science’’ (MIT Press, 1996; second edition, 2005), ‘‘Conceptual Revolutions’’ (Princeton University Press, 1992), and ‘‘Computational Philosophy
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of Science’’ (MIT Press, 1988); and co-author of ‘‘Mental Leaps: Analogy in Creative Thought’’ (MIT Press, 1995) and ‘‘Induction: Processes of Inference, Learning, and Discovery’’ (MIT Press, 1986). Cheng Hock Toh is a Reader in Haematology at the University of Liverpool, UK. He is also an Honorary Consultant in Haematology at the Royal Liverpool University Hospital and Director of the Roald Dahl Haemostasis & Thrombosis Centre. His research programme covers bench to bedside and population studies in the area of haemostatic dysfunction. This is especially applicable to critical care and cardiovascular domains. He is currently co-Chair of the International Society of Thrombosis and Haemostasis Scientific and Standardisation Sub-Committee on Disseminated Intravascular Coagulation. Frank T. Vertosick, Jr., MD, FACS received his undergraduate degree in physics in 1976 and his MD in 1981, both from the University of Pittsburgh. He completed a residency in neurological surgery in 1988 and was board certified in 1991. A Fellow of the American College of Surgeons, he has written more than fifty peer-reviewed articles a wide range of subjects in medicine and medical research and is also the author of three books, including ‘‘The Genius Within’’, an exploration of biological intelligence; ‘‘Why We Hurt’’, a treatise of human pain (and a Library Journal Book of the Year); and ‘‘When the Air Hits Your Brain’’, a whimsical look at the training of a brain surgeon. He has contributed several times to ‘‘Discover’’ and ‘‘Hippocrates’’ magazines. Dr. Vertosick lives in Fox Chapel, Pennsylvania with his wife, two children, one cat and one very large dog. Sir David Weatherall qualified at Liverpool University in 1956 and after a period of National Service in Malaya, spent four years at Johns Hopkins Hospital, Baltimore. He returned to Liverpool in 1965, where he was appointed Professor of Haematology in 1971. In 1974, he moved to Oxford, where he was Nuffield Professor of Clinical Medicine until 1992. In 1992, he was appointed Regius Professor of Medicine at Oxford. In 1979, he became the Honorary Director of the MRC Molecular Haematology Unit, and in 1989, he established the Institute of Molecular Medicine at Oxford, of which he was Honorary Director (later renamed Weatherall Institute of Molecular Medicine). His major research contributions, resulting in some 700 publications, have been in the elucidation of the clinical and molecular basis for the thalassaemias and the application of this information for the control and prevention of these diseases in the developing countries. In 2002, he wrote a major report on the application of genomics for global health for the World Health Organisation. He was knighted in 1987, elected
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FRS in 1977 and a Foreign Associate of the National Academy of Sciences, USA in 1990. In 1992, he was President of the British Association for the Advancement of Science. He became Emeritus Regius Professor of Medicine in September 2000 upon his retirement and was appointed Chancellor of Keele University in 2002. David F. Williams is a Professor of Tissue Engineering at the University of Liverpool and Director of the joint Liverpool-Manchester UK Centre for Tissue Engineering. He was trained as a materials scientist and has worked in the medical applications of materials for 35 years. Professor Williams has published over 350 scientific papers and written or edited 35 books, including the first textbook on medical devices in 1973 (Implants in Surgery) and the recent Williams Dictionary of Biomaterials. He has received the senior awards of the UK, European, and US Societies for Biomaterials and is Editor-in-Chief of the world’s leading journal Biomaterials. Over the last two decades, Professor Williams has been a consultant to both medical device companies and government bodies on a global basis, especially concerning biocompatibility of medical devices and tissue engineering products, complex issues of the scientific basis of regulatory issues and device classification, materials selection for medical devices and failure analysis. He has been heavily involved in litigation, defending device companies in major class actions. Professor Williams has been scientific advisor to the European Commission on public health aspects of medical devices and pharmaceutical products for several years. He was elected as a Fellow of the Royal Academy of Engineering in 1999. Nigel Bruce Wood, whose PhD was in cardiovascular biomechanics, returned to the subject following a career in industry, acquiring funding from 1996 to develop the combination of MRI with CFD in a collaboration between the Royal Brompton Hospital MR Unit and the Mechanical Engineering Department at Imperial College London. In 2001, he joined the combined team of Dr. Yun Xu in the Chemical Engineering Department, and clinical colleagues from the International Centre for Circulatory Health, National Heart & Lung Institute, Imperial College London, as a Principal Research Fellow, since when he has taken part in a wide range of projects, contributing to research proposals, supervisions and publications. He is a Visiting Professor in biofluid mechanics at the University of Surrey. Xiao Yun Xu is a Reader in Bio-fluid Mechanics in the Department of Chemical Engineering, Imperial College London, UK. She obtained her Phd in Mechanical Engineering from City University, London, in 1992.
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She has worked in the field of computational biomechanics for 16 years resulting in over 70 peer-reviewed journal articles, book chapters, and conference papers in this area. Her main contributions are on the development and validation of image-based CFD modelling tools for patient-specific simulation of blood flow in the cardiovascular system under physiologically realistic conditions. Over the last 10 years, she has supervised 5 postdoctoral researchers and 15 PhD students, and has worked closely with clinical researchers, vascular surgeons, radiologists, and medical physicists at the St. Mary’s Hospital and Royal Brompton Hospital in London as well as other British Universities. Her current research interest include computational modelling of flow, mechanical stress, and mass transport in normal and diseased arteries (e.g. aneurysms and plaques), biomechanics of the venous system, and transport processes in bioreactors for tissue engineering. Andrew J. Yates completed a PhD in Theoretical Physics and Cosmology at Imperial College London and held postdoctoral positions in Geneva and Los Alamos before starting work in Theoretical Immunology at ICH in 1998. He is now a postdoctoral fellow in the Biology Department, Emory University. His interests are in modelling T-cell proliferation and differentiation, T-cell homeostasis and within-host evolution of pathogens.
Contents
Series Dedication............................................................................... Foreword........................................................................................... List of contributors ........................................................................... Biographies....................................................................................... 1. Disorders of haemoglobin: from phenotype to genotype, by Sir David J. Weatherall......................................................... 2. Between bleeding and thrombosis or beyond, by Cheng Hock Toh................................................................... 3. The theory of molecular evolution and its medical implications, by Werner Arber ........................................................................ 4. What is a medical theory? by Paul Thagard......................................................................... 5. Medicine as a moral epistemology, by Alfred I. Tauber .................................................................... 6. Theory in medical education – an oxymoron? by Sam Leinster.......................................................................... 7. Knowledge, arguments, and intentions in clinical decision-making, by John Fox and David Glasspool............................................ 8. Analogies, conventions, and expert systems in medicine: some insights from a XIX century physiologist, by Guido Fioretti ....................................................................... 9. Reliability of measurements in medical research and clinical practice, by David Y. Downham, Anna Maria Holmba¨ck and Jan Lexell xxxi
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10. Advanced data mining and predictive modelling at the core of personalised medicine, by Roland Somogyi, John P. McMichael, Sergio E. Baranzini, Parvin Mousavi and Larry D. Greller....................................... 11. Designs and therapies for stochastic neural systems, by Andre Longtin....................................................................... 12. Mining scenarios for hepatitis B and C, by Yukio Ohsawa, Naoaki Okazaki, Naohiro Matsumura, Akio Saiura and Hajime Fujie ................................................... 13. Modelling the in vivo growth rate of HIV: implications for vaccination, by Ruy M. Ribeiro, Narendra M. Dixit and Alan S. Perelson ........................................................................ 14. A flexible, iterative approach to physiological modelling, by Murad Banaji and Stephen Baigent ...................................... 15. Systems biology, cell specificity, and physiology, by Vincent Detours, Jacques E. Dumont and Carine Maenhaut ....................................................................... 16. Modelling T cell activation, proliferation and homeostasis, by Andrew J. Yates, Cliburn C.T. Chan and Robin E. Callard........................................................................ 17. A theory for complex systems: reactive animation, by Sol Efroni, David Harel and Irun R. Cohen ........................ 18. Modelling of haemodynamics in the cardiovascular system by integrating medical imaging techniques and computer modelling tools, by Nigel Bruce Wood and Xiao Yun Xu.................................. 19. Vasopressin and homeostasis – running hard to stay in the same place, by Nancy Sabatier and Gareth Leng......................................... 20. Mathematical modelling of angiogenesis and vascular adaptation, by Tomas Alarcon, Helen Byrne, Philip Maini and Jasmina Panovska...................................................................... 21. Towards understanding the physical basis of re-entrant cardiac arrhythmias, by Oleg V. Aslanidi, Vadim N. Biktashev, Irina V. Biktasheva, Richard H. Clayton and Arun V. Holden ................................
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22. Reflections on the quantitative analysis of liver fibrosis in biopsy specimens, by Nicola Dioguardi .................................................................. 23. A network approach to living tissues, by Frank T. Vertosick, Jr. ......................................................... 24. Genetic algorithms in radiotherapy, by Olivier C. L. Haas and Colin R. Reeves .............................. 25. Tissue engineering: the multidisciplinary epitome of hope and despair, by David F. Williams ................................................................
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
1 Disorders of haemoglobin: from phenotype to genotype Sir David J. Weatherall Weatherall Institute of Molecular Medicine, University of Oxford, Oxford, UK
1. INTRODUCTION Of the several definitions of the word ‘‘theory’’ in the Oxford Compact English Dictionary, two seem to be most appropriate for its use in what is often rather optimistically described as ‘‘scientific medicine’’; ‘‘an idea accounting for or justifying something’’, or ‘‘a set of principles on which an activity is based’’. Even today, much of medical practice is based on accepted theory rather than hard scientific facts. Indeed, it has been suggested that the principal problem for those who educate doctors of the future is how, on the one hand, to encourage a lifelong attitude of critical, scientific thinking to the management of illness and, on the other, to recognise that moment when the scientific approach, because of ignorance, has reached its limits and must be replaced by sympathetic empiricism (Weatherall, 1995). In the second half of the twentieth century, the emphasis of medical research had changed, at least in part, from the study of diseases in patients and their communities, to cells and molecules. This remarkable transition has followed on the back of the new field of molecular biology which emerged in the period after the Second World War. One of the earliest areas of medical research to be affected by this new way of thinking was the study of the inherited disorders of haemoglobin, the commonest single-gene disorders in man. In this chapter, I will outline briefly the multidisciplinary influences that combined to develop the theories, which led to the remarkable expansion in knowledge of disease mechanisms at the molecular level in the inherited haemoglobin disorders in the latter half of the twentieth century. 1
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Because the early development of this field was seminal in the evolution of what became known as ‘‘molecular medicine’’, its early development will repay careful study by medical historians of the future. A more extensive coverage of some aspects of this field is given by Weatherall (2004).
2. SETTING THE SCENE: THE MULTIDISCIPLINARY ROUTE TO THE EARLY DEVELOPMENT OF THE HUMAN HAEMOGLOBIN FIELD As previously suggested, the development of the human haemoglobin field is most easily appreciated by tracing three historical threads that finally came together in the late 1950s (Weatherall and Clegg, 1999, 2001). The first is the discovery of haemoglobin and the elucidation of its structure and function. The second involved the description of sickle cell anaemia, the realisation that it is an inherited disease, and the discovery of sickle cell haemoglobin and the other haemoglobin variants. Finally, there was an amalgamation of observations from many parts of the world which suggested that another group of serious blood disorders of childhood, the thalassaemias, are also genetic disorders of haemoglobin with many features in common with sickle cell anaemia and its variants. It was, in effect, the synthesis of theory and experimentally validated facts from these different routes, together with the interaction of scientists from a variety of different disciplines, that paved the way for a better understanding of the genetic control of human haemoglobin and later, to an understanding of its molecular pathology. The way in which oxygen binds to blood became a subject of intense interest during the second half of the nineteenth century. In 1863, HoppeSeyler coined the term ‘‘haemoglobin’’ to describe the oxygen-carrying pigment of the blood. During the first half of the twentieth century, the study of the function of haemoglobin as an oxygen carrier was largely in the realm of physiologists, including Bohr and Krogh in Denmark, Barcroft, Haldane, Hill, Roughton and others in the UK, and Henderson in the USA. However, by the middle of the twentieth century, the field started to become a major centre of activity for the burgeoning field of protein chemistry. Following the pioneering work on the structure of insulin by Sanger, many protein chemists turned their attention to the structure of haemoglobin, and it was established that it is a tetramer composed of two pairs of unlike chains, which were called and (2 2). Using the newly developed methods of amino acid sequence analysis, their primary structures were soon determined. It was also found that the haemoglobin that is present in fetal life, haemoglobin F, shares chains
Disorders of haemoglobin: from phenotype to genotype
3
with adult haemoglobin but has different non- chains which were called chains (2 2). At about the same time, Perutz and his colleagues arrived at a solution for the three-dimensional structure of haemoglobin by X-ray analysis (Perutz et al., 1960) and a start was made in relating it to its functional properties, which had been described so elegantly by the physiologists. Thus by the late 1950s, a considerable amount was known about the structure of human haemoglobin and some solid theories were already being advanced about its allosteric behaviour as an oxygen carrier. The second thread of the haemoglobin story, which started in the USA in 1910, reflects an even broader spread of scientific disciplines. It began with the work of the physician James Herrick, who first described sickle cell anaemia, the genetic basis of which was worked out later by population geneticists in the USA and Africa. The discovery that sickle cell anaemia results from a structural change in haemoglobin followed a chance conversation between Linus Pauling, a protein chemist, and William Castle, a haematologist from Boston. Castle told Pauling that the red cells of patients with sickle cell anaemia form tactoids after deoxygenation, suggesting to Pauling that this might reflect a change in the structure of haemoglobin. Using the newly developed technique of protein electrophoresis, Pauling and his colleagues discovered that the haemoglobin of patients with sickle cell disease is abnormal; they called the variant haemoglobin, haemoglobin (Hb) S and dubbed sickle cell anaemia a ‘‘molecular disease’’ (Pauling et al., 1949). In 1956, a young protein chemist in Cambridge, Vernon Ingram, on following suggestions by Sanger, Perutz, and others, demonstrated that Hb S differs from normal haemoglobin (Hb A) by a single amino acid substitution in the globin chain (Ingram, 1956). This indicated that the globin chain is the product of a globin gene, entirely compatible with the earlier theory of Beedle and Tatum from their work on Neurospora in which they had suggested that one gene directs the production of one enzyme. Subsequently, many different haemoglobin variants were discovered, most of which resulted from a single amino acid substitution in one or the other of the globin chains. And families were discovered in which two different variants segregated independently, suggesting that the genes for the and chains must reside on different chromosomes. This second thread in the development of the haemoglobin field thus reflects the interaction of widely disparate disciplines, ranging from protein chemistry through population genetics to internal medicine and haematology. The final thread in the early development of the haemoglobin field dates back to 1925, with the independent descriptions of a severe form of childhood anaemia, later called thalassaemia from Greek roots meaning
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‘‘blood’’ and ‘‘sea’’, by an American paediatrician called Thomas Cooley and by several clinicians in Italy. Work by population geneticists in the 1940s showed that this condition is inherited in a Mendelian recessive fashion. By the 1950s, and with the development of simple methods of electrophoresis, haematologists and geneticists in many countries started to study the haemoglobin pattern of patients with thalassaemia and, in particular, of those who had inherited it together with structural haemoglobin variants. It was found that individuals who had inherited the sickle cell gene from one parent and thalassaemia from the other, and who hence had a condition called sickle cell thalassaemia, showed unusual patterns of haemoglobin production compared with those who had inherited the carrier state for the sickle cell gene; the action of the thalassaemia gene seemed to be to reduce the level of Hb A compared with Hb S in those who had inherited both the genes. This suggested that the basic defect in thalassaemia might be a reduced rate of production of the chains of Hb A. Other patients who produced excess chains were discovered and these chains formed abnormal homotetramers (4), called Hb H. This led two protein chemists, Vernon Ingram and Anthony Stretton, to suggest that there might be two forms of thalassaemia, and , reflecting defective or chain production, respectively (Ingram and Stretton, 1959). Thus by 1960, a great deal was already known about the structure and function of haemoglobin and there were already well-based theories about the mechanisms whereby sickling of red cells might occur and for the molecular basis of the thalassaemias. As evidenced by a number of key international meetings at the time, the field had reached this state through the interaction, largely by chance, of fields ranging from protein chemistry, X-ray crystallography, human physiology, population genetics, haematology, to the emerging field of clinical genetics. None of this was planned; it simply followed naturally when a number of different fields reached a particular phase of development and found a common thread in the inherited disorders of human haemoglobin. Although not central to the evolution of the field itself, another discipline started to abut on research into human haemoglobin in the late 1940s. In the immediate post-war period, and following the first use of atomic bombs in Japan, the budding field of human genetics became particularly interested in factors which might alter the mutation rate in humans. At about the same time it was found that the carrier rate for some forms of thalassaemia is particularly high in certain racial groups, notably those of Mediterranean origin. It was suggested therefore that this might reflect a difference in mutation rate between people of different ethnic background. In 1949, J.B.S Haldane (Haldane, 1949) developed
Disorders of haemoglobin: from phenotype to genotype
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another theory to explain the high frequency of this disease in the Mediterranean populations. Not liking the idea of differential mutation rates, Haldane suggested that the frequent occurrence of this gene in those of Mediterranean background might reflect heterozygote advantage against infection by the malarial parasite, a reasonable suggestion since malaria was a devastating disease in Mediterranean populations up until the end of the Second World War. Although it took many years to provide experimental verification for Haldane’s ‘‘malaria hypothesis’’, in the 1950s Anthony Allison and his colleagues provided evidence that the high frequency of the sickle cell gene in Africa is the result of heterozygote advantage against malaria (Allison, 1954). Indeed, the haemoglobin disorders became the prime example of heterozygote advantage and balanced polymorphism in human populations. Although Haldane’s hypothesis had a major effect on our thinking about the origins of human disease, there was little evidence that he thought much about haemoglobin disorders either before or after the meeting in Stockholm at which he proposed his hypothesis. How did this all come about? Undoubtedly Haldane, like all population geneticists at the time, was interested in mutation rates. At about the time of the meeting in Stockholm, he had been a speaker at several other meetings in Italy where he probably became aware of the existence of thalassaemia. In Stockholm, the coming together of those who had actually studied the distribution of disease and their proposal that it might reflect a differential mutation rate in different ethnic groups, may well have been enough to stimulate Haldane to develop an alternative hypothesis. But whatever the reason, the multidisciplinary development of the haemoglobin field during this period underlines the value of interdisciplinary, international scientific meetings.
3. PREPARATION FOR THE MOLECULAR ERA (1960–1980) Although molecular biology developed at a remarkable pace from the late 1950s, it was not until the late 1970s that the critical technology which arose from this field, became available for the study of human disease. Thus, the progress in the haemoglobin field from 1960 until the late 1970s had to rely on clinical, classical-genetic, and population-based studies. However, during this period a new discipline, protein synthesis, encroached the field, bringing with it a completely new set of theories. The notion that the thalassaemias result from defective production of the or chains of haemoglobin required an experimental approach for its validation. In the mid-1960s a method was developed for the in vitro studies of haemoglobin synthesis, which was based on the incorporation of
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radioactive amino acids into red cell precursors followed by the separation of the globin chains in a quantitative fashion (Weatherall et al., 1965). It became apparent that the thalassaemias are disorders of globin chain synthesis and that the key characteristic is imbalanced globin chain production. This observation, which allowed the thalassaemias to be fully defined at the level of defective globin chain production, spawned several multidisciplinary approaches to the further analysis of the disease. At this time, the thalassaemias were of considerable interest to workers from a wide range of disciplines who wanted to try to understand the molecular mechanisms for defective protein synthesis. Those who participated in this work included the few protein chemists who had remained in the field and who had not migrated to the more exciting pastures of the burgeoning world of molecular biology, some clinical scientists who had become at least partly educated in the field of protein synthesis and its abnormalities, and geneticists from a variety of different backgrounds. It was a time of the application of educated guesswork to develop a series of theories, based at least in part, on information which was becoming available from molecular biology. One hypothesis suggested that defective globin synthesis in thalassaemia might reflect structural changes in the affected globin chain which were not amenable to analysis by electrophoresis. That is, the disease might reflect the action of neutral amino acid substitutions. Another, and much more complex series of ideas were derived from the work of Jacob and Monod (1961) which had described the regulation of enzyme production in microorganisms via the operon model. Although it seemed like a major evolutionary jump from E. coli to man, these potential mechanisms had their attractions! Another theory, which came from the interaction of molecular biologists and geneticists had it that the defective synthesis of the globin chains in thalassaemia might result from neutral substitutions for which there was a relative paucity of transfer RNA. Of course with the limited technology available, it was difficult to test these hypotheses experimentally although some progress was made. For example, after a long series of difficult and tedious experiments, it was possible to show that the rates of the globin-chain initiation, assembly, and termination were normal in those forms of thalassaemia in which some gene product was synthesised. This suggested that in these particular cases, the disease might result from a mutation which caused a reduced amount of normal globin messenger RNA. And, of course, there were some lucky findings that came from simple clinical observations of forms of thalassaemia, which did not fit into the usual pattern of the disease. This led to the discovery, for example, of forms of thalassaemia associated with very small quantities of a structural haemoglobin variant. It turned
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out that this variant was elongated by 31 amino acid residues at its C terminal end, suggesting that it might result from a mutation in the chain termination codon, with read-through of messenger RNA which is not normally translated, a hypothesis which was later ratified when it became possible to sequence human messenger RNA (Clegg et al., 1971). The other major interdisciplinary approach of this period saw the beginnings of an understanding of the phenotype–genotype relationships in thalassaemias and why the disease, even when it appeared to result from the same mutant gene, showed wide clinical variability. This work was carried out mainly by clinical scientists who had been trained in certain aspects of molecular and cell biology, a direct result of the interdisciplinary groups that were established in the late 1950s. It was found that the imbalanced globin chain synthesis leads to an excess of chain production in thalassaemia, and vice versa in thalassaemia, and that the major basis for the severe anaemia which characterise these conditions is the deleterious effect of the chains which are produced in excess on red-cell precursor maturation and on red-cell survival (Nathan and Gunn, 1966). It followed, therefore, that if the major factor in causing the profound anaemia of thalassaemia is the deleterious effect of excess chain precipitation on red-cell precursor maturation and on red-cell survival, anything which might reduce the excess of chains in a child with thalassaemia might ameliorate the disease. One way this could happen might be the co-inheritance of thalassaemia; another, would be the persistent production of high levels of the chains of foetal haemoglobin. In the event, both mechanisms were soon found to be involved, though it required the tools of molecular biology, which only became available later, to put these clinically based observations on a stronger experimental footing. While all this work was being carried out at the level of morphological haematology, haemoglobin synthesis, and the study of the heterogeneity of cell populations, and some genuine information was being obtained about the molecular pathology of the thalassaemias, molecular biology was developing at a phenomenal rate. The multidisciplinary nature of the evolution of this field, ranging from physics through microbial genetics to X-ray crystallography, is recounted elsewhere (see Kay, 1993). The early application of the tools of this field to the study of the haemoglobin disorders was carried out by small groups of scientists, nearly all of whom had clinical backgrounds and who had learnt, either themselves or through interactions with molecular biologists, to apply these new tools to clinical problems. By the early 1970s, methods had become available for isolating human globin messenger RNA and for assessing its level in thalassaemic red-cell precursors. At about the same time Temin and Baltimore, independently,
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isolated the enzyme reverse transcriptase which made it possible to synthesise complementary DNA (cDNA) from messenger RNA. Since red-cell precursors contained almost pure globin messenger RNA it soon became feasible to construct radioactively labelled cDNA copies. An extraordinary valuable tool was thus available to probe the human genome. In 1970, it was found that babies with severe forms of thalassaemia synthesised no chains whatsoever. This led to the hypothesis that they might have complete or at least partial deletions of their globin genes. In 1974, two groups were able to show by cDNA/DNA hybridisation that the globin genes in these infants were largely deleted, the first demonstration of the deletion of a human globin gene (Ottolenghi et al., 1974; Taylor et al., 1974). The other seminal advance in the late 1970s was the invention of a technique which became known as Southern blotting, after its discoverer Ed Southern, a molecular biologist (Southern, 1975). This method, which was based on the earlier discovery of restriction enzymes, that is enzymes that cut DNA at specific base sequences, involved a form of hybridisation in which one of the components in the reaction, the DNA under study, is immobilised on a cellulose nitrate filter. Southern blotting offered an approach to gene analysis in which it was possible to build up a picture of the physical organisation and linkage of genes on chromosomes. The technique was relatively simple and was easily adaptable by clinical research laboratories for the study of the thalassaemias. At about the same time, other seminal advances in molecular biology led to methods for cloning and sequencing the globin genes. The molecular era had arrived.
4. 1980–2003 For a brief period during the late 1970s and early 1980s, a number of molecular biologists descended again on the haemoglobin field and all the human haemoglobin genes were rapidly cloned and sequenced. Gratifyingly, there were no great surprises; the careful work on human pedigrees over the previous 20 years had put the genes in the right order on the right chromosomes. And now it was possible to isolate the defective and genes directly from patients with and thalassaemia. Again, the field was soon driven by new technology with the invention of the polymerase chain reaction (PCR), a method which allowed the rapid amplification of specific DNA sequences for analysis. Armed with these extremely powerful new techniques, a number of clinical research laboratories around the world set about defining the molecular pathology of the and thalassaemias. A remarkable picture of the molecular
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diversity of these diseases emerged and at the current time, over 200 different mutations have been found as the basis for thalassaemia and about 100 for thalassaemia. It turns out that every high-frequency population in the world has a different set of mutations, usually two or three common ones and a large number of rare ones. Thus by the late 1980s, a fair idea had been obtained about the repertoire of mutations that can underlie human genetic disease, although the study of other monogenic diseases was to produce some surprises. The availability of these new analytical techniques also allowed a re-evaluation of the reasons for the phenotypic heterogeneity of the thalassaemias in general and the thalassaemia in particular. The early hypothesis that the co-inheritance of different forms of thalassaemia, or genes which lead to more effective chain production, can lead to a reduced severity of the thalassaemia phenotype were fully validated. Heterogeneity of the globin genes or -gene regulatory regions, together with remarkable variation in the types of thalassaemia mutations, could account for much of the heterogeneity of thalassaemia. Later, it became apparent that many of the complications of the disease are also modified by genetic factors. Indeed, it is now clear that the clinical phenotype of the thalassaemias reflects the action of many different layers of genetic heterogeneity, together with a number of environmental factors (Weatherall, 2001). This increasing knowledge of the molecular pathology and pathophysiology of the thalassaemias has led to a number of advances in prevention and treatment. First, using methods for globin chain synthesis, and later PCR-based DNA technology, it became possible to identify the serious forms of thalassaemia early during fetal development and hence to be able to offer prenatal diagnosis for these diseases. This work required the development of new interdisciplinary teams, with expertise in obstetrics, molecular genetics, clinical haematology, and the social aspects of genetics including counselling and bioethics. Similarly, a genuine understanding of the pathophysiology of the thalassaemias led to marked improvements in their treatment, particularly by a better understanding of the use of blood transfusion and chelating drugs that are required to remove iron which accumulates due to chronic administration of red cells. Again, new disciplines were brought together during the development of these therapeutic improvements, including blood transfusion, infectious disease, iron metabolism, and endocrinology. At the time of writing, yet another field has become closely related to thalassaemia research. With the isolation of the globin genes and the development of gene-transfer systems the current hope is that it may be
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possible to correct these genetic defects in the different forms of thalassaemia by somatic cell gene therapy. Again, new disciplines have had to amalgamate including molecular biology, virology, and cell biology. Although progress has been slow, there are signs that this approach may be feasible in the future. The other major area which has brought yet another set of disciplines into the field is bone marrow transplantation. Some thalassaemic patients who are fortunate enough to have matched relatives as potential marrow donors have been cured of the disease by transplantation, an endeavour which has drawn on a number of disciplines including immunology, intensive care, and infectious disease.
5. COMMENT This very brief outline of the way in which the human haemoglobin field, particularly research into thalassaemia, has evolved over the last 40 years has some interesting lessons for those who are interested in the development of multidisciplinary approaches to both the theory and practice of medicine. The early development of the field, at least until 1960, reflects the chance coming together of a number of disciplines at just the right time. This was certainly never planned but shows very clearly how individuals from such unlikely backgrounds as protein chemistry or molecular genetics can become involved in a clinical field, rapidly learn enough about the problems to be able to see the value of their technology for further elucidation, and hence become part of an interactive team, at least for a while. However, it is clear that many basic scientists will not wish to stay in more applied fields like clinical research for very long; they are interested more in the ‘‘big’’ problems in their own fields. This phenomena was well evidenced in the haemoglobin field both in the early 1960s and again in the early 1980s; at both times completely new techniques became available which had exciting implications for the haemoglobin field and which, briefly, allowed molecular biologists to attack problems which were of fundamental biological interest as well as of medical importance. It should be emphasised that these short-term interdisciplinary interactions between scientists from widely different fields and backgrounds were equally important in developing both new ideas and theories to explain many of the problems of the haemoglobin field and in designing the experimental methods required for their validation. On the other hand, the groups that came together which represented different clinical disciplines over this long period tended to interact more naturally and stay together much longer. Although clinical
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haematologists or paediatricians took over the central role of management of the thalassaemias and sickle cell anaemia, they frequently interacted with specialists from a wide range of different medical fields. However, reflecting the increasing divergence of the clinical specialties, there were some downsides. For example, the haemoglobin field became estranged from the newly developing discipline of clinical genetics and from general internal medicine and paediatrics. At least in the developed countries, clinicians evolved who devoted the bulk of their time to the management of haemoglobin disorders, sometimes excluding their patients from the more holistic skills of the rapidly disappearing generalist. During the last part of the twentieth century, the techniques of molecular and cell biology started to be applied right across the field of medical research and there were few diseases which did not become the subject of work in what became known, rather optimistically, as molecular medicine. Clearly, the rather haphazard way in which interdisciplinary theory and practice had evolved in the haemoglobin field would not be good enough for the future. By the mid-1980s, a fundamental series of problems arose. For the most effective application of this new and complex technology to medical research, it was clear that multidisciplinary teams were required, made up both of clinicians with at least some training in the tools of molecular and cell biology and more professional molecular and cell biologists. But where were the clinicians who were to make up these teams to be trained in the tools of molecular and cell biology? And would top-rate molecular biologists wish to develop their careers in clinical departments where they would be isolated from their colleagues? As a model solution to this problem, in Oxford, the Institute of Molecular Medicine was developed in the 1980s. The idea was to house a number of different groups working on specific clinical problems which required the tools of molecular and cell biology. The building would be staffed by clinicians who had been trained in the field, or by young molecular biologists who wished to make their careers in medical research. In this way, it was hoped that a genuine multidisciplinary environment would be achieved which would provide an ideal training ground for both clinical and non-clinical scientists who wished to work in molecular medicine. Young clinicians could be trained in an environment in which the longer-term objective was to apply the sophisticated tools of molecular biology more directly to clinically related problems. At the same time, molecular biologists who wished to learn enough about human disease to be able to apply their tools to its study would find themselves in an environment in which this was possible and where they were not isolated from other scientists in their field. An extension of this model has been subjected to a limited trial by attempting to ensure that both clinicians
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and scientists have a home base in appropriate departments, with their major centre of activity being in the Institute. This model was reasonably successful and has been adapted by many other universities. Indeed, given the complexities of the future evolution of the fields of genomics research, it seems likely that this will be the appropriate way forward for the organisation of research in universities, and to some degree in industry, for the foreseeable future.
6. SUMMARY Using a brief outline of the development of the human haemoglobin field, the characteristics and importance of interdisciplinary research groups for developing both theory and experimental basis for its validation have been described. The subject evolved from the chance coming together of disparate disciplines to the concept of a more organised and integrated approach, at least within the university system. So far, the multidisciplinary group approach has covered only a limited number of disciplines. For the full exploitation of the potential of the remarkable developments in the biological sciences of the last 10 years it may, in the longer term, be necessary to expand the scope of these groups, incorporating the fields of epidemiology, public health, and social sciences. It should be emphasised that these collaborations and integrations cannot be forced on science; they tend to happen naturally when a field is at a particular state of development. Hence it is the role of universities, and other bodies in which medical research is carried out, to ensure that the appropriate facilities are available to house and support integrated groups of this type, or to plan the geography of research facilities such that close interaction, including social contact, is widely encouraged.
REFERENCES Allison, A.C., 1954. Protection afforded by sickle-cell trait against subtertian malarial infection. Br. Med. J. 1, 290–294. Clegg, J.B., Weatherall, D.J., Milner, P.F., 1971. Haemoglobin Constant Spring – a chain termination mutant? Nature 234, 337. Haldane, J.B.S., 1949. Disease and evolution. Ricera Sci. 19, 2. Ingram, V.M., 1956. Specific chemical difference between the globins of Normal human and sickle-cell anaemia haemoglobin. Nature 178, 792–794. Ingram, V.M., Stretton, A.O.W., 1959. Genetic basis of the thalassemia diseases. Nature 184, 1903–1909. Jacob, F., Monod, J., 1961. Genetic regulatory mechanisms in the synthesis of proteins. J. Mol. Biol. 3, 318.
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Kay, L.E., 1993. The Molecular Vision of Life. Oxford University Press, New York and Oxford. Nathan, D.G., Gunn, R.B., 1966. Thalassemia: the consequences of unbalanced hemoglobin synthesis. Am. J. Med. 41, 815–830. Ottolenghi, S., Lanyon, W.G., Paul, J., Williamson, R., Weatherall, D.J., Clegg, J.B., Pritchard, J., Pootrakul, S., Wong, H.B., 1974. The severe form of thalassaemia is caused by a haemoglobin gene deletion. Nature 251, 389–392. Pauling, L., Itano, H.A., Singer, S.J., Wells, I.G., 1949. Sickle-cell anemia, a molecular disease. Science 110, 543–548. Perutz, M.F., Rossman, M.G., Cullis, A.F., Muirhead, H., Will, G., North, A.C.T., 1960. Structure of haemoglobin. Nature 185, 416–422. Southern, E.M., 1975. Detection of specific sequences among DNA fragments separated by gel electrophoresis. J. Mol. Biol. 98, 503. Taylor, J.M., Dozy, A., Kan, Y.W., Varmus, H.E., Lie-Injo, L.E., Ganeson, J., Todd, D., 1974. Genetic lesion in homozygous -thalassaemia (hydrops foetalis). Nature 251, 392–393. Weatherall, D.J., 1995. Science and The Quiet Art. The Role of Research in Medicine. Rockefeller University, W.W. Norton, Oxford University Press, New York. Weatherall, D.J., 2001. Phenotype-genotype relationships in monogenic disease: lessons from the thalassaemias. Nature Reviews Genetics 2, 245–255. Weatherall, D.J., Clegg, J.B., 1999. Genetic disorders of hemoglobin. Semin. Hemat. 36, 24. Weatherall, D.J., Clegg, J.B., 2001. The Thalassaemia Syndromes, 4th Edition. Blackwell Science, Oxford. Weatherall, D.J., Clegg, J.B., Naughton, M.A., 1965. Globin synthesis in thalassemia: an in vitro study. Nature 208, 1061–1065. Weatherall, D.J., 2004. Thalassaemia: the long road from bedside to genome. Nature Reviews Genetics 5(8), 625–631.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
2 Between bleeding and thrombosis or beyond Cheng Hock Toh Department of Haematology, The University of Liverpool, Liverpool, UK
1. INTRODUCTION Coagulation evolved as a means to stem blood loss and as defence against pathogens. Its origins from a basic primitive system, which could support a fluid transport system, lends a central importance to this biological system. It also provides interconnecting relevance to other co- or subsequently evolving processes. Central amongst these is its link to inflammation. Increasingly, paradigms of disease pathogenesis once thought to be solely inflammatory in nature have now shifted to recognise the key role played by coagulation. Some observations have arisen by serendipity but therapies that target the broad inflammatory–coagulation complex have now had successes when previous strategies, derived from linear models of disease pathogenesis, have failed. This chapter discusses coagulation starting from an evolutionary perspective to show how its further understanding, both from the point of complex biology and the pathology of haemorrhagic disorders, can help reduce morbidity as well as mortality in diseases varying from myocardial infarction to sepsis.
2. EVOLUTIONARY RELEVANCE OF COAGULATION The response to injury and the mechanism that arrests bleeding, via formation of an adequate blood clot or coagulum, has been critical to human survival. The central importance of this haemostatic system is also highlighted by its evolutionary history in pre-dating mammalian development itself (Doolittle, 1993; Davidson et al., 2003). Data from biochemical, molecular cloning, and comparative sequence analysis show evidence to support the existence of similar coagulation components in all jawed 15
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vertebrates, thus suggesting that the haemostatic system evolved before the divergence of teleosts over 430 million years ago (Sheehan et al., 2001; Hanumanthaiah et al., 2002). Although the high-amplification response to injury in humans is more exquisitely defined and tightly regulated, a basic blood coagulation network involving a tissue-based initiator is also present in jawless vertebrates (hack fish and lamprey) that diverged over 450 million years ago (Doolittle et al., 1962; Strong et al., 1985; Banfield and MacGillivray, 1992). Phylogenetic analysis of amino acid sequences indicates that the evolution of blood coagulation networks have been through two rounds of gene duplication and this evidence lends support to the hypothesis that vertebrate evolution itself benefited from two global gene duplications (Holland et al., 1994; Abi-Rached et al., 2002). Although the physiologically important components of the mammalian coagulation network now have functionally distinct properties, there are unifying and recurring themes to many of the critical reactions. One example is the assembly of complexes between a vitamin-K-dependent serine protease with a gamma carboxylated glutamic acid domain, divalent cations to bind negatively charged phospholipid surfaces, and a co-factor to facilitate kinetic amplification. The genes for several of these factors relevant to the haemostatic system are located on separate chromosomes in humans. This further suggests that large block or possibly whole genome duplication events contributed to the evolution of the mammalian blood coagulation network. This network, therefore, offers an opportunity to study the molecular evolution of complex biological processes. In vertebrates, the activation of the coagulation cascade by tissue factor is central to both the repair of tissue injury and the host defence towards microbial invasion to retard its dissemination. Cells of the innate immune system participate in the interdependent pathways of coagulation and inflammation (Muta and Iwanaga, 1996). Several factors within the coagulation system share structural similarity to components of the inflammatory pathway. For instance, tissue factor or the primary tissue-based initiator of coagulation has structural homology to the cytokine receptors (Morrisey et al., 1987); the cell-surface receptor thrombomodulin that regulates thrombosis has homology to selectins involved with white blood cell adhesion (Sadler, 1997) and the structure of the endothelial protein C receptor which is also involved in the anticoagulant pathway is almost superimposable over the structure of the corresponding regions of the major histocompatibility complex (MHC) class 1/CD1 family of molecules (Fukudome and Esmon, 1994). Furthermore, linkages to the complement system can be seen in the interaction of complement 4-binding protein with the anticoagulant protein S (Dahlba¨ck, 1991). Together these
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structural observations and interactions suggest that the coagulation and inflammatory pathways interact and that there is tight evolutionary linkage.
3. COMPLEX BIOLOGICAL SYSTEM As in any other physiological system, the haemostatic pathway is finely regulated and homeostatically maintained. The initial event to injury involves a predominately cellular response following blood vessel constriction and the rapid formation of a haemostatic plug, via platelet–von Willebrand factor–collagen dependent interactions (Sjobring et al., 2002). The platelet, like its invertebrate counterpart the haemocyte, sets in motion a cascade of enzymes that ultimately leads to a protein clot. In humans (and other vertebrates), the clottable protein is fibrinogen and its product, fibrin. The mechanism leading to fibrin formation is a complex network of interactions regulated by positive and negative feedback loops and by a series of activation steps based on the conversion of inactive zymogens into enzymatic forms (fig. 1). This is first initiated by the exposure of tissue factor to factor VII (Rapaport and Rao, 1992). Activation of factor VII to its enzymatic form, factor VIIa results in the activation of factor IX and factor X by this tissue factor–factor VIIa complex. This initial factor Xa generated only leads to trace amounts of thrombin generation
Fig. 1. Thrombin action on various cell types and working model of its function at the endothelial cell surface. Its procoagulant function is in the conversion of fibrinogen to fibrin with simultaneous activation of the anticoagulant pathway, via activated protein C (APC) generation and clot consolidation through prevention of lysis, via generation of activated thrombin activatable fibrinolysis inhibitor (TAFIa) in a thrombomodulin (TM) dependent manner. EPCR ¼ endothelial protein C receptor; PAR ¼ protease activated receptor.
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(Lawson et al., 1994). Although insufficient to initiate significant fibrin polymerisation, these trace amounts of thrombin can then back activate factor V and factor VIII into their enzymatic forms, which then lead to the amplified and explosive generation of thrombin (Mann et al., 1988). The reactions to generate further factor Xa (tenase) and thrombin (prothrombinase) are based on this recurring theme of vitamin-K-dependent proteins, divalent cations, and the presence of a co-factor to accelerate the reaction (Naito and Fuijkawa, 1991). It is this propagation phase that ultimately leads to the generation of a stable fibrin clot. Notably, the process of propagation occurs independent of the initiating tissue factor–factor VIIa complex, which is rapidly inactivated by the tissue factor pathway inhibitor. The negative feedback loop to prevent blood from over-coagulating is also dependent on the ubiquity of thrombin in also promoting the anticoagulant pathway. At the cell surface, thrombin can bind to the receptor thrombomodulin, which allosterically alters its substrate specificity so that its pro-coagulant substrates are no longer efficiently proteolysed. Instead, the substrate of the thrombin–thrombomodulin complex is protein C, the vitamin-K-dependent zymogen that is then proteolysed into activated protein C (Esmon, 1989). Activated protein C, in complex with its co-factor protein S and in the presence of calcium and anionic phospholipids can then rapidly inactivate the procoagulant co-factors factor Va and factor VIIIa (Kalafatis et al., 1994). This ability is greatly enhanced by the endothelial protein C receptor, which facilitates presentation of protein C to the thrombin–thrombomodulin complex. Further negative regulation of blood coagulation also occurs through the activity of antithrombin. Antithrombin can complex to thrombin, factor Xa that is then rapidly cleared by the liver. The system of checks and balances also involve the regulation of this endogenous anticoagulant and fibrinolytic pathway (Hockin et al., 2002). Protein C inhibitor is the primary inactivator of activated protein C but other members of the serine protease inhibitor (SERPIN) family with structural homology, such as 1-antitrypsin serve as back-up inhibitors (Scully et al., 1993). Fibrinolysis or the process of fibrin degradation itself has to be well regulated to both prevent premature clot breakdown and ensure appropriate clot clearance in coincidence with tissue healing. Tissue and urokinase-type plasminogen activators of fibrinolysis are readily released from endothelial cells to convert plasminogen into the main fibrinolytic enzyme, plasmin which lyses cross-linked fibrin. Suppression of fibrinolysis is by way of release of plasminogen activator inhibitor-1 and augmented by a thrombin–thrombomodulin-dependent activation of a metallo-carboxypeptidase called thrombin activatable fibrinolysis inhibitor (TAFI) (Bajzar et al., 1996). Activated TAFI exerts
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its anti-fibrinolytic activity by preventing the binding of plasminogen to partially digested fibrin that is the pre-requisite for its conversion to plasmin. The common link of thrombin–thrombomodulin dependence activation for both activated protein C and activated TAFI generation tightly couples the processes of coagulation with fibrinolysis.
4. PATHOLOGY OF COAGULATION: BLEEDING AND THROMBOTIC CONDITIONS 4.1. Localised Whilst bleeding has always been a major health hazard, thrombosis is a relatively modern disease that has arisen as an aberration in the body’s protective haemostatic response due to the increasing discordance between the pace of social and biological evolution. Bleeding or haemorrhagic tendencies can arise from deficiencies in components of the haemostatic system, i.e. from platelets to von Willebrand factor and coagulation factors (Turitto et al., 1985). Historically, haemophilia has been the best known in terms of major morbidity and mortality and this is due to a lack of the coagulation factors VIII and IX, respectively sub-classified as haemophilia A and B (Mannucci and Tuddenbam, 1999). In these conditions, the severity of bleeding is directly related to its numerical circulatory concentration. However, deficiencies of factor VII or XI are less predictable with regard to a bleeding tendency and this may be because of considerable redundancy in the complex system or the relatively little amounts required of the more proximal components of the coagulation system to trigger the amplification cascade (Von dem Borne et al., 1997). The propagationphase of thrombin generation is therefore important in this respect. Conversely, loss of function mutations that occur in the anticoagulant pathway are associated with thrombophilia or a tendency towards venous thromboembolism. However, these are relatively uncommon and deficiencies of antithrombin, proteins C and S together only account for less than 5% of all inherited thrombophilias in the Caucasian population (Simioni et al., 1999). More common is gain of function mutations, for example, in genes affecting the propagation phase of thrombin generation. The factor V Leiden mutation renders the molecule less susceptible to proteolytic degradation by activated protein C and the prothrombin gene mutation G20210A can increase prothrombin levels (Poort et al., 1996; Simioni et al., 1997). These occur in 5 and 3% of the Caucasian population, respectively and this degree of prevalence suggests some evolutionary benefit through possible advantages against haemorrhagic death at
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childbirth and injury. However, even with the inclusion of these analyses, approximately 40% of all thrombophilia are currently unexplained. Cumulative increases in the factor IX (van Hylckama Vlieg et al., 2000) and factor XI (Meijers et al., 2000) towards an unquenched propagation phase of thrombin generation may be contributory in tilting the haemostatic balance towards a prothrombotic state. In addition, inflammatory changes affecting the vessel wall can promote thrombus formation in the arterial circulation when atherosclerotic lesions fissure or rupture to expose tissue factor and trigger off coagulation (Ridker et al., 1997). Atherosclerosis results from an intricate interplay between diverse factors, such as lipid metabolism, coagulation factors, inflammatory cytokines, and behavioural risk factors. The lipid surfaces propagate coagulation by providing anionic phospholipid surfaces and critically affect the size of the thrombus whilst the pattern of inflammation involves macrophage, B and T cell activation, alteration in lymphocyte subset ratios, and elevation of inflammatory cytokines, such as tumour necrosis factor and interleukin-1 (Ray et al., 2002).
4.2. Systemic When coagulation activation is excessive, the fine balance of maintaining haemostasis and preventing thrombosis becomes lost. Such dysfunction can occur as a consequence of major insults, such as sepsis and severe trauma. In vivo, thrombin generation becomes abnormally sustained, pathologically enhanced, to then escape the physiological control that normally keeps the process localised. This is the hallmark of disseminated intravascular coagulation (DIC) and its clinical manifestation can be at any point in the coagulation spectrum from bleeding to microvascular thrombosis and beyond to include capillary leak and oedema; depending on host genetic responses to thrombin (Toh and Dennis, 2003). In addition to affecting coagulation, the inflammatory pathway is also directly stimulated by thrombin (Cirino et al., 1996). Cell signalling occurs via thrombin binding to protease activated receptors to induce the release of inflammatory cytokines (Coughlin, 2000). Pro-inflammatory cytokines, such as tumour necrosis factor- and interleukin-1 are also able to promote further thrombin generation to then fuel the continuous spiral between inflammation and coagulation. The same cytokines that are involved in localised arterial disease also play out here but in far greater magnitude and with more overt mechanisms in the systemic circulation. The ultimate consequence of this unchecked cycle is tissue damage, organ failure, and death.
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Its pathophysiology is complex and includes a non-linear interplay between multiple cell types and soluble mediators that theoretically exemplify the most innate of responses in which inflammation and coagulation processes are inseparable (Aird, 2002). The invoking of simultaneous inflammatory and coagulant responses to a severe injurious insult forms part of this overall host response, which is initially protective (fig. 2). This rapid acute phase reaction is characterised by the release of mediators such as C reactive protein, which are part of host defence. Mice genetically programmed to over express C reactive protein are less vulnerable to sepsis and human as well as mice models heterozygous for the factor V Leiden mutation (with the greater propensity for initial thrombin generation) are also protected from sepsis lethality (Kerlin et al., 2003). The onset of DIC however, appears to be at the point when the adaptive threshold response is crossed and the maladaptive phase of this host response can then have potentially lethal consequences. At this juncture, other mediators that can further enhance thrombin generation become involved. Changes in lipid metabolism favour the predominance of very low density lipoprotein which can then complex with C reactive protein to modulate its activity and provide increased negatively charged phospholipid surfaces to fuel
Fig. 2. The control of coagulation and inflammation by thrombin generation. The square boxes represent the enzymatic amplification steps involving a vitamin-K-dependent enzyme, a cofactor (represented in italics), calcium ions (Caþþ), and phospholipid (PL) surfaces. The propagation phase, when disrupted leads to bleeding and when enhanced, i.e. by factors represented in the hashed rectangular box, produces localised thrombosis or systemic disseminated intravascular coagulation. The inflammatory signalling pathways are triggered via thrombin binding to the protease activated receptors with recruitment of processes including Rho-dependent cytoskeletal responses, calcium mobilisation, and activation of protein kinase C to mediate responses ranging from granule secretion, integrin activation to transcriptional responses. PI3K modifies the inner leaflet of the membrane to provide attachment sites for signalling proteins. IP3 ¼ inositol triphosphate; DAG ¼ diacylglycerol.
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further thrombin generation (Krishnaswamy et al., 1992; Toh et al., 2002). Such surfaces, which can accelerate the prothrombinase reaction dramatically by 250,000-fold are also provided as a consequence of endothelial and circulating cell damage. Translocation of the inner leaflet of cell membranes as well as the formation and release of micro-particles into the circulation can further promote thrombin generation. Such excesses of thrombin formation no longer generate overall benefit to the host and mice models that are homozygous for the factor V Leiden mutation suffer increased lethality to the septic challenge (Kerlin et al., 2003).
5. MEDICAL ASPECTS OF COAGULATION 5.1. Diagnostics Bleeding and thrombosis. Compared to thrombosis, the diagnosis of a bleeding tendency and its prediction of severity is relatively straightforward. This probably reflects evolutionary streamlining in determining the key factors critical for survival. As highlighted above, there is generally good correlation between levels of coagulation factors VIII and IX and the risk of haemophila-related bleeding. By contrast, prediction of primary or recurring thrombosis is still somewhat uncertain despite significant progress in its understanding over the last decade. Added to this is the inherent difference in risk factors between venous and arterial thrombosis. Although both have occlusive clot formation as the final event leading to disease, risk factors for both disorders only partially overlap. In the low-pressure venous vascular bed, stasis and hypercoagulability play major roles as risk factors for venous thrombosis. The occurrence of arterial thrombosis is mainly determined by the development of atherosclerotic changes in the arterial vessel wall. To predict thrombosis in the different vascular trees is important for therapeutic targeting and currently requires knowledge of the risk factors involved. The concept of thrombosis is that of a multigenic and multicausal disease, i.e. disease will only develop in the presence of several interacting determinants. The use of female hormones illustrates this point both for venous and for arterial thrombosis. Several large controlled studies have shown a 3-fold increased risk of venous thromboembolism for oral contraceptive users versus non-users (Bloemenkamp et al., 1995; World Health Organization, 1995). The presence of hereditary thrombophilia however can greatly enhance this risk by up to 15–30-fold, for example in carriers of the factor V Leiden and prothrombin 20210A mutations (Vandenbroucke et al., 1994).
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Many studies have also confirmed an association between oral contraceptive use and the occurrence of myocardial infarction and ischaemic stroke by 3-to-5 fold (Mann et al., 1975; Shapiro et al., 1979; World Health Organization, 1997). In contrast to the case of venous thrombosis, women with factor V Leiden or prothrombin 20210A do not have an increased risk of myocardial infarction when they start using oral contraceptives beyond the risk in women without these mutations (Rosendaal et al., 1997). The risk is however compounded in the presence of metabolic risk factors such as hyperlipidaemia (25-fold), diabetes (17-fold), and smoking (17-fold). The mechanism in operation for arterial thrombosis appears to be that linking inflammation, lipid metabolism, and coagulation. The evidence for atherosclerosis being an inflammatory state is now considerable and circulating levels of C reactive protein, the archetypal biomarker of inflammation, have recently been shown to better predict cardiovascular events than traditional markers of lipid disturbance, such as cholesterol (Ridker et al., 2002). Apart from marking the process of inflammation, there is also evidence of its direct participation in atherosclerosis (Yeh et al., 2001). The pathophysiological basis of thrombosis therefore involves multiple genes and pleiotropic environmental factors (Freeman et al., 2002). Most of our current knowledge regarding genetic factors are limited to association studies that employ case-control design to look at known variations in candidate genes. Studies are required that will map genes influencing quantitative variation in thrombosis susceptibility. Such approaches have been applied in other common complex diseases, such as type 2 diabetes, gallbladder disease, and obesity (Hager et al., 1998). Identification of underlying quantitative trait loci that influence disease susceptibility can also identify novel genetic contributors to the underlying biologic pathway (Blangero et al., 2000). Beyond localising these quantitative trait loci, a further need is for statistical identification of functional polymorphisms (Almasy and Blangero, 1998). Analyses to date have used Bayesian quantitative trait nucleotide analysis, which is extremely computer intensive, but through biocomputational modeling, could rapidly expand understanding in this field. Disseminated intravascular coagulation. When derangement of coagulation is extensive to the point of extremis, the diagnosis of DIC is straightforward. The classically characterised laboratory findings are prolonged clotting times (e.g. prothrombin time, activated partial thromboplastin time, elevated products of fibrin breakdown, low platelet counts, and fibrinogen (Toh and Dennis, 2003). However, the diagnosis of DIC at this overt stage is usually relatively late for therapeutic benefit due to the irreversible decompensation that would have occurred. There are
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moves therefore, to try and identify this earlier at a non-overt stage of DIC (Taylor et al., 2001). By identifying circulating biomarkers that propagate rather than initiate thrombin generation and which indicate an early stage of the disseminating process, promising data has now emerged for prognostication in DIC. Such diagnostic tools can predict, monitor, and guide therapeutic targeting. Of interest is that the same biomarkers that predict DIC are equally also useful in the forewarning of sepsis development (Toh et al., 2003). This is probably reflecting the tight and inseparable links between the processes of coagulation and inflammation within the critically ill, irrespective of whether the phenotypic manifestation is predominantly coagulant or septic in nature. This close convergence of the same markers for predicting adverse outcome also applies to mortality prognostication. Mapping the topology of these links and connections is likely to banish consideration of sepsis and DIC as separate entities, except only at the time of initiation. Convergence on a common and complex but individually determined course from genetic host differences poses a challenge for the revised model to be workable. However, novel therapeutic strategies might then emerge to improve on currently dismal survival figures of less than 30%.
5.2. THERAPEUTICS Bleeding. Haemophilia treatment has been relatively straightforward through replacement of the missing coagulation factor. Progress in the last three decades, has seen haemophilia moving from the status of a neglected and often fatal hereditary disorder to that of a fully defined group of molecular-pathological entities for which safe and effective treatment is available (Mannucci and Tuddenbam, 1999). Indeed, haemophilia is widely considered to be the first widespread severe genetic condition to be cured by gene therapy in the third millennium. The condition is well suited for gene therapies since it is due to a single-gene defect and the therapeutic window is relatively broad (High, 2002). A slight increase in plasma factors VIII or IX can potentially convert severe to mild haemophilia and this would obviate the risk of spontaneous bleeding, the need for repeated replacement factor infusions, and the risk of viral infection associated with plasma-derived factor replacement. Thrombosis. Although treatment in this field has had a major impact, mortality in this area of public health is still very high. The decrease in cardiovascular mortality has been through thrombolytic therapies, such as
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streptokinase and tissue plasminogen activator (Fibrinolytic Therapy Trialists’ Collaborative Group, 1994), in the acute management of myocardial infarctions and the wider use of anti-platelet and anticoagulant agents for prevention. Whilst drugs such as aspirin and warfarin have been generally beneficial, there are treatment failures as well as persistent concerns over individual bleeding risk when decisions are still based on fairly empirical risk:benefit evaluations (Sarasin and Bournameaux, 1998; Lindmarker et al., 1999). This might benefit from improved estimation of quantitative risk of recurrent thrombosis (including fatal pulmonary embolus) and major bleeding (including fatal bleeding) over time (Prandoni et al., 2002). Advancements in pharmacogenetics, for example have recognised that sequence variations within genes and coding metabolising enzymes like CYP2D6 can increase response to warfarin and increase the risk of bleeding (Aithal et al., 1999). Equally, development of therapies that target critical elements of the coagulationinflammatory axis are of importance for the future of arterial thrombotic management. The concept that the same mediators act out in chronic arthrosclerosis as in acute sepsis, but at a localised level rather than systemically, would suggest that lessons learnt in one condition might have ramifications for the other. Disseminated intravascular coagulation. The recent success of a recombinant form of human-activated protein C in severe sepsis (Bernard et al., 2001), whereby mortality at 28 days was significantly reduced from 30.8 to 24.7%, has been an important breakthrough, both from a therapeutic angle as well as from a mechanistic perspective. This is of significance especially as all other therapies have failed to improve survival in patients with severe sepsis who can continue to deteriorate even when appropriate antibiotics have been used. This therapeutic success also focuses relevance upon the role of thrombin in sepsis, as it does in DIC. As indicated earlier, activated protein C is an anticoagulant but it also has direct anti-inflammatory and antiapoptotic properties (Joyce et al., 2001). These dual properties are highly relevant, as therapies that have only targeted the inflammatory cascade or only the coagulation pathway have not improved survival. However, the biologic plausibility of activated protein C treatment results are mired in a maze as inflammation and coagulation pathways remain to be clearly deciphered. It does at least promise new hope and a step in the right direction for these patients with overwhelmingly high mortality rates. A better model of knowledge in DIC-sepsis could also translate to treatment benefits in arterial thrombosis as previously discussed. Many of the same players are involved, suggesting evolutionary linkage constitutive of an
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innate inflammatory–coagulation response. The more overt playing field of sepsis-DIC potentially offers an easier panorama of the multi-faceted events than in the more insidious localised pathology of arterial thrombosis.
6. CONCLUSIONS The molecular refinement that has made the coagulation system a successful evolutionary development has somewhat fallen foul of human adaptation to its social environment. The coagulation system has now become a target in the treatment of modern disease such as thrombosis. However, it appears that interrupting clot formation with the use of anticoagulants and anti-platelet drugs is not sufficient, as cardiovascular mortality remains high. The new knowledge that the cycle of inflammation, coagulation, and lipid metabolism is closely linked poses the big challenge to decipher its non-linear dynamics and the large number of components involved. These components can display both marked variability over time as well as high degrees of connectivity or interdependence. The extraordinary durability of coagulation over the past 450 million years does however make this a worthwhile challenge for future, far-reaching rewards especially as the information may also be highly relevant to the area of sepsis. Potentially, modelling prediction and treatment in one area can have positive ramifications for other areas. This kind of work will require crossdisciplinary interactions; from evolutionary to molecular and cellular biology, statistics and biocomputational science to pharmacogenetics and developmental therapeutics to the clinical sciences involving at the very least cardiology, haematology, and intensive care in the present time.
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Banfield, D.K., MacGillivray, R.T., 1992. Partial characterization of vertebrate prothrombin cDNAs: amplification and sequence analysis of the B chain of thrombin from nine different species. Proc. Natl. Acad. Sci. USA 89, 2779–2783. Bernard, G.R., Vincent, J.L., Laterre, P.F., LaRosa, S.P., Dhainaut, J.F., Lopez-Rodriguez, A., Steingrub, J.S., Garber, G.E., Helterbrand, J.D., Ely, E.W., Fisher, C.J. Jr., 2001. Efficacy and safety of recombinant human activated protein C for severe sepsis. N. Engl. J. Med. 344, 759–762. Blangero, J., Williams, J.T., Almasy, L., 2000. Quantitative trait locus mapping using human pedigrees. Hum. Biol. 72, 35–62. Bloemenkamp, K.W.M., Rosendaal, F.R., Helmerhorst, F.M., Bu¨ller, H.R., Vandenbroucke, J.P., 1995. Enhancement by factor V Leiden mutation of risk of deep-vein thrombosis associated with oral contraceptives containing a third-generation progestagen. Lancet 346, 1593–1596. Cirino, G., Cicala, C., Bucci, M.R., Sorrentino, L., Maraganore, J.M., Stone, S.R., 1996. Thrombin functions as an inflammatory mediator through activation of its receptor. J. Exp. Med. 183, 821–827. Coughlin, S.R., 2000. Thrombin signalling and protease-activated receptors. Nature 407, 258–264. Dahlba¨ck, B., 1991. Protein S and C4b-binding protein: components involved in the regulations of the protein C anticoagulant system. Thromb. Haemost. 66, 49–61. Davidson, C.J., Hirt, R.P., Lal, K., Snell, P., Elgar, G., Tuddenham, E.G.D., McVey, J., 2003. Molecular evolution of the vertebrate blood coagulation network. Thromb. Haemost. 89, 420–428. Doolittle, R.F., Oncley, J.L., Surgenor, D.M., 1962. Species differences in the interaction of thrombin and fibrinogen. J. Biol. Chem. 237, 3123–3127. Doolittle, R.F., 1993. The evolution of vertebrate blood coagulation; a case of Yin and Yang. Thromb. Haemost. 70, 24–28. Esmon, C.T., 1989. The roles of protein C and thrombomodulin in the regulation of blood coagulation. J. Biol. Chem. 267, 4743–4746. Fibrinolytic Therapy Trialists’ (FTT) Collaborative Group, 1994. Indications for fibrinolytic therapy in suspected acute myocardial infarction; collaborative overview of early mortality and major morbidity results from all randomised trials of more than 1000 patients. Lancet 343, 311–322. Freeman, M.S., Mansfield, M.W., Barret, J.H., Grant, P.J., 2002. Genetic contribution to circulating levels of hemostatic factors in healthy families with effects of known genetic polymorphisms on heritabilty. Arterioscler. Thromb. Vasc. Biol. 22, 506–510. Fukudome, K., Esmon, C.T., 1994. Identification, cloning and regulations of a novel endothelial cell protein C/activated protein C receptor. J. Biol. Chem. 269, 6486–6491. Hager, J., Dina, C., Francke, S., Dubois, S., Hourari, M., Vatin, V., Vaillant, E., Lorentz, N., Basedevant, A., Clement, K., Guy-Grande, B., Froguel, P., 1998. A genome-wide scan for human obesity genes reveals a major susceptibility locus on chromosome 10. Nat. Genet. 20, 304–308. Hanumanthaiah, R., Day, K., Jagadeeswaran, P., 2002. Comprehensive analysis of blood coagulation pathways in teleostei, evolution of coagulation factor genes and identification of zebrafish factor VIII. Blood Cells Mol. Dis. 29, 57–68. High, K., 2002. AAV-mediated gene transfer for hemophilia. Genet. Med. 4, 56S–62S. Hockin, M.F., Jones, K.C., Everse, S.J., Mann, K.G., 2002. A model for the stoichiometric regulation of blood coagulation. J. Biol. Chem. 277, 18322–18333.
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Rapaport, S.I., Rao, L.V.M., 1992. Initiation and regulation of tissue factor dependent blood coagulation. Arterioscler. Thromb. 12, 1111–1121. Ray, K.K., Camp, N.J., Bennett, C.E., Francis, S.E., Crossman, D.C., 2002. Genetic Variation at the interleukin-1 locus is a determinant of change in soluble endothelial factors in patients with acute coronary syndromes. Clin. Sci. (Lond). 103, 303–310. Ridker, P.M., Cushman, M., Stampfer, M.J., et al., 1997. Inflammation, asprin, and the risk of cardiovascular disease in apparently healthy men. N. Engl. J. Med. 336, 973–999. Ridker, P.M., Rifai, N., Rose, L., et al., 2002. Comparison of C-reactive protein and lowdensity lipoprotein cholesterol levels in the prediction of first prediction of first cardiovascular events. N. Engl. J. Med. 347, 1557–1565. Rosendaal, F.R., Siscovick, D.S., Schwartz, S.M., Psaty, B.M., Raghunathan, T.E., Vos, H.L., 1997. A common prothrombin variant (20210 G to A) increase the risk of myocardial infarction in young women. Blood 90, 1747–1750. Sadler, J.E., 1997. Thrombomodulin structure and function. Thromb. Haemost. 78, 392–395. Sarasin, F.P., Bournameaux, H., 1998. Decision analysis model of the prolonged oral anticoagulant treatment in factor V Leiden carriers with first episode of DVT. BMJ 316, 95–99. Scully, M.F., Toh, C.H., Hoogendoorn, H., Manuel, R.P., Nesheim, M.E., Solymoss, S., Giles, A.R., 1993. Activation of protein C and its distribution between its inhibitors, protein C inhibitor, alpha 1-antitrypsin and alpha-2 macroglobulin, in patients with disseminated intravascular coagulation. Thromb. Haemost. 69, 448–453. Shapiro, S., Slone, D., Rosenberg, L., Kaufman, D.W., Stolley, P.D., Miettinen, O.S., 1979. Oral-contraceptive use in relation to myocardial infarction. Lancet 1, 743–747. Sheehan, J., Templer, M., Gregory, M., Hanumanthaiah, R., Troyer, D., Phan, T., Thankavel, B., Jagadeeswaran, P., 2001. Demonstration of the extrinsic coagulation pathway in teleostei: identification of zebrafish coagulation factor VII. Proc. Natl. Acad. Sci. USA 98, 8768–8773. Simioni, P., Prandoni, P., Lensing, A.W.A., Scudeller, A., Sardella, C., Prins, M.H., Villalta, S., Dazzi, F., Girolami, A., 1997. The Risk of recurrent venous thromboembolism in patients with an Arg506 ! G1n mutation in the gene for factor V (factor V Leiden). N. Engl. J. Med. 336, 399–403. Simioni, P., Sanson, B.J., Prandoni, P., Tormene, D., Friederich, P.W., Girolami, B., Gavasso, S., Huisman, M.V., Bu¨ller, H.R., ten Cate, J.W., Girolami, A., Prins, M.H., 1999. Incidence of venous thromboembolism in families with inherited thrombophilia. Thromb. Haemost. 81, 198–202. Sjobring, U., Ringdahl, U., Ruggeri, Z.M., 2002. Induction of platelet thrombin by bacteria and antibodies. Blood 100, 4470–4477. Strong, D.D., Moore, M., Cottrel, B.A., Bohonus, V.L., Pontes, M., Evans, B., Riley, M., Doolittle, R.F., 1985. Lamprey fibrinogen gamma chain: cloning, cDNA sequencing, and general characterization. Biochem. 24, 92–101. Taylor, F.B., Jr. Toh, C.H., Hoots, W.K., Wada, H., Levi, M., Scientific Subcommittee on Disseminated Intravascular Coagulation (DIC) of the International Society on Thrombosis and Haemostasis (ISTH), 2001. Towards definition, clinical and laboratory criteria, and a scoring system disseminated intravascular coagulation. Thromb. Haemost. 86, 1327–1330. Toh, C.H., Samis, J., Downey, C., Walker, J., Becker, L., Brufatto, N., Tejidor, L., Jones, G., Houdijk, W., Giles, A., Koschinsky, M., Ticknor, L.O., Paton, R., Wenstone, R., Nesheim, M., 2002. Biphasic transmittance waveform in the APTT coagulation of
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
3 The theory of molecular evolution and its medical implications Werner Arber Division of Molecular Microbiology, Biozentrum, University of Basel, Basel, Switzerland
1. INTRODUCTION The Neodarwinian theory of biological evolution occurred towards the middle of the twentieth century from the synthesis of lines of thought (1) of Darwin’s theory of descent under the pressure of natural selection and (2) of classical genetics in which genes are identified by occasional mutations resulting in observable alterations of phenotypical traits that are transmitted to the progeny. In brief, biological evolution is then driven by the occasional spontaneous occurrence of genetic variations, it is directed by natural selection favouring some of the available genetic variants, and it is modulated by isolation which can be either geographic or reproductive such as infertility in crosses between distantly related organisms. Around 1950, it became clear that genetic information is carried in the linear sequences of nucleotides of long filamentous molecules of DNA. This insight gave rise to molecular genetics and eventually to genomics. It has thus principally become possible to identify genetic variations as spontaneous changes in the inherited nucleotide sequences. Identifying causes and mechanisms of genetic variation on the DNA molecules leads to a confirmation of the Neodarwinian theory of biological evolution at the molecular level. The underlying novel synthesis leads to the theory of molecular evolution. This theory identifies a multitude of specific mechanisms contributing to the overall genetic variation. These mechanisms can be classified into a few natural strategies of genetic variation. This knowledge prompts us to postulate that nature cares actively for occasional genetic variation and thus for biological evolution. It does so by making use 31
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(1) of intrinsic properties of matter and (2) of products of specific evolution genes. Ideas behind and evidence for the theory of molecular evolution shall be briefly outlined in this chapter before medical implications of this theory will be addressed. The multidisciplinary nature of these considerations shall become obvious, and it may also be a principal reason why possible interrelations between the process of molecular evolution and specific medical problems have so far only rarely been discussed.
2. HOW TO IDENTIFY GENETIC VARIATIONS Classical genetics is based on the availability of occasional individuals which differ in one of their phenotypical traits from the majority of individuals of the concerned species. If the change in the phenotype is transferred to the progeny, the novel phenotype is attributed to a mutation or genetic variation, i.e. an alteration in the genetic information. In the meantime, it has become obvious that by far not all spontaneous changes in the inherited nucleotide sequences of a genome result in a detectable alteration of a phenotype. Many such changes are silent or neutral and have, for various explainable reasons, no immediate influence on the biological functions of the concerned individual and its offspring. Various studies also indicated that, as a general rule, spontaneous mutations are not occurring in response to an identified evolutionary need, although some exceptions to this rule may exist and find a very specific causal explanation for such directed adaptation. But there is no reason to generalise such observations. Rather, overall spontaneous mutagenesis causing DNA sequence alterations gives only exceptionally rise to beneficial mutations providing a selective advantage, much less frequently than to either detrimental or silent mutations. With the advent of molecular genetics and DNA sequence comparison it has become possible to identify molecular mechanisms of spontaneous DNA sequence alterations, particularly for relatively small genomes such as those of bacteria and viruses. In the following sections, we will focus our attention to mechanisms and general strategies causing DNA sequence alterations. The reader is advised to pay thereby attention to the difference in the definition of the term mutation. Recall that in classical genetics, a mutation is identified by a change in a phenotypical trait. In contrast, it has become customary in molecular genetics to call any alteration of the inherited DNA sequences a mutation. We mainly follow here the molecular genetic definition. Increasing knowledge on the molecular mechanisms of genetic variation enables one to postulate past events of genetic separation as testified by
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DNA sequence differences between more or less closely related genes, groups of genes, and genomes as revealed by appropriate DNA sequence comparisons. The so far available data of such comparisons suggest that evolutionary models based on relatively few well studied, mainly microbial organisms, are likely to apply to all living beings.
3. MOLECULAR MECHANISMS AND NATURAL STRATEGIES OF GENETIC VARIATION A schematic overview on the process of biological evolution is given in fig. 1. A multitude of different specific mechanisms steadily generates genetic diversity, the majority of which is, however, rejected by natural selection. As was already mentioned, isolation modulates the process of modulates biological evolution
Sources of genetic diversity
Limitation of genetic diversity
Geographic ISOLATION Reproductive
Organisms Ecosystems MUTATION NATURAL SELECTION GENETIC VARIATION drives biological evolution Strategies: Local change of DNA sequence
DNA rearrangement
directs biological evolution Mechanisms:
Physico-chemical environment
Replication infidelities
Biological environment Carrier capacity of biosphere
Mutagens -internal -environmental Recombinational reshuffling of genomic DNA segments
DNA acquisition
Horizontal gene transfer
Fig. 1. Schematic representation of major features of the theory of molecular evolution.
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biological evolution. The directions of evolution in the various ecosystems are determined by natural selection together with the available genetic variants. Genetic variation is the driving force of evolution. A complete genetic stability would not allow biological evolution to occur, while a very high genetic instability would not allow a concerned species to persist, not at least in view of the abundance of detrimental mutations among the genetic variants. The different processes contributing to the generation of genetic variants can be classified into three major natural strategies of genetic variation. In the following brief characterisation of these strategies, we will pay particular attention to the different qualities of their contributions to biological evolution.
3.1. Small local changes in the DNA sequences The fidelity of the replication of genetic information is ensured by the specificity of base pairing of the double-stranded DNA molecules. However, it is well known that this fidelity is limited for a number of different reasons, such as a structural flexibility of nucleotides known as tautomerism, limited chemical stability of nucleotides, slippage of the DNA polymerase on its template, and the interaction of chemical and physical mutagens with DNA. As a matter of fact, mutagenesis due to these causes would be quite high, if living organisms would not possess enzymatic repair systems to prevent nascent mutations to become fixed. The local DNA changes resulting from this kind of mutagenesis include nucleotide substitution, the deletion and the insertion of one or a few nucleotides, and a scrambling of a few adjacent nucleotides. A local sequence alteration within an open reading frame risks to change the quality of a gene product, while a change within an expression control signal may affect the availability and quantity of such product. Due to of the lack of directedness of mutagenesis, beneficial mutations will be rare, but still frequent enough to allow for evolutionary progress. These types of alteration of the genetic information mainly contribute to a stepwise improvement of genetic functions, as long as the concerned gene product represents a target for natural selection.
3.2. Intragenomic DNA rearrangements Mostly enzyme-mediated systems of genetic recombination can bring about a reshuffling of genomic DNA segments. In prokaryotic genomes, this can result in translocation, inversion, deletion, duplication, and higher
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amplification of parts of the genome. The kinds of recombination involved can be (a) general recombination between homologous segments of the genome, (b) transposition of mobile genetic elements, (c) site-specific recombination which usually acts at specific or consensus nucleotide sequences, but which can occasionally also act at so-called secondary sites of recombination differing considerably from the consensus, or (d) finally still other, less well-understood events of DNA reshuffling. Some of these processes can give rise to the rare inversion of any given DNA segment within the genome. This represents an interesting source for the fusion of previously unrelated functional domains to form novel sequence combinations. Another source of novel fusions of DNA sequences is deletion formation. By these and other reshuffling activities, nature occasionally tinkers with existing capacities. This tinkering represents a source for novel biological functions. Similarly, these kinds of processes can bring a given reading frame under an alternative control of its expression.
3.3. DNA acquisition by horizontal gene transfer The horizontal transfer of genetic information by transformation, conjugation, and virus-mediated transduction represents the well-studied basis of bacterial genetics. These processes are counteracted by a number of natural barriers, such as the requirement of surface compatibility of the interacting partners and restriction and modification systems. As a result, horizontal transfer of genetic information is widespread in microorganisms, but it usually occurs only occasionally and in small steps, i.e. by the acquisition of a relatively small part of a foreign genome. More and more upcoming evidence indicates that the same may apply to higher organisms. The acquisition of foreign genetic information represents a very efficient strategy of evolutionary development. In view of the universal nature of the genetic code, genetic information that had been developed in a potential donor organism has a fair chance to also serve the same purpose in a recipient organism that had not yet possessed the genetic information for the acquired function. The classification of specific mechanisms of genetic change into the three major strategies of genetic variation as outlined above should serve the purpose to better distinguish the qualities of contribution of the specific classified mechanisms to genetic diversification. In order to prevent misunderstandings, it should be said clearly that in the strategy of DNA rearrangements, small local sequence changes might also occur. A good example is the target duplication in transpositional events. Similarly, DNA recombination is generally also involved in the strategy of DNA
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acquisition, e.g. in the loading and unloading of transferred genes to and from a natural gene vector as well as in the incorporation of the DNA to be acquired into the recipient genome.
4. PRINCIPLES AND CONCEPTUAL ASPECTS OF THE THEORY OF MOLECULAR EVOLUTION The description of mechanisms and strategies of genetic variation given in the preceding section is largely based on empirical data. The given classification into strategies relies on evidence-based knowledge. In this section, we will discuss rather conceptual points of view, based on rational reflections. Some of the claims to be made rather reflect an attitude towards intrinsic potentialities of nature. It is thus advisable to continue for the time being to talk on a theory of molecular evolution rather than an established knowledge on the evolutionary process.
4.1. The postulate of the involvement of products of evolution genes In the outline of mechanisms of genetic variation we mentioned several times the involvement of specific enzymes, e.g. in DNA rearrangement processes and in the avoidance of mutagenesis by repair systems. If we consider the specific functions of these enzyme systems in single-cellular organisms such as bacteria, we can raise the question whether their presence is essential for each of the cells of a bacterial population while they are growing from one generation to the next. The answer will often be no, for example with regard to the transposition of a mobile genetic element. In contrast, their role is obvious in the generation of genetic variations, and it is thus of evolutionary relevance. We consider this kind of genes and their products as principally serving the needs of biological evolution. As a matter of fact, the enzyme transposase acts as a generator of genetic variations, and so do other recombinases. On the other hand, enzymatic DNA repair systems as well as bacterial restriction endonucleases seriously limit the frequencies of local sequence change and of DNA acquisition, respectively. They serve as modulators of the frequencies of genetic variation. We therefore define as evolution genes any genetic information for products which primarily serve the purpose of biological evolution.
4.2. Nature cares actively for biological evolution In addition to the activities of products of evolution genes, intrinsic properties of matter also represent sources of genetic variation. As we have
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already discussed, local sequence changes are often initiated by structural flexibilities or chemical instability of nucleotides, while the effective frequency of this mutagenesis is modulated by enzymatic repair activities. We see here, as in other examples, a close cooperation between the use of fundamental properties of matter and the modulating activities of evolution genes. We oppose this view that nature makes active use of intrinsic properties of matter for the purpose of biological evolution to another widespread view that genetic variation largely relies on errors of replication and accidents happening to DNA. The difference between these two views is conceptual rather than mechanistic. We consider biological evolution as of similar importance as the accomplishment of each individual life. In this light the joint involvement of products of evolution genes and of nongenetic elements in the generation of genetic variants represents a rational postulate.
4.3. The postulate of an evolutionary fine-tuning of the evolution genes Like many conventional genes, evolution genes must have been developed at early times of evolution of life on our planet. However, the products of evolution genes could not have been selected for directly. Rather, their activities exerted at the level of populations must have favoured subpopulations that produce genetic variants of conventional genes at frequencies appropriate for the evolutionary progress. The underlying selection and functional fine-tuning of evolution genes is called secondorder selection. A very strict classification of genes into those serving the individual for the accomplishment of its lifespan on the one hand, and those serving the needs of biological evolution on the other hand, would not correspond to reality. We are aware that some gene products serve both purposes. Possibly, these have also been selected and fine-tuned for both tasks. However, as has already been said, some genes accomplishing evolutionary functions are absolutely unessential for the life of individuals.
4.4. The duality of the genomic information It is still widely assumed that all active genes carried in the genome serve the needs of the concerned individual. However, the presence of evolution genes in the genome requires a revision of this view. The encountered situation implies a duality of the functional role or purpose of the information carried in the genome. At the same time, we become aware that the
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presence of generators of genetic variations will occasionally affect the life of an individual by the occurrence of a deleterious mutation in view of the discussed non-directional nature of genetic variation. This is a sacrifice that nature makes to the benefit of the evolutionary progress of the population under various environmental conditions, in some of which a given genetic variation may provide an advantage while the same mutation may be of disadvantage in other ecological niches.
4.5. Evolutionary fitness We have seen that a relatively large number of specific mechanisms can make contributions to genetic variation. Depending on their belonging to different strategies of genetic variation, their contributions may be of different qualities. Possibly, mechanisms of the same strategic class may often substitute for each other, but not those belonging to different strategies. Therefore, we define here as a good evolutionary fitness if the genome is equipped with a few specific mechanisms for each of the three strategies of genetic variation. In early biological evolution of prokaryotes, it may have taken a considerable time span to reach this kind of evolutionary fitness, which then could have allowed for the steps towards the development of more complex multicellular and higher organisms.
4.6. The role of evolution genes in multicellular higher organisms We here postulate that in higher organisms, genetic variation principally follows the same rules as in prokaryotes, according to which the scheme in fig. 1 was designed. However, some of the evolution genes may locally as well as temporally also accomplish functions to the service of the concerned individual. One may think on the repair of DNA lesions in somatic cells. Another well-studied example is the DNA rearrangement giving rise to antibody diversity in the immune system of higher organisms. The gene products thereby involved clearly carry out a developmental function at the somatic level. This situation is fully compatible with the view that whatever can serve a purpose can be made use of in living systems. Nevertheless, it is highly probable that all living beings also make use of evolution genes for their evolutionary progress by the occasional generation of genetic variations that become transmitted to their progeny. Functional genomics and proteomics should pay particular attention to this question.
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4.7. Gene concept to be revised A certain reluctance of biologists and in particular biochemists and molecular biologists, to accept the concept of evolution genes may reside in the fact that evolution genes acting as generators of genetic variations are in their activities neither efficient nor reproducible with regard to the final result of the reactions that they catalyze. Indeed, genetic variation must occur at rather low frequencies only and the resulting alteration in the genomic sequences must not be identical from case to case. This contrasts with the efficiency and reliability of most enzyme reactions that biochemists have so far studied with success. However, there is no reason to believe that all genes and gene products follow the same rules. Rather, knowledge on generators of genetic variations such as transposases should stimulate biologists to reconsider and widen the customary concept of the gene.
5. MEDICAL IMPLICATIONS OF GENETIC VARIATION AS THE DRIVER OF BIOLOGICAL EVOLUTION It has since long been perceived and discussed that genetic variation represents an important source of many medical problems. We know that genetic variation in the germ line represents the basis for inherited diseases. We also know that genetic variation occurring in somatic cells may lead to a serious malfunctioning of the affected genes and cells. The purpose of this chapter is to discuss some of the medical implications of genetic variation in the light of the novel knowledge and concepts regarding molecular evolution. This is clearly a multidisciplinary exercise. The specific examples to be discussed here shall also illustrate conceptual aspects related to the crossing of disciplinary borders. They are given without any claim for a complete encyclopaedic covering of relevant situations. Thereby, we will focus our attention on human medicine; however, what applies to humans also applies to other living organisms. Our discussion is thus also relevant for the health of animals and plants, as well as for the robustness of microorganisms.
5.1. Can a genome ever be optimal? At a superficial view, one may believe that the evolutionary progress will sooner or later result in an optimisation of the genomic functions. After all, according to the theory of evolution, a progressive improvement of functions might be expected to result in an ever better functional harmony
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of an organism. However, one has to be aware that the pressure of natural selection which is mainly exerted on gene functions is neither temporally nor spatially constant. Therefore, there cannot be an optimal structure of the genome of organisms exposed to ever changing living conditions. As postulated by the theory of molecular evolution, spontaneous genetic variations occasionally introduce alterations into the genomic DNA sequences. Depending on the specific mechanisms of mutagenesis involved, these alterations can be either local sequence changes, the rearrangement of genomic DNA segments, or the uptake and acquisition of a segment of foreign genetic information. Local changes of the inherited DNA sequences are probably the most abundant alterations. Intragenomic DNA rearrangements have been well documented in a number of different organisms, but they may occur less frequently than local sequence changes. Horizontal gene transfer is well documented for microorganisms. It is also known to occur, e.g. with viral gene vectors, in higher organisms, but more specific research is required to reach more insight into its relative importance, particularly in symbiotic associations between different organisms. In the following sections, we will discuss specific implications of medical importance of genetic variation.
5.2. Inherited diseases: a consequence of genetic variation affecting the germ line Genetic variation is of highest evolutionary significance if it occurs in the germ line. We are aware that a majority of spontaneous alterations in the genomic information is either detrimental or neutral, while relatively few changes are beneficial and provide a selective advantage. Medicine has to cope with those detrimental variants which are not lethal but affect life to some degree. Novel mutations in the germ line can thus lead to the transmission of the genetic defect to the progeny of the individual having been the target of the genetic variation. In recent years, diagnostic tools have been developed to identify the affected genes as well as the DNA sequence alterations causing the disease. This is a good basis to search for appropriate therapies that might cure or at least attenuate the defect. Depending on the biological functions affected, therapies may range from treatment with drugs able to compensate for the missing functions up to somatic gene therapy and cell therapy, which may one day, and in specific cases, represent the most direct way to cure an individual from an inherited disease. Whether in specific cases germ line gene therapy may in future times become a sure and reliable as well as ethically justifiable treatment that can assure also the health of the progeny of an affected person remains an open question.
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5.3. Somatic genetic variation As a consequence of the discussed duality of the genome with the presence of evolution genes besides the housekeeping genes, the genes for developmental functions, and additional genes of relevance for cell populations under particular conditions, we have to face the possibility of genetic activities generating genetic variations in somatic cells. We know that some of the involved enzyme systems are heavily inhibited to do so, but biological barriers are usually not complete. Take the case of general recombination; in somatic cells this enzymatic activity is normally not present. It exerts its evolutionary activity at a particular moment of the life cycle, upon meiotic division, and it represents an important source of novel assortments of chromosomal information for individuals of the progeny. However, general recombination also plays some role in the repair of broken DNA molecules due to the impact of high energy radiation. Hence, this and other types of DNA rearrangements can also occasionally occur in somatic cells. It appears quite difficult to entirely prevent such activities. However, nature itself has learned to deal with such situations. Apoptosis is a good example, by which incapacitated cells eliminate themselves from a functional tissue. None of these natural devices is foolproof, though. Cancer has been described as resulting from uncontrolled growth of a somatic cell having suffered some critical mutations and having escaped the biological control of the suffered defect. Some of the somatic mutations go back to those intrinsic properties of matter known to cause local sequence changes, being it upon DNA replication or by the action of mutagens. In these cases, it is essential that repair systems encoded by evolution genes exert their activities also at the level of somatic cells in order to preserve the genetic integrity with a high probability. However, these probabilities are never 100% and some detrimental mutations may occasionally occur. Knowledge on the multitude of sources of somatic mutations and on their specific molecular mechanisms may help future investigations in search of means to reduce the frequencies of somatic mutagenesis as well as in search of therapies to prevent detrimental consequences of fixed genetic variations. For this latter aim, therapies might best be searched for on the basis of their possible stimulation of natural ways to eliminate malfunctioning cells, such as by apoptosis.
5.4. Infectious diseases In the course of evolutionary times many living organisms have taken profit of other organisms by forming close associations with each other.
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These are known as symbiotic associations. In most of these cases, each partner takes some advantage of the others present in that kind of cohabitation. As a matter of fact, genetic functions of the partners have often been evolutionarily adapted to this kind of symbiotic life. There may be just a few additional steps from such a friendly equilibrium to a more one-sided situation of taking profit, which we tend to call pathogenicity. In this situation one of the partners takes big advantage of the other partner, while the latter rather suffers from this cohabitation. Various degrees of virulence reflect different degrees of damage caused to the partner suffering by the cohabitation. A considerable number of viruses, bacteria and protozoan microorganisms are known to be pathogenic for higher organisms including for man. The degree of pathogenicity may vary, both by genetic variations occurring to the pathogens and by the genetic setup and the general health constitution of the infected host. Here again, the medical treatments for prevention and therapy profit considerably from a deep understanding of the process of molecular evolution. As a rule, microorganisms, and in particular viruses, undergo evolutionary alterations faster than higher organisms. This explains the occasional emergence of novel infective agents. A fast analysis of their genetic and functional setup can often help to identify appropriate targets for prevention and therapy by drugs and specific vaccination. It is thereby good to know that evolutionary adaptation can often occur by the pathogen and that hosts may similarly undergo evolutionary adaptation towards better resistance. This kind of mutual evolutionary development is part of the phenomenon of co-evolution, which has also its relevance in beneficial symbiosis. Related to the power for evolutionary development of pathogens is their possibility to develop drug resistance. We know that horizontal gene transfer between different microorganisms plays a considerable role in the rapid expansion of drug resistance, particularly in the widespread presence of the antimicrobial drug exerting in these cases a specific pressure of natural selection in favor of organisms able to propagate in the presence of the drug. Another evolutionary aspect of relevance for pathogenicity is the fact that genes involved in pathogenesis are often found grouped into so-called pathogenicity islands which may behave as mobile genetic elements and can thus easily spread horizontally to render non-pathogenic microorganisms pathogenic.
5.5. Immune proficiency of higher organisms One of the most efficient natural defense mechanisms against infectious diseases is a well functioning immune system. By eliminating infectious
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agents the immune system also reduces the possibility of horizontal transfer of genes brought in by invading microorganisms serving as gene vectors. More importantly, the immune system prevents serious functional damage which could be caused to the host by infecting agents. We know that the functional setup of immune capacities depends on somatic mutation, which includes local sequence changes and the rearrangement of DNA segments. These fundamental developmental activities use the strategies of evolutionarily relevant genetic variation. Immune deficiencies can be based on improper development and they represent very serious medical problems.
6. CONCLUDING OBSERVATIONS Genetic variation is a relatively rare, or inefficient, event that results in an alteration of the sequences of nucleotides of DNA molecules. From case to case, these alterations differ from each other. The resulting genetic variants form the substrate for natural selection, by which relatively few of the variants are favoured, while many variations provide selective disadvantage and many other variations have no immediate influence on natural selection. Under these conditions it is understandable that genetic variants had generally been attributed to errors occurring upon DNA replication and to different kinds of accidents happening to DNA such as by the impact of chemical or physical mutagens. Under these presumptions biological evolution was seen as depending on errors and accidents reducing to some degree the genetic stability of the genomes. This widespread view is now challenged by results of molecular genetic studies and by the investigation of molecular mechanisms of genetic variation. In contrast to previous views, the theory of molecular evolution postulates biological evolution to be an active process in which fine-tuned mechanisms bring about occasional variants in the nucleotide sequences of DNA molecules. A multitude of different molecular mechanisms contribute to the overall mutagenesis, and these mechanisms can be classified into a few qualitatively different natural strategies to generate genetic variations. Two principally different types of sources for the alterations in the DNA sequences serve the purpose of genetic variation. One of them relates to intrinsic properties of nature such as a structural flexibility of nucleotides and of enzymes interacting with DNA, the chemical instability of nucleotides, or also the random interaction of natural mutagens with DNA. The second kind of actors in mutagenesis are the products of evolution genes serving as generators of genetic variations. Many of these enzyme systems exert their functions in an intragenomic rearrangement of DNA segments
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as well as in DNA acquisition by horizontal gene transfer. The products of other evolution genes rather modulate the frequencies of genetic variation, so that these frequencies insure a certain genetic stability but still allow for evolutionary developments at the level of populations. In brief, nature cares actively for biological evolution in providing qualitatively different mechanisms of genetic variation acting in populations at frequencies that are fine-tuned for the purpose of evolution which is at the origin of biological diversity and which has the intrinsic power to replenish biological diversity under changing living conditions. The concept that we have just outlined in its major lines has deep philosophical relevance. It merits to be widely reflected and recognised as cultural value to become integrated into our world view. This interdisciplinary task is still far from being completed. Nevertheless, we may reflect on the medical importance of the proposed change of attitude towards the basis of biological evolution. In the updated optic of this process we realise that the genomes of any organisms are of a dual nature. Clearly, many specific genes serve for the life fulfillment of the carrier organism. Other genes, however, serve for the needs of biological evolution and they do so at the level of populations. A number of other genes serve for both purposes. We then realise that evolutionary gene functions may occasionally affect the health of a particular organism of a healthy population. This happens if an occasionally occurring genetic variation ends up in a detrimental mutation. Examples of these have been described above. They may relate to inherited diseases or to a somatic malfunctioning. In addition, genetic variation has also its medical impact on infectious diseases. In all of these cases, a better knowledge on purpose and mechanisms of genetic instability may provide novel means in the search for diagnostic and therapeutic tools in the fight against the disease. A comprehensive knowledge of the natural processes driving biological evolution and forming the basis of the rich biodiversity may, in many cases, represent a mental help for a patient confronted with the medical consequences of genetic variation. One may expect that at least for some human beings it makes a difference to explain their disease as a testimony of the wonderful natural forces which drive biological evolution rather than to be the victims of an accident or an error affecting their genetic information. This difference in perception might exert psychological and sometimes even psychosomatic influences on the patients in question. It should become a routine for physicians to strengthen their patients in reflections on the basis of their disease in the light of updated knowledge on molecular evolution.
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RECOMMENDED READING Arber, W., 1995. The generation of variation in bacterial genomes. J. Mol. Evol. 40, 7–12. Arber, W., 2000. Genetic variation: molecular mechanisms and impact on microbial evolution. FEMS Microbiol. Rev. 24, 1–7. Arber, W., 2003. Elements for a theory of molecular evolution. Gene 317, 3–11. Arber, W., 2003. Cultural aspects of the theory of molecular evolution. In: The Cultural Values of Science. Pontifical Academy of Sciences Scripta Varia, 105, pp. 45–58. Arber, W., 2004. Genetic variation and molecular evolution. In: Meyers, R.A. (Ed.), Encyclopedia of Molecular Cell Biology and Molecular Medicine. Wiley-VCH, Weinheim, Germany, 5, pp. 331–352. Caporale, L.H. (Ed.), 1999. Molecular Strategies in Biological Evolution. Annals of the New York Academy of Sciences, 870. Hacker, J., Kaper, J.B. (Eds.), 2002. Pathogenicity Islands and the Evolution of Pathogenic Microbes, Current Topics in Microbiology and Immunology, Vol. 264, I & II. SpringerVerlag, Berlin, Heidelberg.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
4 What is a medical theory? Paul Thagard Philosophy Department, University of Waterloo, Ontario, Canada
1. INTRODUCTION Modern medicine has produced many successful theories concerning the causes of diseases. For example, we know that tuberculosis is caused by the bacterium Mycobacterium tuberculosis, and that scurvy is caused by a deficiency of vitamin C. This chapter discusses the nature of medical theories from the perspective of the philosophy, history, and psychology of science. I will review prominent philosophical accounts of what constitutes a scientific theory, and develop a new account of medical theories as representations of mechanisms that explain disease. An account of the nature of medical theories should illuminate many aspects of the development and application of medical knowledge. Most importantly, it should contribute to understanding of medical explanation, both at the general level of causes of diseases and at the individual level of diagnosis of particular cases of a disease. Medical researchers seek to explain the causes of diseases such as tuberculosis, while physicians seek to identify diseases that explain symptoms such as fever. A medical theory such as the bacterial theory of tuberculosis provides good explanations at both the general and individual levels. The primary aim of this chapter is to show how these explanations work. A secondary aim is to show how an account of medical theories can shed light on other aspects of medical research and practice, including the nature of medical discovery, the process of evaluation of competing medical theories, and the ways in which effective treatments of disease depend on the development of good mechanistic theories about diseases.
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2. SOME MEDICAL THEORIES Before examining various accounts of what theories are, it is useful to review some important examples of medical theories. Until the advent of modern scientific medicine in the middle of the nineteenth century, the world’s predominant medical theories attributed diseases to various kinds of bodily imbalances. In Europe, the humoral theory of disease originated with Hippocrates around 400 B.C. It held that diseases arise because of imbalances in the body’s four humors: blood, phlegm, yellow bile, and black bile. Treatment consisted of attempts to restore the proper balance by ridding the body of excessive quantities of blood, bile, or phlegm by techniques, such as bloodletting and purgatives. Humoral medicine is no longer practiced, unlike traditional Chinese medicine which is also based on a theory that diseases are caused by imbalances. According to Chinese medicine, which is even older than the Hippocratic theory, everything in the universe including the human body is governed by principles of yin and yang. Diseases arise when the body has an improper balance of these principles, and they can be treated by herbs and other techniques that restore the proper balance. Thagard and Zhu (2003) describe the conceptual structure and explanation patterns of traditional Chinese medicine. Traditional Indian medicine is similarly ancient, and also explains diseases as arising from imbalances. Lad (2003) describes the doctrine of Ayurveda as follows: According to Ayurveda, health is a state of balance between the body, mind and consciousness. Within the body, Ayurveda recognises the three doshas, or bodily humors vata, pitta and kapha; seven dhatus, or tissues, plasma, blood, muscle, fat, bone, nerve, and reproductive; three malas, or wastes; feces, urine and sweat; and agni, the energy of metabolism. Disease is a condition of disharmony in any of these factors. The root cause of imbalance, or disease, is an aggravation of dosha, vata-pitta-kapha, caused by a wide variety of internal and external factors. Thus ancient theories of medicine all attributed diseases to imbalances. Modern scientific medicine emerged in the 1860s and 1870s, when Louis Pasteur and others originated the germ theory of disease, according to which contagious diseases such as cholera are caused by microorganisms like bacteria. The germ theory is really a class of theories applying to many specific diseases, each of which is associated with a specific infectious agent. These include the bacterium that causes cholera, the virus that causes
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AIDS, the protozoan that cause malaria, the fungus that causes athelete’s foot, and the prions that cause spongiform encephalopathies (e.g. mad cow disease). The twentieth century saw development of additional classes of medical theories. Nutritional diseases, such as scurvy and beriberi are explained by deficiencies in nutrients such as vitamins. Autoimmune diseases such as lupus erythematosus are explained by the immune system becoming overactive and attacking bodily tissues. Genetic diseases such as cystic fibrosis are explained by mutated genes that cause defects in the physiological functioning. Other maladies, such as heart disease and cancer are often caused by combinations of genetic and environmental factors. See Thagard (1999) for a review of the explanation patterns associated with these classes of disease. All these medical explanations are consistent with the following first attempt to provide an account of the nature of medical theories: Analysis 1: A medical theory is a hypothesis about the cause or causes of a particular disease. This account does not go very far, however, because it says nothing about the nature of hypotheses and the causal explanations intended to link diseases with causes. In search of a deeper account, I will now examine the major philosophical views of the nature of scientific theories.
3. PHILOSOPHICAL VIEWS OF THEORIES Here are the most influential accounts of the nature of theories that philosophers have so far proposed: Syntactic: A theory is a collection of universal generalisations in a formal language. Model-theoretic: A theory is a set-theoretic structure. Paradigm: A theory is a world view based on exemplars. Third-world: A theory is an abstract entity in an autonomous, nonphysical, non-mental world. Cognitive: A theory is a mental representation of mechanisms. I will explain each of these accounts and assess them with respect to how well they apply to the history of medicine and with respect to how much they shed light on the nature of explanation, evaluation, discovery, and treatment. In the 1950s and 1960s, the syntactic view was the accepted one in the philosophy of science (see, for example, Nagel, 1961; Hempel, 1965; Suppe, 1977). The logical positivists thought that theories could be represented
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by universal generalisations in a formal language such as predicate calculus. For example, we might formalise the Plasmidium theory of malaria by an expression such as (x)(Px ! Mx) and (x)(Mx ! Px), which say that anyone infected by this parasite gets malaria, and that anyone with malaria has been infected by the parasite. There are many problems with this syntactic account that I can mention only briefly. First, relationship between causes and diseases are rarely universal, because there are usually many interacting factors involved, some of them unknown. In contagious diseases, there are usually many more people infected by the relevant microorganism than those that come down with the disease. Second, universal generalisations are inadequate to characterise causality, because they cannot distinguish between cases where a generalisation is true accidentally and ones where it derives from underlying causal structure. Third, the syntactic view of theories assumes that explanation is a matter of logical deduction from universal generalisations, but it is rare outside physics for scientists to be able to generate deductive explanations. In medicine, there is rarely a tight deductive relationship between hypotheses about causes and the diseases they explain. Finally, the syntactic account of theories has nothing to say about how medical hypotheses can be discovered or about how they can be used to suggest treatments of disease. The model-theoretic (sometimes called the semantic) account of theories was devised to overcome the excessively linguistic nature of the syntactic account (see Suppe, 1977). A model in the relevant sense is a structure consisting of a set of objects that provides an interpretation for sentences in a formal language. On this account, what matters about a theory is not its particular linguistic expression, but rather its specification of a set of models that are intended to include the world. The model-theoretic account is difficult to apply to medical theories because they are rarely susceptible to formalisation. Moreover, this account has nothing to say about the nature of explanation, causality, discovery, and treatment. Hence it is clear that we need a richer conception of medical theories. In 1962, Thomas Kuhn published The Structure of Scientific Revolutions, which introduced the term paradigm into the philosophy and history of science. Should we consider a medical theory as a paradigm? Kuhn’s use of the term was notoriously vague, but he eventually identified two key senses, as a world view and as a set of exemplars, which are standard examples of problem solutions (Kuhn, 1977). Neither of these senses applies well to medical theories. Even the most general medical theory, the germ theory of disease, does not constitute a world view, and it is not evident what in medical science constitutes an exemplar. Kuhn had some important insights about scientific theories as a part of conceptual systems
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and about the magnitude of conceptual change in the development of knowledge, but these can be pursued more fruitfully within the cognitive account of theories discussed in the next section. Karl Popper’s (1959) early work in the philosophy of science was similar to the logical positivist’s view of theories as syntactic structures. But he later proposed that theories are part of a third world of intelligibles distinct from the first world of physical objects and the second world of mental states. The third world is ‘‘the world of possible objects of thought; the world of theories in themselves, and their logical relations; of arguments in themselves; of problem situations in themselves’’ (Popper, 1972, p. 154). I fail to see, however, what is gained by postulating this mysterious additional world. In accord with contemporary cognitive science, I would deny even the division between Popper’s first and second worlds: mental states are physical states of the brain. Moreover, Popper’s treatment of theories as abstract entities in an autonomous world sheds no light on questions of evaluation, causality, and discovery, and we have already seen reasons to doubt the deductive view of explanation that Popper assumes. Hence I will now turn to what I think is a more plausible view of medical theories.
4. THE COGNITIVE CONCEPTION OF THEORIES Cognitive science is the interdisciplinary investigation of mind and intelligence, embracing the fields of psychology, neuroscience, linguistics, philosophy, and artificial intelligence. Since its origins in the 1950s, the central hypothesis of cognitive science has been that thinking is a kind of computational process in which algorithmic procedures operate on mental representations. A mental representation is a structure in the mind/brain that stands for something. This hypothesis has been fertile in generating explanations of many aspects of thinking, such as problem solving, learning, and language use. From the perspective of cognitive science, it is natural to think of a scientific theory as a complex of mental representations, including concepts, rules, and visual images (see Thagard, 1988, 1992, 1999; and Giere 1988, 1999). Moreover, the main processes involving scientific theories, including discovery, explanation, and evaluation, can be understood computationally. Discovery is an algorithmic process of building new representations, and medical explanation is a process of connecting a representation of a disease with a representation of a relevant cause. Evaluation of competing theories is a computational process that determines which is the best explanation of all the evidence.
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The cognitive perspective suggests the following answer to the question of what is a medical theory: Analysis 2: A medical theory is a mental representation of the cause or causes of a disease. This analysis is still very general, however, because it neither specifies the kinds of mental representations that are involved in the explanation of diseases, nor does it detail the particular kinds of mental procedures that produce discovery, explanation, and evaluation. To show how the cognitive conception can give a rich account of medical theories, I will work through a case history of a novel disease, SARS.
5. CASE STUDY: SARS Severe acute respiratory syndrome (SARS) was first reported in China in February, 2003, and quickly spread to other countries (CDC, 2004). More than 8,000 people became sick with SARS, of whom more than 900 died. The symptoms of SARS include high fever, headache, discomfort, body aches, dry cough, and the development of pneumonia. SARS is spread by close contact involving respiratory droplets. The cause of SARS was identified with remarkable speed. In March, 2003, a novel coronavirus, now called SARS-CoV, was discovered in patients with cases of SARS. By April, there was strong evidence that this virus caused the disease (Ksiazek et al., 2003). Moreover, by May, investigators had sequenced the complete genome of SARS-CoV, showing that it is not closely related to previously characterised coronaviruses (Rota et al., 2003). Thus in a matter of months medical researchers managed to discover the plausible cause of the new disease. The medical theory here is: SARS is caused by the virus SARS-CoV. Let us now look at this theory as a kind of mental representation. First, what is the mental form of the concept of SARS? The traditional view of concepts is that they are defined by necessary and sufficient conditions, so that we would have a definition of the form: person P has SARS if and only if P has the symptoms X, Y, and Z. There is abundant psychological evidence, however that the traditional view does not adequately characterise mental concepts (Murphy, 2002). A prominent alternative theory of concepts is that they consist of prototypes that describe typical rather than universal features of the objects that fall under a concept. Accordingly, we should think of a disease concept as involving the specification of a set of typical features involving symptoms as well as the usual course of the disease. Here is an approximate prototype for SARS, in the form of a structure
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that artificial intelligence researchers such as Winston (1993) call a frame: SARS: A kind of: infectious disease. Typical symptoms: high fever, dry cough, lung infection. Typical course: fever, then cough, then pneumonia. Typical treatment: antiviral drugs, isolation. Cause: SARS-CoV. This structure is flexible enough to allow the existence of SARS patients whose symptoms and disease development are not typical. How are symptoms mentally represented? In some cases, a purely verbal representation is adequate; for example, ‘‘temperature greater than 38 degree Celsius’’. But there is enough evidence that human minds also operate with visual, auditory, and other kinds of representations. A physician’s representation of dry cough, for example, may be an auditory and visual prototype based on extensive clinical experience with many patients with dry and wet coughs. Similarly, part of the mental representation of pneumonia may be based on visual images of X-rays that show what pneumonia typically looks like. Even more obviously visual is the representation of the cause of SARS, the virus SARS-CoV. Pictures and diagrams of this virus and its relatives are available on the web, at such sites as: http://www-micro.msb.le.ac.uk/3035/Coronaviruses.html http://www.rkm.com.au/VIRUS/CORONAVIRUS/index.html. Viruses are too small to be photographed through ordinary microscopes, but electron microscopy reveals their basic structure. The term ‘‘coronavirus’’ derives from the crown-like appearance of this class of viruses in images generated by electron microscopes. Hence the mental representation of the SARS virus is multimodal, including both verbal information such as that its genome has 29,727 nucleotides, and visuospatial information about its shape and structure. Diagrams are also very useful for displaying the genome organization and protein structure of the SARS virus (Rota et al., 2003). It is not unusual for human concepts to be grounded in modality-specific systems: Barsalou et al., (2003) reviewed experimental evidence that conceptual processing activates modality-specific brain areas. Thus it is plausible that the mental representation of both the disease SARS and its cause, the SARS-CoV coronavirus, are multimodal,
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involving visual as well as verbal representations. Now we get to the hard part: how does the mind represent cause? Philosophers have attempted to give verbal reconstructions of the concept of causality, from Hume on constant conjunction to Kant on the causal schema to modern philosophers who have tried to tie causality to probability theory. I suspect that all these attempts have failed to characterise causal knowledge because they neglect the fact that people’s understanding of causality is also multimodal. I do not know whether this understanding is innate or learned very early, but people acquire or instantiate the concept of causality through non-verbal perceptual experiences, including ones that are visual, tactile, and kinesthetic (Michotte, 1963). Even infants have strong expectations about what they can expect to see and what they can expect to happen when they interact with the world. Baillargeon, et al. (1995) report that infants as young as 2.5 months expect a stationary object to be displaced when it is hit by a moving object. By around 6 months, infants believe that the distance traveled by the stationary object is proportional to the sise of the moving object. Thus at a very primitive stage of verbal development children seem to have some understanding of causality based on their visual and tactile experiences. The brain contains regions of the parietal and prefrontal cortices that serve to integrate information from numerous perceptual sources, and I speculate that understanding of causality resides in higher-level nonverbal representations that tie together such visual/tactile/kinesthetic perceptual inputs. Various writers in philosophy and psychology have postulated causal powers that go beyond relationships, such as co-occurrence and conditional probability (Harre´ and Madden, 1975; Cheng, 1997). My multimodal hypothesis suggests how this appreciation of causal powers may operate in the mind. Children know little about logic and probability, but they quickly acquire a sense of what it is for one event to make another happen. Understanding of simple mechanisms such as the lever and even of complex ones such as disease production depends on this preverbal sense of event causation. In sum, the mental representation of the seemingly straightforward hypothesis that SARS is caused by a newly discovered coronavirus is highly complex and multimodal. Hence from the perspective of the cognitive conception of theories a medical theory is an integrated multimodal representation. Formation of such theories requires building verbal, visual, and other perceptual representations of the disease and its cause. Cognitive science is replete with detailed computational theories of the acquisition of concepts, so the cognitive approach can easily address the problem of understanding how medical theories are discovered. Similarly, there is a well-developed psychological theory and computational
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model of explanatory coherence that describes how competing theories can be evaluated using artificial neural networks (Thagard, 1992). This leaves the major problem of saying how the cognitive conception of theories can shed light on the nature of medical explanation, which requires attention to the topic of mechanisms. This discussion will also illuminate the relationship between diseases and their causes.
6. MECHANISMS AND EXPLANATIONS As I have argued elsewhere, modern explanations of disease based on molecular biology are largely concerned with biochemical mechanisms (Thagard, 2003). To understand what biological mechanisms are, it is useful to examine the nature of machines created by people. In general, a machine is an assemblage of parts that transmit forces, motion, and energy to each other in order to accomplish some task. To describe a machine and explain its operation, we need to specify its parts, their properties, and their relation with other parts. Most importantly, we need to describe how changes to the properties and relationships of the parts with respect to force, motion, and energy enable the machine to accomplish its tasks. Consider the basic lever shown in fig. 1. It consists of only two parts, a stick and a rock. But levers are very powerful and have enabled people to build huge structures such as the Egyptian pyramids. The lever in fig. 1 operates by virtue of the fact that the stick is rigid and is on top of the rock, which is solid. Applying force to the top of the stick (tactile and kinesthetic perception) makes the bottom of the stick to move and lift the block (visual perception), thus accomplishing the machine’s task. Similarly, biological mechanisms can be explained by identifying the relevant parts and interactions. My approach to medical theories is in keeping with the mechanismbased view of explanation espoused by such philosophers of science as
Fig. 1. A simple machine, the lever.
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Salmon (1984) and Bechtel and Richardson (1993). Machamer, et al. (2000, p. 3) characterise the mechanisms as ‘‘entities and activities organised such that they are productive of regular changes from start or set-up to finish or termination conditions’’. I prefer the term ‘‘part’’ to ‘‘entity’’ because it indicates that the objects in a mechanism are part of a larger system; and I prefer ‘‘interaction’’ and ‘‘change’’ to ‘‘activity’’ because they sound less anthropomorphic. More importantly, I find the reference to start and finish conditions highly misleading, because the biochemical mechanisms needed to explain biological functioning often involve ongoing feedback processes rather than unidirectional changes. Hence I will simply say that a mechanism consists of a group of parts that have properties and relationship with each other that produce regular changes in those properties and relationships, as well as to the properties and relationships of the whole group. To apply this to medical explanations, we need to identify for a particular disease the biochemical mechanisms that cause it. The general mechanisms for viral infection and disease causation are well understood (e.g. Freudenrich, 2004). A virus typically has three parts: nucleic acid, consisting of DNA or RNA, which contains genetic instructions; a coat of protein that protects the nucleic acid; and a lipid membrane or envelope that surrounds the coat. For the SARS coronavirus, the envelope carries three glycoproteins, including a spike protein that enables the virus to bind to the cell receptors. Once a virus has attached itself to a cell, it enters it and releases its genetic instructions that recruit the cell’s enzymes to make parts for new viruses. The parts are assembled into new viruses, which then break out of the cell and can infect other cells. Schematically, the mechanism is: Attachment ! entry ! assembly ! replication ! release: Viral replication in itself does not produce disease symptoms, which can arise from two sorts of mechanisms. First, viral release may directly cause cell damage or death, as when the SARS virus infects epithelial cells in the lower respiratory tract. Second, the presence of the virus will prompt an autoimmune response in which the body attempts to defend itself against the invading virus; this response can induce symptoms such as fever that serves to slow down the virus replication. Schematically, these two mechanisms are: Viral infection ! cell damage ! symptoms; Viral infection ! immune response ! symptoms:
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Obviously, these mechanisms of disease symptom causation can be broken down much further by specifying the relevant parts, such as the proteins responsible for viral replication and the autoimmune cells that attack viruses, and the relevant processes, such as cell destruction and autoimmune responses. These two kinds of mechanisms, in company with the mechanisms of viral activity, together explain how viruses such as the SARS-CoV cause diseases like SARS. A similar mechanistic account of medical explanation can be given for many other genetic, nutritional, autoimmune, and cancerous diseases. Hence we can enhance the cognitive conception of the nature of medical theories as follows: Analysis 3: A medical theory is a mental representation of mechanisms that generate the states and symptoms of a disease. Note that the parts and changes in biological mechanisms are often represented visually as well as verbally, so for most medical theories the mental representation is multimodal. Disease explanation is a mental process of manipulating representations of mechanisms to link their parts and changes to representations, which may also be multimodal, of states and symptoms of diseases. I use the phrase ‘‘states and symptoms’’ to acknowledge that people may have diseases before they display any symptoms. Although the word ‘‘cause’’ has been dropped in the enhancement of analysis 2 by analysis 3, I do not mean to suggest that causality can be replaced by mechanism in the explanation of disease. Saying that the parts and interactions of a mechanism produce regular changes are equivalent to saying that they cause regular changes, so we need to maintain the unanalysed, multimodal concept of causality that I proposed earlier. Attempts to analyse causality away by means of concepts of universality or probability have been unsuccessful, and my account of medical explanation does not try to eliminate causality from understanding of theories and explanations. Rather, I propose that people’s comprehension of machines and mechanisms presupposes an intuitive notion of causality that derives from non-verbal experience. Analysis 3 gives a good account of the nature of medical theories as they are currently used by medical researchers and practitioners. Discovery of disease explanations involves formation of hypotheses about mechanisms that link causal factors such as microorganisms with disease states and symptoms. Evaluation of competing theories involves determining the most plausible set of mechanisms for producing a set of symptoms. In the case of SARS, a dominant theory of disease causation was generated with remarkable speed, although many other diseases remain unexplained. However, there is a serious limitation in analysis 3 that I now want to address.
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7. DISTRIBUTED COGNITION Medical theories are representations of biochemical mechanisms, but increasingly such representations are to be found, not in minds or books, but in computer databases. I will briefly describe several such databases and then discuss their implications for understanding the nature of medical knowledge. Here are six major computer databases of the sort that are becoming increasingly important for understanding the causes of diseases. 1. Metabolic Pathways of Biochememistry URL: http://www.gwu.edu/mpb/ Function: Graphically represents, in 2D and 3D, all major metabolic pathways, including those important to human biochemistry. 2. ExPASy (Expert Protein Analysis System) Molecular Biology Server URL: http://us.expasy.org/ Function: Dedicated to the analysis of protein sequences and structures. 3. Biomolecular Interaction Network Database (BIND) URL: http://www.bind.ca/index.phtml Function: Designed to store full descriptions of interactions, molecular complexes, and pathways. 4. The MetaCyc metabolic pathway database URL: http://MetaCyc.org/ Function: Contains pathways from over 150 different organisms, describing metabolic pathways, reactions, enzymes, and substrate compounds. 5. KEGG: Kyoto Encyclopedia of Genes and Genomes URL: http://www.genome.ad.jp/kegg Function: A bioinformatics resource for understanding higher order functional meanings and utilities of the cell or the organism from its genome information. 6. Biocarta Pathways Database URL: http://www.biocarta.com/ Function: Uses dynamical graphical models to display how genes interact to determine molecular relationships. Figure 2 is a vivid example of the kind of pictorial information that is available in these databases. It shows a pathway that is necessary for understanding how defects in regulation of the protein CFTR can lead to cystic fibrosis. With rapid developments in genomics and proteomics, the biochemical bases for a number of diseases are being understood. The development of these computer databases demonstrates a stark difference between theories in physics and those in biomedicine. A theory in physics such as Newtonian mechanics or relativity can be stated in a small
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Fig. 2. Depiction of the pathway for CFTR regulation, whose defects are believed to be the major cause for cystic fibrosis. This diagram can be found on the web at http://biocarta.com/pathfiles/h_cftrPathway.asp. Reprinted with permission of BioCarta.
number of equations that can be grasped by anyone who has taken the time to learn them. But no single human being has the time, energy, or memory capacity to learn even just the metabolic pathways for a simple organisms such as E. coli: the EcoCyc database contains information on 4363 E. coli genes, 165 pathways, and 2604 chemical reactions (Karp et al., 2002). Hence the biochemical understanding of any disease by a human scientist needs to be supplemented by access to computer databases that describe genes, proteins, and their interactions. Because biomedical mechanisms are being represented in computer databases, and not minds or books, the representation of the mechanisms for understanding diseases are distributed among various human minds and computers. Giere (2002) reached a similar conclusion about physics, arguing that research in high-energy physics is performed by a complex cognitive system consisting of an accelerator, detectors, computers, and all the people working on an experiment. Accordingly, I propose my final analysis of the nature of medical theories: Analysis 4: A medical theory is a representation, possibly distributed among human minds and computer databases, of mechanisms whose proper and improper functioning generate the states and symptoms of a disease. Analysis 4 does not contradict any of the previous 3 analyses offered above, but it expands them to allow the increasing role of bioinformatics
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in medical theorising. I have added the clause about ‘‘proper and improper functioning’’ to indicate that explanations of disease presuppose a background of normal biological operation that has broken down.
8. CONCLUSIONS The extension of my analysis of medical theories to encompass bioinformatics does not undermine any of the criticisms made in section 3 of various philosophical accounts of the nature of theories. The syntactic, model-theoretic, paradigm, and third-world accounts still fail to capture the complexity of medical theories and explanations. In particular, they do not illuminate the ways in which multimodal representations of mechanisms are crucial to the explanation of disease. Explanations of disease do not always need to go down to the deep biochemical level displayed in fig. 2. Depending on the problem and audience at hand, a medical explanation may operate at a superficial level, for example when physicians tell ordinary patients how they got sick. But explanation is not merely pragmatic: it should draw on established knowledge of mechanisms described at the level of detail appropriate for the task at hand. The most important task in medical research after determining the causes of diseases is developing treatments for them. Whereas drug discovery used to be largely a matter of serendipity or exhaustive search, current pharmaceutical research is based on deep understanding of the molecular bases of disease. Once investigators have identified how defective pathways lead to various diseases, they can search selectively for drugs that correct the defects (Thagard, 2003). I have defended a cognitive account of medical theories, but there is a great need for further research in cognitive science to describe the mental structures and processes that are used in medical theory and practice. Psychology and the other fields of cognitive science have contributed to powerful theories of mental representation and processing, for example, theories of concepts, rules, images, and neural networks (Thagard, 2005). But here are some difficult unanswered questions that are crucial to further our understanding of how minds do medicine: 1. How do brains represent changes of the sort that mechanisms produce? 2. How do brains operate cooperatively with multimodal representations, for example combining verbal and visual information? 3. How do brains accomplish an innate or learned intuitive understanding of causality that emanates from integrated multimodal representations? 4. What would it take for computers to be able not only to contain information about genes, proteins, and pathways, but also to use that
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information to reason about them in order to generate explanations and treatments? Thus there is much work to be done to develop the cognitive conception of medical theories from a philosophical account into a full-fledged psychological/computational theory of medical reasoning.
REFERENCES Baillargeon, R., Kotovsky, L., Needham, A., 1995. The acquisition of physical knowledge in infancy. In: Sperber, D., Premack, D., Premack, A. J., (Eds.), Causal Cognition: A Multidisciplinary Debate. Clarendon Press, Oxford, pp. 79–116. Barsalou, L.W., Simmons, W.K., Barbey, A.K., Wilson, C.D., 2003. Grounding conceptual knowledge in modality-specific systems. Trends Cogn. Sci. 7, 84–91. Bechtel, W., Richardson, R.C., 1993. Discovering Complexity. Princeton University Press, Princeton. CDC, 2004. Severe Acute Respiratory Syndrome (SARS). Retrieved January 14, 2004, from http://www.cdc.gov/ncidod/sars/. Cheng, P.W., 1997. From covariation to causation: A causal power theory. Psychol. Rev. 104, 367–405. Freudenrich, C.C., 2004. How Viruses Work. Retrieved January 14, 2004, from http:// www.howstuffworks.com/virus-human.htm. Giere, R., 1988. Explaining science: A Cognitive Approach. University of Chicago Press, Chicago. Giere, R., 1999. Science Without Laws. University of Chicago Press, Chicago. Giere, R., 2002. Scientific cognition as distributed cognition. In: Carruthers, P., (Eds.), The Cognitive Basis of Science. Cambridge University Press, Cambridge, pp. 285–299. Harre´, R., Madden, E., 1975. Causal Powers. Blackwell, Oxford. Hempel, C.G., 1965. Aspects of Scientific Explanation. The Free Press, New York. Karp, P.D., 2002. The EcoCyc database. Nucleic Acids Res. 2002, 56–58. Ksiazek, T.G., 2003. A novel coronavirus associated with severe acute respiratory syndrome. N. Engl. J. Med. 348, 1593–1966. Kuhn, T.S., 1970. The Structure of Scientific Revolutions, 2nd Edition. University of Chicago Press, Chicago. Kuhn, T.S., 1977. The Essential Tension. University of Chicago Press, Chicago. Lad, V., 2003. An Introduction to Ayurveda. Retrieved Sept. 22, 2003. from http:// www.healthy.net/asp/templates/article.asp?PageType¼Article&ID¼373. Machamer, P., Darden, L., Craver, C.F., 2000. Thinking about mechanisms. Philos. Sci. 67, 1–25. Michotte, A., 1963. The Perception of Causality, Translation: Miles, T. R., Miles, E., Methuen, London. Murphy, G.L., 2002. The Big Book of Concepts. MIT Press, Cambridge, MA. Nagel, E., 1961. The Structure of Science. Harcourt Brace, New York. Popper, K., 1959. The Logic of Scientific Discovery. Hutchinson, London. Popper, K., 1972. Objective Knowledge. Oxford University Press, Oxford.
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Rota, P.A., 2003. Characterization of a novel coronavirus associated with severe acute respiratory syndrome. Science 3000, 1394–1399. Salmon, W., 1984. Scientific Explanation and the Causal Structure of the World. Princeton University Press, Princeton. Suppe, F., 1977. The Structure of Scientific Theories 2nd Edition. University of Illinois Press, Urbana. Thagard, P., 1988. Computational Philosophy of Science. MIT Press/Bradford Books, Cambridge, MA. Thagard, P., 1992. Conceptual Revolutions. Princeton University Press, Princeton. Thagard, P., 1999. How Scientists Explain Disease. Princeton University Press, Princeton. Thagard, P., 2003. Pathways to biomedical discovery. Philos. Sci. 70, 235–254. Thagard, P., 2005. Mind: Introduction to Cognitive Science 2nd Edition. MIT Press, Cambridge, MA. Thagard, P., Zhu, J., 2003. Acupuncture, incommensurability, and conceptual change. In: Sinatra, G. M., Pintrich, P. R., (Eds.), Intentional Conceptual Change. Erlbaum, Mahwah, NJ. pp. 79–102. Winston, P., 1993. Artificial Intelligence 3rd Edition. Reading, Addison Wesley, MA.
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
5 Medicine as a moral epistemology Alfred I. Tauber Center for Philosophy and History of Science, Boston University, Boston, MA, USA
1. INTRODUCTION This collection of essays addresses the multidisciplinary character of contemporary medicine, and I suggest that the key question posed by this project is, What binds medicine’s various elements and approaches together? I submit that the answer is not to be found in medicine’s epistemology, its forms of knowledge and manner of understanding, when conceived narrowly. As my title suggests, I wish to expand the idea of knowledge and form a synthesis between two branches of philosophical discourse – the moral and the epistemological. These are generally regarded as separate, but my underlying thesis is that any form of knowledge, no matter how objective and divorced from subjective bias, is still imbued with value. And here, value is construed as moral. And in the case of medicine, because of its dual character of scientific practice and ethics of care, the distinction between facts and values collapses in a particularly interesting way. Moral is not simply the discourse about good and evil, but includes all those aspects that underlie such determinations. In other words, values presuppose judgment, and in this sense ethics is based on structures of values. Even objective science is ordered by its own values: objectivity, coherence, predictability, comprehensiveness, simplicity, etc. (Putnam, 1990, 2002). These values, at least for the past sixteen decades or so, have conferred a particular cast to scientific knowledge, a form of positivism, which assumes that objective facts are freed of bias, subjectivity, and value. Positivists would not deny the utility of such values, and consequently the door is left ajar for considering how facts and values may be linked. But they do restrict the kind of value allowed to participate in the scientific endeavor: Objectivity divorced from personal value is embraced precisely 63
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because such knowledge is regarded as making facts universal. Indeed, it is the universality of scientific knowledge that affords its authority. I would hardly argue against science’s successes, and indeed, who could quarrel with the triumphs of such an approach? To be sure, science is governed by its own values, and these have served medicine well. However, I claim that the limitations of these values for the care of the ill require a reformulation of medicine’s scientific aspirations. For the view from nowhere, the absent perspective, is not only inappropriate for medicine, it is unattainable as well. Medicine’s fundamental scientific assumption, namely, that medicine may become a branch of science, is a false conceit, one that must be modified by admitting that medicine’s epistemology is thoroughly embedded in non-positivist values, and that these competing values reflect a moral structure that ultimately orders and defines clinical science. In short, I maintain that the glue holding together the various epistemological strands of contemporary medicine is of a personal moral character, and what we seek is a better understanding of medicine’s moral epistemology as it is guided by responsibility and an ethics of care. What this means is the subject of this essay.1 My thesis, simply, is that the practice of medicine employs certain tools – scientific and technologic – to fulfill its moral mandate, the care of the person. That entity – the person – defines an ethical response, and physicians optimally adhere to understanding that the multiple dimensions of care demand attention by the underlying moral calling of responsibility for the welfare of the patient. Clinical science scrutinises and treats the disease; the doctor treats the person, and this difference is what makes medicine a normative science, for its practitioners must synthesise the various strands of its faculties in the service of the afflicted individual (Richman, 2004). This is ultimately a moral calling – the responsibility of care orders all the rest. So this claim, that medicine is most deeply a moral enterprise – defining and executing the ethics of care – constitutes my response to how we might tie together the multiple dimensions of clinical medicine. I begin by describing nineteenth century positivism and a philosophical argument that has been waged since the eighteenth century, the so-called fact/value distinction. This historical and philosophical overview explains the conceptual issues at the foundation of medicine’s scientific epistemology
1 Note that I will not employ the characteristic usage of ‘‘moral epistemology’’, which addresses the epistemic status and relations of moral judgments and principles, e.g. justification of statements or beliefs, in epistemology, or validation of judgments of actions, in ethics. Rather, I am seeking a synthesis of the moral and epistemological domains, or to put it another way, I am exploring the value-laden characteristics of knowledge.
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and will serve to explain how and why medicine is only in part a scientific enterprise. The collapse of the fact/value distinction, generally, and more specifically in medicine, lies at the heart of medicine’s epistemology. Specifically, dissecting this issue explains why the physician cannot, under any circumstances, simply rely on facts independent of values and judgments dictated by the circumstances of an individual patient. The ethical thread of care is thereby inextricably woven into the epistemological project simply because the individual person demands, solely by his or her status as a person, a personal response. Why this is the case will then be explored, and the conclusion is concerned with the implications of this position.
2. HISTORICAL SUMMARY OF POSITIVISM AND THE FACT/VALUE DISTINCTION For over a century, medicine has prided itself on its scientific orientation and technological feats. To be sure, the accomplishments based on the scientific attitude have had an enormous success, and only those adherents to a metaphysics deeply at odds with Western rationality would disparage or deny the dominance of clinical science. But two caveats should be accepted: The first is that scientific medicine is limited to certain maladies (albeit growing), and second, the costs for the scientific approach to disease has had certain untoward effects on what might be best called the humanistic treatment of illness. The initial caveat premises that not all ailments are susceptible, in principle, to a biomedical approach. Such psychological and existential crises in life that may lead to illness may be symptomatically alleviated by drug or cognitive therapies, but the personal and social contingencies that have so much to do with the health of persons are, strictly speaking, outside the purview of scientific medicine. Such problems have, to be sure, their own professional specialties committed to understanding and relieving them, e.g. psychology and social medicine, but scientific medicine has not traditionally considered itself concerned with such matters. However, the boundaries separating what is amenable to scientific inquiry and therapy, and what is not, remains hotly contested. For instance, the growing conviction that genetics lies at the root of complex human behavior belies a narrow definition of medicine’s future, while those more skeptical of genetic determinism argue that these problems, in principle, are not subjects for a reductionist approach (Tauber and Sarkar, 1993). Putting aside the boundary question, the second caveat addresses the complaint, evident since the romanticists first cautioned about the perils of science, that scientific medicine reduces the ill to the study of a disease,
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and in that reduction the ‘‘whole person’’ is lost. This dehumanising process has been successfully countervailed by the appeal of complementary and alternative medicine (CAM), which, despite myriad schools of thought, is unified by a holistic approach to the patient (Callahan, 2002). I have had occasion to discuss the claims of CAM approaches to illness elsewhere (Tauber, 2002a), and here I wish to slice out a particular response to the latter criticism about medicine’s seeming abandonment of its more humane orientation. To do so, we must excavate some of the history leading us to the present moment. The historical development of Western medicine as it became a product of the scientific ethos of the mid-nineteenth century is well-known. At that time, two philosophies of science – positivism and reductionism – emerged, which decisively shifted the character of medicine towards a new scientific ideal. Neither were totally novel philosophical strategies, indeed each have venerable histories dating to at least the early modern period, but by the 1850s they were articulated within a new context and were joined to set a new agenda for clinical medicine. By the end of the century, medical training had been transformed and application of a laboratory-based approach to diagnostics and therapeutics established revolutionary aspirations for medical practice. While there are strong social and political reasons for this shift (Foucault, 1963, 1973), I wish to emphasise the reification of the patient as a consequence of positivism, and highlight the moral consequences of that approach. For the past century and a half, mainstream science has assumed a positivist stance, one which increasingly seeks to describe the world in non-personal terms (Simon, 1963; Kolakowski, 1968). Positivism carries several meanings and has been notoriously difficult to define, yet certain precepts may be identified, especially as espoused in its nineteenth century format: Foremost, it championed a new form of objectivity, one that radically removed the personal report to one that was universally accessible. Thus knowledge, to be ‘‘true’’ and ‘‘real’’, must be attested to by a community of observers who shared common observation. This move from the private sphere of experience to a communal one had begun at the dawn of modern science, but in the mid-nineteenth century this ideal of truth became clearly enunciated as a scientific principle. Thus, positivism sought a collection of rules and evaluative criteria to provide a normative attitude, which would regulate how we use such terms as ‘‘knowledge’’, ‘‘science’’, ‘‘cognition’’, and ‘‘information’’. As developed in the 1850s, positivism came to be understood as a philosophical belief which held that the methods of natural science offer the only viable way of thinking correctly about human affairs (Tauber, 2001, 105ff.). Accordingly, empirical experience – processed with a
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self-conscious fear of subjective contamination – served as the basis of all knowledge. Facts, the products of sensory experience, and, by extrapolation, the data derived from machines and instruments built as extensions of that faculty, were first ascertained, and then classified. Positivism contrasted with – indeed, was constructed in opposition to – the romantic view of the world by denying any cognitive value to value judgments. Experience, positivists maintained, contains no such qualities of men or events as ‘‘noble’’, ‘‘good’’, ‘‘evil’’, or ‘‘beautiful’’. In radical reaction against romanticism, positivists sought instead to objectify nature, banishing human prejudice from scientific judgment. The total separation of observer from the object of observation – an epistemological ideal – reinforced the positivist disavowal of ‘‘value’’ as part of the process of observation. One might interpret, but such evaluative judgments had no scientific (i.e. objective) standing. Simply put, where the romantics privileged human interpretation (exemplified by artistic imagination), the positivists championed mechanical objectivity (e.g. thermometer, voltmeter, chemical analysis) (Daston, 2000). But by the end of the eighteenth century, Goethe, resisting the allure of a radically objective science, appreciated that ‘‘facts’’ do not reside independent of a theory or hypothesis which must ‘‘support’’ them (a point well developed in twentieth century philosophy of science). Goethe’s precept that ‘‘everything factual is already theory’’ (Tauber, 1993), was offered as a warning about the epistemological complexity of supposedly objective knowledge. He understood the potential danger of subjective contamination of scientific observation, and more to the point, the tenuous grounds of any objective ‘‘fact’’ that relied in any way on interpretation. ‘‘Interpretation’’ stretches from inference to direct observation, for any perception must ultimately be processed to fit into a larger picture of nature and must cohere with previous experience. The synthetic project of building a world view thus begins by placing ‘‘facts’’ within their supporting theory, and continues with integrating that scientific picture with the broader and less obvious intellectual and cultural forces in which science itself is situated. Thus ‘‘facts’’ as independent products of sensory experience are always processed – interpreted, placed into some over-arching hypothesis or theory. In short, observations assume their meanings within a particular context, for facts are not just products of sensation or measurement as the positivists averred, but rather they reside within a conceptual framework which ‘‘places’’ the fact into an intelligible picture of the world. To varying degrees, this constructivist interpretation was denied by the positivists. A world built from their principles would appear essentially the same to all viewers, because ‘‘facts’’ have independent standing and
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universal accessibility, so that irrespective of individual knowers, facts constitute shared knowledge. The romantics placed important caveats on that approach to nature, both on epistemological grounds, as well as metaphysical ones. From their perspective, each inviolate observer held a privileged vantage, and the vision so obtained was jealously protected. The conflict between the ‘‘objectified’’ world of scientific facts and the private domain of personalised experience of those facts dates from the very origins of science, which aspired to discover facts ‘‘out there’’ divorced from a subjective projection of the mind upon nature. Descartes initiated and Locke completed the philosophical stance of a newly defined science, which in separating mind and body, split the I and the world. In this view, humans are subject to an irreducible duality: the mind, res cogito, surveys the world, res extensa. This division, irreparable and absolute, framed epistemology for the next four centuries and, in the context of a positivistinclined science, to study natural phenomena demanded a dissociated self: To see ‘‘objectively’’, disallowed projection of the self, a contamination of attaining neutral knowledge. But this dualism bequeathed the dilemma of rendering whole what was broken in the division between self and world. The Cartesian reductive method imparts an irresolvable anxiety: After dissecting the world into parts, how are those elements to be reintegrated (Tauber, 1996)? Cartesianism itself offers no solution. Further, the epistemological standing of the observer is ambiguous: How indeed does the observer know? The positivist movement was a response to this problem. If facts could be universalisable, the ‘‘private’’ mind could be ‘‘opened’’ to public discourse. Objectivity at its most basic calling is the attempt to solve the imbroglio of unifying minds, which are not only separated from the world, but also dangerously isolated from each other. So the Cartesian mind/world split resurfaces in the public and private scientific experience of ‘‘fact’’. Specifically, in a community of distinct knowers, Who ‘‘knows’’ facts? How are facts used? What do they mean? Although the discovery – or more precisely, the construction – of a fact is intimately linked to the observer, the dynamics of the fact can hardly be limited to the private domain of the observer’s experience. Others have a claim to a fact, which is often shared in the narrow proprietary sense, but always as the expected outcome of the scientific process. A scientific fact is fundamentally public, for it must be universalised by the scientific community at large. A hidden fact is useless to that community; discourse demands scrutiny. Scientific objectivity focuses upon the discovery or creation of facts and the public debates surrounding them. Scientific facts acquire the status of public entities as they become objectified, circulated, and finally identified increasingly less with the subjective, private report of the scientist.
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Critical to the development of modern science was precisely this process by which shared experience was universalised among scientific practitioners. Within this domain ‘‘objectivity’’ is attained. Yet there remains a second, private sphere of the fact, which arises from the scientist’s identity as an autonomous epistemological agent. The integrity of the scientist as a private, knowing agent remains an implicit and critical characteristic of scientific activity. To know the world remains a fundamental individual aspiration in the age of the Self (Tauber, 1994, 141 ff.), and while we emphasise the social aspects of science as a cultural activity, the scientist remains that Cartesian agent who experiences the world independently. Scientific knowledge thus has strong commitments to Cartesian dualism, especially to its concept of a universalised corpus of fact and theory, which arises as the product of individual experience. We are left with a complex dialectic between the observer’s ‘‘personal’’ relations to those facts as the product of his autonomous personhood and the need for entering that experience into the public sector. From the positivist orientation, this independence of the known fact rests on its correspondence to a reality which any objective observer might know. This assumes both a universal perspective, that ‘‘view from nowhere’’ and a correspondence theory of reality. But the subjective components cannot be entirely eliminated, and as stubborn as the positivists might have been in attempting to stamp out subjective influences, they only succeeded in making them seem disreputable (Daston, 2000). There is no escape from the constraints of an observer fixed by his individual perspective, contextualised in some observational setting, and committed to processing information through some interpretative (viz. subjective) schema. Such an observer cannot adhere to a rigid identification of ‘‘facts’’ based on an idealised separation of the knower and the known.2 The radical separation of the observing/knowing subject and his object of scrutiny is the single most important characteristic of positivist epistemology (Tauber, 2001). Because of this understanding, positivists claimed that science should rest on a foundation of neutral and dispassionate observation. The more careful the design of the experimental conditions, the more precise the characterisation of phenomena, the 2
From this short overview, it seems obvious that what constitutes a fact depends upon the metaphysics, epistemology, theory of truth, and semantics that determine its definition. Insofar as facts are what makes true statements true, inquiries that do not distinguish the metaphysical nature of truth from epistemological concerns or from the linguistic use of truth will hopelessly muddle important distinctions. Notwithstanding debates about correspondence theories of truth (Russell, Austin, and Strawson) and the empirical status of facts (scientific realism versus social constructivism), it is apparent that descriptive medical science encompasses a wide variety of facts, whose epistemological status and linguistic uses vary.
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more likely the diminution of subjective contaminants. Thus, the strict positivist confined himself to phenomena and their ascertainable relationships through a vigorous mechanical objectivity. In the life sciences, positivism exercised new standards in the study of physiology that applied the objective methodologies of chemistry and physics to organic processes. This approach allowed newly adopted laboratory techniques to establish physiology as a new discipline and gave birth to biochemistry, whose central tenets held that the fundamental principles of organic and inorganic chemistries were identical, differing only inasmuch as the molecular constituents of living organisms were governed by complex constraints of metabolism. This led to a new declaration for the application of a reductionist strategy to biology and medicine, and, indeed, in positivism’s philosophical basin, reductionism was baptised. Positivism’s methodology was intimately linked to the assumption that all of nature was of one piece, and the study of life was potentially no different in kind than the study of chemical reactions, the movement of heavenly bodies, or the evolution of mountains. Thus, if all of nature was unified – constituted of the same elements and governed by the same fundamental laws – then the organic world was simply on a continuum with the inorganic. According to this set of beliefs, there was no essential difference between animate and inanimate physics and chemistry, and the organic world was therefore subject to the same kinds of study so successfully applied in physics. On this view, medicine studied the body essentially as a machine, which was governed by uniform chemistry, and thus susceptible to mechanical repair. The new problem was to reduce the organic to the inorganic, that is, to exhibit the continuity of substance and operation, and concomitantly understand the distinct character of life processes. To accomplish this twofold agenda, reductionism was coupled to positivism. The reductionists were initially a group of German physiologists, led by Hermann Helmholtz, who in the 1840s openly declared their manifesto of scientific inquiry (Galaty, 1974). They did not argue that certain organic phenomena were not unique, only that all causes must have certain elements in common. They connected biology and physics by equating the ultimate basis of the respective explanations. Reductionism, specifically physical reductionism as opposed to the later development of genetic reductionism, was also a reaction to romanticism’s lingering attachment to vitalism, that notion that life possessed a special ‘‘life force’’. Vitalism was seised upon because it belied the unity of nature offered by various mechanistic philosophies. The debate was largely resolved by three key discoveries at mid-century: the heat generated by contracting muscle could be accounted for by chemical metabolism (no special vitalistic force was
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necessary); bacteria did not arise through spontaneous (vitalistic) generation; and finally, the blind materialism of natural selection could explain the evolution of species. The appeal of vitalism was not totally extinguished by mid-century, but certainly a new scientific ethos had taken over the life sciences by 1890. And medicine was radically changed as a result of these developments. The impact of reductionism was to offer a complementary method to enact the positivists’ philosophical programme. This dual attitude had a profound influence on the doctor-patient relationship, and even more importantly gave new meaning to illness and the body (Foucault, 1963, 1973). The holistic construct of Man and the medicine which served him were replaced by a fragmenting clinical science that, in its powerful ability to dissect the body into its molecular components, remained unconcerned with addressing what had traditionally organised the clinical perspective: Laboratory analysis replaced the holistic construct of the individual patient with a different standard of fragmenting analysis.3
3. THE LIMITS OF THE FACT/VALUE DISTINCTION IN MEDICINE The holist rejoinder to reductionist medicine is both epistemological and moral. From the moral perspective, we begin by acknowledging that the doctor-patient encounter is, by its very nature, a negotiated attempt to coordinate, if not combine, different frames of reference – treating disease (medical science) and experiencing illness (the patient). The recurrent question plaguing a reductionist, positivistic clinical medicine is to what extent the mechanistic, dehumanising experience of becoming a medical object of scrutiny and therapy can be mitigated by counterbalancing factors. I have argued that a response to this question must begin with re-evaluating the doctor-patient relationship and seeing it as fundamentally ethical in character (Tauber, 1999). My thesis, as already stated, is that science and technology are in the employ of medicine’s primary moral
3 Medicine, of course, was never monolithic, and well into our own century renewed challenges to reductive orthodoxy have appeared, even within mainstream conventional medicine: constitutionalism, psychosomatic medicine, neo-Hippocratic medicine, neo-humoralism, social medicine, Catholic humanism, and, in Europe, homeopathy and naturpathy (Lawrence and Weisz, 1998). These ‘‘holistic’’ systems have been espoused not only by various kinds of practitioners, but in noteworthy instances, championed by ‘‘legitimate’’ basic scientists, e.g. Henry Head, Walter B. Canon, and Alexandre Besredka (ibid.). Through historical reflection, we can see that the discussions of today are directly linked to similar debates held between 1920 and 1950, which in turn were re-framed arguments dating to the nineteenth century.
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responsibility, and that the ethical dimension of care organises all other aspects of medicine. By this, I mean that the requirement of recovering the full personhood of the patient to again become an autonomous free-living individual is the fundamental telos of medicine. This is an ethical venture, and from this perspective, science is fundamentally in the employ of a moral goal (Tauber, 2002b). Accordingly, a humane doctor–patient relationship remains a basic requirement of contemporary medicine. The logic for understanding the relationship of biomedical reductionism to its complementary orientation, holism, takes this form: 1. In any clinical encounter, the experience of the suffering patient and his or her reification as a medical object requires a negotiation between the two points of view; 2. While the successful application of rational, scientific knowledge is expected, this application can only be framed by the particular context of care; 3. This so-called ‘‘context of care’’ is fundamentally moral in character inasmuch as it is framed by the particular values and needs of the patient; 4. Based on those values, science has been developed to address disease, but the care of illness, the care of the suffering patient, requires more; 5. Ergo, effective medicine is humane medicine, and the reductive practice must be regarded, always, as only part of the therapeutic encounter. Note, there is no argument against reductionism per se, but there is a complaint lodged against radical positivism, where the patient is regarded as the disease, e.g. ‘‘The cancer in bed 3’’, or ‘‘the pneumonia in room 506’’ (Tauber, 2002b). Such references to persons are jarring. Why? Simply, the reification of disease is not easily extrapolated to the treatment of persons, or put another way, ‘‘disease’’ is ordered by one set of values and ‘‘persons’’ are understood by another. Each set of values has their own legitimacy within the particular domain in which they are appropriately applied. The issue is not that the objective values governing the understanding and treatment of disease are in competition with humane values, which organise the care of patients, but we must be aware of the appropriate application of each set. However, I would go one step further: In medicine the ‘‘set’’ of objective values and the ‘‘set’’ of humane values are inextricable. Both are at play in the same arena of patient care, simultaneously. Their proper integration is the challenge. In a trivial sense, values direct knowing. For instance, we constantly choose to pay attention to certain elements of our experienced world and
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ignore the vast majority. Values determine what we study and indeed, as Hilary Putnam has cogently argued (1990), even the positivist standards or aspirations of science are values, historically arrived at and chosen in everyday practice.4 In medicine, this view is overwhelmingly self-evident and hardly needs recitation: From the socially-based policy decisions of health care administrators to the attention paid to the individual patient, the care delivered is allocated by a distillation of value choices. Medicine is embedded in a value system, and patients are subject to complex moral choices, whether declared or not. The ill demand, and expect, that their physician will negotiate the maze of choices for them, be their advocate, and protect their interests. For instance, whether I administer an aggressive chemotherapy to an elderly patient depends on many factors beyond the stage of her cancer, and must include such factors as expected quality of life, support structures, other confounding medical problems, etc. These are options that must be negotiated with the patient and family. Simply put, medicine is hardly objective in its applications, nor in its practices, and doctors must engage the social world of the sufferer, as much as the biophysical and genetic domains of the body. The boundaries are not firmly demarcated. The positivist attitude simply will not suffice in the care of the patient. But more, it is an encumbrance. Patients are social creatures as well as organic ones, and the caring physician must recognise that care is multidimensional. The existential state of being a patient is perhaps an even more immediate domain of the moral. The loss of autonomy, the fear of the unknown, the dissolution of identity accompanying pain in its multifarious forms, the dehumanisation of being subjected to the administrative processes of health care, and the psychological dependence each of these challenges fosters combine to make the patient emotionally dependent on health care providers (Tauber, 2003a). In this setting, individual concerns are paramount, and the most immediate response must be a humane one. But physicians are trained to be medical scientists and testaments to the
4 ‘‘[I]f values seem a bit suspect from a narrowly scientific point of view, they have, at the very least, a lot of ‘‘companions in the guilt’’: justification, coherence, simplicity, reference, truth, and so on, all exhibit the same problems that goodness and kindness do, from an epistemological point of view. None of them is reducible to physical notions; none of them is governed by syntactically precise rules. Rather than give up all of them . . . and rather than do what we are doing, which is to reject some – the ones which do not fit in with a narrow instrumentalist conception of rationality which itself lacks all intellectual justification – we should recognise that all values, including the cognitive ones, derive their authority from our idea of human flourishing and our idea of reason. These two ideas are interconnected: our image of an ideal theoretical intelligence is simply part of our ideal of total human flourishing, and makes no sense wrenched out of the total ideal, as Plato and Aristotle saw’’. (Putnam, 1990, p. 141)
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conflict inherent in that orientation are legion. The issue is succinctly stated in a recent book review about the care of schizophrenics: Despite their reputation for vanity, many mental health professionals, and medical students in particular, fail to recognise their own importance. They ‘come and go among patients as if their knowledge and skills were all that counted, their persons not at all’. The remark is pertinent, for it points to the underlying vision that drives the profession. The medical students are not looking for personal engagement with the patient. They don’t really want their ‘person’ to make a difference. That is not the ‘importance’ they are after. Rather they want to learn (why not?) to heal the patient with a precise and controlled intervention, the exact dosage of the exact drug chosen after an exact diagnosis based on meticulous and exact analysis of spinal fluids and brain scans. They are in thrall, that is, to the great and credible dream of Western medicine. (Parks, 2000, p. 15) This positivist attitude is well-established in the biomedical world, and, to be sure, it was hard-won and hardly to be disparaged. But at the same time, the price for making disease objective has diluted, if not too often replaced medicine’s ancient calling of care. I mean by ‘‘care’’, attention to each facet of the individual, namely, treating the patient as a person, as a whole. A medicine that fails to address those elements of personhood that have no scientific basis – the social, the emotional, the moral – is ultimately fractional and therefore incomplete. Only by the physician committing to comprehensive care can the diverse elements of being ill be addressed effectively. Patients may have surrogate advocates, for instance, family members or friends, but in the end, no one is better situated to assume the responsibility of advocacy than the patient’s physicians and nurses, and to that end we must invoke the ethics of responsibility (Tauber, 1999, 2005a). Ultimately, the argument between reductionism and holism is a hollow one. From the epistemological perspective, the organism as an integrated, functioning entity frames all approaches to the patient. Medicine is, by its very character, holistic in orientation, endeavoring to address all systems at once and to effect full function of each. This requires a global view of function, from molecule to intact organism. But medicine is more than a science of an organic entity, and ultimately must be judged as how effectively it addresses the person, the individual with illness. Disease is an objective account of pathology, but disease is only one component of illness, and all those other elements of dysfunction that might arise from disease also require care. In this sense, the patient has moved from being an entity – an organic construct – to one of personhood. This latter
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characterisation is a moral one, one laden with values and choices. If one regards medicine as dealing finally with this larger conception of the patient, then reductionism must be viewed as a tool, albeit a powerful one when applied to certain questions, but only an instrument in the employ of another agenda. The ethical demand of medicine simply disallows satisfaction with the positivist stance, either in practice or as an aspiration. To accede to the resulting fragmentation of reductionism is to surrender medicine’s ultimate concern, the care of the patient.
4. IMPLICATIONS But the question remains, how is a balance struck between the ‘‘holistic’’ – often translated to a humanistic concern for the patient – with the positivist/reductionist perspective, which draws upon immense resources of technical success, and which, because of these successes, has imperialistic designs on what hitherto has been the domain of the social and humanistic disciplines. For instance, the ‘‘biological imperative’’ of genetics is increasingly regarded as the blueprint of identities by designating to some unknown, but suspected large extent, the physical, cognitive, and emotional characteristics of complex human behavior. This primary level of biological organisation is thought then to serve as the foundation for social identities that are made by adding the contingencies of family, social strata, religion, and all the other various factors that play in cultural character. The naturenurture debate is seemingly never-ending, but one conclusion is inescapable: Biology is bedrock to our personhood, and while it may be altered or controlled, in the end, biological constitution confers a large, and sometimes over-whelming definition of who we are and what we might do. This genetic determinant, notwithstanding the power of its associated technology and recent advances, is ultimately sustained by the belief that humans – both their bodily functions as well as their social behaviors – are ultimately reducible to biochemistry, biophysics, and genes. This is the so-called naturalised view of humans and the power of its vision have transformed the way we think of ourselves, and to balance this view with an older humanism is a challenge as yet not met. The repercussions of this celebration of reductive scrutiny left medicine with a deep contradiction: Initially designed to address the patient’s illness as experienced in an array of meanings directly accessible to the sufferer, disease of a system, or organ became the focus of concern, and medicine thereby made a Faustian pact with a putatively valueless science: Amending, and often times foregoing integrated care – one that addressed
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the psychological and spiritual dimensions of illness as well as the pathophysiological – medicine too often was accused of losing its deepest commitment to the patient. The doctor-patient encounter is by its very nature a negotiated attempt to coordinate, if not combine, different frames of reference: In treating disease, medical science employs a reductive approach, while the patient experiencing illness assumes a holistic stance. Each has its place and each must accommodate the other. So it seems to me that the recurrent question plaguing a reductionist, positivistic clinical medicine is to what extent the mechanistic, dehumanising experience of becoming a medical object of scrutiny and therapy can be mitigated by counterbalancing factors. Simply, scientific biomedicine, for all of its power and promise, still must treat persons, and persons are only in part defined by their biology. A more expansive medicine is required.
5. RECASTING CONTEMPORARY MEDICINE The clinician is committed to a scientific ethos. She scrutinises the patient as an individual with a disease, and the diagnosis of that condition determines therapy. This is a commonplace understanding of the basis of the physician’s craft. But more is required, for the fact/value distinction has a particularly malodorous quality when applied to the ill. Crucial as medical facts are to the clinician’s art, she remains an artist, or more accurately a priestess of care. So the most important fact in medicine is the irreducibility of the patient’s personhood. In the end, it is this category of moral agency that defines the doctor-patient relationship, determining the physician’s epistemology and the ethics of her care. Here, I wish to explore how facts are inextricable from values of care and thereby offer a useful example of how the fact/value distinction collapses more generally. Disease is a synthesis and condensation of signs and symptoms, test findings, and a web of sorting categories. Indeed, in the Unites States, every disease has an international bar code, and if a patient does not have such a code, the doctor does not get paid! Illness, on the other hand, is a composite of all those elements that conspire to incapacitate a person. Disease in its biological formulation is optimally based on objective, i.e. public, fact. But what, indeed, is the status of objective fact in this setting? First, and foremost, all clinical facts are contextualised at several levels. From the strictly biological perspective, and this, as we will see is already a false depiction, organic dysfunction is witnessed in a complex array of other integrated elements. No fact resides alone. One of the first lessons medical students must learn is that a laboratory finding or anatomic
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description is only the beginning of building an integrated clinical picture. What does it mean that a serum sodium level is low? To understand that ‘‘fact’’ is to understand the entire physiology of renal and endocrine regulation of electrolytes; the hormones effecting secretion or retention; the anatomic structures – kidney, intestines, lungs, skin – which are the targets of metabolism – absorption and excretion. No fact stands alone. And the focus of the array of facts is the function of the whole person. For instance, sickle cell anemia has a precise pathophysiological description at the molecular level, while the symptom, lethargy, does not. The nature of the fact describing each condition is thus quite different. One might say that sickle cell disease is factual and lethargy is not, because the latter is subjective, unobservable, and thus unverifiable. But the meaning of the so-called fact of sickle cell disease’s etiology and the subjectivity of lethargy is not so easily divided between a factual account and a valued one. Consider, how a keenly defined molecular lesion for sickle cell disease is insufficient for understanding the protean manifestations of the illness. Some patients are virtually asymptomatic while others have debilitating pain crisis, organ damage, hemolytic anemia, and other co-morbid states that lead to a shortened life span. The molecular ‘‘fact’’ of an abnormal hemoglobin precisely defined goes only part way in describing an illness that requires individually-specified care. This general observation has important implications for understanding the contextual character of any scientific fact, and how in medical science in particular, each so-called ‘‘fact’’ exists in a context which confers a distinctive meaning. That meaning is determined by factors usually un-recognised, and thus the grounding of the molecular fact, its valuation so to speak, only can assume its significance in the context of the individual patient. That contextualisation immediately shifts the ontological character of clinical facts from a positivist aspiration to a more complex value-dependent ontology. Perhaps the most striking irony in treating sickle cell patients is the physician’s reliance on the patient’s report of pain as the principle criteria of therapy. But are these other descriptive facts merely raw data as a radical positivism might espouse? Absolutely not! Clinical data, in themselves fall into an intricate continuum of ‘‘normality’’ which has its individual, or idiosyncratic parameters, which in turn require judgment to assess their significance. George Canguilhem, in his celebrated The Normal and the Pathological (1966, 1989), showed the ever-changing shifts of the normal and the pathological as constructs, both as understood in their scientific context, but also as understood and then experienced by the suffering patient. Medicine both exists in, and helps create a complex web of values in which disease and illness are suspended. Therapeutic tolerance or intervention require a balanced judgment of diverse modes of
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interpretation, so that the cardinal decision in any clinical encounter is to distinguish what may be done diagnostically or therapeutically, from what, in a universe of choices, is actually selected (Pellegrino and Thomasma, 1981). In other words, what may be done is narrowed to what should be done, and that winnowing is determined by an array of value-based decisions. In a trivial sense, whether to intubate a patient with respiratory failure at the end stage of cancer of the lung is a judgment governed by values: What is the life expectancy if successful? What are the chances of success? Indeed, what is ‘‘success’’? What resources must be allocated at the expense of another patient? What is the quality of life to begin with? What are the patient’s wishes? Such decisions, usually not as dramatic, nor as easily formulated, arise in virtually all clinical decisions. And beyond this contextualisation, the physician must place ‘‘disease’’ within an everchanging nosography, a system of medical theory and classification that accounts for these facts. Considering the incompleteness of our scientific theory, the social construction of much of it, and the intimate relation of psychological and social factors in defining disease, commentators are increasingly appreciating that the model of clinical medicine based on impersonal ‘‘facts’’ is not only incomplete, it is distorting. The literature dealing with this general issue is immense, and here I wish to sketch in only two general ways of approaching the fact/value relationship in medicine. The first pertains to the efforts at establishing a medical heuristics, the so-called ‘‘silent adjudicators of clinical practice’’ (McDonald, 1996; see also Fox and Glasspool, this volume). If we simply look at this decision-making process as an epistemological exercise, the intermingling of facts and values is obvious: Robust scientific conclusions are too sparse to fully inform clinical decisions for the simple reason that few patients fall exactly into the same criteria of study groups. Physicians routinely must extrapolate from small study groups to the general population in which they must situate their particular patient (McDonald, 1996). For instance, we treat moderately hypertensive women as we treat men, but the study upon which we base such treatment was conducted by the Veterans Administration and no women were enrolled! (Veterans Administration Cooperative Study Group, 1970) Given the increasing concern about sexual differences in the natural history of the same disease, this compromise is seen for what it is, a necessary extrapolation for the lack of good data for women. To counter such myopia, Bayesian inference, a statistical method that includes all previous data to assess likely future outcomes, is increasingly gaining favor. Such meta-analyses represent formal methods to make these kinds of assessments, which are, in a sense, attempts to develop a better heuristic for clinical judgment. Instead of blind intuition, value is
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actually calculated as a likelihood ratio. Such tools are part of the new discipline of evidence-based medicine, a relatively new movement in modern medicine (Evidence-Based Medicine Working Group, 1992). In the early 1990s a growing self-consciousness about the spotty nature of medical knowledge became widespread, not only by an increasingly skeptical public, personified by third party payers who were aghast at medical costs with no obvious criteria for success, but also the medical profession itself, which was being newly challenged by its own members to justify its interventions. That academic champions have emerged as self-appointed guardians of a more vigilant clinical science might strike one as curious, since for over a century, the dominant model of clinical care has claimed to be based on sound scientific information and its objective application. Indeed, that claim is the rationale for discrediting all other practitioners. Medical facts are rarely ‘‘simple facts’’, which means that while physicians must decide how to interpret a test or treat a patient from a limited ying/yang choice, no test, nor intervention, falls into a clearly defined positive or negative domain (Murphy, 1976, 1997; Weinstein and Fineberg, 1980). Every test result has false positives and false negatives as compared to some gold standard, which in itself may not be absolute. And every drug has toxicities and failure rates that not only vary within sub-groups of patients, but more to the point, are unpredictable beyond a frequency figure as determined for a large population. This means that when applied to any given patient, a test result or a therapeutic outcome may only be described as an odds ratio. And when the confounding uncertainty of diagnosis is factored into this complex calculus of therapeutic choice, then the circularity of decision-making begins to look like the dog chasing its tail. More often then not, the probabilities are inferred, not known, and even when clearly defined, probabilities change the ground rules of what constitutes an objective decision. The choice is made with only certain degrees of certainty, and these depend on variables more often then not untested, and if they have been accounted for, these characteristics may not be applicable because of other confounding factors, whether biological or social in nature. The variation problem is simply beyond the horizon of most factual information bases in clinical science or the knowledge base of even the most earnest physician. Clinicians are increasingly aware that the choice of strategy is largely intuited from experience and hidden judgments that are biased in ways usually unrecognised, and as noted, extrapolated by measures hardly supported by rigorous analysis. Nevertheless, decisions must be made and the call for a clinical science that might address the particular concerns of proper development and application of clinical data has many origins. The randomised clinical trial, double-blinded and thus ostensibly neutral,
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was introduced in the late 1940s and quickly became the gold standard of assessment. But given the limitations already alluded to, more ambitious tools for clinical judgment have been proposed, beginning with statistical formalised methods introduced by Alvan Feinstein in the 1960s (Feinstein, 1967) to formal decision analysis programs inaugurated in the 1970s (Weinstein and Fineberg, 1980). But such efforts, despite their obvious utility for measuring cost-benefit ratios in certain well-studied cases, have also pointed to how clinical choices are irreducibly value-laden. The ‘‘facts’’ of clinical care are only the beginning of the decision tree of options, exercised, or forsaken. Due to the health care crisis, the social implications are apparent to all, and these discussions have moved from the theoretical concerns of a few philosophically minded to the domain of public debate (e.g. Bodenheimer, 1997; Ham, 1998).5
6. PERSON-CENTERED MEDICINE Many critics have maintained that the medical model is insufficient for treating patients, since the biomedical approach is focused upon ‘‘disease’’, and persons suffer ‘‘illness’’. This distinction has both epistemological and moral implications. The suffering person is an individual who, precisely because of his or her standing as an individual, is marked by various kinds
5 There are many parameters now in use to assess the character of medical knowledge and its application. I will describe one of them, QALY’s – Quality Adjusted Life Year (Normand, 1991) – for it clearly shows how values are embedded in policy decisions about health care, which in turn determines the options available to patients and their health care providers. QALY is a measurement to assess how much it costs to provide the same quality of life for each patient in a health care system for a given period of time, i.e. one year. So, irrespective of the disease any patient might suffer, calculations are made to determine the cost for each to maintain the same quality of life. Once that is determined, policy makers, faced with limited resources, are then in a position to decide whether, for instance, an elderly woman with diabetes and hypertension or a child with diabetes is more deserving of restricted resources. This is of course a rigged example. But it highlights what is increasingly becoming apparent: We need rational planning for the health care budget; to do so we require formal quality control measures, and, finally, we must have a basis for determining allocations based on some common denominator for cost comparisons. When this calculation is completed, choices must be made. For instance, in this example, the probability of hospitalising the elderly woman with complications must be gauged against all the expenses and possible dire complications of the child with diabetes, whose life span is in all likelihood shortened. This is hardly an academic exercise. Physicians engage in this kind of decision-making all the time, informally. Recent surveys have demonstrated that doctors lie to third party payers to obtain services for their patients (Freeman et al., 1999; Wynia et al., 2000), and in the converse situation, physicians not infrequently do not offer patients possibly useful choices in consideration that their medical insurance does not cover such services or medications (Wynia et al., 2003). This is rationing at the bedside, and the moral difficulties it entails are clearly shown whenever the debate about rationing becomes public (Tauber, 2002b,c, 2003b).
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of specificity, both moral and epistemological. In the latter context, different patients may be infected with the same bacteria and suffer very different symptoms; hypertension of a certain severity will cause different degrees of organ damage; each orthopedic repair addresses a different fracture; each appendectomy demands a particular solution; each cancer has its unique natural history in presentation, response to therapy, and survivorship. Medical science, which seeks general explanations based on universal scientific laws is still oriented around a specific disease, which may follow some general rules, but is always individualised. Indeed, the epistemological investigation begins with an historical account of the illness, which in itself confers specificity. The individuality of each case makes the physician a peculiar kind of scientist: ‘‘However specialised and fragmented the technical practice of medicine may become, the true physician remains – as he has always been – the person who takes the patient’s history’’ (Toulmin, 1993, p. 240). This claim of physician as historian makes several demands: From the epistemological point of view, variation must be sorted out to discern the universal, which means, simply, that the particular constellation of signs and symptoms must be assigned to a diagnosis. The significance of each datum must be weighed and factored. This requires both certain kinds of scientific assessment and a degree of intuition – what is often referred to as ‘‘the art of medicine’’. The intuitive, creative synthesis of information is hardly reduced to rigorous scientific assessment, and, indeed, commentators have fashioned many ways of describing medical knowledge and its application (e.g. Delkeskamp-Hayes and Cutter, 1993). Beyond the epistemological configuration of the physician as historian is a moral dimension – the ability to hear the patient. To truly listen yields an appreciation of the psychological and existential elements of a person’s illness. This becomes a moral exercise, because without an empathetic hearing, how might a physician begin to address a person’s suffering? The detached attitude of a natural scientist cheats the physician of a comprehensive understanding of the ‘‘whole person’’, and without that engagement, according to the basic thesis of this essay, the physician shirks her full moral responsibility. Stephen Toulmin puts the case succinctly: If one does not wish to accept some real psychic involvement with sick people and is not really willing to involve one’s whole personality in that interaction – and it is not just a case of the physician treating the patient as a ‘‘whole man’’, but rather one of the physician himself, as a ‘‘whole man’’, dealing with the patient as a ‘‘whole man’’ – then, I would ask, why be a physician at all? (1993, p. 248) Indeed.
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I have also maintained that this orientation orders the entire practice of medicine, namely that clinical science and technology is in the employ of the ethical mandate of caring for the person, which requires the physician’s full moral engagement with her charge (Tauber, 1999). Accordingly, we must seek a more comprehensive alternative to the dominant disease model of contemporary medicine. This model approaches patients with an ‘‘analysis by which symptoms and physical signs – the complex, mostly subjective phenomena known as illness – are reduced to a more specific disordered part, the disease, to which science can then be applied’’ (Barbour, 1995, p. 9). The biomedical model assumes that this analysis of the illness, as described by the patient, indicates a disordered part, or pathology, called the disease or disorder, which is the cause or basis of illness. This model works very efficiently when the disordered part diagnosed fully accounts for the illness and its treatment restores the person to health. But in most cases, the model is inadequate to the patient’s psychological needs. As Allen Barbour explains, The disease is not the illness, even when the disease, especially chronic disease, fully explains the disability and there are no other contributory factors exacerbating the illness. . . No disease is disembodied. . . to understand the illness we must understand the person. (ibid. p. 28) When doctors adhere too closely to the disease model, ignoring the unique characteristics of each person’s disease, several problems may result: (1) incorrect diagnosis, (2) inappropriate diagnostic procedures, (3) ineffective therapy, (4) unnecessary hospitalisation, (5) prolonged disability, and most importantly, the patient is left dissatisfied that his or her true needs have not been addressed. A more comprehensive biopsychosocial model is required, and it demands different resources than the commonly appreciated technical skills of clinical medicine (Laine and Davidoff, 1996). The ‘‘biopsychosocial model of illness’’ was formally introduced by George Engel in 1977, whose essential precept was that ‘‘emotional, behavioral, and social processes are implicated in the development, course, and outcome of illness’’.6
6
An important antecedent to Engel’s efforts were those of Milton Winternitz, Dean of Yale Medical School (1920–1935), who envisioned an Institute for Human Relations for the comprehensive study of the patient as a bio-psycho-social being. The Institute was designed to integrate various university departments and schools, and his critics rallied against him on the charge that such an inter-disciplinary structure would severely compromise the scientific agenda of the medical school faculty. His efforts were thereby effectively resisted by those committed to a strict biomedical research agenda, and the Institute collapsed with Winternitz’s resignation (Spiro and Norton, 2003).
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In other words, disease occurs in a complex context that is only in part – sometimes greater, sometimes less – ‘‘biological’’. In other words, there is no isolated locus in which physicians might function as applied biologists – geneticists, biochemists, biophysicists, or whatever. Indeed, the physician would also assume the mantles of the sociologist, psychologist, priest, and humanist (Chapman and Chapman, 1983). Accordingly, proponents of this patient-centered approach would expand the focus of professional interest from the disease, its diagnosis and treatment, to also encompass the multiple social and psychological dimensions of a person who is ill. This revised responsibility recasts physician identity by advocating a more comprehensive vision of what it means to heal. Barbour, schematises these differing visions by differentiating the doctor’s responsibilities for a patient’s disease (the biomedical model) from those responsibilities for the care of the ill person (biopsychosocial model) (Barbour, 1995, p. 32). Physicians must seek a judicious balance between these competing claims, and because the choices of individual patients will vary, no formulae are possible. So, while many illnesses can be managed effectively from a biophysical attitude, others demand a more comprehensive approach. The crucial moral element in this rendering of the medical scenario is that a patient-centered, holistic approach is adopted. The patient holds onto her personhood, resisting the reduction of illness to disease. Instead of unilateral treatment, collaboration between the two parties prompts the patient, guided by the doctor, to take personal responsibility for attaining health (Barbour, 1995, p. 34). And by the criteria discussed earlier, selfresponsibility must be the functional definition of autonomous actions. So it is not ‘‘what the doctor does to the patient’’ that serves as the therapeutic goal, but rather an expanded agenda that includes the doctor’s capacity to help the patient understand the specific personal sources of the problem and the effects of the disease. Accordingly, care is not simply the performance of necessary services, but also entails interest, concern, and understanding. Taking care of and caring for are not the same, but in medicine they are interdependent. . . Taking care of patients by taking over is not necessarily caring for them. The patient often needs a doctor who is more guide than therapist. (Ibid. 43-4) Person-centered care sets different criteria for care, and for our purposes provides the moral framework in which patient autonomy and physician responsibility might easily co-exist side-by-side to effect the same ends, the attainment of health. This depiction of the physician would require a major revision in medical education, indeed, in the very conception of medicine that is so
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enamored with the power of biochemistry and genetics. Doctors, although educated to detect disease know how to ask questions pertinent to their biomedical mission, but not necessarily how to listen to suffering patients.7 Finally, the E-word. Contemporary medicine must find a moral space for empathy. ‘‘In clinical medicine, empathy is the ability to understand the patient’s situation, perspective, and feelings and to communicate that understanding to the patient’’ (Coulehan et al., 2001). The term was coined by Titchener in 1909 from the Greek em and pathy – feeling into – and for the next fifty years the psychological literature discussed empathy as a type of emotional response (ibid.). But, empathy is more fairly regarded as a form of ‘‘emotional reasoning’’ (Halpern, 2001). Much of our evaluation of the world and others is coloured by subjectivity, and, indeed, emotions are evaluative, not in the same way as logical precision commands, but as lenses by which perceptions are refracted by personal experience and temper (Nussbaum, 2001; Tauber, 2001). So empathy is more than mere emotionalism – it is also a substrate for thought with at least distinct three domains: (1) a cognitive orientation, where the physician enters into the patient’s experience, yet maintains a clinical perspective; (2) an emotional focus where emotions resonate between doctor and patient, and (3) an action component, where dialogue establishes enhanced communication and understanding. This last category may foster increased diagnostic accuracy, therapeutic compliance, and patient satisfaction, because patients feel better understood and respected (Beckman and Frankel, 1984; Roter et al., 1997; Levinson et al., 2000). Because of its general salutary effects on patient management, empathy is increasingly taught in medical schools and residency training programs, and the increased attention to developing these skills highlight the growing legitimacy of this dimension of care (Delbanco, 1992; Matthews et al., 1993; Coulehan et al., 2001). In sum, to treat the person in his entirety requires more than reliance on some sterile objectivity, whatever that might be. Empathy remains the responsibility of the care giver, and while technical competency is expected, and under certain situations may even be sufficient, illness requires more
7
In a recent small study, the mean elapsed time from the moment patients began to express their primary concern to the doctor’s first interruption was 18 s (Beckman and Frankel, 1984) and in another study, 22 s (Marvel et al., 1999). From there on the doctors took control of the interview by asking increasingly specific, closed-end questions. By so structuring the fact-gathering, only certain kinds of information become available. Indeed, when patients are allowed to tell their full story uninterrupted, the time spent is hardly excessive, even by the most structured time analysts. In a recent large Swiss study of 335 patients referred to a tertiary care center, the mean spontaneous talking time was 92 s; 78% of the patients finished their initial statements in 2 min, and only 7 patients talked for longer than 5 min (Langewitz et al., 2002). The doctors thought the time was well-spent.
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comprehensive care. Psychological and social supports are absolute requirements, and if framed differently, spiritual and existential challenges also demand address. Clinical tools are only instruments for application. They are in service to the doctor’s craft. The exercise of that craft requires more than technical expertise. Judgment, moral sensitivity, and self-awareness are pre-requisites to the healing relationship. So, in my view, medicine is fundamentally ethical. At the bedside the epistemological consequence of integrating facts and value points to the moral product of that union – the effective integration of various faculties to make the self whole, both the cognitive functions of the physician and the dignity of the individual. There, Knowledge may not be separated from Value.
7. CONCLUSIONS Ultimately, the fact/value distinction collapses when faced with the ‘‘ur fact’’, the person. How one functions and what determines one’s relationships, choices, and obligations is inseparable from understanding the character of the knowledge framed by personal values. Judgment is not arbitrary or frivolously contingent, but takes its own bearings from the interplay of social and natural realities understood in the context of adaptation and creative growth. The synthetic project of building a world view begins by placing ‘‘facts’’ within their supporting theory, and continues with integrating that scientific picture with the broader and less obvious intellectual and cultural forces in which science itself is situated. Thus ‘‘facts’’ as independent products of sensory experience are always processed – interpreted, placed into some over-arching hypothesis or theory. In short, observations assume their meanings within a particular context, for facts are not just products of sensation or measurement as the positivists’ averred, but rather they reside within a conceptual framework which ‘‘places’’ the fact into an intelligible picture of the world. Inextricable from context, facts must assume their meaning from an universe of other valued facts. In a sense, value is the glue that holds our world together. Thus, Knowledge is inexorably valued; it is both useless and irrelevant divorced from the reality of personal choice. Medicine offers a fecund example of this view. At the heart, then, of what I am calling a moral epistemology is the quest for the elusive synthesis of ‘‘personal’’ and ‘‘objective’’ – a search for their common foundation. Indeed, much of twentieth century philosophy peered into the metaphysical divide created by a self-conscious dismay at a disjointed epistemology and sought, in their distinctive fashions,
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to offer solutions (Tauber, 1996). I would call this venture, ‘‘moral epistemology’’, and by tracing it as I have done, we rightly see medicine as an exemplary case of both the problem and its possible solution.
ACKNOWLEDGEMENT This paper expands earlier published materials (Tauber, 2002c and 2005b) and closely draws from Chapters 1 and 2 of my most recent book on medical ethics (Tauber, 2005a).
REFERENCES Barbour, A., 1995. Caring for Patients: A Critique of the Medical Model. Stanford University Press, Stanford. Beckman, H.B., Frankel, R.M., 1984. The effect of physician behavior on the collection of data. Ann. Intern. Med. 101, 692–696. Bodenheimer, T., 1997. The Oregon Health Plan – Lessons for the Nation. N. Engl. J. Med. 337, 651–655; 720–723. Callahan, D. (Ed.), 2002. The Role of Complementary and Alternative Medicine. Accommodating Pluralism. Georgetown University Press, Washington, D.C. Canguilhem, G., 1966, 1989. The Normal and the Pathological. Translated by C.R. Fawcett. Zone Books, New York. Chapman, J.E., Chapman, H.H., 1983. The Psychology of Health Care. A Humanistic Perspective. Wadsworth Health Sciences, Monterey. Coulehan, J.L., Platt, F.W., Egener, B., Frankel, R., Lin, C.-T., Lown, B., Salazar, W.H., 2001. ‘‘Let me see if I have this right. . .’’: Words that build empathy. Ann. Intern. Med. 135, 221–227. Daston, L., 2000. Scientific objectivity with and without words. In: Becker, P., Clark, W. (Eds.), Little Tools of Knowledge: Historical Essays on Academic and Bureaucratic Practice. The University of Michigan Press, Ann Arbor, pp. 259–284. Delbanco, T.L., 1992. Enriching the doctor-patient relationship by inviting the patient’s perspective. Ann. Intern. Med. 116, 414–418. Delkeskamp-Hayes, C., Cutter, M.A.G. (Eds.), 1993. Science, Technology, and the Art of Medicine. European-American Dialogues. Kluwer Academic Publishers, Dordrecht. Engel, G., 1977. The need for a new medical model: a challenge for biomedicine. Science 196, 129–136. Evidence-based Medicine Group, 1992. Evidence-based medicine: a new approach to teaching the practice of medicine. JAMA 268, 2420–2425. Feinstein, A., 1967. Clinical Judgment. Williams & Wilkins, Baltimore. Foucault, M., 1963, 1973. The Birth of the Clinic. An Archaeology of Medical Perception. Vintage, New York. Freeman, V.G., Rathmore, S.S., Weinfurt, K.P., Schulman, K.A., Sulmasy, D.P., 1999. Lying for patients: physician deception of third party payers. Arch. Intern. Med. 159, 2263–2270.
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Galaty, D.H., 1974. The philosophical basis for mid-nineteenth century German reductionism. J. Hist. Med. Allied Sci. 29, 295–316. Ham, C., 1998. Retracing the Oregon trail: The experience of rationing and the Oregon health plan. Br. Med. J. 316, 1965–1969. Halpern, J., 2001. From Detached Concern to Empathy. Oxford University Press, New York. Kolakowski, L., 1968. The Alienation of Reason. History of Positivist Thought. Doubleday, Garden City. Laine, C., Davidoff, F., 1996. Patient-centered medicine. JAMA 275, 152–156. Langewitz, W., Denz, M., Keller, A., Kiss, A., Ruttimann, S., Wossmer, B., 2002. Spontaneous talking at start of consultation in outpatient clinic: Cohort study. Br. Med. J. 325, 682–683. Lawrence, C., Weisz, G. (Eds.), 1998. Greater than the Parts. Holism in Biomedicine, 1920–1950. Oxford University Press, Oxford and New York. Levinson, W., Gorawara-Bhat, R., Lamb, J., 2000. A study of patient clues and physician responses in primary care and surgical settings. JAMA 284, 1021–1027. Marvel, M.K., Epstein, R.M., Flowers, K., Beckman, H.B., 1999. Soliciting the patient’s agenda: have we improved? JAMA 281, 283–287. Matthews, D.A., Suchman, A.L., Branch, W.T. Jr., 1993. Making ‘connexions’: enhancing the therapeutic potential of patient-clinician relationships. Ann. Intern. Med. 118, 973–977. McDonald, C.J., 1996. Medical heuristics: the silent adjudicators of clinical practice. Ann. Intern. Med. 124, 56–62. Murphy, E.A., 1976, 1997. The Logic of Medicine, 2nd Edition. The Johns Hopkins University Press, Baltimore. Normand, C., 1991. Economics, health and the economics of health. Br. Med. J. 303, 1572–1575. Nussbaum, M., 2001. Upheavals of Thought. The Intelligence of Emotions. Cambridge University Press, Cambridge. Parks, T., 2000. In the locked ward. New York Review of Books (Feb. 24, 2000) 47, pp. 14–15. Pellegrino, E.D., Thomasma, D.C., 1981. A Philosophical Basis of Medical Practice. Toward a Philosophy and Ethic of the Healing Professions. Oxford University Press, New York and Oxford. Putnam, H., 1990. Beyond the fact/value dichotomy. In: Realism with a Human Face. Harvard University Press, Cambridge, pp. 135–141. Idem, 2002. The Collapse of the Fact/Value Dichotomy and Other Essays. Harvard University Press, Cambridge. Richman, K.A., 2004. Ethics and the Metaphysics of Medicine. Reflections on Health and Beneficence. The MIT Press, Cambridge. Roter, D.L., Stewart, M., Putnam, S.M., Lipkin, M., Jr., Stiles, W., Inui, T.S. 1997. Communication patterns of primary care physicians. JAMA 277, 350–356. Simon, W.M., 1963. European Positivism in the Nineteenth Century. Cornell University Press, Ithaca. Spiro, H., Norton, P.W., 2003. Dean Milton C. Winternitz at Yale. Perspect. Biol. Med. 46, 403–412. Tauber, A.I., 1993. Goethe’s philosophy of science: Modern resonances. Perspect. Biol. Med. 36, 244–257.
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Tauber, A.I., 1994. The Immune Self: Theory or Metaphor? Cambridge University Press, New York and Cambridge. Tauber, A.I., 1996. From Descartes’ dream to Husserl’s nightmare. The Elusive Synthesis: Aesthetics and Science. Kluwer Academic Publishers, Dordrecht, pp. 289–312. Tauber, A.I., 1999. Confessions of a Medicine Man. An Essay in Popular Philosophy. The MIT Press, Cambridge. Tauber, A.I., 2001. Henry David Thoreau and the Moral Agency of Knowing. University of California Press, Berkeley and Los Angeles. Tauber, A.I., 2002a. The quest for holism in medicine. In: Callahan, D. (Ed.), The Role of Complementary and Alternative Medicine: Accommodating Pluralism. Georgetown University Press, Washington, D.C., pp. 172–189. Tauber, A.I., 2002b. The ethical imperative of holism in medicine. In: Van Regenmortel M.H.V., Hull D.L. (Eds.), Promises and Limits of Reductionism in the Biomedical Sciences. John Wiley & Sons, West Sussex, pp. 261–278. Tauber, A.I., 2002c. Medicine, public health and the ethics of rationing. Perspect. Biol. Med. 45, 16–30. Tauber, A.I., 2003a. Sick autonomy. Perspect. Biol. Med. 46, 484–495. Tauber, A.I., 2003b. A philosophical approach to rationing. Med. J. Australia 178, 454–456. Tauber, A.I., 2005. Medicine and the call for a moral epistemology. Perspect. Biol. Med. 48, 42–53. Tauber, A.I., 2005a. Patient Autonomy and the Ethics of Responsibility. The MIT Press, Cambridge. Tauber A.I., Sarkar, S., 1993. The ideological basis of the Human Genome Project. J. R. Soc. Med. 86, 537–540. Toulmin, S., 1993. Knowledge and art in the practice of medicine: clinical judgment and historical reconstruction. In: Delkeskamp-Hayes, C., Cutter M.A.G. (Eds.), Science, Technology and the Art of Medicine. Kluwer Academic Publishers, Dordrecht, pp. 231–250. Veterans Administration Cooperative Study Group, 1970. Effects of treatment on morbidity in hypertension. II. Results in patients with diastolic blood pressure averaging 90 through 115 mm Hg. JAMA 213, 1143–1152. Weinstein, M.C. Fineberg, H.V., 1980. Clinical Decision Analysis. W.B. Saunders, Philadelphia. Wynia, M.K., Cummins, D.S., VanGeest, J.B. Wilson, I.B., 2000. Physician manipulation of reimbursement rules for patients: Between a rock and a hard place. JAMA 283, 1858–1865. Wynia, M.K., Van Geest, J.B., Cummins, D.S., Wilson, I.B., 2003. Do physicians not offer useful services because of coverage restriction? Health Aff. 22, 190–197.
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
6 Theory in medical education – an oxymoron? Sam Leinster School of Medicine, Health Policy and Practice, University of East Anglia, Norwich, UK
1. INTRODUCTION Medical education aspires at being a scientifically based discipline. The Association for the Study of Medical Education was founded in UK in 1960 with the aim, among others, of carrying out research in medical education. In the past ten years there has been an effervescence in the creation of chairs in medical education within UK and most medical schools now have medical education units or departments. There are a number of national and international journals dedicated to this subject. Nevertheless, if medical education is to be recognised as truly scientific it must develop an agreed theoretical grounding. Kuhn (1970) suggests that science is defined by the existence of an agreed paradigm. The current state of disorganised and diverse activity in the study of medical education corresponds to Kuhn’s pre-science theory (Chalmers, 1982). If medical education is to become a truly scientific endeavour it must become grounded in theory (Kuhn, 1970; Latakos, 1974), but it is debatable whether it is possible to define a theoretical basis that is acceptable to all medical educationalists. Much of the discussion in this chapter is based on the recent experiences of change in medical schools of UK, but the principles apply more widely.
2. WHY DO WE HAVE MEDICAL EDUCATION? The purpose of medical education is to produce medical practitioners who are capable of practising medicine safely and effectively. Most senior practitioners regard it as axiomatic that this includes a thorough training 89
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in science. This concept was clearly articulated by Flexner in his advice to the President of the United States of America (Flexner, 1910). Various approaches to the process of this education at the undergraduate level coexist. For most of the twentieth century in most parts of the world a period of pre-clinical studies was followed by a roughly equal period of clinical studies. During the pre-clinical phase the students studied the basic sciences (originally anatomy and physiology, but expanding in scope and content as new sciences developed and became relevant to the practice of medicine). The clinical phase concentrated on clinical sciences and was characterised by attachments to hospital clinicians in an observational and apprenticeship role known as ‘‘clerkships’’ (USA) or ‘‘firms’’ (UK). This model is still widely followed. In the late 1960s, Barrow, at McMaster University, developed a new approach called ‘‘problem-based learning’’ (PBL) (Barrows, 1986). This became the dominant innovation in medical education over the next 40 years and is now found in medical schools around the world. Other medical schools have adopted alternative approaches, such as case-based (Epling et al., 2003) or presentation-based learning (Mandin et al., 1995). Most medical schools in the world retain the pre-clinical/clinical split but there is a movement for increasing integration, which in the UK has been encouraged by the General Medical Council (GMC) in their recommendations for medical undergraduate education Tomorrow’s Doctors (General Medical Council, 2002). Considerable time and effort has been expended on trying to decide what medical graduates should know. The days have long since passed when it was realistic to expect a new graduate to have sufficient knowledge to practise in all the branches of medicine from the moment of graduation. In the 1940s, the UK government recognised that new graduates would need a period of supervised practice before they were awarded full registration as an independent medical practitioner. It introduced the preregistration year for newly qualified doctors in 1953. The graduate was still expected to learn all the necessary basic science. Since then medical knowledge has grown in extent and complexity. No individual can learn all that is now known during a lifetime of practice, let alone within the limits of the undergraduate course.
3. WHO IS A MEDICAL PRACTITIONER? Individuals on the Medical Register fulfil a wide range of roles. Many are clinicians undertaking direct clinical care of patients but others may be laboratory scientists, public health specialists, or administrators. All of
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them would have undergone a similar basic medical education but their subsequent training and experience is very diverse. It is difficult to identify the defining characteristic that allows them all to be classified as medical practitioners. Knowledge is an insufficient demarcation, as other professional groups possess the same knowledge. The claim that doctors have wider range of knowledge than other professions is no longer sustainable in practice. The junior doctor does not have the breadth of knowledge of an experienced practitioner in any of the health- related disciplines. As the doctor attains seniority in a given speciality, his or her knowledge deepens in some areas but may diminish or become obsolete in areas unrelated to the speciality. The core knowledge common to all medical practitioners is relatively small. The core knowledge exclusive to medical practitioners is even smaller. In the past, there were some tasks that were unique to medical practitioners. As other professions have extended their roles the number of exclusively medical tasks has diminished. Perhaps the two defining tasks were diagnosis and prescription. Nurse practitioners and consultant physiotherapists are now seeing patients without direct medical supervision, ordering investigations, and making diagnoses. Prescribing, albeit of a limited range of drugs, is now being undertaken in the United Kingdom by nurses and pharmacists who have undergone extra training. Even the assumption that the doctor should always lead the health team is gradually being broken down. In the end, the only thing which distinguishes doctors as a group is being on the Medical Register. This does not provide a useful means of determining what medical education needs to deliver. Curriculum planning has, therefore, concentrated on the immediate outcomes of the undergraduate course (Harden, 2002). Newly graduated doctors need clinical and communication skills to enable them to deal with patients. They need basic knowledge about the structure and function of the human body, about the effects of disease and their mode of action, and utility of available treatments. Above all they need to be able to apply their knowledge appropriately. The way in which we frame our understanding of how they use their knowledge and skills will to a large extent determine how we plan their learning to achieve the desired outcomes.
4. THE THEORY OF MEDICAL EDUCATION A substantial body of literature has grown up around medical education. Most of the early literature is descriptive with little attempt at evaluation. When evaluation was undertaken it was often of low grade merely reporting faculty and student satisfaction levels. Concerted attempts are being
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made to raise the quality of research in medical education but much of it remains observational (Regehr, 2004). Very often the study design is based on medical models. Controlled trials have been undertaken but they are most useful in testing different methods in discrete units (Davidson et al., 2001; Holloway et al., 2004). It is more difficult to carry out research on major curricular changes (Prideaux and Bligh, 2002; Norman, 2003). A major deficiency in most of the studies is the lack of a firm theoretical basis for the interventions that are being investigated (Wolf, Shea and Albenese, 2001). The problem that faces us is the difficulty in deciding which theoretical paradigm is the most useful. Some writers seek enlightenment from learning state; others are more attracted to theories of cognition while others look to sociological constructs. It may be that all these areas and more are needed if we are to gain an adequate understanding of the process of producing an effective doctor. An effective theoretical framework will explain how doctors think and behave as well as how they learn.
5. HOW DO DOCTORS THINK? Bacon’s theory of scientific activity suggests that observation leads by induction to the creation of laws and theories. These laws and theories in turn allow predictions and explanations to be made by the process of deduction. These predictions can be tested and if they prove to be true the laws and theories are taken to be confirmed. There are weaknesses in this model. Observation is not a purely objective phenomenon. The observations that we make are governed by the theoretical framework in which we make them. A clear example of this is found in a study of the ability to make a diagnosis from an electrocardiogram (ECG) tracing accompanied by a clinical history (Hatala et al., 1999). Two groups of subjects were given the same abnormal ECG tracings but each group was given a different clinical history. Unsurprisingly, the groups came to different diagnoses. Of more interest, the groups saw different abnormalities in the ECG with each group seeing only the abnormality that supported their diagnosis. If observation were objective this could not happen. Clearly the subjects had formed a theory about the diagnosis based on their interpretation of the history and only saw the facts that supported their theory. Nevertheless, it is widely accepted that doctors make diagnoses using a hypothetico–deductive model. It is postulated that a good doctor collects information about the patient’s clinical condition by careful history taking and a thorough examination. This information is processed in the light
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of the doctor’s pre-existing knowledge and a hypothesis is formed as to the possible causes for the condition. This is commonly referred to as reaching a differential diagnosis. This hypothesis is tested by further history taking and examination and by relevant investigations. The hypothesis is refined and the process continues until a firm diagnosis is reached. In computing terms, the data is being processed serially. This pattern of behaviour can be seen in novice doctors (Bordage and Lemieux, 1991). It is not seen in experts. The expert clinician reaches a diagnosis very quickly after meeting the patient. The history taking is very focussed and is directed to confirming the judgement that has already been made rather than collecting information in order to form a hypothesis (Grant and Marsden, 1988). In order to explain this phenomenon, it is suggested that the expert is using a cognitive schema. Cognitive schemas are postulated as the way in which we organise all our knowledge. Knowledge is not filed in the long-term memory as separate items but is organised into patterns. These patterns may identify objects or concepts or actions. Whenever the pattern is encountered it is recognised immediately and identified without conscious effort. These patterns are known as schemas. There are many sorts of schemas. Those which govern actions are often known as cognitive scripts and govern all our routine activities (Stein, 1992). When the concept is applied to clinical behaviour it suggests that the features of a given condition or diagnosis are linked to one another in the memory. When the necessary triggers are present the condition is recognised and the diagnosis is made. There is a debate about the nature and number of the schemas used by clinicians. Some researchers believe that there are a limited number of typical schemas that cover all the possible cases of a given diagnosis (Schmidt et al., 1990). Other researchers believe that each case of a given condition is represented by a different schema (Papa et al., 1996). In either case, the diagnosis is made as a matter of recognition not as a matter of reason (Corderre et al., 2003; Norman and Eva, 2003). In a similar way, action in routine cases is through cognitive scripts. The appropriate series of actions are associated with one another in the memory and triggered by a specific stimulus. These scripts extend to such things as the appropriate style and content of communication with a patient (Humphris, 2002) as well as the selection of the correct treatment.
6. HOW ARE SCHEMAS FORMED? Standard cognitive theory recognises four stages of learning. The first stage is activation of prior knowledge. When a novel situation is
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encountered apparently related facts are mobilised from the memory. The new material is perceived and then passes into a buffer zone. From there it enters the short-term memory. The capacity of the short-term memory is limited to six or seven items. If it is to be retained, the material must pass into the long-term memory. According to the information processing theory this takes place through encoding (Schmidt, 1983). The new material is linked to the old material and then stored. The encoding is specific and the new material firmly associated with the old material is retrieved along with it. Apparently irrelevant material may be included in this association leading to the phenomenon of context-specific recall. The encoding is encouraged by rehearsal. Constant repetition is a timehonoured way of memorising and is the basis of rote learning. The final stage of learning is elaboration. As the new information is used, further connections are made in the memory. These serve to strengthen the retention of the material and increase the routes by which it can be recalled. Elaboration includes explanation of new but similar examples to oneself or to others. The learnt material may be brought into consciousness by recall or recognition. The latter is the least demanding. Presented with a number of alternatives the individual can pick out the one that is correct. In order to recall it is necessary to remember the correct answer without any cues. Concern is often expressed that some forms of examination, test the recognition rather than recall. However, in real life there are often cues that aid recognition. The practising clinician rarely has to remember something in a vacuum. For this reason the context of learning is important as it may influence remembering. Cognitive schemas operate below the level of conscious recall but it is postulated that the learning process is the same. However, the process of remembering is different since the schema itself is never consciously perceived. In a given situation an observer will note certain features. Up to six or seven schemas with similar features will be brought from the longterm memory into the short-term memory. Those with the closest match will be retained; the remainder will be rejected. Further schemas may be examined before the final match is made. This process takes place very rapidly at a subconscious level. A useful metaphorical comparison can be made between this kind of problem-solving and parallel processing in a computer. Parallel processing is much quicker than serial processing allowing many more hypotheses to be examined in a given time. This is consistent with the speed with which the expert doctor takes clinical decisions. This model has consequences for the way in which undergraduate medical learning is structured. As long as it was thought that knowledge
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was retained in the memory as discrete facts and that medical reasoning took place in a linear fashion, it made sense to teach medical facts in separate disciplines. The argument was that specialists in an individual discipline knew more about that discipline and therefore were better able to teach it. Teaching was understood as the transference of facts from one individual to another, so the more facts that could be transferred, the better. The awareness that the recipients of this transfer retained only a small proportion of the facts transmitted led to the attempt to transfer more facts. A fixed proportion of a lot of facts is more than a fixed proportion of a few facts. In the end this led to the complaints of factual overload addressed by the GMC in Tomorrow’s Doctors (GMC, 2002). If knowledge is retained in integrated schemas, then it makes sense to teach in an integrated way. The complex linkages needed to understand a clinical case are made in the phase of learning about the condition not at the point of making the diagnosis. The clinician will activate the appropriate schema; not recall and process the separate facts relating to the case. The challenge is how one achieves integration in the learning process. A number of medical schools have independently come up with the solution of defining what the student needs to know in terms of the cases or presentations they will need to be familiar with, in their practice (see above). The cases themselves act as the focus for integration and may act as embryo schemas.
7. HOW DO DOCTORS LEARN? Cognitive theory addresses the internal processes that lead to learning. Educational theories address the external factors which influence learning. When attempting to characterise those factors there is a tendency to concentrate on the teacher, the material, and the environment. The student’s attitude is just as important. Learning for small children is most effective when it is task based and repetitive. Children need to form relationships with their teachers and will tend to believe what they are told by a teacher to whom they are bonded. In contrast, adults learn best when they have a specific purpose in mind (Knowles, 1990). They will then be voluntary participants in learning. If their learning is to be effective it must have meaning and relevance to their own personal goals and objectives. This does not mean that the student will necessarily choose the specific knowledge that will be learnt but they will need to be brought to accept its relevance to their personal agenda. Adults need an active approach to learning rather than a passive transfer of facts. They will tend to be reflective and to check that
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the learning experience is meeting their self-identified needs. As a corollary, they need feedback to reassure them that their learning is accurate, adequate, and appropriate. This implies a much more equal relationship with the teacher than is the case with young children. It is important that the students’ status as ‘‘adult learners’’ is recognised in the teaching methods used in the course although the way in which this is achieved will vary from course to course. The transition from ‘‘learning as a child’’ to ‘‘learning as an adult’’ is gradual rather than abrupt, but by the time students are entering tertiary education they are mainly in adult learning mode. Higher education is not compulsory and the subjects chosen are usually those that the student has himself chosen. The sophisticated student will even have selected the courses to which they apply because of the approach to the chosen subject. Even within medicine where the subjects studied are in part determined by the need for the graduates to meet the minimum standards needed to practice medicine, there is variation in emphasis and approach between different courses. The students are, therefore, in a very real sense voluntary participants in the learning even if parts of the curriculum are designated as ‘‘compulsory’’ by the medical school. Kolb viewed learning as a cyclical experience (Kolb, 1984). When we have a new experience or encounter a new piece of information, we build a theory based on the interaction between our previous knowledge and the new experience. These theories are not the explicit constructs of the professional thinker but rather the implicit constructs formed by the association of facts in our memory. On the basis of the new theory we take action which leads to further new experiences and so to new theories. Kolb suggested that individuals prefer certain sectors of the learning cycle. He defined these preferences as ‘‘learning styles’’ and suggested that teachers should identify the learning style of their students in order to match the learning experience to the students’ styles. In practice, most groups of students will have a mixture of learning styles and providing a range of learning experiences is on offer, the majority of students will be satisfied. A different (and in many ways more useful) interpretation of learning styles is the classification of students into superficial, deep, and strategic learners (Newble and Entwhistle, 1986). Superficial learners learn by rote and do not achieve an understanding of the subject matter. The material learnt is rapidly forgotten. All learners will tend to adopt this style when the amount of material to be learnt is too large. Deep learners attempt to understand the subject. They do not aim simply to regurgitate the facts but rather to explain connections. The learnt material is remembered indefinitely. The majority of highly achieving students are strategic learners, using a combination of deep and superficial approaches
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predicated on their perception of which bits of knowledge are needed for understanding and which will be sought in the examinations. Most educators pay lip service to the need to encourage a deep learning style in students. However, assessment procedures in medical schools throughout the world tend to encourage a strategic style. There is clearly a dissonance between our stated aims and our behaviour. The interaction between the student’s learning style and the way in which the material is presented will clearly influence learning. However, learning is also affected by motivation. In a study of the selection process for medical students, Powis et al. (1988) found that motivation at the time of admission to medical school was the best predictor of performance at medical school and after graduation. Williams et al. (1999) describe two forms of motivation – controlled and autonomous. Controlled motivation is built on internalised contingencies (‘‘this is what I ought to do’’) derived from other people, and based on external rewards. This pattern was commonplace in medical education in the past. Students were often motivated by success in examination whether at the level of ‘‘I must pass this examination in order to continue with my studies’’ or ‘‘I must do well in this examination to prove I am as good as/better than my peers’’. Autonomous motivation is built on learning material because it is personally endorsed as important or because it is intrinsically interesting to the individual. When motivation is controlled, students tend to learn the material by rote with the result that the memory of it is short-lived. The new material is poorly integrated into the student’s own values and skills. In contrast, when motivation is autonomous the students show greater understanding of the subject. Their performance and their confidence in their performance are both improved. Students who are autonomously motivated show enhanced creativity. The congruence between this construct and Knowles’ theory of adult learning is clear.
8. THE CONTEXT OF LEARNING The approaches to learning theory discussed so far focus on the individual and the effect of individual characteristics on learning. Learning rarely takes place in isolation. Even when an individual is studying alone they are usually drawing on materials from a wider community in the form of books, journal articles, and increasingly the internet. While the social context of learning has received considerable attention in the studies of child development and the education of children, it has only recently been applied to medical education.
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Soviet psychologists who were influenced by Marxist sociology did much of the early work on the social dimensions of education. Vygotsky and his students were particularly influential in developing the concept that the social context of learning was fundamental to the process. Whereas Western psychologists tend to develop models in which the individual’s characteristics are formed and then interact with the outside world, Vygotsky maintains that it was only through interactions with the outside world that the characteristics are formed. Clearly our thinking depends on language (or symbolism). Language is acquired by social interaction, so our thought processes are rooted in social interaction. One important example of the influence of social context on learning is Vygotsky’s concept of the Zone of Proximal Development (ZPD) (Vygotsky, 1978). In its original form, Vygotsky applied it to the development of young children. If children of a given chronological age are left to themselves to complete a graduated series of tasks they will, if their development is normal, complete them to a level commensurate with their chronological age. If they are asked to complete the same tasks in the presence of knowledgeable peers or informed adults, they will complete the tasks to a higher level. Children will differ in the extent to which their performance is augmented by working with others. Take the example, given by Vygotsky, of two 7-year-old children. Left to themselves both will perform at 7-year-old level. With assistance, however, one may improve to 9-year-old level while the other reaches 12-year-old level. The difference between their unaided efforts and what they do with assistance is labelled the Zone of Proximal Development. Although at first sight there is no difference between the children, the second has greater potential for development in the class setting. Efforts have been made to describe the way in which students learn surgical skills in terms of the Zone of Proximal Development (ZPD) (Kneebone, 2003). It is not entirely clear how the concept of the ZPD can be applied to adults who are not undergoing development in the same sense as children but the suggestion is useful as a reminder that the context of learning in medical education is as important as the content. A similar message can be derived from the concept of Co-operative Learning. Older styles of teaching emphasised the competitive aspects of learning. Great importance was placed on ranking students within the class. It was tacitly understood that the way to achieve excellence was to reward those who did best. At the same time the poorer students could be encouraged to improve by the fear of coming last. There is no evidence other than anecdote and the accumulated wisdom of the years to support this idea. A meta-analysis of 63 studies of co-operative versus competitive learning showed clearly that co-operative learning is more effective
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(Qin et al., 1995). Students who learnt co-operatively were better able to understand problems and to plan effective solutions. They executed the plans and checked the outcomes more effectively. The awareness of the social dimensions of learning has led to the concept of communities of learning. This concept is helpful in visualising what is taking place in a group of individuals who are working as a team. The individuals learn from the experience they gain in the team task (e.g. patient care). They learn from personal study and they learn from one another. However, the team itself is an entity and the learning of the team as a whole is greater than the sum of the learning of the individual members of the team (Lave and Wagner, 1991). If a naı¨ ve learner is attached to the team, they have a different relationship with the learning community from that of the team members. They will participate in some of the team interactions and will be permitted to undertake a limited number of the activities of the team. If the naı¨ ve learner subsequently joins the team there is a step change in the relationship. The new team member is seen as possessing the team’s values and knowledge and becomes a full member of the learning community. Within the health-care environment individuals belong concurrently to a number of different teams. These teams may be entirely distinct from one another or may overlap. A multidisciplinary team may comprise several smaller uni-professional teams or may have within it a senior team with a greater level of responsibility. The move from junior team member to senior team member (for example, from specialist registrar to consultant) is particularly interesting. There is a sudden shift in the individual’s own perception of their knowledge and ability which is echoed by a shift in the perceptions of others including other members of the team. Tasks and decisions that would have been referred to a mentor are suddenly within the individual’s competence. The team validates this assumption of competence by expecting engagement with the team’s tasks at a higher level of responsibility. In one sense, the new consultant knows no more than they did on the previous day but their performance suggests a sudden increase in learning. The effect is more noticeable if the more senior post is in a new locality. When promotion occurs within the team some memory of the previous status and relationship might linger. In a new team, the individual is assumed to have the competencies needed for their new role.
9. ATTEMPTING A SYNTHESIS Health-care delivery is changing rapidly in response to the technological and social changes. The attitudes and expectations of those entering the
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health-care professions are also changing. Medical education must operate within this framework. It is no longer possible to carry on training doctors in the same old ways that worked in the past but it is proving difficult to determine what is the best approach. Education is a complex phenomenon affected by a multiplicity of variables. Each of the different theoretical approaches address a subset of the variables. No one theoretical approach is sufficient in itself. Until further research produces a comprehensive theoretical framework, medical education must be informed by all the approaches. Fortunately, the logical conclusions of the theories discussed result in the same pragmatic approach to teaching and learning. Knowledge should be acquired within the context in which it is to be applied. Learning should be active and should be student-centred. The social context of learning should encourage a team-based approach recognising the inter-professional dimension of modern health-care delivery. Within these parameters there is scope for a variety of approaches to learning and teaching in medicine. It is to be hoped that educators will grasp the opportunity that these varied approaches provide in order to carry out the research needed to develop a unifying theory.
REFERENCES Barrows, H.S., 1986. A taxonomy of problem based learning methods. Med. Educ. 20, 481–486. Bordage, G., and Lemieux, M., 1991. Semantic structures and diagnostic thinking of experts and novices. Acad. Med. 66 (Suppl 9), S70–72. Chalmers, A.F., 1982. What is this Thing Called Science? University of Queensland Press, St Lucia, Queensland, p. 90. Coderre, S., Mandin, H., Harasym, P.H., Fick, G.H., 2003. Diagnostic reasoning strategies and diagnostic success. 37, 695–703. Davidson, R., Duerson, M., Rathe, R., Pauly, R., Watson, R.T., 2001. Using structured patients as teachers: a concurrent, controlled trial. Acad. Med. 76, 840–843. Epling, J.W., Morrow, C.B., Sulphet, S.M., Novick, L.E., 2003. Case based teaching in preventive medicine: rationale, development and implementation. Am. J. Prev. Med. 24, 85–89. Flexner, A., 1910. Medical Education in the United States and Canada: A Report to the Carnegie Foundation for the Advancement of Teaching, Bulletin 4. The Carnegie Foundation, New York [Reprinted in Birmingham, AL: Classics of Medicine Library; 1990]. General Medical Council., 2002. Tomorrow’s Doctors. GMC, London. Grant, J., Marsden, P., 1988. Primary knowledge, medical education and consultant expertise. Med. Educ. 22, 173–179.
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Harden, R.M., 2002. Developments in outcome-based education. Med. Teach. 24, 117. Holloway, R., Nesbit, K., Bordley, D., Noyes, K., 2004. Teaching and evaluating first and second year students’ practice of evidence based medicine. Med. Educ. 38, 868–878. Hatala, R., Norman, G.R., Brooks, L.R., 1999. Impact of a clinical scenario on accuracy electrocardiogram interpretation. J. Gen. Intern. Med. 14, 126–129. Humphris, G.M., 2002. Communication skills knowledge, understanding and OSCE performance in medical trainees: a multivariate prospective study using structured equation modelling. Med. Educ. 36, 842–852. Kneebone, R., 2003. PhD Thesis, University of Bath. Knowles, M.S., 1990. The Adult Learner: A Neglected Species, 4th Edition. Gulf Publishing, Houston, Texas. Kolb, D.A., 1984. Experiential Learning: Experience as a Source of Learning and Development. Prentice Hall, Eaglewood Williams Cliffs, Chicago. Kuhn, T.S., 1970. The Structure of Scientific Revolutions. University of Chicago Press, Chicago. Latakos, I., 1974. Falsification and the methodology of scientific research programmes. In: Latakos, I., Musgrave, A. (Eds.), Criticism and the Growth of Knowledge. Cambridge University Press, Cambridge, pp. 91–196. Lave, J., Wagner, E., 1991. Situated Learning: Legitimate Peripheral Participation. Cambridge University Press, Cambridge. Mandin, H., Harasym, P., Eagle, C., Watanbe, M., 1995. Developing a ‘‘clinical presentation’’ curriculum at the University of Calgary. Acad. Med. 70, 186–193. Newble, D.I., Entwhistle, N.J., 1986. Learning styles and approaches: implications in medical education. Med. Educ. 20, 162–175. Norman, G.R., 2003. RCT results confounded and trivial: the perils of grand educational experiments. Med. Educ. 37, 582–584. Norman, G.R., Eva, K.W., 2003. Diagnostic reasoning strategies: an alternative view. Med. Educ. 37, 676–677. Papa, F.J., Stone, R.C., Aldrich, D.G., 1996. Further evidence of the relationship between case typicality and diagnostic performance: implications for medical education. Acad. Med. 71 (Suppl 1), S10–12. Powis, D.A., Neame, R.L., Bristow, T., Murphy, L.B., 1988. The objective structured interview for medical student selection. Br. Med. J. 296, 765–768. Prideaux, D., Bligh, J., 2002. Research in medical education: asking the right questions. Med. Educ. 36, 1114–1115. Qin, Z., Johnson, D.W., Johnson, R.T., 1995. Co-operative versus competitive efforts and problem-solving. Rev. Educ. Res. 65, 129–143. Regehr, G., 2004. Trends in medical education research. Acad. Med. 79, 939–947. Schmidt, H.G., Norman, G.R., Boshuisen, H.P.A., 1990. A cognitive perspective on medical expertise: theory and implications. Acad. Med. 65, 611–621. Stein, D.J., 1992. Schemas in the cognitive and clinical sciences: an integrative construct. J. Psychother. 2, 45–63. Schmidt, H.G., 1983. Problem-based learning: rationale and description. Med. Educ. 17, 11–16. Vygotsky, L.S., 1978. Mind and society: The Development of Higher Mental Processes. Harvard University Press, Cambridge, MA.
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Williams, G.C., Saizow, R.B., Ryan, R.M., 1999. The importance of self determination theory for medical education. Acad. Med. 74, 992–995. Wolf, F.M., Shea, J.A., Albenese, M.A., 2001. Towards setting a research agenda for systematic reviews of evidence of the effects of medical education. Teach. Learn. Med. 13, 54–60.
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
7 Knowledge, arguments, and intentions in clinical decision-making John Fox and David Glasspool Cancer Research UK, Advanced Computation Laboratory, London, UK
1. INTRODUCTION Until relatively recently, the most influential theories of reasoning and decision-making were developed by mathematicians and logicians, often informed by problems in some practical domain such as medicine or economics. Their work led to theoretical concepts with great intellectual depth and formal rigour, such as statistical decision theory (SDT). Dennis Lindley summarises the basic tenets of SDT as follows: ‘‘ . . . there is essentially only one way to reach a decision sensibly. First, the uncertainties present in the situation must be quantified in terms of values called probabilities. Second, the consequences of the courses of action must be similarly described in terms of utilities. Third, that decision must be taken which is expected, on the basis of the calculated probabilities, to give the greatest utility. The force of ‘must’ used in three places there is simply that any deviation from the precepts is liable to lead the decision maker in procedures which are demonstrably absurd’’ (Lindley, 1985, p. vii). The mathematical arguments for this claim are well known and need not be repeated here (Lindley provides an excellent source). However, despite the force of Lindley’s assertion, there are difficulties with expected-utility and other mathematical techniques for practical decision-making. First of all, any quantitative decision procedure depends upon the ability to estimate the required parameters, in this case the probabilities and utilities, associated with the application domain. This can be problematic in real-world applications. In clinical settings, for example, even 103
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highly routine ones, these data are not easily obtained. The cost of obtaining good probability estimates frequently outweighs the perceived benefits, and there are deep philosophical and technical difficulties in trying to capture human values and preferences as quantitative utilities. A second issue is that classical decision theory focuses on only a small part of the decision process, making the choice. Lindley continues: ‘‘The first task in any decision problem is to draw up a list of the possible actions that are available. Considerable attention should be paid to the compilation of this list [though] we can provide no scientific advice as to how this should be done.’’ His unwillingness to give ‘‘scientific advice’’ on how to determine the possible decision options seems strange. In medicine, for example, the determination of these things is at the heart of clinical work. Even in routine medicine, practitioners need to be able to structure their decisions: they need to decide what hypotheses to consider, sources of evidence that are relevant, and even the type of decision that is required: ‘‘Should I attempt a diagnosis? Or just make a risk assessment? Is it sufficiently urgent that I should go straight for a treatment? Or should I refer the patient to a colleague who is more experienced?’’ Finally there are deep issues about the adequacy of quantitative formalisms to represent the kinds of knowledge and forms of reasoning that are routinely employed in medical thinking (Schwartz and Griffin, 1986). The development of an alternative framework that is formally sound but avoids the shortcomings of standard quantitative decision procedures, is the theme of this chapter. Before we present this approach, however, let us introduce the challenge with some real clinical decisions in routine medicine.
1.1. Assessing genetic cancer risk More and more diseases are found to have a genetic component, and the identification of people who have a genetic predisposition to some disease is becoming a leading public health problem. The RAGs software package (Risk Assessment in Genetics) is designed to assist general practitioners in assessing the risk that a healthy woman has a genetic predisposition for a disease such as breast or ovarian cancer (Coulson et al., 2001). RAGs takes a family history, prompting for information about the relationship between the woman and her relatives, any cancers or other diseases they may have had, their ages at diagnosis, and so on. RAGs then, applies a set of ‘‘if . . . then . . .’’ rules to identify risk factors in the family history,
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and then assesses the overall risk that the woman is a gene carrier. The result is an assessment of whether she is at population risk, moderately elevated risk, or high risk. A typical risk-factor rule used in RAGs is, ‘‘If the woman has two or more first-degree relatives diagnosed with breast cancer and both relatives were diagnosed under the age of 40, then this is a risk factor for genetic predisposition to breast cancer’’. Although the rule has a logical form, it is not conclusive, but is a ‘‘reason’’ to suspect that the woman may have a predisposition to cancer. RAGs’ rules incorporate simple weights to represent the relative significance of different risk factors: low significance ¼ 1, medium ¼ 2, high ¼ 3. The overall risk for the woman being a gene carrier is determined by establishing which rules are true in her case and summing the associated weights. The risk assessments produced by RAGs was compared with that provided by a leading statistical risk assessment system (Cyrillic). Despite the simplicity of RAGs, the two systems produced identical risk assessments for 50 families with known genetics (Emery et al., 2000).
1.2. Prescribing drugs for common conditions One of the major tasks facing doctors is associated with high level of error is prescribing drugs. CAPSULE (Computer Aided Prescribing Using Logic Engineering) is a program that was developed to help general practitioners in carrying out routine prescribing decisions (Walton et al., 1997). CAPSULE is equipped with a database of information about drugs and a set of rules for deducing benefits, potential harms, and other advantages and disadvantages of particular drugs. When the system is invoked, the rules are evaluated against information from the patient notes and with knowledge from the drug database. It generates a list of candidate medications based on its drug knowledge, and then applies its prescribing rules in order to construct arguments for and against each candidate medication. For example, if CAPSULE is considering drug A, and drug A is relatively cheap by comparison with the alternatives, this is an argument in favour of A. On the other hand, if the patient is already taking drug B, and B is known to have an undesirable interaction with A, then this is an argument against A. CAPSULE can construct arguments based on a number of general factors. The main ones are as follows. Arguments for prescribing a drug if: The patient has already used the drug, and there are no side-effects It is recommended for the condition in the British National Formulary
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It is local policy to use the drug The drug is moderately priced Arguments against a drug if: The drug has undesirable side effects It is contraindicated by other patient conditions There are known interactions with other drugs the patient is taking The drug is expensive In order to make a recommendation among alternative medications, CAPSULE simply counts up the arguments for and against each one and recommends the alternative with the highest overall support. CAPSULE demonstrated major benefits in improving prescribing decisions in general (Walton et al., 1997).
1.3. Interpreting medical images In the UK, all women between the ages of 50 and 70 are invited to be screened for breast cancer every 3 years, a process which consists of taking X-rays of the breasts and scrutinising the images for evidence of significant abnormalities. CADMIUM, or Computer Aided Decision Making and Image Understanding in Medicine, is designed to support this process by conducting a partially automated image analysis and making a recommendation about whether any abnormalities are cancerous. Although the raw data is in the form of an image, the decision-making process is logical in form. CADMIUM’s image processing is primarily concerned with finding abnormalities called micro-calcifications which are small bright flecks in the image. The program then characterises properties of these features, such as their density, shape, clustering, and size. The decision process considers these properties and uses them as the basis for arguments for the abnormalities being caused by cancer or some benign cause. CADMIUM was evaluated as a practical tool in a study that assessed its efficacy in improving the diagnostic accuracy of trainee radiographers, with very promising results (Taylor et al., 1999). Each of the three decisions outlined here depends upon various kinds of knowledge. CAPSULE contains knowledge about drugs and their uses; RAGs has rules about genetics and inheritance, while CADMIUM incorporates knowledge of disease processes and their effects on the appearance and morphology of abnormal features. Traditional theories of decision-making abstract away from such forms of knowledge in their pursuit of methods that focus on precise, quantitative relationships between variables, but let go much of our human understanding of the concepts being dealt with and the complex relationships between them that forms
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the medical knowledge base. We believe that this strategy is mistaken as it ignores the decision-makers’ understanding of the world, including understanding of normal and abnormal function and structure, time and causation, and a wide range of strategies for reasoning and decision-making which can be selected to deal with different circumstances. We shall argue that non-numerical and logical methods have many technical and other advantages even if there is sometimes a loss in quantitative precision.
1.4. Cognitive processes in reasoning and decision-making Despite the apparent clarity and lack of ambiguity of mathematical approaches to judgement and decision-making, the whole field of reasoning under uncertainty has been dogged by philosophical as well as technical disputes for many years. For example, Kyburg (1990) observes that ‘‘Many proponents of many [different] views have argued that their interpretation of probability is the correct (or the most useful, or the only useful) interpretation’’. Indeed, ideas about probability and human ‘‘rationality’’ have been debated by mathematicians and philosophers for centuries (Hacking, 1975). This is a challenging background against which to try to understand clinical decision-making, but a fascinating one as a new set of ideas promises new insights and perhaps, new solutions.
1.5. The contribution of cognitive science In recent years, a new group, the cognitive scientists, has entered the debate about rational judgement. Among their important contributions was the demonstration that normative frameworks for decision-making have surprisingly little to say about how people actually make decisions or reason under uncertainty. A massive body of empirical work, and theoretical ideas ranging from Herbert Simon’s concept of bounded rationality (1956) to Kahneman and Tversky’s programme of research into the ‘‘heuristics and biases’’ that underpin human reasoning under uncertainty (1974a,b) attests to the now generally accepted conclusion that human reasoning and decision-making are cognitive processes that are based on rather different principles from those which have been the preoccupation of statisticians and decision theorists. Few researchers now believe that normative probability and decision theory are the best bases for understanding human decision-making, and many doubt that they even represent gold standards against which human cognitive processes should be assessed. The programme of
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Gigerenzer et al. (1999) has indeed sought to extend Kahneman and Tversky’s heuristics and biases perspective by suggesting that human judgement is not a degenerate form of mathematical thinking, but has its own rationality. They specifically suggest that people must make decisions in a ‘‘fast and frugal’’ way that is optimised for speed at the cost of occasional but usually inconsequential errors. It now seems likely that biological, environmental, and other demands on mammalian cognitive function created a far wider range of needs and constraints than those addressed by the abstract norms of expected-utility and other mathematical theories. Animals must operate in a world in which information and knowledge are limited, time is of the essence, and environments are unpredictable and even capricious. The challenge from the cognitive sciences to the whole mathematical paradigm of uncertain reasoning and decision-making goes even deeper than this. A mathematical characterisation of any process necessarily involves creating an abstraction of that process, removing extraneous detail to facilitate formal analysis and development. However, if abstraction goes too far in the search for elegant and parsimonious mathematical solutions, there is a danger of oversimplifying the problem, decontextualising the clinical process we are trying to understand. For example, it is strange to insist, as Lindley does, that a theory is the only correct account of decision-making, and that all alternatives are demonstrably absurd, while also admitting that there are important parts of the decision process for which no ‘‘scientific advice’’ can be given (Lindley, op. cit.). Human decision-makers have strengths that are not acknowledged within the classical decision theory perspective. For example, Shanteau (1987) discusses ‘‘factors that lead to competence in experts, as opposed to the usual emphasis on incompetence’’. He observes that expert decisionmakers know what is relevant to specific decisions and what to give priority to in a busy environment. They can also make decisions about their own decision processes: which decisions to make, and when to make exceptions to general rules.1 Experts frequently ‘‘know a lot about what they know’’ and often have good communication skills and the ability to articulate their decisions and how they arrived at them. They can adapt to changing task conditions and are able to find novel solutions to problems. Classical accounts of decision-making do not deal with these meta-cognitive capabilities.
1 ‘‘Good surgeons, the saying goes, know how to operate, better surgeons know when to operate and the best surgeons know when not to operate. That’s true for all of medicine’’ Richard Smith, Editor of the British Medical Journal.
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Our long-term objective has been a new framework for understanding clinical decision-making that gives a more general account of cognitive and decision processes. Among the requirements that this seeks to address are: A description of the ‘‘complete’’ decision cycle, from the point where the goal of a clinical decision is formulated, through the selection of relevant evidence and its interpretation, to the final choice. The nature and role of ‘‘knowledge’’ within decision processes. The assessment of decision options in the absence of quantitative probabilities and utilities. The basis of ‘‘meta-cognitive’’ skills, when decision-makers reflect on their own performance, as in ‘‘is my decision sound, appropriate and safe?’’ Subsequent sections will briefly review a research programme which has addressed these questions within the field of medical cognition, drawing out results which illuminate the processes of routine clinical decisionmaking, and some of the sophisticated, non-routine capabilities that traditional accounts neglect. In the next section, we introduce a general framework for understanding cognition that has emerged from this work. We then home in on the decision-making component of this framework, and particularly on a theory of reasoning under uncertainty called argumentation. This offers both an explanatory account of cognitive processing in reasoning and decision-making, and a formal tool for analysing decision-making in complex domains. The use of the tool is demonstrated in one such domain: the detection, diagnosis, and treatment of breast cancer. Finally, we review our objectives and discuss the extent to which the model meets requirements I to IV above.
1.6. A general model of cognition and decision The domino model of decision making in cognition is a model of a general cognitive ‘‘agent’’ that has emerged from a variety of lines of research on medical reasoning, decision-making, planning, and other tasks (Fox and Das, 2000) (fig. 1). The left hand side of the domino deals primarily with decision making, while the right deals primarily with the organisation and enactment of plans. The nodes of the domino are state variables, while the arrows are inference functions. Inference mechanisms derive data of the type at the head of the arrow based on data of the type at the tail together with general and specific medical knowledge. The outer labels on the nodes (in italic) show the kinds of information that are involved in particular classes of decision in the particular domain of medicine (e.g. diagnosis and
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J. Fox and D. Glasspool Clinical goals
Patient data [1]
Problem goals
[2]
Candidate solutions Possible Diagnoses, Treatments etc.
Clinical orders [7]
Situation beliefs
Actions
Commit [4]
[6]
Commit Decisions [3]
Plans [5]
Selected Diagnoses Treatments etc.
Treatments and care plans
Fig. 1. The domino model of decision-making in cognition.
treatment decisions) while the inner labels (in bold) refer to equivalent but more general concepts which are independent of any specific domain of decision-making. The development of the domino model drew upon analysis of a wide range of medical decisions (including the risk assessment, diagnosis, and prescribing decisions outlined in the introduction) and the execution of care plans. It was developed as a parsimonious description of the processes involved here. The domino incorporates a number of steps that are required for general cognition, including decision-making. To illustrate this, consider a clinical situation in which we are presented with a patient who has inexplicably lost a great deal of weight. This could indicate a possible disease, so the first step is to establish a clinical goal to diagnose the cause of the weight loss (the inference process required to establish the goal is represented by arrow [1]). According to the model, the goal gives rise to a set of inferences about the possible explanations of the weight loss (arrow [2]). Taken together, these two steps represent the ‘‘framing’’ of the diagnosis decision. Once the frame of diagnostic alternatives has been created, we need to formulate a set of arguments for and against the competing explanations (arrow [3]). The argumentation process may take into account various types of knowledge, including known causes of weight loss, statistical associations between this symptom and alternative diagnoses, and so on. The final step in the decision process is to assess the arguments in order to arrive at a specific diagnosis decision (arrow [4]) such as cancer.
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Whatever the chosen diagnosis, it becomes a new piece of data or a belief which can give rise to a new goal. In this example, it may be to choose the best treatment of the condition. Once again several treatment options may be identified (arrow [2]), such as chemotherapy, surgery, and radiotherapy, and there are varied arguments for and against these options (arrow [3]). Arguments may take into account a variety of knowledge about the treatments including their expected efficacy, undesirable side-effects, interactions with other treatments, and possibly, safety. Once the arguments have been formulated, we need to assess the overall force of the arguments for each alternative in order to arrive at the choice of an appropriate therapy plan (arrow [5]). The plan that implements a medical treatment decision typically consists of a number of component actions. The domino model also extends to cover the implementation phase, in which actions of the plan are scheduled to meet various constraints on time and other resources (arrow [6]). Some actions can lead to new information such as new beliefs about the patient’s state, response to treatment, and so on (arrow [7]). This may result in additional goals being raised (e.g. to manage unexpected sideeffects or failures to achieve original goals). These will initiate further cycles of decision-making and planning. The domino model can be viewed as a competence model of cognitive processes, in the Chomskian sense (Chomsky, 1969). Its primary function is to formalise the core concepts and functions that are required in realworld decision-making. Like traditional decision-theoretic models (such as expected-utility models), the scheme is intended to provide a general inference model that can be used in any knowledge domain, but it introduces a wider range of inference types, that are required for a comprehensive account of decision-making. These inference types are represented by the arrows of the model and have been given a formal interpretation2 (Fox and Das, 2000) and therefore, a normative status. There are two areas where our account of decision-making differs strongly from traditional normative accounts like expected utility theory. First, the domino is intended to provide a framework for understanding and formalising the context within which decision-making is carried out. The account is thus widened to cover those areas which are traditionally excluded from mathematical approaches – specifically the purpose or goal of a decision, its framing (how decision options and relevant sources of knowledge and evidence are identified), and the processes which implement the decisions.
2
A model-theoretic semantics which has been proved to be sound and complete.
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Second, the reasoning that is at the heart of decision-making in this model is not some form of degenerate expected-utility calculation, but a versatile form of logical reasoning called argumentation. Argumentation is the pivot around which our proposed account of decision-making turns, and the focus of the remainder of the chapter. In the next section, we introduce the concept in more detail, explaining the theoretical basis of the idea. After that we turn to assessing how the concept can contribute to understanding routine medical decision-making in a complex medical domain, that of diagnosis and treatment of breast cancer.
2. ARGUMENTS AND DECISIONS 2.1. The nature of argument Informally, arguments are reasons to believe in possible states of the world (e.g. reasons to believe a patient has a disease) and reasons to act in particular ways in order to bring about or prevent anticipated states of affairs (e.g. reasons for selecting one particular medical treatment rather than another). Arguments are lines of reasoning that support or oppose claims. The differences between everyday informal argument and the arguments of formal logic was emphasised by the philosopher Stephen Toulmin. In The Uses of Argument (1957) he explored the question of why standard theories of reasoning, notably logical deduction and probabilistic reasoning, have little apparent relevance to everyday reasoning. Toulmin proposed a famous schema for characterising informal argument, in which ideas like the ‘‘warrants’’ ( justifications) for arguments and their ‘‘backings’’ and ideas like ‘‘rebuttal’’ and ‘‘qualifiers’’ for ‘‘claims’’ were central. However, Toulmin was focused on reasoning, not decision-making, and provided little detail. Recent developments, particularly in cognitive science, allow us to take his ideas further. Visualisation of an argumentation process represents a hypothetical agent that is required to take a decision (fig. 2). We adopt the neutral term ‘‘agent’’ to refer to any cognitive entity that has goals that it wishes to achieve and a body of knowledge that it can apply in achieving these goals; the agent might be a person, an artificial intelligence or an abstract theoretical entity. The large ellipse at the top left of the figure represents the agent’s knowledge base, which may include general knowledge about the world (dealing with time, space, properties of physical objects, and so forth) or they may represent technical information like medical knowledge (e.g. knowledge of anatomy, biochemistry, physiology, nosology,
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Commitment
Theory 3 Situation
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Epistemic modalities (e.g. Possible, probable, suspected, believed
Theory n
Theory 1 Argument annotations
Force of Arguments, degree of confidence
Argument 1
Argument 3 Argument 2
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Fig. 2. Visualisation of an argumentation process.
immunology, epidemiology, and so forth). The knowledge base is partitioned into a number of different segments that reflect these ontological distinctions; we call these ‘‘theories’’. Theories can be thought of as collections of assertions in some formal language. Some will assert general facts about the world (e.g. ‘‘all cancers are diseases’’) while others represent assertions about a specific situation (e.g. ‘‘this patient may be suffering from breast cancer’’); still others will represent rules like, ‘‘If there is an abnormality, we should establish the cause’’. A special theory is what the agent knows or believes about the present situation; what a doctor knows about a patient, for example. Suppose that a decision-making agent of this kind acquires some information about a particular situation, such as a patient complaining of unexplained weight loss. In such circumstances, the agent adopts the goal of finding the most likely explanation of this abnormal situation. According to the domino model, the first step is to identify candidate explanations, such as the loss of weight being caused by a gastric ulcer or the patient covertly dieting. In fig. 2, these alternative explanations are called ‘‘claims’’, which the agent can use to focus the application of its knowledge in order to construct arguments for and against the competing claims. For example, the agent could argue for the hypothesis of gastric ulcer on the grounds that the patient has pain after meals, using a causal theory that gastric acids irritate pain receptors in the lining of the stomach, which are exposed by the ulceration process. On the other hand, it may argue on statistical
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grounds that peptic ulcer is unlikely because the patient is only 20, and a gastric ulcer in a patient under 50 is very rare. In fact, we can develop any number of arguments for and against the alternative claims, drawing on different subsets of knowledge and applying different common-sense modes of reasoning (causal, statistical etc.) and technical knowledge (e.g. knowledge of anatomy, physiology, immunology).
2.2. Taking decisions, making commitments In an argumentation system, we may have arguments for and against a claim. In order to make a decision between competing claims, we have to assess the various pros and cons, combining them into a case for each claim, and then deciding which case is the strongest. For example, we might use a simple but effective method famously described by Ben Franklin (Schwartz and Griffin, 1986) in which the more positive arguments for a claim, the greater our confidence in it; the more negative ones, the greater our doubt. Such linear models with uniform weights have proved to be highly effective in a range of applications (Fox et al., 2001). It is also possible to attach different weights to arguments, as was done in the RAGs risk assessment system described earlier, in which the arguments were weighted with integers representing low, medium, and high strength of arguments. Many mathematical functions can be used to represent ideas like ‘‘weight of evidence’’ and ‘‘strength of argument’’, and to aggregate the weighted arguments into some overall measure of confidence. In fact, we can take this further by attaching real numbers to the arguments, such as the numbers between 0 and 1, and if we are careful with the design of our argumentation rules and aggregation function, we can capture the strength of argument as a conventional probability or expected value (Fox and Parsons, 1998). There are pros and cons of different argument aggregation schemes. Linear models with uniform weights are simple to use and robust and do not depend upon large bodies of quantitative information, while expectedutility and other statistical decision models are technically sound and offer precise results but are relatively difficult to formulate and use. Whatever scheme one chooses, however, the general contribution of the aggregation process is to bring together collections of arguments in order to define a preference order over the set of competing claims. Establishing an order of preference over a set of decision options is an important part of decision-making but the complete decision cycle requires one last step. From the domino model, we can see that taking a decision is
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to commit to one or other of the competing claims, to adopt a plan of action, or to accept a hypothesis about the present situation that will determine future actions. This basic aspect of all decision-making gets surprisingly little attention in the research literature. Figure 2 indicates decision-makers can take two different routes from a collection of arguments to a commitment. The ‘‘aggregation’’ route involves acting on the strength of the set of arguments for a claim or comparing the force of arguments for the competing claims expressed as a number, the traditional approach. However, there is a second route to making decisions that has not been much studied. We call this the ‘‘annotation’’ route, because it considers logical properties of collections of arguments in order to annotate the claim. For example, we may say ‘‘it is possible’’ that a patient has cancer on the grounds that there is at least one argument in favour and no arguments to exclude cancer. Similarly we may say that ‘‘cancer is probable’’ if, say, there are more arguments in favour than against. No arithmetic operations are needed. Elvang-Gøransson et al. (1993) have demonstrated a formal annotation system based on this idea. They present a consistent set of logical terms for expressing confidence in a claim which allows claims to be placed into a total preference order (from least confidence to highest confidence) on purely logical grounds: Claim is open if the claim is any well-formed proposition without argument Claim is supported if an argument, possibly using inconsistent data, can be constructed for the claim Claim is plausible if a consistent argument can be constructed for the claim (we may also be able to construct a consistent argument against) Claim is probable if a consistent argument can be constructed for it, and no consistent argument can be constructed against it Claim is confirmed if it satisfies the conditions of being probable and, in addition, no consistent arguments can be constructed against any of the premises used in its supporting argument
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Claim is certain if it is a tautology of the knowledge base (meaning that its validity is not contingent on any other data in the knowledge base). The existence of annotation systems, whether formal or informal, is an important insight for understanding much human decision-making, because it potentially explains both how people can arrive at new beliefs on purely qualitative grounds, and the reason for the rich variety of uncertainty terms in English and other natural languages. In the next section, we use these ideas to develop a system for modelling routine decisions, and apply it in a complex medical domain.
3. MODELLING ROUTINE CLINICAL DECISIONS For the purposes of this discussion, we view ‘‘routine decisions’’ as decisions that are taken frequently, employing forms of evidence or argument that are normal for those who make the decisions. Routine decisions depend upon shared knowledge that is uncontroversial and may well be explicitly documented. Prescribing the drug, genetic risk assessment, and cancer screening decisions described in the introduction are examples of routine decisions in this sense.
3.1. An argument schema for routine decisions Conventional decision theory offers a set of concepts and procedures for modelling routine decisions (options, evidence, prior and conditional probabilities and probability revision, etc.). In this section, we describe an analogous set of concepts that are intended to facilitate understanding and modelling of decisions within the argumentation framework. The core concepts draw on terminology from Toulmin (1957): Claim: A hypothetical situation or action that is under consideration but has not been committed. Grounds: Specific situational data that are the basis of a line of argument for or against the claim. Qualifier: The modality of the argument (supporting, opposing, confirming, etc.) or a label representing the strength of the argument. Theory: The body of knowledge that sanctions or warrants the argument. Backing: The justification for assuming that the theory is valid, sound, or true.
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In what follows, we use this scheme to analyse the knowledge and arguments in a complex real-world domains: the detection, diagnosis, and treatment of breast cancer.
3.2. Modelling routine decisions in breast cancer medicine Breast cancer is one of the most common cancers. Nearly 40,000 women are diagnosed with breast cancer in the UK every year, making it by far the most common cancer in women (CancerStats, 2002). The treatment of breast cancer typically follows four phases: the detection of possible or potential disease, the work-up of the case to decide appropriate action, enactment of active treatment or other intervention, and post-treatment follow up of the patient. Figure 3 summarises the main processes that are involved in their care. Each process, represented by a rounded rectangle, consists of a number of tasks and one or more decisions. The specific pathway followed by a patient varies from case to case, depending on the type of cancer and other specific characteristics of the patient, response to treatment, and so on. There are many different kinds of decision, including diagnosis, situation assessment, and treatment decisions. The ontological classification of decisions is a complex subject but for present purposes, we shall consider just two broad categories: decisions about what to believe about a situation (e.g. ‘‘Does this patient have cancer? Is she at risk of developing cancer? What type of cancer is present and what stage has the disease progressed to?’’) and what to do (e.g. ‘‘how should the risk of cancer be managed? Detection
Primary care
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Psychosocial
Treatment Follow-up
Surgery
Palliative care
Radiotherapy
Diagnosis Screening Staging
Therapy planning
Systemic Therapy
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Fig. 3.
Primary Care
Follow up Clinics Pathology
Radiology
Multidisciplinary patient reviews
Main processes in the care of patients with potential, suspected, or confirmed breast cancer.
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What type of therapy should be used to treat the cancer? What further services are required?’’). In the next section, we analyse a number of the decisions which clinicians routinely take in this domain, identifying the knowledge and arguments that are relevant to each. In each case, we shall present one example of an argument for one possible decision option using the format introduced above. Appendix A provides a summary of the arguments required for each decision.
3.3. Urgent referral of patients with suspected cancer The UK Department of Health (DoH) requires that patients who show any signs of early cancer should be seen and assessed by a cancer specialist within 2 weeks of their family doctor deciding that they need to be investigated. The DoH has developed and published criteria to assist doctors in deciding whether or not a particular patient needs to be referred under the 2-week standard, or non-urgent referral to a breast specialist. An example of an argument for making the decision to refer to a breast specialist is shown here (see appendix A, table 1 for a fuller analysis). Claim: Patient should be referred to a breast specialist Grounds: Abscess or breast inflammation that does not settle after one course of antibiotics Qualifier: The argument supports referral Warranted by: Specialist epidemiological and oncological knowledge and general knowledge about time and urgency Backing: Authorised by UK Department of Health
3.4. Risk of being at elevated genetic risk for breast cancer In recent years, it has become increasingly evident that susceptibility to many diseases can be inherited. Breast cancer is a well-known example of such a disease, where the lifetime risk of developing the disease for some women is as much as 80%. However, only one case in 20 is genetically predisposed. Sporadic incidence of disease tends to follow a different pattern within a family predisposed to inherited disease, so an assessment of the pattern of disease within a family can provide an initial indication of the presence or absence of a predisposing gene (see appendix A, table 2). Claim: Subject has a genetic predisposition to breast cancer Grounds: One first degree relative with (bilateral breast cancer OR breast and ovarian cancer)
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Qualifier: Supporting argument Warranted by: Knowledge of aetiology, epidemiology and genetics Backing: Scottish Intercollegiate Guidelines Network
3.5. Detection of breast cancer through imaging The UK runs a breast cancer screening service where X-rays of the breasts are taken every 3 years and examined for signs that breast cancer may be developing. If there are abnormal features, the patient will be referred for detailed investigation (only about 1 in 10 of patients with suspicious features will actually have cancer). Alberdi et al. (2002) investigated radiologists’ interpretations of an important class of abnormality in mammograms called micro-calcifications. They developed a standard terminology that discriminated benign and malignant outcomes and were generally highly correlated with radiologists’ assessment of risk. Taylor, Lee and Alberdi characterise the arguments that underpin this decision, and these are summarised in appendix A, table 3. One of these arguments is as follows: Claim: Calcifications are of benign origin Grounds: All calcifications occur within fatty tissue Qualifier: Supporting argument Warranted by: Statistical association between feature and disease Backing: Alberdi et al. (2002)
3.6. Staging of breast cancer Cancer is a disease that goes through a number of stages as it develops. It is important to establish the stage of the disease as this has important implications for the choice of treatment. A common system for staging breast cancer is the TNM (Tumour, Nodes, Metastases) classification system developed by the International Union against Cancer. The classification actually consists of 3 independent decisions, one to establish how advanced the primary tumour is (T), the second concerns whether the disease has migrated to lymph nodes (N) and the last concerns whether there are any metastatic tumours (M). This scheme has been designed to simplify the staging process by using categorical criteria. An example of one TNM argument is shown here, the complete TNM scheme for breast cancer is in appendix A, table 4. Claim: Tumour stage is T1 Grounds: Tumour size is 2 cm or less in greatest dimension
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Qualifier: Conclusive Warranted by: The TNM staging system for breast cancer Backing: International Union against Cancer, Geneva
3.7. Referral for further investigation after screening Once there are established grounds to believe that breast cancer may be present, the patient is referred for specialist assessment and confirmation or exclusion of disease. Simple guidelines may govern the assessment referral, for example those in table 5. The following is one example taken from table 5: Claim: Further investigation is required Grounds: Localised abnormality is present Qualifier: Conclusive Warranted by: Oncological and epidemiological knowledge about the disease process and its consequences Backing: Scottish Intercollegiate Guidelines Network
3.8. Treatment selection Patients with breast cancer will typically have a combination of three different types of treatment: chemotherapy, radiotherapy, and surgery. Each treatment has a number of different options and associated arguments. An argument for one particular chemotherapy regime is shown below: table 6 in appendix A shows the arguments for all three decisions. Claim: An anthracycline regimen is appropriate Grounds: Patient is at high risk of relapse Qualifier: Conclusive Warranted by: Knowledge of tumour type and cytotoxic effects Backing: SIGN guideline 29 (Breast Cancer)
4. DISCUSSION It is generally accepted that accounts of human decision-making will depend upon different representations and operations than those used in traditional mathematical theories. We share with others (e.g. Gigerenzer) the view that human decision-making is optimised to meet a wider range of requirements and performance constraints than are considered in classical accounts of decision-making and, further, question the idea
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that existing prescriptive models truly offer gold standards against which human judgement must be made. In fact, we argue that such theories are incomplete in important ways. For example, they do not explain how decisions can be made in the absence of statistical and other quantitative data. Argumentation provides a natural and expressive way of making decisions based on qualitative criteria when that is all that is possible, yet can incorporate quantitative weights when this is practical and helpful. We have not provided a mathematical treatment of argumentation and decision-making here, but focused on how these ideas can be used to articulate the kinds of knowledge people bring to bear in making routine decisions in knowledge-based domains like medicine. Formal treatments have been developed, however (e.g. Fox et al., 1992; Krause et al., 1994; Fox and Parsons, 1998) which we believe addresses any charges of incoherence that are regularly levelled at ‘‘ad hoc’’ decision theories. Under certain technical assumptions, argumentation systems can in fact be shown to be closely related to classical ideas in probability theory (Krause et al., 1994) and may indeed shed some light on the history of the emergence of probabilistic concepts (Fox, 2003). Another important area where traditional theories concerns are how agents frame their decisions in ways that are consistent with their goals (this is ‘‘upstream’’ of argumentation in the domino model). Obviously, clinical decisions are generally carried out for a reason, to decide how to bring about or prevent some desired or undesired situation, for example. If a process of care fails to achieve the desired outcome, then the clinical goal has not been achieved and the decision must at least be reviewed. One might suggest that ‘‘goal’’ is really just another name for a measure of utility in conventional decision theory. However, analysis suggests that utilities may again represent an abstraction too far. Shahar et al. (1998) identify three distinct dimensions to be considered when trying to formalise a clinical goal: Whether the goal is to achieve, maintain, or avoid some situation; Whether the goal refers to a clinical state or action; Whether the goal holds during enactment of a clinical process or after it has been completed. Hashmi et al. (2003) have proposed an extended model in which goals are modelled in terms of 5 dimensions: The initial state or context in which the goal applies The target, which can refer to states of anatomical structures, diseases or disorders, or physiological functions The intention, a verb that specifies whether the target function is to be achieved, avoided, etc.
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Timing constraints The priority of the goal, which can be used to select and rank from among competing goals There is much to be learned by addressing this issue in a medical context where being clear about goals and objectives is so critical. In our view, a clinical goal is naturally described as a sentence in natural language, which is highly expressive if relatively informal. Many examples consist of just a verb phrase and a noun phrase. Shahar et al. (1998) model the goal as a verb (achieve, maintain, and avoid) and an object (state or action). Hashmi et al. (2003) speaks of a verb and a target. Huang et al. (1993) model decision-making goals as a [Task, Focus] pair as in ‘‘diagnose weight loss’’; ‘‘treat joint pain’’ or ‘‘prescribe analgesics’’. While goals can often be described in terms of hverb phraseihnoun phrasei constructions, natural language can express further constraints. Shahar et al. (1998) and Hashmi et al. (2003) emphasise the importance of temporal constraints, for example, but there are any number of possible constraints that could limit the scope of a goal, from objective matters like budgetary restrictions to subjective factors like clinician priorities and patient preferences. An important property of goals is that they can usually be grouped into classes, based on the fact that they have a common verb (such as ‘‘diagnose’’) or some other shared feature. This can help when framing a decision. For example, we can have a general strategy for determining which treatments might be useful for treating a condition (e.g. treatments that eradicate or ameliorate the condition) and the kinds of argument that are relevant (e.g. argue from side-effects, interactions, cost, availability, and so forth). We recently explored this idea in the domain of breast cancer, identifying 222 different services that are provided through the process of care, from initial detection of disease through the work-up, treatment planning and treatment execution, and long-term follow-up. For each service we defined a goal in terms of a hverb phraseihnoun phrasei pair. Among these services were 65 different decisions, which we organised into classes, as shown below. Decide between alternative beliefs Detect (Decide presence/absence of something) Classify Stage of disease Eligibility (determine whether criteria are satisfied) {Investigation, Referral, Therapy, Research trial} Level of a parameter {Urgency, Risk, Need, Quality} Predict
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Diagnosis Prognosis Decide between alternative actions Whether to carry out intervention or not Type of intervention Timing of intervention Current work is concerned with how such a logical ontology can inform the design of methods for decision-making, with the aim of finding out what general strategies of argument are relevant to common classes of decision. Research in artificial intelligence (AI) has also contributed insights into the nature of goals. AI starts with the premise that to build intelligent systems like planning systems or robots which must cope with complex and unpredictable environments, it is necessary to separate the behavioural aspects of intelligence (what a robot should do in the world) from the cognitive aspects (what the robot may reasonably believe and how it should decide to act with respect to its beliefs given its goals). The questions for theorists are: what intuitive properties do goals have, and what formal constraints should be placed on them? Winikoff et al. (2002) suggest that goals must be: Explicit (if the agent is to reason about them) Consistent (an agent should not adopt goals that conflict) Persistent (goals exist so long as their success conditions are not satisfied) Unachieved (a goal is only valid when its success conditions are false) Possible (a goal is abandoned when it becomes impossible to achieve) Such properties can be defined formally with a logical semantics that defines the rules that goals must obey. To conclude, we believe that a logical perspective is highly productive in understanding decision-making, whether in medicine or other domains. We earlier noted four general issues for such an account. I. Can we describe a ‘‘complete’’ decision cycle, from the framing of a decision to the final choice? II. What is the nature and role of ‘‘knowledge’’ within everyday decision processes? III. How can agents make decisions in the absence of quantitative data (e.g. probabilities and utilities) and indeed in the absence of knowledge generally? IV. What is the basis of meta-cognitive skills? The domino model is our general proposal for a complete decision process (fig. 1), and the argumentation process describes how knowledge, in the form of diverse theories about the world, is brought to bear in making decisions (fig. 2). Despite the fact that an agent’s knowledge
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may be incomplete, we have shown in a number of experimental studies that argumentation is a robust mechanism by which a decision-maker can generate ‘‘reasons to believe and reasons to act’’, in order to establish preferences and make decisions (Fox and Das, 2000; Fox et al., 2001). We believe that an account of meta-cognitive functions in decisionmaking is also an important theoretical and practical challenge for decision theorists. How can an agent explain the reasons for its beliefs or actions? How can it reflect critically upon its goals and its knowledge? A recent discussion of the professional responsibilities of a doctor (Pritchard, 2004) provides compelling illustrations of how important this is: I am committed to putting the patient first I practice honestly, truthfully, and with integrity I respect empathically the patient’s identity, dignity, beliefs, and values I maintain confidentiality at all times I am open to self-criticism and self-audit I am open to peer criticism and peer audit I try to provide care of high quality and apply evidence-based medicine where appropriate I am dedicated to lifelong reflection and learning. If we ignore the complexity of medical knowledge and the varied cognitive processes involved in clinical decisions, then we will be unable to arrive at a credible account of practical decision-making, or an understanding of the strengths and weaknesses of human decision-making. If we insist that the only correct approach to decision-making must be strictly quantitative then we, like Lindley, will continue to be unable to offer scientific advice that will improve all aspects of the decision process.
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APPENDIX A: ARGUMENTATION IN BREAST CANCER CARE Table 1 Urgent referrals: criteria for urgent referral of women with possible breast cancer Claim
Arguments
Should be referred to breast specialist
Any new discrete lump New lump in pre-existing nodularity Asymmetrical nodularity that persists at review after menstruation Abscess or breast inflammation which does not settle after one course of antibiotics Cyst persistently refilling or recurrent Pain associated with lump Intractable pain Unilateral persistent pain in post-menopausal women Nipple discharge in woman aged 50 and over Bloodstained discharge in women under 50 Bilateral discharge sufficient to stain clothes Persistent single duct discharge Nipple retraction or distortion Nipple eczema Change in skin contour
Table 2 Risk assessment decision: arguments for referral of patient due to possible inherited cancer risk Claim
Supporting arguments
Subject is at moderate risk of being a gene carrier
One first degree relative with bilateral breast cancer or breast and ovarian cancer One first degree relative with breast cancer diagnosed under the age of 40 or one first degree male relative with breast cancer diagnosed at any age Two first or second degree relatives with breast cancer diagnosed under the age of 60; or ovarian cancer at any age on the same side of the family Three first or second degree relatives with breast or ovarian cancer on the same side of the family Four or more relatives affected with either breast or ovarian cancer in three generations and one alive affected relative
Subject is at high risk of being a gene carrier
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Table 3 Detection decision: arguments about features of mammographic calcifications Claim
Conclusive arguments
Supporting arguments
Calcifications of benign origin
Big Within fat Similar density Curvilinear With a rim Well defined Homogeneous
Calcifications of malignant origin
Segmental Pleomorphic
Isolated Lucent centre 1–5 flecks Scattered Vascular distribution In skin Adjacent Oval Few specks Variable density Towards nipple Ill-defined Variable size Linear shape Branching Ductal/linear Distribution Clustered
Table 4 Staging decision: TNM staging of breast cancer (UICC) Primary Tumour TX T0 Tis
T1 T2 T3 T4
Primary tumour cannot be assessed No evidence of primary tumour Carcinoma in situ: intraductal carcinoma, or lobular carcinoma in situ, or Paget disease of the nipple with no tumour Tumour 2 cm or less in greatest dimension Tumour more than 2 cm but not more than 5 cm in greatest dimension Tumour more than 5 cm in greatest dimension Tumour of any size with direct extension to chest wall or skin
Regional Lymph Nodes NX N0 N1 N2 N3
Regional lymph nodes cannot be assessed (e.g. previously removed) No regional lymph node metastasis Metastasis to movable ipsilateral axillary node(s) Metastasis to ipsilateral axillary node(s) fixed to one another or to other structures Metastasis to ipsilateral internal mammary lymph node(s)
Distant Metastasis MX M0 M1
Distant metastasis cannot be assessed No distant metastasis Distant metastasis
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Table 5 Referral of suspected cancer: arguments concerning referral of tumour patients for assessment. From SIGN guideline 29 Claim
Arguments
Patient should have a full clinical examination Patient should have imaging usually followed by FNAC or core biopsy Patient should have histopathological confirmation of malignancy before any definitive surgical procedure
Always A localised abnormality is present
Lesion is considered malignant on either clinical examination, imaging or cytology alone
Table 6 Selection of treatment: arguments concerning the treatment of confirmed breast cancer Claim Chemotherapy Standard CMF chemotherapy An anthracycline based regimen Other cytotoxic regimens, including high-dose chemotherapy Radiotherapy Radiotherapy should be given to the breast Wide local excision should be combined with radiotherapy and systemic therapy as appropriate Radiotherapy should be given to the chest wall after mastectomy The axilla should be irradiated The axilla should not be irradiated Surgery Mastectomy
Breast conservation
Supporting arguments Normally, outside clinical trials Women at high risk of relapse or patient in clinical trial Normally, only within clinical trials
Normally, following wide local excision Patient outside a clinical trial
Patient judged to be at high risk of local recurrence After axillary sampling, if node positive or inadequately sampled After axillary clearance Operable breast cancer which is either large or at multiple sites Radiotherapy is to be avoided Patient preference for mastectomy Smaller tumours in larger breasts Specific pathological features of the tumour Age of patient is young Stated patient preference Fitness for surgery and/or radiotherapy
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REFERENCES Alberdi, E., Taylor, P., Lee, R., Fox, J., Todd-Pokropek, A., 2002. Eliciting a terminology for mammographic calcifications. Clin. Radiol. 57, 1007–1013. CancerStats, 2002. Breast cancer statistics: Source: Cancer Research UK, September. Chomsky, N., 1969. Aspects of the Theory of Syntax. MIT Press, Cambridge, MA. Coulson, A.S., Glasspool, D.W., Fox, J., Emery, J., 2001. RAGs: a novel approach to computerized genetic risk assessment and decision support from pedigrees. Meth. Inf. Med. 4, 315–322. Elvang-Gøransson, M., Krause, P.J., Fox, J., 1993. Dialectic reasoning with inconsistent information. In: Heckerman, D., Mandani, A. (Eds.), Uncertainty in Artificial Intelligence. Proceedings of the 9th Conference, Morgan Kaufman, San Mateo, CA. Emery, J., Walton, R., Coulson, A., Glasspool, D., Ziebland, S., Fox, J., 1999. Computer support for recording and interpreting family histories of breast and ovarian cancer in primary care (RAGs): qualitative evaluation with simulated patients. Br. Med. J. 319, 32–36. Emery, J., Walton, R., Murphy, M., Austoker, J., Yudkin, P., Chapman, C., Coulson, A., Glasspool, D., Fox, J., 2000. Computer support for interpreting family histories of breast and ovarian cancer in primary care: comparative study with simulated cases. Br. Med. J. 321, 28–32. Fox, J., 2003. Logic, probability and the cognitive foundations of rational belief. J. Appl. Log. 1, 197–224. Fox, J., Das, S., 2000. Safe and Sound: Artificial Intelligence in Hazardous Applications. MIT Press, Cambridge, MA. Fox, J., Parsons, S., 1998. Arguing about beliefs and actions. In: Hunter, A., Parsons, S. (Eds.), Applications of Uncertainty Formalisms, Springer-Verlag, New York. Fox, J., Krause, P., Ambler, P., 1992. Arguments, contradictions and practical reasoning, Proceedings of the European Conference on Artificial Intelligence, Vienna. John Wiley, Chichester, pp. 623–626. Fox, J., Glasspool, D., Bury, J., 2001. Quantitative and qualitative approaches to reasoning under uncertainty in medical decision making. In: Quaglini, S., Barahona, P., Andreasson, S. (Eds.), Proceedings of AIME. Springer-Verlag, Berlin, pp. 272–282. Gigerenzer, G., Todd, PM., ABC Research Group Staff, 1999. Simple Heuristics That Make Us Smart, Oxford University Press, Oxford. Hacking, I., 1975. The Emergence of probability. Cambridge University Press, Cambridge. Hashmi, N., Boxwala, A., Zaccagnini, D., Fox, J., 2003. Formal Representation of Medical Goals for Medical Guidelines, Medinfo. Huang, J., Fox, J., Gordon, C., Jackson-Smale, A., 1993. Symbolic decision support in medical care. Artif. Intell. Med. 5, 415–430. Krause, P.J., Ambler, S.J., Fox, J., 1995. A logic of argumentation for uncertain reasoning. Computational Intelligence 11(1), 113–131. Kyburg, H., 1990. Science and Reason. Oxford University Press, Oxford. Lindley, D.V., 1985. Making Decisions, 2nd Edition. Chichester, Wiley, UK. Pritchard, P., 2004. Professional values and informatics: what is the connection? Inform. Prim. Care 12(2), 91–96. Schwartz, S., Griffin, T., 1986. Medical Thinking: The Psychology of Medical Judgment and Decision Making, Springer-Verlag, New York.
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Shahar, Y., Miksch, S., Johnson, P., 1998. The Asgaard project: a task-specific framework for the application and critiquing of time-oriented clinical guidelines. Artif. Intel. Med. 14, 29–51. Shanteau, J., 1987. Psychological characteristics of expert decision makers. In: Mumpower, J. (Ed.), Expert Judgment and Expert Systems, NATO: ASI Series. (F35). Simon, H. A., 1956. The Sciences of the Artificial. MIT Press, Cambridge, MA. Sobin, L.H., Wittekind, C. (Eds.), 1997. TNM Classification of malignant tumours, UICC International Union Against Cancer, Wiley-Liss, New York. Taylor, P., Fox, J., Pokropek, A., 1999. The development and evaluation of CADMIUM: a prototype system to assist in the interpretation of mammograms. Med. Image Anal. 3, 321–337. Toulmin, S., 1957. The Uses of Argument. Cambridge University Press, Cambridge, UK. Walton, R.T., Gierl, C., Yudkin, P., Mistry, H., Vessey, M.P., Fox, J., 1997. Evaluation of computer support for prescribing (CAPSULE) using simulated cases. Br. Med. J. 315, 791–795. Winikoff, M., Padgham, L., Harland, J., Thangarajah, J., 2002. Declarative and Procedural Goals in Intelligent Agent Systems. Proceedings of the Eighth International Conference on Principles of Knowledge Representation and Reasoning (KR2002), Toulouse, France.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
8 Analogies, conventions, and expert systems in medicine: some insights from a XIX century physiologist Guido Fioretti1 Department of Quantitative Social and Cognitive Sciences, University of Modena and Reggio Emilia, Italy
1. INTRODUCTION Like detective stories, art critique, and history, medical diagnoses rest on highlighting minuscule cues that may shed a beam of light on a grand hidden picture that may be inferred by induction but will never be deduced from general principles. This method is inherently and profoundly different from making a priori generalisations, as is often the case in the natural sciences, where empirical regularities inspire the definition of a set of possibilities (Ginzburg, 1986). Probability theory, with its emphasis on games of chance where the set of possibilities is known and given once and for all (e.g. the six faces of a die, or the two faces of a coin), reflects the needs and the methods of natural sciences. As such, it may not be appropriate for investigative practices such as medicine. For this reason, it is interesting to see how a concept of probability was eventually developed by a medical practitioner who was skilled enough in logic to develop one of his own. In the second half of the nineteenth century, a physiologist named Johannes von Kries was attempting to apply probability theory to the evaluation of the effectiveness of new drugs. Like many developers of expert systems for medical applications today, von Kries realised that the main difficulty lay in the very definition of events (Fox, 2003). What should count as a ‘‘healing’’? That a particular drug prolonged a patient’s life a little longer than if he had not taken it? That a patient recovered from one disease, then succumbed to another? Furthermore, in some cases it is not 1
I wish to thank Peter McBurney for giving me a chance to contribute to this voume.
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obvious where the border between two or more diseases lies. Consequently, the classification of symptoms is never obvious. von Kries became deeply involved in this issue and, as a side interest to his academic career as a physiology professor, he became a logician and a probability theorist. von Kries is interesting precisely because, unlike most probabilists, his background was not in mathematics. Contrary to nearly all other probability theorists, he did not consider games of chance as the prototypical situation where uncertainty would arise. As a physician, he knew that in practical situations uncertainty means a lot more than the occurrence of one out of a given list of possibilities. von Kries viewed probability as a logical relation based on analogy. By drawing analogies between the present and the past, e.g. between the present symptoms and the past ones, a decision-maker may arrive at the conclusion that a certain event, e.g. a particular disease, is more or less ‘‘probable’’. von Kries was very much ahead of his time. Notably, he did not think of mental categories as sets of elements exhibiting certain commonalities but rather as incremental collections to which a new element is added because of some similarity with existing members. He did so because he had in mind the way a doctor knows a disease, as a series of practical cases that collectively add to a label whose meaning is shared with colleagues. This is not an ex ante definition that is the equivalent of the face of a die, but rather a never-ending construction resting on analogies and similarities between a continuous flow of cases. von Kries stressed that, since similarity is a subjective judgement between phenomena that are objectively different, objective numerical probabilities are not possible for the very same reason why one cannot sum apples to pears. Thus, any assessment of a numerical probability is to some extent arbitrary. More precisely, it is arbitrary to the extent the judgement of similarity on which it rests is itself arbitrary. In medical contexts, this degree of arbitrariness may be very high. von Kries focused his research activities on the physiology of the sensory organs and their activation by the nervous system. In the nineteenth century, that was the closest thing to a physiology of psychology. He never arrived at a physical foundation of probability judgements. However, he stands as a leading scholarly figure who included logic and psychology in a course of physiology (von Kries, 1923), as well as a man whose interests spanned several disciplinary boundaries (von Kries, 1925). Nowadays, it is still interesting to see how von Kries characterised probability. It is interesting also because expert systems for medical applications face the same kind of difficulties, and their eventual diffusion may establish or stabilise conventions as envisaged by von Kries’s probability theory.
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2. THE PROBABILITY THEORY OF A PHYSIOLOGIST According to von Kries, it is by drawing analogies between the present and the past that an individual becomes able to describe that a certain course of events is more or less ‘‘probable’’. However, the reliability of an analogy depends on the similarity between the past cases and the present one: strictly speaking, situations are almost never the same, and analogies are almost never perfect. Consequently, in general, probabilities cannot be expressed numerically: ‘‘(. . .) there exist logical relations that link things known with certainty to others for which they provide a large or small probability, without a numerical mass existing for it. Actually only the strict dependency that in deductive reasoning links premise to conclusion can transpose to the second the certainty of the first. With other logical relations, it is not so. Less even with analogy. If we observed one or more cases of a certain kind occurring in a certain way, and we expect the same course for a similar case, this expectation does not share the certainty of the premises on which it is based. Taken for granted these premises, this expectation is more or less probable. But this logical relation cannot be expressed numerically. The probability of an outcome increases with the number of cases that have come to be known, but it depends also on the grade and the kind of similarity of these cases, and especially on the similarity between the case the current expectation refers to, and the cases that occurred in the past. However, there is no reason to assume that the [similarity] assumptions have the same value’’.2 (von Kries, 1886: 26)
2 (. . .) Verha¨ltnisse des logischen Zusammenhanges giebt, welche, indem gewisse Dinge als sicher gelten, fu¨r andere eine mehr oder weniger grosse Wahrscheinlichkeit constituiren, ohne dass fu¨r diese ein numerisches Maas existirt. In der That kann ja nur der vo¨llig feste Zusammenhang, welcher bei dem deductiven Schlusse die Conclusion an die Pra¨missen knu¨pft, die Sicherheit dieser letzteren unvera¨ndert und ohne Abzug auf jene u¨bertragen. Bei anderen logischen Verha¨ltnissen ist dies anders. So zuna¨chst beim Analogie-Schlusse. Wenn wir einen oder mehrere Fa¨lle von gewisser Art in einer bestimmten Weise haben verlaufen sehen und fu¨r einen a¨hnlichen Fall den gleichen Verlauf erwarten, so teilt diese Erwartung ja selbstversta¨ndlich nicht die Sicherheit derjenigen Voraussetzungen, auf welche sie sich gru¨ndet; sie ist – jene als sicher angenommen – immer nur mehr oder weniger wahrscheinlich. Das hier Statt findende logische Verha¨ltniss hat nun gar nichts zahlenma¨ssig Darstellbares; die Wahrscheinlichkeit des fru¨her beobachteten Erfolges steigt mit der Zahl der bekannt gewordenen Fa¨lle und ha¨ngt ausserdem von dem Grade und der Art der Aenlichkeit ab, welche die einzelnen Fa¨lle untereinander und insbesondere der gegenwa¨rtig zu beurteilende mit den fru¨heren zeigt. Fu¨r eine Aufstellung gleichwertiger Annahmen aber fehlt hier jeder Anhalt.
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Similarly, probability cannot be numerical when induction is involved. In fact, induction and analogy are closely linked to one another: ‘‘The considerations we made regarding analogy hold for induction as well, which is the process whereby we derive general statements from single experiences. This is particularly so when a general statement has numerous consequences and finds a number of applications, which implies that it can be suggested by very many different experiences. In this case, a numerical measure of its soundness does not exist’’.3 (von Kries, 1886: 29) ‘‘The difference between induction and analogy can be expressed by saying that the first is a relation from the particular to the particular, the second a relation from the particular to the general. Thus, the connections involved in the two cases are definitely of a different kind. But however precise and irrefutable this distinction might be, it is quite an unimportant one. On the one hand, the general statement that results from an induction is the summary of an unlimited or unknown number of particular statements, and each of them could be reached by simple analogy. (. . .) On the other hand, at least in many cases we can recognise in analogy an implicit induction’’.4 (von Kries, 1916: 403) Exceptions exist, and in certain cases probabilities can be expressed numerically. This happens when empirical facts are qualitatively equal to one another, so that it is not necessary to draw any analogy at all. This is the case, for example, of the games of chance we usually refer to when we 3
Ganz dasselbe, wie fu¨r die Analogie, gilt nun auch fu¨r das logische Verha¨ltniss, welches bei dem Inductionsverfahren Statt findet; hierunter soll ein solches verstanden sein, bei dem wir aus einem mehr oder weniger ausgedehnten Erfahrungs-Wissen Sa¨tze allgemeinen Inhaltes ableiten. Insbesondere wenn ein solcher Satz sehr mannigfaltige Consequenzen besitzt, sehr vielfach Anwendung findet, also auch durch sehr verschiedenartige Erfahrungs-Resultate begru¨ndet werden kann, wird nicht in Abrede zu stellen sein, dass ein numeriscgı` hes Maass diesere Begru¨ndung oder erfahrungsma¨ssigen Besta¨tigung nicht existirt.
4
Was das Verha¨ltnis der Induktion zum Aalogie-Schluß anlangt, so wird man den Unterschied beider zuna¨chst dahin zu fixieren geneigt sein, daß in dem einen Falle der Schluß von einem Einzelnen auf ein enderes koordiniertes Einzelnes, im anderen vom Einzelnen auf eine Gesamtheit gehe, daß also die in einen und andern Falle zugrunde liegenden Geltungsbeziehungen streng verschieden seien. Indessen la¨ßt sich doch nicht u¨bersehen, daß wir hiermit eine zwar pra¨zise und formell einwandsfreie, sachlich aber meist wenig belangreiche Unterscheidung machen. Zuna¨chst na¨mlich versteht sich, daß der allgemeine Satz, der das Ergebnis des Induktions-Schlusses, die Zusammenfassung einer allerdings unbegrenzten oder mindestens unu¨bersehbaren Menge von Einzelsa¨tzen darstellt, deren jeder auch direkt per analogiam erschlossen werden kann. (. . .) Anderseits aber ko¨nnen wir auch im Analogie-Schluß wenigstens in vielen Fa¨llen die Anwendung eines allerdings nicht ausdru¨cklich zum Bewußtsein gebrachten und ausgesprochenen, aber doch stillschweigend supponierten Induktions-Schlusses erblicken.
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talk about probability. Nonetheless, in the reality of our daily experiences situations are never perfectly equal to one another. von Kries acknowledged that, in practice, it is useful to express uncertainty numerically even when the arbitrariness of analogy undermines the theoretical foundations of any numerical probability measure, and that this is what people actually do. The rationale for doing this, according to von Kries, is the application to non-numerical probabilities of a subjective Taxirung (evaluation) that expresses the confidence in the reliability of the analogies underlying them. However, von Kries worried about the arbitrariness of this procedure: ‘‘We can now examine the question of whether probabilities of any kind can be expressed in numerical form, so that they can be compared with truly numerical probabilities. It seems possible to evaluate a generic probability in such a way as to produce a numerical probability that has the same degree of certainty. In principle there is no objection to such a procedure, but it is necessary to be aware of what it means and of the difficulties that underlie it. If we evaluate numerically the probability of an analogy at 5⁄6 and then consider a case of an expectation where the dimensions of the possibility spaces of alternative outcomes are in the ratio 1:5, we are dealing with heterogeneous contexts, that are incomparable by their very nature. Consequently, their point of equivalence is merely a psychological one. What is compared is the psychological certitude in the two contexts: this is all they have in common’’.5 (von Kries, 1886: 181) If most of our numerical probabilities depend on arbitrary similarity judgements, how do we assess the reliability of a probability value? von Kries built upon Sigwart (1873), Lotze (1874), and Lange (1877), who claimed that probability calculus can be applied after a set of equally possible events has been singled out. Subsequently, higher order probabilities would derive from the combination of these elementary events. von Kries
5
Es darf nun die Frage aufgeworfen werden, ob nicht eine zahlenma¨ssige Darstellung auch anderer, ganz beliebiger Wahrscheinlichkeiten in der Weise Statt finden kann, dass dieselben mit eigentlich numerischen verglichen werden; es erscheint denkbar, jede Wahrscheinlichkeit zu taxiren, indem man diejenige zahlenma¨ssige Wahrscheinlichkeit angiebt, welche mit ihr gleichen Sicherheits-Grad zu haben scheint. Gegen derartige Abscha¨tzungen ist nun zwar principiell gar nichts einzuwenden; es ist aber notwendig, wol zu beachten, welche Bedeutung sie haben und welchen Schwierigkeiten sie unterliegen. Wenn wir den Wahrscheinlichkeits-Wert eines Analogie-Schlusses zahlenma¨ssig taxiren und auf 5/6 angeben, so sind die logischen Verha¨ltnisse jener Analogie und einer freien Erwartungsbildung, bei welcher die Spielra¨ume in dem Gro¨ssen-Verha¨ltniss 1:5 stehen, vollsta¨ndig heterogen und ihrer Natur nach unvergleichbar. Der Vergleichspunkt beider ist demgema¨ss ein lediglich psychologischer; verglichen wird die psychologische Gewissheit, welche in dem einen und dem anderen Falle Statt findet; diese ist das einzige beiden Fa¨llen Gemeinsame.
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thought of a geometrical representation of possibility spaces as they are conceived by the human mind. He called these possibility spaces Spielra¨ume. However, it is of utmost importance to bear in mind that the German word Spielraum means ‘‘space’’ as well as ‘‘clearance’’. Only in the particular case of games of chance do Spielra¨ume exist as crisp sets whose sizes can be compared. However, in general, Spielra¨ume do not have precise boundaries. Rather, they should be thought as fuzzy sets that entail the necessary clearance for events whose probabilities derive from imperfect analogies. To be absolutely precise, even games of chance cannot be grasped by perfectly crisp Spielra¨ume; for instance, because the barycenter of a die is not known with absolute precision, or because frictions on a roulette cannot be distributed with absolute uniformity. Games of chance offer the simplest instances of Spielra¨ume. In this case, the Spielra¨ume conceived by a human mind can be deduced from the objective description of a game: ‘‘Games of chance can be seen as the best approximation to an ideal case where the relationships between Spielra¨ume can be deduced, with a great improvement of our understanding. In fact, the meaning of the Spielraum principle is much easier to grasp if we can proceed from a description of Spielra¨ume’’.6 (von Kries, 1916: 621) In the limiting case of Spielra¨ume that correspond to elementary events that exhaust all possibilities, and if the dimensions of these Spielra¨ume can be compared to one another, probabilities can be expressed numerically: ‘‘The final result of our logical research is that hypotheses can be cast into numerical probability relations if they correspond to elementary Spielra¨ume whose dimensions can be compared to each another, and that particular probability values arise if these hypotheses exhaust all possibilities’’.7 (von Kries, 1886: 36)
6 Ja, man kann sagen, daß das, was in den realen Zufalls-Spielen gegeben und beachtenswert ist, gerade als eine weitgehende Anna¨herung an jenen idealen Fall am einfachsten und zutreffendsten beschrieben wird. Und namentlich darf auch bemerkt werden, daß die deduktive Betrachtung der Spielraums-Verha¨ltnisse unser Versta¨ndnis in wertvoller Weise vervollsta¨ndigt. Denn die Bedeutung des Spielraums-Prinzips gewinnt ohne Zweifel in hohem Maße dadurch an Greifbarkeit und Anschaulichkeit, daß wir die Spielra¨ume, um die es sich handelt, in ganz direkter Weise angeben und bezeichnen ko¨nnen. 7 Als Gesamt-Ergebniss der logischen Untersuchung erhalten wir somit den Satz, dass Annahmen in einen zahlenma¨ssig angebbaren Wahrscheinlichkeits-Verha¨ltniss stehen, wenn sie indifferente und ihrer Gro¨sse nach vergleichbare urspru¨ngliche Spielra¨ume umfassen, und dass bestimmte Wahrscheinlichkeits-Werte sich daher da ergeben, wo die Gesammtheit aller Mo¨glichkeiten durch eine Anzahl solcher Annahmen erscho¨pft werden kann.
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von Kries was eager to stress that Spielra¨ume are by no means objective properties of dice or anything else we can express a probability about. On the contrary, they are constructed by the person who evaluates a probability subjectively, though not without reference to empirical knowledge: ‘‘Any probability statement requires first of all a list of cases that appear equally possible to our present and individual state of knowledge. Thus, they are of a subjective nature. However, since probability statements are only possible in connection with a particular knowledge having an objective meaning, and since this knowledge contributes to probability expressions, we can say that probability statements have an objective meaning, too’’.8 (von Kries, 1886: 76) Contrary to modern subjectivists, however, von Kries did not prescribe any numerical probability judgement in cases where no empirical knowledge is available. The following discussion of a well-known paradox highlights that the ‘‘principle of sufficient reason’’ is actually not sufficient to establish numerical probabilities everybody would agree upon: ‘‘If we know that an urn contains an equal number of black and white balls, we estimate the probability of drawing a black (white) ball as 1⁄2. According to the principle [of sufficient reason], we should reach the same result if we only knew that the urn contains black and white balls, without knowing anything about their proportions’’.9 (von Kries, 1886: 8) ‘‘Let us come back to the example of an urn containing black and white balls in unknown proportions. The idea that each single ball could be indifferently black or white appears to be just as sensible as the idea that black and white balls are present in equal proportions. But this consideration leads to a uniform probability over all possible proportions of black and white balls! Moreover, further reflections lead us to still different claims. We could say equally well 8
Wahrscheinlicjkeits-Satz entha¨lt zuna¨chst und unmittelbar eine Aufstellung von Fa¨llen, welche bei unserem gegenwa¨rtigen individuellen Wissens-Stande gleich mo¨glich erscheinen, hat also eine subjective Bedeutung. Da aber eine solche Aufstellung num im Anschluss an gewisse Kenntnisse von objectiver Bedeutung mo¨glich ist, so gelangen auch diese in dem Wahrscheinlichkeitssatze zum Ausdruck, und man darf daher sagen, dass derselbe implicite auch einen objectiven Sinn besitzt.
9
Wenn wir wissen, dass in einem Gefa¨sse gleich viele schwarze und weisse Kugeln enthalten sind, so setzen wir die Wahrscheinlichkeit, bei einer Ziehung eine weisse oder eine schwarze Kugel zu erhalten, gleich, und beziffern beide mit 1⁄2. Dieselbe Ansetzung der Wahrscheinlichkeit wu¨rde unserem Princip nach auch dann gerechtfertigt sein, wenn wir u¨berhaupt nur wu¨ssten, dass schwarze und weisse Kugeln in dem Gefa¨sse sind, wa¨hrend ihr Zahlen-Verha¨ltniss uns ganz unbekannt wa¨re.
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that the simplest assumption is that the urn is either filled with balls of only one color, or with a mixture of balls of both colors. Hence, if the urn contains 1000 balls we should attach higher probabilities to the urn containing a thousand, five hundred or no black balls than, to say, the urn containing 873 black balls. Clearly, the attempt of a comprehensive decomposition of all possibilities gets lost in a maze’’.10 (von Kries, 1886: 33) Neither a frequentist nor a subjectivist, von Kries was essentially an advocate of the logical view of probability. But his was a very original version of the logical view, one that called for a novel logic. Without pretending to lay down a comprehensive list of the forms of human thinking, von Kries distinguished between Werturteile (value judgements), Real-Urteile (reality judgements), and Beziehungs-Urteile or Reflexions-Urteile (relation judgements). Value judgements, which include aesthetic and moral judgements, fell outside the scope of his investigation. Reality judgements represent ‘‘the first, basic way a subject grasps reality’’ (von Kries, 1916: 36), purely subjective understanding such as ‘‘sweet’’ or ‘‘red’’ (von Kries, 1916: 38), symbols that acquire a meaning when they are linked to the corresponding properties of an empirical object (von Kries, 1916: 40). von Kries devoted much attention to reality judgements, but not the whole of his Logik (von Kries, 1916) can be reported here. Rather, we shall focus on relation judgements, which include probability judgements. Relation judgements connect mental representations to one another (von Kries, 1916: 33). von Kries did not claim that it is possible to provide an exhaustive list of relation judgements, but deemed it sensible to focus on the following ones: analytische Urteile (analytical judgements), Subsumtions-Urteile or Inzidenz-Urteile (subsumption judgements),
10
Kommen wir nunmehr auf das Beispiel eines Gefa¨sses, welches mit teils schwarzen teils weissen Kugeln gefu¨llt ist, nochmals zuru¨ck. Auch hier erscheint zuna¨chst die Vorstellung, dass jede einzelne Kugel ebensowol schwarz wie weiss sein ko¨nne, im Allgemeinen ebenso berechtigt, wie die oben erwa¨hnte; nach dieser letzteren sollte die Annahme, dass irgend eine beliebige Zahl der Kugeln schwarz und die anderen weiss seien, einen bestimmten, fu¨r jede hier gewa¨hlte Zahl gleichen Wahrscheinlichkeits-Wert haben; nach der ersteren wu¨rde mit u¨berwiegender Wahrscheinlichkeit zu erwarten sein, dass anna¨hrend gleich viele schwarze und weisse Kugeln vorhanden sind. Auch hier aber fu¨hren weitere Ueberlegungen zu noch ganz anderen Ansa¨tzen. Wir ko¨nnten recht wol auch sagen, dass die Fu¨llung des Gefa¨sses mit Kugeln bloss einer Sorte, und anderseits eine zufa¨llige Durcheinandermischung beider Sorten am ehesten anzunehmen sei; es wu¨rde danach, wenn tausend Kugeln vorhanden sind, den Annahmen, dass tausend, dass fu¨nfhundert oder dass gar keine schwarz sei, gro¨ssere Wahrscheinlichkeit zugeschrieben werden mu¨ssen, als etwa der, dass 873 schwarz seien. Der Versuch einer vollsta¨ndigen Zergliederung aller Mo¨glichkeiten wu¨rde sich in ein endloses Labyrinth verlieren und notwendig resultatlos bleiben.
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judgements value judgements relation judgements
reality judgements
subsumption judgements
analytical judgements logical judgements analogy
mathematical judgements
induction
Fig. 1. von Kries’s classification of relation judgements.
mathematische Urteile (mathematical judgements) and judgements that establish a dependence, of which the logische Urteile (logical judgements) are the most important ones. Among logical judgements we find analogy and induction, which originate probability statements. Figure 1 summarises von Kries’s classification, where empty ovals are there to remind that von Kries did not pretend it to be exhaustive. According to this scheme, probability arises as a logical judgement, from analogy and induction. However, in order to understand analogy and induction, it is necessary to explain the difference between analytical judgements and subsumption judgements. Analytical judgements establish a relation between a synthetic concept and its components. A synthetic concept can be explained by means of a definition, and its parts can be derived by means of deductive logic. Subsumption judgements, on the other hand, establish what von Kries called a ‘‘synchytic’’ concept. In contrast to synthetic concepts, synchytic concepts cannot be explained by means of a definition, but only by means of examples. ‘‘The [subsumption] judgement is to the construction of a synchytic concept like the analytical judgement is to the construction of a synthetic concept. Both processes provide the material of our thinking out of given elements, but [in the case of the construction of a synchytic concept] we are not able to overview these elements.
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Consequently, we can describe the ensuing concepts and relationships only by means of examples’’.11 (von Kries, 1916: 11) Furthermore, synchytic concepts cannot be crisp and clear-cut: ‘‘In most cases we are not able to overview all the elements that such concepts entail. And where we can provide a systematic description of the multiplicity of our sensations, as e.g. for the concept ‘‘red’’, we are not able to fix a precise sensation as the border of the concept. Even less with more complex concepts like accident, State, etc. We must conclude that, because of their very construction process, all synchytic concepts are to some extent imprecise’’.12 (von Kries, 1916: 12) Although von Kries did not use the modern terminology, he was actually dealing with mental categories and the way they aggregate information. In particular, the two passages quoted above anticipate the following basic tenets of modern psychology: 1. In general, mental categories have fuzzy boundaries; 2. Each member of a mental category has a similarity with some other members of the category, but not necessarily with all of them. Consequently, mental categories may not entail a group of objects that share common features. Both circumstances prevent categories like. ‘‘game’’ from being described by means of a definition, although a few examples suffice to convey their meaning. Using his personal terminology, von Kries defined probability judgements as subsumption judgements that, in general, would arrive at synchytic concepts. As such, they are not susceptible of a numerical evaluation: ‘‘When we judge two expectations or two hypotheses to be equally probable, we make a comparison of the same kind as when we 11
Wie schon bemerkt, steht ja das Inzidenz-Urteil in der na¨mlichen Beziehung zu der synchitischen, wie das analytische zu der synthetische Begriffsbildung. Mit diesen beiden Arten der Begriffsbildung sind die Funktionen bezeichnet, vermo¨ge deren wir das begriffliche Material unseres Denkens aus irgendwelchen in anderer Weise gegebenen Elementen bilden. Wir sind aber nicht in der Lage, diese Elemente selbst ohne weiteres zu u¨bersehen oder aufzuza¨hlen. Und wir ko¨nnen dem gema¨ß jene logischen Funktionen und die aus ihnen resultierenden Beziehungen zuna¨chst nur an einzelnen Beispielen aufweisen. 12
In der Tat sind wir ja meist nicht in der Lage, die Gesamtheit des Einzelnen, was ein solcher Begriff umfassen soll, u¨bersichtlich darzustellen. Und wo wir, wie z.B. beim Begriffe Rot, eine systematische Darstellung der hierhergeho¨rigen Empfindungs-Mannigfaltigkeit geben ko¨nnen, sind wir doch nicht in der Lage, irgendeine bestimmte Empfindung zu fixieren, die die Grenze des rot zu nennende ausmachte. Noch weniger ko¨nnen wir bei verwickelteren Begriffen, wie Unfall, Staat u. dgl., daran denken, sie als Zusammenfassung einer aufza¨hlbaren Menge scharf angebbarer Beispiele zu betrachten. Alle synchytischen Begriffe sind also, wie das mit der ganzen psychologischen Natur ihrer Bildung zusammenha¨ngt, mehr oder weniger unbestimmt.
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say that two sensations are equally strong, or that two differences of sensations are equally large or equally clear, and so on. Now, (. . .) we must distinguish very carefully this concept of equality from the strict and definitive equality concept of mathematical expressions. The equalities that are expressed in these statements basically mean that the relationships between the objects to be compared can neither be expressed in terms of more nor in terms of less, but the broad range spanned by these comparisons rests on an even broader and correspondingly imprecise meaning of this more or less, stronger or weaker, and so on. Thus, we can consider these comparisons as [subsumption] judgements (...) that construct an imprecise [equality] concept’’.13 (von Kries, 1916: 596) At this point, we can summarise von Kries’s probability theory along the following lines. Probability judgements are analogy and induction relations, linking statements that can be represented by Spielra¨ume in a possibility space. Depending on the goodness of the underlying analogies, Spielra¨ume can be grasped with varying degree of precision. Strictly speaking, only in the abstract case of games of chance that are known with absolute precision (i.e. a perfect die) Spielra¨ume can be compared in a mathematical sense and probabilities can be calculated. In all other cases, probabilities are subsumption judgements, which are not numerical because their comparison is inherently imprecise. However, even in these cases a subjective Taxirung can provide a numerical, although arbitrary, probability value. In practice, real-world games of chance are so close to being perfectly known that the amount of Taxirung is negligible. Consequently, probabilities can be safely considered to be numerical. In other fields, such as medical or social statistics, a remarkable amount of subjective Taxirung is necessary in order to yield numerical values but arbitrariness (e.g. in the definition of macroeconomic magnitudes) may be covered up by conventions. Finally, there are situations where analogies are so poor that the 13
Das Urteil, das wir aussprechen, indem wir zwei Erwartungen oder zwei Annahmen in diesem Sinne gleich wahrscheinlich nennen, ist offenbar ein Vergleichungs-Urteil in dem fru¨her des Genaueren besprochenen Sinne, ganz a¨hnlich wie wenn wir zwei Empfindungen gleich stark, zwei Empfindungs-Unterschiede gleich groß oder gleich deutlich nennen usw. Nun wurde schon oben betont, daß wir den in solche Sa¨tze eingehenden Gleichheits-Begriff wohl unterscheiden mu¨ssen von dem strengen und endgu¨ltigen der mathematischen Sa¨tze. Die Gleichsetzungen, die in diesen Sa¨tzen ausgesprochen werden, bedeuten im Grunde, daß die Beziehungen der beiden verglichenen Objekte sich weder als ein Mehr noch als ein Minder bezeichnen lassen. Der weite Umfang, in dem solche Vergleichungen ausgefu¨hrt werden ko¨nnen, beruht auf dem u¨beraus weiten, aber auch entsprechend unbestimmten Sinne dieses Mehr oder Weniger, Sta¨rker oder Schwa¨cher usw. Wir ko¨nnen solche Vergleichungen also auch auffassen als Aussagen einer Inzidenz (einer durch den Sinn des allgemeinen Begriffes gegebenen Zugeho¨rigkeit) zu jenen unbestimmten Begriffen.
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amount of Taxirung necessary to yield a numerical probability is so high, and conventions so shaky, that individuals are not able to express any numerical probability at all. This does not mean that they are unable to point out that a certain event is ‘‘probable’’, but merely that this probability cannot take a numerical value.
3. SOME CONSEQUENCES FOR EXPERT SYSTEMS Through a series of passages and in spite of serious misunderstandings, von Kries had a strong influence on John Maynard Keynes (Fioretti, 1998, 2001, 2003), the economist whose name is associated with the possibility of underemployment equilibria (Keynes, 1936). Keynes realised that, if numerical probabilities arise out of subjective evaluations that may have a tenuous relationship with the objective reality, then the only possibility for reaching an agreement is that of sticking to a convention. If we are in a traditional domain where age-old conventions exist, they will probably persist. But how do people behave if a convention has to be established? Keynes illustrated the point by means of a simple example: a beauty contest launched in his times by a popular magazine. Readers were confronted with a series of pictures of women whose beauty they were asked to rate. The winning reader was the one who ranked the pictures in the same order as the average reader would. Readers would not be motivated to express their vote according to a personal idea of beauty, but rather according to what they thought the mean idea of beauty probably was. Clearly, this game has no fixed point. The idea of beauty can never settle at a stable equilibrium. Even if a conventional equilibrium is eventually reached, it will not be stable with respect to exogenous perturbations. In general, the oscillations of the idea of beauty will depend on the structure of the communications between the subjects involved, on how many magazines there are and how many readers each has or, in our age, on more powerful visual media, such as television or the internet. Many domains of applied research rely heavily on conventions in order to yield numerical values. Computational models of climate change are a case in point. Variables are numerous, there are multiple feedback loops among variables and, as if that is not enough, climate is characterised by sharp and unpredictable phase transitions. Under such conditions, computer models may potentially yield any number of conceivable results. Instead, researchers have observed some convergence towards a series of conventional estimates. This is not to say that models never differ in their outcomes: differences do occur, and frequently enough to spur strident policy debates. However, researchers apparently care that
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some key outputs of their models such as the prospective annual variations of temperature in particular areas of the planet are not too distant from the outcomes of previous models. Too different a result may suggest that the new model is wrong, so it is safer for a researcher to maintain received wisdom rather than reject it altogether (van der Sluijs, 1997). Medicine may be no less complex than global warming. As von Kries pointed out long ago, not only do a large number of variables interact with one another to produce surprising outcomes, but even the very definition of outcomes is subject to interpretation. How may expert systems impact on such a field? Surely, they will help eliminating wrong diagnoses. May be they will eliminate innovative, better diagnoses as well? A main rationale for making use of expert systems in medical diagnosis is that they may reduce the variance of treatments by diffusing best practices (Fox and Das, 2000). At the time expert systems are first introduced, it is clear what the best practices are. Thus, the initial adoption of expert systems has only advantages for patients. The question is, what happens after that? How will the knowledge embedded in expert systems be updated? In particular, the following two difficulties may be envisioned: 1. As von Kries pointed out, the identification of a set of possibilities may not be straightforward in medicine. Indeed, the very process of defining a new category for a disease, of recognizing a new symptom or aggregating well-known symptoms in a novel way, may conduct to fundamental discoveries and substantial improvements. It is a ‘‘synchytic’’ judgement, one that requires openness of mind and readiness to accept and formulate novel hypotheses. To the extent that a physician delegates diagnosis to an expert system, the process of hypothesis formulation is constrained by the accepted wisdom. Innovating may become difficult. 2. Suppose that an innovation is made, but not necessarily in a major research centre of big science. A better procedure for making diagnoses, a more effective drug for a particular disease, an improvement of a surgical procedure. How can this innovation be included in the next generation of expert systems? Innovations may be many and not very visible to software houses, they may compete with one another, a judgement on their validity may be influenced by personal idiosyncrasies or preferential commercial relations, and the very relevance of an innovation may be subject to subjective guess and unwarranted beliefs. Similar to the case of the beauty contest, the adoption of innovations by expert systems depends on the shape of the network of relations that channels and distributes information. Hopefully, we may find ways to avoid such undesirable developments. Most importantly, expert systems should be so designed that physicians
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understand what the machine is doing and are allowed to re-program it, perhaps by means of a visual programming language. If flexible enough, expert systems may even help physicians to formulate novel ‘‘synchytic’’ judgements. Possibly, expert systems for medical diagnoses should not be monopolised by a few software houses. Indeed, the successful experience of open source and free software stands as a strong indication of what may be done in order to keep network structures flexible and productive (Raymond, 1999). Creative expert systems that are able to stimulate tentative ‘‘synchytic’’ judgements by their users would have a positive impact on information networks, from professional associations to chat rooms to mailing lists. To the extent that people understand what a machine is doing and are empowered to change what it is doing, they can ensure that conventions, as encoded in expert systems, evolve rapidly towards the emerging best practice.
4. CONCLUSIONS von Kries stands as a prominent figure in the development of probability theory, a very original thinker who has been unduly neglected. His greatest originality lies in considering the cognitive processes that originate a set of possibilities in the mind of a decision-maker. Essentially, he singled out conditions for the validity of the premises from which every probability theory starts. His experience as a physician enabled him to think creatively because he was not biased to consider throwing dice or playing roulette as prototypical situations in which uncertainty arises. Incidentally, it is interesting to note that another fundamental development in the mathematics of uncertain reasoning, Evidence Theory, originated from a scenario in which the thinking process of a judge evaluating testimonies is used as the prototypical setting for uncertainty (Shafer, 1976). In effect, a physician evaluating symptoms is in quite a similar situation as a judge evaluating testimonies: moreover, both of them are conceptually far from playing dice. Once again, we find a similarity between medicine and other disciplines in which the development of problem solving strategies begins with the recognition of clues. von Kries was incredibly ahead of his time and it is curious that his work has received so little scholarly attention. To my knowledge, no English translation of his works yet exists. Only recently have English-speaking cognitive scientists arrived at the same understanding of mental categories that von Kries developed over a century ago. Perhaps von Kries would
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have received greater credit for his work, had not the destruction of German culture under the Nazis and the ensuing disaster of World War II occurred. A more important reason may be the predominance of subjective probability theory, which emerged in the 1930s. Within a paradigm that pretends to mathematise any form of uncertainty by forcing people to make bets, the questions posed by von Kries make no sense. Nowadays, expert systems for medical applications are making us understand that these questions do make sense, and that they are very important indeed.
REFERENCES Fioretti, G., 1998. John Maynard Keynes and Johannes von Kries. Hist. Econ. Ideas 6, 51–80. Fioretti, G., 2001. von Kries and the other ‘‘German Logicians’’: Non-numerical probabilities before Keynes. Econ. Philos. 17, 245–273. Fioretti, G., 2003. No faith, no conversion: The evolution of Keynes’s ideas on uncertainty under the influence of Johannes von Kries. In: Runde, J., Mizuhara, S. (Eds.), Perspectives on the Philosophy of Keynes’s Economics: Probability, Uncertainty and Convention. Routledge, London, pp. 130–139. Fox, J., 2003. Probability, logic and the cognitive foundations of rational belief. J. Appl. Logic 1, 197–224. Fox, J., Das, S., 2000. Safe and Sound: Artificial Intelligence in Hazardous Applications. MIT Press, Cambridge, USA. Ginzburg, C., 1986. Spie: radici di un paradigma indiziario. In: Miti, emblemi, spie: morfologia e storia. Einaudi, Turin, pp. 158–209. Keynes, J.M., 1936. The General Theory of Employment, Interest and Money. MacMillan, London. Kries, J. von, 1886. Die Principien der Wahrscheinlichkeitsrechnung. Verlag von J.C.B. Mohr (Paul Siebeck), Tu¨bingen. Kries, J. von, 1916. Logik. Verlag von J.C.B. Mohr (Paul Siebeck), Tu¨bingen. Kries, J. von, 1923. Allgemeine Sinnesphysiologie. Verlag von F.C.W. Vogel, Leipzig. Kries, J. von, 1925. Johannes von Kries. In: Grote, L.R. (Ed.), Die Medizin der Gegenwart in Selbstdarstellungen. Verlag von Felix Meiner, Leipzig. Lange, F.A., 1877. Logische Studien. Verlag von J. Baedecker, Iserlohn. Lotze, R.H., 1874. Logik. Verlag von S. Hirzel, Leipzig. Raymond, E.S., 1999. The Cathedral and the Bazaar. O’Reilly, Sebastopol, USA. Shafer, G., 1976. A Mathematical Theory of Evidence. Princeton University Press, Princeton. Sigwart, C., 1873. Logik. Verlag der H. Laupp’schen Buchhandlung, Tu¨bingen. Sluijs, J. van der, 1997. Anchoring amid Uncertainty. CIP˜ Gegevens Koniklijke Bibliotheek, Den Haag.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
9 Reliability of measurements in medical research and clinical practice David Y. Downhama, Anna Maria Holmba¨ckb and Jan Lexellb,c,d a
Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK b Department of Physical Therapy, Lund University, Lund, Sweden c Department of Rehabilitation, Lund University Hospital, Lund, Sweden d Department of Health Sciences, Lulea˚ University of Technology, Lulea˚, Sweden
1. INTRODUCTION In medical research and clinical practice, measurements are regularly obtained for different purposes: for example, to detect and to diagnose a disease, to plan an appropriate intervention for a patient, to assess the short-term effects of an intervention on a patient, and to assess the longterm effects on a group of patients. To be clinically and scientifically useful, any method of measurement should be valid, reliable, and sufficiently sensitive. Measurements are valid if they measure what they purport to measure. They are reliable if they are reproducible and stable over time, and if they display adequate absence of measurement errors. The method of measurement must also be sufficiently sensitive for a specific purpose: if the main purpose of a measurement of a patient’s performance in several tasks is to identify clinically important changes, then the method should be sufficiently sensitive to detect such changes. By applying well-defined techniques, studies can be undertaken to ascertain whether or not a method of measurement is reliable. If a method of measurement is found to be reliable, it could be used in research on many individuals, and/or for clinical practice where a medical intervention for an individual is evaluated. Reliability in medical research and clinical practice is often determined for continuous data in inter-rater (between 147
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raters) or intra-rater (between occasions) studies (Rothstein, 1985; Bland and Altman, 1986; Atkinson and Nevill, 1998). The first two parts of the evaluation of reliability are: 1. The analysis of agreement between measurements, commonly referred to as ‘‘relative reliability’’, and 2. Assessments of measurement errors and systematic changes in the mean, commonly referred to as ‘‘absolute reliability’’. The analysis of agreement between measurements examines the relationship between two or more sets of repeated measurements, whereas the analysis of measurement errors and systematic changes in the mean examines the variability of the scores from one measurement to the other measurement. The third part of a reliability analysis is to assess whether the method of measurement is sufficiently sensitive to do a particular task: if the intended use is to identify a ‘‘clinically relevant’’ or ‘‘true’’ change, then the method should be sufficiently sensitive to detect such a change. This notion is sometimes referred to as ‘‘responsiveness’’. Many different approaches have been described to evaluate ‘‘clinically relevant changes’’ in measurements, but there is no general agreement on which approach to use (Terwee et al., 2003). Several methods are required to fully address the reliability of a method of measurement (see, for example, Rothstein, 1985; Atkinson and Nevill, 1998; Bland and Altman, 1999; Holmba¨ck et al., 1999, 2001). In this chapter we review methods of assessing reliability for continuous data in medical research. We address briefly related issues such as sample size and power, and discuss the concept of responsiveness. The analyses are illustrated using measurements of muscle performance. We also discuss how reliability studies can aid scientists and clinicians in the interpretation of results from interventions, both at the group level and for individual patients.
2. MUSCLE STRENGTH Isokinetic dynamometry is frequently used to assess muscle performance, both in research and in clinical practice. The applicability of an isokinetic dynamometer depends upon the reliability of the measurements, which in turn depends upon both the equipment and the test protocol. Holmba¨ck et al. (1999, 2001) studied the test–retest reliability of several different measurements of isokinetic ankle dorsiflexor muscle strength using the Biodex dynamometer, one of the several dynamometers commercially available. We utilise some of the data from these studies to illustrate the evaluation of reliability for continuous medical data.
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60
Test session 2
50 40 30 20 10 10
20
30
40
50
60
Test session 1
Fig. 1. To illustrate the analysis of reliability, measurements of isokinetic ankle dorsiflexor muscle strength are used. The data were obtained from 30 healthy young men and women at two test sessions seven days apart.
Ankle dorsiflexor muscles are important for gait and balance. To establish if the Biodex dynamometer could be used to reliably measure the performance of the ankle dorsiflexor muscles, strength was measured for each of 30 healthy young men and women on two occasions separated by one week (Holmba¨ck et al., 1999). At each test session, three non-consecutive maximal concentric contractions were performed for each of five angular velocities in the following order: 30, 60, 90, 120, and 1508/s. Strength is recorded as Newton meter (Nm) and the strength measurements at 308/s from the two test sessions are used in this chapter to illustrate the evaluation of reliability. The measurements are plotted in fig. 1.
3. ASSESSMENT OF RELIABILITY WITH CONTINUOUS DATA Reliability refers to the consistency of a measurement, when all conditions are thought to be constant (Rothstein, 1985). For measurements to be considered reliable, they must be comparable when performed on several occasions with the same subject by the same rater (intra-rater reliability), or when performed with the same subject by different raters (inter-rater reliability) (Baumgartner, 1989). Different types of reliability data require different statistical methods, but there is a lack of consensus in the literature as to which methods are most appropriate (Atkinson and Nevill, 1998; Rankin and Stokes, 1998). The main statistical measures in reliability
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studies with continuous data are different forms of analysis of agreement between measurements and of analysis of measurement errors, which include measures of the within subject variation and the detection of systematic changes in the mean between test sessions (Baumgartner, 1989; Domholdt, 1993; Atkinson and Nevill, 1998; Hopkins, 2000).
4. ANALYSIS OF AGREEMENT BETWEEN MEASUREMENTS Here, the relationship between two or more sets of repeated measurements is examined by the intra-class correlation coefficient (ICC) and/or Pearson’s r. If each subject has an identical value in the two test sessions, both ICC and Pearson’s r have value 1, and in a plot of the values of the two test sessions all points lie on the straight line with gradient 1 that passes through the origin. The ICC assesses the closeness of the points to the line with gradient 1, whereas Pearson’s r assesses the proximity to any straight line. Furthermore, the ICC can be applied more readily in the evaluation of the reliability for more than two sets of measurements. However, both ICC and Pearson’s r can give misleading results because their values are highly sensitive to the heterogeneity (or spread) of the measurements between subjects. It follows that the analysis of reliability cannot be based only on ICC or Pearson’s r and must be complemented by an analysis of measurement errors.
4.1. Intraclass correlation coefficient (ICC) Different ICCs are available for different study designs. The three commonly used ICCs are ICC1,1, ICC2,1, and ICC3,1. From a statistical standpoint the differences between these ICCs are how error variance (lack of reliability) is accommodated (Shrout and Fleiss, 1979; Baumgartner, 1989). ICC can be calculated from repeated measures analysis of variance (a one-way or two-way ANOVA) and is obtained by dividing the true variance by the total variance. When individuals are the objects of the measurements, the ‘‘true’’ variance represents the variance among individuals (Shrout and Fleiss, 1979; Roebroeck et al., 1993; Stratford and Goldsmith, 1997). For intra-rater test-retest reliability, ICC1,1 or ICC2,1 are appropriate (Fleiss, 1986; Rankin and Stokes, 1998). To examine inter-rater test-retest reliability, ICC2,1 or ICC3,1 are recommended, depending on the study design (Shrout and Fleiss, 1979). Generally, in clinical practice or in scientific research, ICC2,1 is often appropriate as the raters can be considered to be randomly selected from a
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large population of raters. If testing is only to be performed by a limited number of raters, i.e. a fixed number, ICC3,1 is used. ICC2,1 and ICC3,1 can be calculated from a two-way random or fixed effects model, whereas ICC1,1 is calculated from a one-way random effects model (Rankin and Stokes, 1998). In practice, the values of the different ICCs are often very similar and the choice between different ICCs can be considered to be almost philosophical (Baumgartner, 1989; Holmba¨ck et al., 2001). The three forms of ICC for n subjects and for two test sessions are expressed in Equations (1), (2), and (3) in terms of three mean squares terms: ICC1,1 ¼ ðBMS WMSÞ=ðBMS þ WMSÞ
ðEq: 1Þ
ICC2,1 ¼ ðBMS EMSÞ=ðBMS þ EMS þ 2ðJMS EMSÞ=nÞ
ðEq: 2Þ
ICC3,1 ¼ ðBMS EMSÞ=ðBMS þ EMSÞ
ðEq: 3Þ
where BMS represents the variability between subjects, WMS the variability in the measurements within subjects, JMS represents the variability between test sessions and EMS represents the variability remaining when the between and within subjects variability has been accommodated. In particular, BMS is the between subjects mean square, WMS is the within subjects mean square, EMS is the residual mean square, and n is the number of subjects. The equivalent expressions for more test sessions and more testers have been reported (Shrout and Fleiss, 1979). Data from fig. 1 for the 30 men and women from the two test sessions are used to illustrate the terminology and the calculations of ICC2,1. A two-way analysis of variance (ANOVA) for the model peak torque at 30=s ¼ K þ subject effect þ test session effect
ðEq: 4Þ
is presented in table 1. The value of ICC2,1 for the peak torque at 308/s for the 30 men and women is 0.915 and an approximate 95% confidence interval is (0.83, 0.96). Equations for approximate confidence intervals for the ICCs have been expressed in terms of the entries in the ANOVA table (Shrout and Fleiss, 1979). They are algebraically complicated, especially for ICC2,1.
4.2. Comparison between ICC and Pearson’s r As previously mentioned, ICC assesses the proximity of the points to the straight line with gradient 1 that passes through the origin, whereas Pearson’s r assesses the proximity to any straight line. In other words,
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Table 1 Two-way analysis of variance (ANOVA) for Equation (4) Source of variation Between subjects With subjects Between test sessions Residual Total
Degrees of freedom
Sum of squares
Mean squares
Name
29 30 1 29 59
2608.25 119.94 0.0135 119.92 2728.19
89.94 4.00 0.0135 4.14
BMS WMS JMS EMS
ICC assesses the agreement between repeated measurements whereas Pearson’s r assesses the closeness to a linear fit. Consequently, Pearson’s r could indicate high reliability, even when there is systematic bias in the data. When the data in fig. 1 are analysed using ICC and Pearson’s r, the values for the two coefficients are both 0.91. Holmba¨ck et al. (1999) calculated ICC and Pearson’s r for several sets of data and found the pairs of values to be close, especially if systematic bias in the data was low: the largest difference in any pair was 4%. In the investigation of the closeness of Pearson’s r and ICC2,1, Pearson’s r was expressed in terms of ICC2,1: r ¼ ICC2,1 0:5 ðk þ 1=kÞð1 þ ½2 ðJMS EMSÞ=ðn ðBMS þ EMSÞÞÞ ðEq: 5Þ where k2 is the ratio of the variances of the measurements in test 1 and test 2 and n is the number of subjects (Holmba¨ck et al., 1999). Let K ¼ 0.5 (k þ 1/k); when k is close to one, which occurs often in practice, K is close to unity. If the variance pffiffiffiffiffiffiffi of the measurements in test 1 is 50% more than in test 2, then k ¼ 1:5 and the value of K is 1.021. For n not small, the value of (1 þ [2(JMS EMS)/(n(BMS þ EMS))]) is close to unity. If JMS exceeds EMS, then r is larger than ICC. If JMS is less than EMS, ICC2,1 may be larger than r, but r could be less than ICC2,1 for K close to one. Thus, it is not surprising that ICC2,1 and Pearson’s r often take similar values.
4.3. Interpretation of the values of ICC Shrout and Fleiss (1979) suggested that specific values of ICC could be considered to represent acceptable, good, and fair reliability. They suggested that the minimally acceptable ICC coefficient for reliability is 0.75 to 0.80. Fleiss (1986) later recommended that ICC values above 0.75
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represent excellent reliability and values between 0.4 and 0.75 represent fair to good reliability. Some authors have adopted these recommendations. However, Atkinson and Nevill (1998) argued that no clear definition of acceptable ICC ‘‘cut-off ’’ points for practical use has yet been presented. As the acceptable degree of repeatability depends upon the purpose of the measurements – that is, the specific application – the global use of terms such as ‘‘good reliability’’ should be avoided.
4.4. Sample size and power of ICC In comparison with clinical trials, sample sizes have received little attention in the reliability literature. Some researchers have recommended specific sample sizes. As these recommendations are based more upon experience than power considerations, they are likely to reflect the sort of applications addressed by the researcher. A sample size of 15 to 20 individuals has been recommended for reliability studies with continuous data (Fleiss, 1986), and this size has been adopted in many reliability studies. Larger sample sizes, 30 to 50 individuals, have been suggested more recently (Baumgartner, 1989; Hopkins, 2000). The calculation of sample sizes has been addressed (Donner and Eliasziw, 1987; Walter et al., 1998), but has not been exploited in the medical field. We summarise here the arguments, which are based on the hypothesis tests of ICC1,1 ¼ say. The null hypothesis H0 : ¼ 0 is tested against the alternative hypothesis H1 : ¼ 1 4 0 for a given significance level and power 1-. Donner and Eliasziw (1987) display contours for the sample sizes necessary to reject H0 for values of 1 that are meant to represent ‘‘slight’’, ‘‘fair’’, ‘‘moderate’’, ‘‘substantial’’ and ‘‘almost perfect’’ reliability. Their calculations and contours were based upon ¼ 0.05 and ¼ 0.2, which represent a significance level of 5% and a power of 80% – typical values in sample size calculations for clinical trials. As this method for determining exact sample sizes is difficult to interpret and computationally expensive, it cannot be easily exploited. Walter et al. (1998) developed the following method that provides close approximations and is easy to interpret. Consider n measurements per subject, significance level and power 1-. If U is the 100(1 ) per cent
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point in the cumulative normal distribution, U and U can be obtained for given and , and C is as follows: C ¼ ð11 Þð1 þ ðn 1Þ0 Þ=fð1 0 Þð1 þ ðn 1Þ1 Þg
ðEq: 6Þ
The number of subjects, required to reject H0 in favour of H1 at a given significance level and power (1-) is approximately 2 1 þ 2ðn=ðn 1ÞÞ ðU þ U Þ=lnðC ÞÞ
ðEq: 7Þ
As the number of subjects for different values of n can easily be calculated, resources and cost at the planning stage can be included into the design of a study. However, there is still the problem of the formulation of H0 and H1: that is, the specification of the problem in terms of 0 and 1.
5. ASSESSMENTS OF MEASUREMENT ERRORS AND SYSTEMATIC CHANGES IN THE MEAN Basing a reliability argument only upon ICC has been questioned (Madsen, 2002): for example, the comparison of ICCs calculated in different reliability studies should be made with caution. As the reliability of a method of measurement cannot be assessed comprehensively by considering only ICC, the reliability analysis must also include the assessments of measurement errors and systematic changes in the mean. Several methods and indices of measurement errors and systematic changes in the mean have been considered in the literature (see, for example, Atkinson and Nevill, 1998). The most commonly used are described in this section, and the data from fig. 1 are used to illustrate the calculations of these indices of measurement error and and systematic changes in the mean.
5.1. Indices of measurement errors Errors of measurement quantify the within subject variation and represent the degree by which repeated measurements vary for individuals (Baumgartner, 1989; Domholdt, 1993), often referred to as the within subject variation (Hopkins, 2000). These measurements are some of the most important types of reliability measures for scientists and clinicians to use when, for example, changes in a group of individuals’ or in a single individual’s performance are to be detected. A change in performance is easier to detect when the within subject variation is small (Atkinson and Nevill, 1998; Hopkins, 2000). The within subject variation, sometimes
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referred to as the ‘‘typical error’’ (Hopkins, 2000) or the ‘‘method error (ME)’’ (Portney and Watkins, 1993), can be calculated simply by dividing the pstandard deviation of the mean difference scores for each individual ffiffiffi by 2 pffiffiffi ME ¼ SDdiff = 2
ðEq: 8Þ
where SDdiff is the standard deviation of the differences between two measurements. It can be shown that, if there are n pairs, then ME2 ¼ EMS
ðEq: 9Þ
where EMS is defined in the ANOVA table (cf. table 1). The within subject variation, expressed as the standard error of the measurement (SEM), is calculated as follows SEM ¼ SDð1 ICCÞ0:5
ðEq: 10Þ
where SEM is the standard error of measurement, SD is the sample standard deviation and ICC is the calculated intra-class correlation coefficient (Baumgartner and Jackson, 1991; Stratford and Goldsmith, 1997; Atkinson and Nevill, 1998). (The customary terminology is adopted here, but SEM is sometimes used to represent the standard error of the mean.) The statistic calculated this way is affected by sample heterogeneity in the same way as the ICC. We prefer to calculate the SEM as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffi SEM ¼ WMS
ðEq: 11Þ
where WMS is the mean square error term in a repeated measures ANOVA (cf. table 1). This statistic is less affected than the expression in Equation (10) by the range (or spread) of the measured values (Stratford and Goldsmith, 1997; Atkinson and Nevill, 1998). If n is sufficiently large and the mean difference small, both highly likely conditions, then ME and SEM take similar values. For many measures in medical research and clinical practice, the within subject variation has been expressed as a coefficient of variation: in particular, the within subject standard deviation has been divided by the mean of all the measurements and multiplied by 100 to give a percentage, often reported as SEM% SEM% ¼ ðSEM=meanÞ 100
ðEq: 12Þ
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2.03 2.01 6.3 6.4
Sometimes this has been called the coefficient of variation and written as CV%. We prefer to define CV% in terms of ME CV% ¼ 100 ME=mean
ðEq: 13Þ
Both SEM% and CV% are independent of the units of measurement and have been used as descriptive tools: for example, to compare methods or samples. When inferences at the individual level are wanted, the CV% should only be used when the error depends on the value of the measurement, usually being larger for larger values (Bland, 2000). The values of ME, SEM, SEM% and CV% for the data for peak torque of the 30 men and women (fig. 1) were calculated using expressions in Equations (8), (10), (12), and (13). These values are presented in table 2. The values SEM and ME are seen to be very close.
5.2. Detection of systematic changes in the mean The techniques used to detect systematic changes in the means are here encompassed by the term ‘‘Bland and Altman analysis’’. We consider the change in the mean value between two test sessions. The change consists of two components: a systematic change, i.e. a systematic bias, and a random component, due to biological variation. For the example illustrating the methods, a systematic change could be a learning effect. The mean of the intra-subject differences (d ) is an index of a systematic change in the mean d ¼ the mean difference between the two sessions
ðEq: 14Þ
The variation about the mean difference for all subjects is assessed by SDdiff ¼ the standard deviation of the differences
ðEq: 15Þ
and the variation about the mean is assessed by the standard error of the mean (SE) pffiffiffi SE ¼ SDdiff = n
ðEq: 16Þ
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Table 3 Systematic changes in the mean between test sessions Mean difference between the two test sessions d Standard deviation of the differences between test sessions (SDdiff) Standard error of d (SE) 95% confidence intervals of d (95% CI)
0.03 2.88 0.53 1.10–1.04
where n is the number of subjects. A 95% confidence interval (95% CI) can be calculated. The approximate 95% CI is 95%CI ¼ d 2 SE
ðEq: 17Þ
The multiplier of SE in Equation (17) depends upon the number of subjects, but 2 is a good approximation when the number of subjects exceeds 20: to be precise, the multiplier in the data illustrated in fig. 1 is 2.045 which is obtained from the t-table with 29 ¼ (n 1) degrees of freedom. The d and 95% CI are easily interpreted. If the value of d is positive (or negative), then the measurements from the first session tend to be larger (or smaller) than those from the second session. If zero is included in the 95% CI, it is inferred that there is no systematic change in the mean (Bland, 2000); this is equivalent to a paired t-test (5% significance level) or a repeated measures ANOVA. The SDdiff is a useful measure of agreement and the differences between the two measurements will be, with probability 0.95, approximately within two SDdiff either side of the mean. The values of d , SDdiff, SE of d and the 95% CI are presented in table 3 for the data illustrated in fig. 1. The measurements in the second session tend to be larger than those in the first session. As zero is included in the 95% CI, it is inferred that there is no systematic change in the mean between the two test sessions.
5.3. Formation of graphs (‘‘Bland and Altman plots’’) A graphical approach is useful in the analysis of systematic changes in the mean between test sessions. The so-called ‘‘Bland and Altman plots’’ can be formed and easily interpreted. The differences between measurements at the two test sessions are plotted against the mean of the two test sessions for each subject. Such a plot clearly illustrates any systematic bias and/or outliers and/or relationship between difference and magnitude. The Bland and Altman plot for the data in fig. 1 is displayed in fig. 2: d and the 95% CI are also included. It is clearly seen that d is close to zero and zero is included in the 95% CI.
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Difference
6
95% LOA
3 95% CI 0 −3 −6 −9 10
95% CI
95% LOA
20
30
40
50
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Mean
Fig. 2. The ‘‘Bland and Altman plot’’ for the data in fig. 1 with d (solid line) and the 95% confidence interval (95% CI) and the 95% limits of agreement (95% LOA).
It is possible that the variance is related to the size of the mean, which is commonly referred to as ‘‘heteroscedasticity’’ in the data. Heteroscedasticity can be examined by calculating the Pearson’s correlation coefficient for the absolute differences and the mean of the two test values. If heteroscedasticity is suspected, Bland (2000) suggests that a logarithmic transformation of the data should be done before the analysis. Although the transformed data display less heteroscedasticity, the logarithmic transformation can cause other technical problems, in particular, when the results are interpreted in terms of the original measurements. If the heteroscedasticity correlation is close to zero and if the differences can be considered normally distributed, one may proceed with the interpretation using the original data. For the data in fig. 1, the correlation coefficient, r, is 0.06 ( p 4 0.05) so we continued the analysis as though heteroscedasticity was not present.
6. EVALUATION OF CLINICALLY IMPORTANT CHANGES IN SCORE Once the reliability has been established, it is necessary to determine if a method of measurement is sufficiently sensitive for a specific purpose in medical research and clinical practice: for example, to assess whether the method is sufficiently sensitive to detect a clinically important change for measurements made before and after an intervention. The term ‘‘responsiveness’’ has been used for this concept, especially in the literature about the quality of life (see, for example, Guyatt et al., 1992).
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In a review of the methods for the assessment of responsiveness, Terwee et al. (2003) identified 25 definitions of responsiveness and separated them into three main groups: 1. Change in general; 2. Clinically important change; 3. Real change in the concept being measured. The definitions were obtained from many sources and from a wide range of applications, and responsiveness must be put into the context of how the measurements are to be used. Terwee et al. (2003) also identified 26 measures that had been used by authors writing about responsiveness. Most of the measures and methods are equivalent to those used in methods assessing reliability: in fact, several have been defined and used in this chapter. In summarising, Terwee et al. (2003) considered the term ‘‘responsiveness’’ to be redundant as the methods are incorporated within reliability analyses. An attractive way to establish the sensitivity of a measurement is to use the reliability data to calculate an interval surrounding the true score. The smaller the interval width the more sensitive is the method of measurement. Importantly, this expands the notion of reliability: a method of measurement can be considered reliable as indicated by various reliability measures, but the interval in which the score is likely to lie is too wide to be clinically useful, even though it might be satisfactory for other purposes, such as research. In practice, small measurement errors usually imply narrow intervals and so represent a sensitive method of measurement. To assess the sensitivity of a measurement, the ‘‘limits of agreement’’ (LOA) have been proposed (see, for example, Bland and Altman, 1986, 1999). This approach is applied when a clinician wants to assess whether the difference between two measurements from an individual represents a ‘‘clinically relevant’’ or ‘‘true’’ difference. Ideally, the LOA is an interval such that if the difference between those measurements made before and after an intervention is outside (or within) the LOA, it does (or does not) represent a real change in performance. The first steps in this approach are to plot the data as a simple scatterplot, to form the Bland and Altman plot, and to check for heteroscedasticity of the data. Provided the heteroscedasticity is acceptable, the mean difference (d ) and the standard deviation of the differences (SDdiff) are then calculated. Approximately 95% of the differences between test sessions will lie within two standard deviations either side of the mean difference (d ). The 95% LOA are formed by d 2 SDdiff
ðEq: 18Þ
The 95% LOA are included in fig. 2: they are the outer parallel lines.
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Clinical judgement is required to assess the acceptability, or agreement, associated with the LOA interval (Bland and Altman, 1999). As mentioned earlier, sample size considerations have received less attention in reliability analysis than in other areas (such as clinical trials). It is generally perceived that a fairly large sample size is required to form reliable 95% LOA. One suggestion has been that the sample sizes should exceed 50 (Altman, 1991; Rankin and Stokes, 1998). An alternative approach for detecting clinically important changes was introduced by Beckerman et al. (2001). The ‘‘smallest real difference’’, SRD, is the limit for the smallest change between two measurements that indicates a real (clinical) change for a single individual following, for example, an intervention. The SRD is defined by pffiffiffi SRD ¼ 1:96 SEM 2 ðEq: 19Þ The value 1.96 is appropriate when many subjects are used in calculating SEM; a value from the t-distribution is preferred when SEM is calculated from fewer than 30 subjects. Beckerman et al., suggested the calculation of an ‘‘error band’’ around the mean difference of the two measurements, d ; the 95% SRD was defined by 95% SRD ¼ d SRD
ðEq: 20Þ
To allow the SRD to be independent of the units of measurement, Flansbjer et al. (2005) defined the following relative measure: SRD% ¼ ðSRD=meanÞ 100
ðEq: 21Þ
where mean is the mean of all measurements. Such a measure is likely to be attractive to the clinician, because the criteria for identifying a clinical change becomes that of calculating whether or not a simply calculated percentage exceeds a specific value. Furthermore, this approach accommodates, to some extent, heteroscedasticity, but the statistical argument is still incomplete. In table 4, data for the 95% LOA, the 95% SRD, and the SRD% are presented. It is not surprising that the 95% LOA and the 95% SRD are very similar, as they are algebraically similar. The SRD% is 18%, which
Table 4 Evaluation of clinically important changes in measurements Limits of agreement (95% LOA) Smallest real difference (95% SRD) Smallest real difference (% SRD)
5.92–5.86 5.84–5.78 18.1
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indicates that the difference in a measurement should exceed 18% to indicate a ‘‘clinically relevant’’ or ‘‘true’’ change. Taking the mean value of muscle performance presented in fig. 1, we can calculate the relative improvement needed to detect a ‘‘clinically relevant’’ change for a subject. The mean muscle strength was 31.9 Nm, and this has to change 5.7 Nm to indicate a ‘‘clinically relevant’’ or ‘‘true’’ improvement. From a clinical standpoint, this SRD% value is most reasonable, and confirm that this measurement can be useful for the detection of ‘‘clinically relevant’’ or ‘‘true’’ changes following, for example, strength training. One should be aware that there is an essential difference between a ‘‘clinically relevant change’’ and the ‘‘SRD’’ or the ‘‘LOA’’. Beckerman et al. (2001) stated: ‘‘SRD is a clinimetric property of a measurement tool, whereas ‘‘clinically relevant change’’ is an arbitrarily chosen amount of change indicating which change clinicians and researchers minimally judge as important’’. An interesting area for future research is to explore the clinimetric property of a measurement tool and how that corresponds to what clinicians judge as ‘‘clinically relevant’’. Such research will help us define the optimal outcome measure for medical research and clinical practice.
7. CONCLUSIONS Any test–retest reliability investigation of intra- or inter-rater evaluation using continuous data should include a specified ICC (relative reliability), assessments of measurement errors (absolute reliability), and analyses of systematic change in the mean. The reliability methods described here should be used when deciding whether or not a method of measurement is sufficiently reliable for a specific purpose, and can be applied to develop an algorithm for identifying clinically important changes in individual patients.
REFERENCES Altman, D.G., 1991. Some common problems in medical research. In: Altman, D.G. (Ed.), Practical Statistics for Medical Research, 1st edition. Chapman & Hall, London, pp. 396–403. Atkinson, G., Nevill, A.M., 1998. Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine. Sports Med. 26, 217–238. Baumgartner, T.A., 1989. Norm-referenced measurement: reliability. In: Safrit, M, Wood, T. (Eds.), Measurement Concepts in Physical Education and Exercise Science. Human Kinetics, Champaign (IL), pp. 45–72.
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Baumgartner, T.A., Jackson, A.S., 1991. Measurement for Evaluation in Physical Education and Exercise Science. Wm.C. Brown Publishers, Dubuque. Beckerman, H., Roebroeck, M.E., Lankhorst, G.J., Becher, J.G., Bezemer, P.D., Verbeek, A.L.M., 2001. Smallest real difference, a link between reproducibility and responsiveness. Qual. Life Res. 10, 571–578. Bland, J.M., 2000. An introduction to medical statistics. 3rd Edition. Oxford University Press, Oxford. Bland, J.M., Altman, D.G., 1986. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet Feb 8, 1, 307–310. Bland, J.M., Altman, D.G., 1999. Measuring agreement in method comparison studies. Stat. Methods Med. Res. 8, 135–160. Donner, A., Eliasziw, M., 1987. Sample size requirements for reliability studies. Stat. Med. 6, 441–448. Domholdt, E., 1993. Physical Therapy Research: Principles and Applications. W.B. Saunders Company, Philadelphia. Flansbjer, U.B., Holmba¨ck, A.M., Downham, D.Y., Patten, C., Lexell, J. (in press). Reliability of gait performance test in men and women with hemiparesis after stroke. J. Rehab. Med. 37, 75–82. Fleiss, J.L., 1986. The Design and Analysis of Clinical Experiments. John Wiley & Sons, New York. Guyatt, G.H., Kirshner, B., Jaeschkle, R., 1992. Measuring health status: what are the necessary measurement properties? J. Clin. Epidemiol. 45, 1341–1345. Holmba¨ck, A.M., Porter, M.M., Downham, D.Y., Lexell, J., 1999. Reliability of isokinetic ankle dorsiflexor strength measurements in healthy young men and women. Scand. J. Rehab. Med. 31, 229–239. Holmba¨ck, A.M., Porter, M.M., Downham, D.Y., Lexell, J., 2001. Ankle dorsiflexor muscle performance in healthy young men and women: reliability of eccentric peak torque and work. J. Rehab. Med. 33, 90–96. Hopkins, W.G., 2000. Measures of reliability in sports medicine and science. Sports Med. 30, 1–15. Madsen, O.R., 2002. Reliability of muscle strength testing quantified by the intra class correlation coefficient. Arch. Phys. Med. Rehabil. 883, 582. Portney, L.G., Watkins, M.P., 1993. Statistical measures of reliability. In: Portney, L.G., Watkins, M.P. (Eds.), Foundations of Clinical Research: Applications to Practice. Englewood Cliffs, Prentice Hall, NJ, pp. 525–526. Rankin, G., Stokes, M., 1998. Reliability of assessment tools in rehabilitation: an illustration of appropriate statistical analyses. Clin. Rehab. 12, 187–199. Roebroeck, M.E., Harlaar, J., Lankhorst, G.J., 1993. The application of generalisability theory to reliability assessment: an illustration using isometric force measurements. Phys. Ther. 73, 386–400. Rothstein, J.M., 1985. Measurement and clinical practise: theory and application. In: Rothstein, J.M. (Ed.), Measurement in Physical Therapy. Churchill, Livingstone, New York. Shrout, P.E., Fleiss, J.L., 1979. Intraclass correlations: uses in assessing rater reliability. Psychol. Bull. 86, 420–428. Stratford, P.W., Goldsmith, C.H., 1997. Use of the standard error as a reliability index of interest: an applied example using elbow flexor strength data. Phys. Ther. 77, 745–750.
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Terwee, C.B., Dekker, F.W., Wiersinga, W.M., Prummel, M.F., Bossuyt, P.M.M., 2003. On assessing responsiveness of health-related quality of life instruments: guidelines for instrument evaluation. Qual. Life Res. 12, 349–362. Walter, S.D., Elisziw, M., Donner, A., 1998. Sample size and optimal designs for reliability studies. Stat. Med. 17, 101–110.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
10 Advanced data mining and predictive modelling at the core of personalised medicine Roland Somogyi a, John P. McMichael b, Sergio E. Baranzini c, Parvin Mousavi d and Larry D. Greller a a
Biosystemix, Ltd., Sydenham, ON, Canada Management Science Associates, Tarentum, PA, USA c Department of Neurology, University of California at San Francisco, San Francisco, CA, USA d School of Computing, Queen’s University, Kingston, ON, Canada b
1. INTRODUCTION Extensive medical experience and our growing molecular-mechanistic knowledge have clearly established that most diseases represent a complex web of symptoms and causes with a high degree of individual variation. What we label as a disease may effectively not be just one disease with a specific cause. How many types, subtypes, and mixtures of cancers are there? How many variations of cardiovascular disease should we consider with differing physiological, dietary, and behavioural components? How strong and complex are the genetic components causing a disease and influencing its progression for a particular individual? The effectiveness of treatments varies greatly from individual to individual. To what degree may a chemotherapeutic agent that reduces one individual’s form of cancer be effective, ineffective, or even detrimental in another individual? To what extent may a generally effective drug cause toxic side effects in a genetically predisposed subpopulation? Personalised medicine is challenged to provide solutions for treating these complex and individual forms of disease. This goal can be achieved only if sufficient knowledge exists to (a) distinguish detailed variants of disease, (b) reliably classify therapeutic outcomes in terms of past experience, 165
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(c) capture key individual genetic, medical, and molecular profiling variables associated with disease type, therapeutic, and potential toxic outcomes, and (d) adjust dosing and therapeutic regimens accordingly (Sections 3–5 provide practical examples of solutions associated with points c and d). There has been significant progress in capturing this type of knowledge in a variety of clinical and biomolecular databases. These databases cover specific clinical trial and research projects, and include information on treatment regimens and outcomes, clinical assay variables of patients, and increasingly detailed molecular profiling data. With respect to the latter, genomics technologies have made it possible to collect information on individuals on a large scale. This provides key information on patterns of genetic variation (genomic markers and SNPs) and gene activity (RNA and protein expression characteristic of specific patient tissues, such as blood or disease tissue biopsies). One can make the case that the fundamental information required for the design of better targeted, personalised treatments already exists or will soon find its way into these databases (see fig. 1). However, today’s growing biomedical information sources that characterise disease and therapeutic outcome are perhaps just as complex as the diseases they describe. How can one draw sensible and valuable conclusions from these datasets? Given the nature of the data primarily in the form of databases of clinical and research study records, direct human evaluation of the data is obviously not practical because of the sheer scale of the data processing challenge. Neither can the analysis simply be carried out through the application of conventional statistical tools. These are often constrained to idealised models and simplified relationship types that cannot capture the complexity of the biomedical relationships that may be most informative and valuable. However, advanced computational, statistical, and mathematical data mining approaches have the ability to sift the data for the key patterns and complex relationships that are required for a personalised medicine application. The full predictive model is the product of personalised medicine that ultimately will be applied in a practical therapeutic setting. Patients and health professionals will depend on this model for in-depth recommendations on therapeutic decisions based on a complex set of patient information and past medical experience on which the model is trained. Models integrate selected results from data mining with domain knowledge within a suitable mathematical framework. Extensive statistical and computational validation of these models assure their robustness and resistance to measurement noise and error that is part of any data collection.
Advanced data mining and predictive modelling of personalised medicine target & marker qualification
RNA, protein, metabolite profiling genetic variation
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Fig. 1. The central role of data mining and predictive modelling. On the left we highlight data sources that reflect our clinical and biomolecular knowledge foundation; this information continues to grow in depth, quality, and scale. On the right we see development steps of a personalised medicine solution. The bottom lists the molecular and information products that ultimately reach the patient. Data mining and predictive modelling occupy the central position in this process. All the information from the raw data must be carefully evaluated and passed on to various stages of development. Validation essentially represents a continued refinement (or rejection) of the predictive model and its constituent molecular and biomedical variables. Optimising the data mining and predictive modelling component implies great efficiency and quality gains. Errors in this process can also lead to failed investments and losses through the selection of ineffective markers, targets, and predictive rules.
Of course, before broad application in the field, models must be clinically validated in the appropriate settings. The medical and economic benefits of a comprehensive application of personalised medicine are many and profound. For one, a majority of the therapeutic decisions made today are based on an incomplete characterisation of the patient and disease, such that the most-likely-to-succeed therapy is often not known, and therefore not prescribed. Improvements through more in-depth patient characterisation and individually-targeted therapeutic decision making should clearly result in improved patient well being and reduced cost of long-term medical care. Drugs and therapies that work very well on only specific forms of a disease may now be more effectively targeted based on more readily accessible knowledge on which individuals are suitable. In other words, treatments that do not work well on a population as a whole may get approved for a defined subset of patients, and may, therefore, not have been considered effective in the past. Moreover, toxic side effects in small subpopulations have blocked the application of otherwise effective treatments because the individuals showing adverse
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effects could not readily have been identified. Such drugs and treatments could be rescued by identifying the personalised profiles of individuals that are likely to benefit versus the ones likely to exhibit adverse effects. In summary, a carefully executed, comprehensive personalised medicine programme should lead to major improvements in patient well being and survival and provide new economic opportunities in the health care and pharmaceutical fields. Economic growth in these sectors should be expected due to (a) increased value through more effective deployment of existing treatments, (b) the generation of novel, personalised drugs, and (c) diagnostic/prognostic products to be used hand-in-hand with a therapeutic agent. However, the medical and economic success of personalised medicine solutions will largely depend on the effectiveness of the core computational tasks of translating the data generated in the development process into predictive and therapeutically powerful models (summarised in fig. 1).
2. THE FOUNDATIONS FOR PERSONALISED MEDICINE In terms of practical success, it will help to clearly define what we expect of an effort to advance technologies and solutions for personalised medicine. Increased accounting for individual, molecular, and genetic variants of a disease in diagnostic and prognostic applications. Systematic consideration of past therapeutic experience on medical decisions with respect to the treatment planning for a variant of a disease. Clear identification of clinical, molecular, or genetic markers for the patients that may respond adversely to an otherwise widely effective and beneficial treatment. Better understanding of molecular pathways linking a selected treatment to a disease variant in a patient. A patient should expect to receive an informative and dependable, biosystemic description or diagnosis for his/her disorder, and a projection or prognosis of whether the disorder will simply go away, or become more unpleasant, harmful, or fatal in the future. For diagnosis and prognosis to be effective and dependable, however, sufficient information on the manifestation and cause of a disease in a patient must be provided. This requires data much beyond a superficial characterisation of symptoms, and should be broad enough to characterise the set of disease-associated system variables in an individual. Such a biosystemic evaluation should
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include measurements of key physiological, cellular, molecular, and genetic profiles that are associated with the etiology of a disease. On the one hand, extensive diagnostic profiling of clinical and molecular variables could be prohibitively expensive in a clinical setting. On the other hand, evolving cost-efficient measurement technologies and dependable knowledge of which subset of variables may be relevant to a general disease should make costs manageable. Moreover, an investment in improved biosystemic diagnosis and prognosis should lead to significant overall cost savings in medical care. Assuming that an in-depth, biosystemic diagnosis and prognosis of a patient’s condition are available, how might that help us with respect to choosing a treatment? What is required here is a link from a patient’s biosystemic profile to past therapeutic experience from patients with comparable profiles. While the required patient information is increasingly becoming available, there are many data analysis challenges in establishing exactly what the valuable links are. Since one patient profile will rarely be exactly the same as another patient profile, key patterns and variables must be identified that have general predictive power. In other words, the challenge in making effective predictions for therapeutic decisions lies as much in the computational data mining efforts as in providing the information foundation. After all, the value of a personalised medicine outcome will ultimately lie in the performance and reliability of the predictive model that will be used to guide the patient’s therapy.
3. THE GROWING CLINICAL AND GENOMIC DATA FOUNDATION There is an expanding array of databases covering patient clinical histories, new treatment trial data, and detailed measurements on patient clinical assays, genetic variation, and genomic molecular activity profiling. The information in these databases is allowing specialists to define an increasingly detailed biosystemic patient profile, linking the microscopic with the macroscopic patient variables. By introducing such a systems-level characterisation, analysts are beginning to capture at once the diagnostic, prognostic, and causal variables as one set. Availability of this information is invaluable for successful downstream data mining and predictive modelling. Patient record databases do not yet represent a unified, coordinated set. Different hospitals, medical institutions, and health-related businesses collect data as part of their general record keeping and for the purpose of novel treatment development in investigative therapeutic trials. These
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studies may be managed and funded by mixed groups including public health research organisations, and the pharmaceutical and biotechnology industries. Individual studies reported in these databases take into account in their design, the scope and depth required to draw statistically meaningful conclusions. At a minimum, the likely disease and treatment-related variables must be recorded. Ideally, to enable the discovery of novel molecular markers and causal links, genomic technologies may be used to monitor genetic variation and molecular activity profiles on a broad scale. Depending on the complexity of the disease and treatment, many patients must be sampled over time to provide a sufficiently large dataset that can provide statistical support for inferring general conclusions. When monitoring clinical variables, several levels of data are usually considered within a particular study. A foundation is provided by general macroscopic and physiological variables, such as age, sex, body temperature, blood pressure, etc. Depending on diseased area, further straightforward tests involving readily available patient samples may be considered for cellular and molecular assay. These might cover white and red blood cell distributions, and levels of metabolites (blood glucose in diabetes) and specific antibodies (infectious and autoimmune diseases) in various bodily fluids, such as blood serum, urine, cerebro-spinal fluid, etc. More in-depth assays are often carried out on samples, such as excised tumors and disease-organ-specific fluids and tissue biopsies. Tissue samples may be evaluated on morphological features (often reported within a diseasespecific scoring regimen) and processed for specific molecular marker assays specifying varying forms and degrees of a disease. Over all, these features are recorded as discrete and continuous variables and begin to define a broad biosystemic patient profile that may be complemented with more detailed genomic molecular profiling data. While many morphological, physiological, and molecular assay features have been painstakingly developed through decades of medical practice, a revolution in scale is in progress based on genomic technologies. Fundamentally, all the molecules an organism involved in a disease response have their origin in the genes that directly encode RNA transcripts as indicators of gene activity, the ensuing translated proteins, and the metabolites resulting from protein-mediated catalysis. The extensive knowledge of whole genome sequences has enabled the design of gene-specific hybridisation probes for use in chip and quantitative RT-PCR (reverse transcription polymerase chain reaction) RNA expression assays. Moreover, protein assay technologies are becoming comparable in scale to those used for RNA profiling. These may be based on two-dimensional gel electrophoresis, or on antibody or high diversity affinity surface array
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technologies. A challenge following the detection of differentially expressed proteins lies in assigning protein identity. This is accomplished through mass spectrometry based technologies that provide protein-specific amino acid sequence signatures for searching genomic databases for the defining molecules. Together, these assays are now widely used to monitor RNA and protein activity on a genomic scale, enabling the discovery of novel disease-associated genes from uncharted regions of functional pathways. This is an important step, since many protein-encoding genes discovered in the genomic sequencing projects have no known function or purpose associated with them, and therefore represent a valuable reservoir of potential therapeutic markers and targets. In a complementary fashion, databases of genetic diversity studies between individuals and populations are allowing us to define the units of genetic variation, known as single nucleotide polymorphisms (SNPs). This knowledge in turn is used to generate DNA-sequence-specific probes for the genome-wide monitoring of genetic variation in individuals. Associating the frequencies of specific genetic variants with specific diseases and therapeutic outcomes provides additional information for solving the diagnostic/prognostic puzzle (Roses, 2000; Roden and George, 2002). Overall, the discoveries from genomic studies of RNA expression, protein abundance, and genetic variation in clinical research should increase by orders of magnitude the number of clinical markers and causal disease genes for novel therapeutic drug targeting. In addition to the challenge of collecting and organising clinical and genomic patient assay data, we are also faced with the ubiquitous issues of data quality and consistency. These may have various sources. For example, due to assay or recording failure, gaps with unknown values find their way into datasets. Values will be misrepresented due to instrument noise and human error. Moreover, the lack of assay reporting standards makes it difficult to compare results across different studies; this may seriously curtail potential statistical support for key study conclusions. While measurement noise and recording error may never be entirely eliminated, international institutional initiatives in biomedical data acquisition and management may help provide common standards for measurements and database structures (Brazma et al., 2001). Such standardisation should vastly increase the sets of commensurable samples. Ultimately this should lead to great gains in statistical support and confidence in the biomedical conclusions and predictions derived from these data. Investments in building and standardising these clinical and genomic patient databases should lead to substantial value in terms of cost savings through more efficiently administered medical care, larger profits through the development and sale of more effective therapeutic products, and increased human well-being through reduced disease-based suffering.
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4. VALUE EXTRACTION WITH ADVANCED DATA MINING The growing clinical and genomic patient databases provide us with raw materials from which we expect to refine personalised medicine solutions. However, the mountains of generated data within which these markers, targets, and novel therapeutic insights are hidden represent a formidable data mining challenge. This challenge is proving to be the ultimate gatekeeper separating us from the rewards of these novel technologies and information sources. The data mining challenge is not just one of scale with respect to the computational and personnel resources required to process the data according to routine data analysis protocols. The crux lies in the complexity of the underlying biomedical relationships that we need to understand to make the ultimate discoveries possible. This level of complexity is generally not accessible to the routine application of conventional statistical analysis, as we will illustrate below with examples. We are faced with three major issues in data-driven, computational mining for complex, high-value biomedical relationships (fig. 2): networks, nonlinearity, and the combinatorial explosion. At the fundamental level, the genes underlying an organism’s function interact in complex regulatory networks through the proteins and catalytic protein products which they encode (Kauffman, 1993; Somogyi and Sniegoski, 1996; Somogyi and Greller, 2001). Taking a systems view beyond these basic genetic networks, all the variables, (ranging from molecular activity, to cell function, organ activity and overall physiological parameters) are connected in a causal biosystemic network (see top right panel, fig. 2), that ultimately determines system output, e.g. measured as ‘‘health’’ or ‘‘disease’’. Through better understanding of this network, we will discover the key signature variables and root causes for each disease and its variations. This represents the knowledge required for precision, personalised therapeutic targeting. Solving the structure of biosystemic control networks is not a simple task that can be carried out one variable at a time with conventional statistical inference tools. For one, the complexity of regulatory interactions in genetic, biochemical, or system-level networks typically involves nonlinearities. This is illustrated in the lower left panel of fig. 2. For statistical inference purposes, analysts often, by default, assume that variables are related in a linear fashion for simplicity (black line). However, the reality is more often reflected in sigmoid interactions (green dotted line; typical of dose–response or molecular binding behaviour), or in dome-shaped, response maximisation/optimisation curves type (red broken line; typical of desensitisation and depletion behaviour). These interactions cannot be
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well, or at all, inferred using typical statistical measures such as Pearson correlation coefficient, or p-values generated from ANOVA tests (see below for specific examples). Advanced continuous and discrete data mining algorithms are required to solve these types of inference problems. In addition to nonlinearity, complexity is often reflected through combinatorial interactions. It is an established fact that (a) most diseases have multiple, interacting causes, (b) variations of multiple genes are required to explain genetic predisposition towards a disease, (c) proteins interact through regulatory complexes, and (d) expression of genes are regulated by the activity of multiple other genes and their protein products. The widespread use of combinatorial control in biological systems provides a daunting data mining challenge: the combinatorial explosion (lower right panel, fig. 2). For a typical genomic data mining task such as examining gene expression microarray data, we may already encounter difficulties when mining for combinatorial interactions. For example, if we presume that an interaction of four genes (this number could very well be higher) may be required to explain a particular outcome, we would need to search for all the combinations of four genes in a typical 10,000 gene chip to identify the combination that is most closely associated with the outcome. However, the number of combinations that are required to be searched is 4 1014, i.e. 400 million. The computational time and memory required to search this many combinations (or many more for the case of five or more interactions) would not be practical using any readily available advanced computational platform operating today. However, through the use of heuristic association mining algorithms, such as sublinear association mining (SLAMTM), useful approximations to an exhaustive search for combinatorial interactions can be made. While a ‘‘perfect’’ solution to the combinatorial explosion short of exhaustive search does not exist in principle, the appropriate algorithms allow us to make valuable discoveries in the higher order interaction domain.
4.1. Towards a personalised medicine solution in an autoimmune disorder We will discuss below several aspects of data mining to achieve progress in a personalised medicine solution: (i) drug response in multiple sclerosis (MS), and (ii) adaptive customisation of an individual patient’s drug dosing (section 5). The principal investigators of the MS project, Dr. Jorge Oksenberg and Dr. Sergio Baranzini (University of California,
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Fig. 2. Fundamental challenges in data mining and predictive modelling. Top left panel: Biological complexity manifests itself in (1) interwoven, molecular and physiological signalling networks, (2) nonlinear interactions in the control functions and predictive associations, and (3) high degree of combinatorial interaction connectivity in high-dimensional molecular variable spaces. Top right panel: From the perspective of the overarching, general ‘‘biosystemic network’’, it is not only important to recognise that multiple variables contribute to a particular outcome, but that they do so through combinatorial interactions and that cannot be decomposed into single interactions (see main text for details and examples). Bottom left panel: While in a first-cut data mining exercise, practitioners often assume linear interactions by default (black line), important features and interactions are missed when the prevalent nonlinearities are ignored by the inference methods. For example, while a sigmoid (green dotted line) interaction may be somewhat approximated by a linear fit, an optimisation/desensitisation type dome-shaped interaction cannot be inferred at all through linear fits. Bottom right panel: When searching for higher order variable interactions, even the analyst just wishes to examine, e.g. all combinations of four genes in a 10,000 gene chip variable set, the computations are faced with choosing from 4 1014 combinations. This daunting task cannot be achieved by ‘‘brute force’’ exhaustive search methods due to the physical limitations of today’s computational technologies. Thus, advanced heuristic-search data mining algorithms are required to make progress in these areas.
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San Francisco, USA) and Xavier Montalban (Hospital Vall d’Hebron, Barcelona, Spain), have focused on the study of blood samples from MS patients before and after the treatment with interferon beta (IFNbeta)(Oksenberg et al., 2001). An additional analysis of this data from this study using a three-dimensional IBIS model (Baranzini et al., 2005) (compared to the two-dimensional approaches discussed below), and a review of expression-based predictions of drug response studies have recently been published (Kaminski and Achiron, 2005). IFNbeta is the most widely prescribed drug for this disorder (Jacobs et al., 1981, 1986). However, not all the patients respond well to this drug. Of the 52 patients surveyed here, 32 represent good responders, and 20 represent bad responders. The investigators pursued a genomics approach to discover novel markers and further elucidate mechanisms of this disease. Blood samples were processed and assayed for the RNA expression of 33 selected genes from immune signaling pathways using a high-precision RTPCR method (reverse transcription polymerase chain reaction). RNA measurements were carried out in duplicate, resulting in a set of 104 samples per gene. The goal is to gain answers to several questions from these individual patient gene-expression data points: 1. Can the assay of selected genes before the treatment help us predict therapeutic outcome? 2. Can the assay of selected genes during the course of treatment help us predict continued therapeutic outcome? 3. Does the analysis of gene-expression time series using ‘‘reverse engineering’’ methods allow us to reconstruct the structure of the regulatory network functionally linking these genes? While we can address results with respect to (1) and (3) below, more analysis needs to be completed before a substantial report on (2) can be provided (the flavour of the analysis would be very much along the lines of question (1)) We will focus below on (1) – finding predictors of drug response from gene-expression data before the treatment in the remaining part of this section. Using principal component analysis (PCA), a routine method from linear algebra and exploratory statistics, we can visually evaluate whether the expression of 33 genes helps separate good from poor IFNbeta responders on a coarse level (fig. 3). PCA linearly transforms the 33 dimensions of the individual gene elements to new dimensions that each tries to capture the highest degree of variance in the data. The first principal components displayed in fig. 3 provides a three-dimensional view that captures most of the variance of the experimental data. We note that most of the poor (blue) and good (red) responder samples blend evenly within a cluster in the center of this projection. However, towards the right of the plot along the
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Fig. 3. Principal Component Analysis provides a reduced gene-expression space for the visualisation of sample similarity in the MS study. For high-dimensional datasets (e.g. 33 genes here), it is impossible to visualise the data points on all 33 orthogonal axes since we only have 2–3 orthogonal dimensions at our disposal. One approach to providing a useful visualisation is to linearly transform the 33 dimensions to the most informative top 3 ‘‘principal components’’, i.e. the dimensions which carry the most variation. We see that good (red) and poor (blue) IFNbeta responders mix more or less evenly in the centre of the graph, and that a cluster of good responders is isolated in the right part of the graph on the PC1 axis. The analysis and visualisation shown here were generated with the GeneLinkerTM Platinum software (Predictive Patterns Software, www.predictivepatterns.com).
PC1 axis, we see a group of good responders (red) that are well separated from the main cluster. Overall, PCA suggests that gene expression bears some relationship to patient drug response, but that distinguishing good from poor responders is not a simple matter of finding a boundary in the PCA space. The main mission of data mining here is to find the patterns and key variable sets that have predictive value with respect to the biomedical outcome. We therefore seek algorithms that enable a targeted search for these variables, allowing for the capture of simple as well as complex relationships. Before embarking on the pattern search, fundamental statistical considerations must be taken into account. For one, there is the risk of ‘‘overfitting’’ the data. That means variables and values may be found that distinguish
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certain sample groups in a spurious idiosyncratic, nongeneralisable fashion. A simple strategy to avoid this is to separate the samples into training and test data sets. This parallels the ‘‘real life’’ situation of designing a clinical application and predictive model based on experimental data, and then using it within the setting of new patient test data that is not part of the training data set. If the predictive model is sufficiently general and reliable, it should perform nearly as well on the new data as on the training data. For this purpose, we have divided the 104 RNA measurements per gene along an 80/20 division into 82 training samples (32 poor and 50 good responders) and 22 test samples (8 poor and 14 good responders). Following the principle of Occam’s Razor, it should first be determined whether a single variable can adequately determine the outcome according to a simple relationship. Figure 4 (top row) shows the results of onedimensional linear discriminant analysis (LDA 1D), as implemented in the IBISTM (Integrated Bayesian Inference System). This advanced data mining algorithm incorporates a complete leave-one-out cross-validation loop with several independently trained classifiers integrated to predict an outcome based on a voting scheme. The top left panel clearly illustrates a good, yet not perfect, fit of the model prediction corresponding to the colour of the background shading, with the measured data annotated through the colour of the measurement points. To assess generalisability of this relationship, we also note a good fit of the model with the measured samples in the independent test data set (right panel, top row). The key gene identified here, NFkB, is known to be a major transcription factor controlling the expression of immunogenic genes. It appears plausible that high levels of this gene are associated with the poor responder (blue) range of the data. Simple reasoning may suggest that increased expression of the immunogenic genes by high levels of NFkB exacerbates the autoimmune response underlying MS symptoms. This might explain why standard IFNbeta treatment is less effective in these individuals. One might also speculate whether more frequent or higher doses of the drug might help overcome increased autoimmune activity in the case of NFkB highexpressors. While NFkB is providing helpful information, a more in-depth understanding of this autoimmune disorder would require more complex interactions involving additional factors. Could we discover some of these as building blocks for a more accurate predictive model of IFNbeta response? Using the two-dimensional, quadratic discriminant analysis variant (QDA 2D) of the IBISTM algorithm, we can expand our search to also include complex, nonlinear, and combinatorial (pair-wise) interactions. The lower left panel in fig. 4 illustrates the model probability distribution (background shading) according to which two genes, MX1 and
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Fig. 4. Advanced data mining for the discovery of genes and relationships that predict drug response in MS. The four panels show how good (red) and poor (blue) IFNbeta responders are separated according to predictions from model probability distributions (red and blue background shadings) discovered using the IBISTM search algorithm (Integrated Bayesian Inference System). Top left panel: A single-gene, linear search resulted in the discovery of the NFkB as a determinant of drug response in the training data set. Top right panel: The independent test data set is superimposed on the predictive distribution of the training data set. Lower left panel: A two-gene, nonlinear search resulted in the discovery of MX1 and NFkB as a combinatorial separator of drug response in the training dataset. Note that the good responder (cyan circle) misclassified by the single-gene predictor (top left panel) is correctly classified by the more informative two-gene model (cyan circle is now in the red region of good drug response). Bottom right panel: The independent test data set is superimposed on the predictive distribution of the training data set. Note that the poor responder (magenta circle) marginally classified in the simpler single-gene model (top right panel) is now firmly placed in the deep blue region clearly predictive of poor drug response. The analysis and visualisation shown here were generated with the GeneLinkerTM Platinum software (Predictive Patterns Software, www.predictivepatterns.com).
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NFkB60, separate poor (blue) from good (red) responders in the training data set. Note that one of the good responders that was clearly misclassified in the training data set for NFkB alone (upper left panel, highlighted cyan circle), was ‘‘rescued’’ in the two-dimensional NFkB, MX1 model, i.e. the highlighted cyan circle clearly falls in the predicted red, good responder region (lower left panel). We note that the two-dimensional distribution better defines the region of poor responders as the area where MX1 is low and NFkB is high. This essentially represents a logical AND relationship, i.e. if NFkB is high AND MX1 is low, we predict a high probability of being a poor drug responder. Moreover, in the case of the independent test data set, the NFkB and MX1 distribution more clearly separates the blue, poor responders compared to the single NFkB distribution, in which many blue samples occupy the boundary region to the red, good responders. Note that a poor responder in the uncertain, red-to-blue boundary region in the single gene model (magenta circle, upper right panel), is unambiguously located in the blue region predictive of poor responders (magenta circle, lower right panel). We see that the increased information content of the nonlinear, two-gene predictive pattern better approximates the biomedical response complexity and provides clearer predictions in the test dataset. In our search of this dataset for genes that help us better explain MS therapeutic outcome, would it not be most efficient to select the top genes using a conventional statistical test, and consider them as the most promising building blocks for a multi-gene, predictive model? Using an ANOVA (analysis of variance) F-test approach on single genes to separate responders, we determined which genes co-aryl with the responder outcome variable with high statistical significance. It is to no surprise that NFkB was determined to be the best F-test gene with a p-value of 0.00001. There are nine genes with p 5 0.02 from the analysis shown in the right panel of fig. 5 (see check-marks). However, when comparing this prioritisation to the genes that were identified using the nonlinear, combinatorial IBISTM method, we see that many of the best IBISTM performers (all highlighted in gray in fig. 5), are not captured by the top F-test list. In fact, MX1 from the example above only scores with a completely insignificant p-value of 0.54. However, we demonstrated that MX1 together with NFkB better define the poor responder samples in both the test and training data sets. The fact that MX1 has a poor p-value is due to the limitations of the linear model, single variable statistical model underlying the F-test. The key here is that the combinatorial predictors must be sought as a set, and cannot be discovered simply by aggregation of the ‘‘best’’ single variable predictors. We will discuss further in the next section how variable selection through advanced data mining is an important first step in model building.
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5. PREDICTIVE MODELS AS THE KEY COMPONENT FOR DELIVERING PERSONALISED MEDICINE Developing a personalised medicine solution is a step by step process with the goal of providing a predictive model for making decisions for diagnosis, prognosis, and therapy. Moreover, in-depth predictive models that take into account the causal molecular and physiological variables provide invaluable guidance towards new therapies and targets. We have discussed above aspects of advanced data mining as a required step for extracting the variables and patterns from which predictive models can be built. There are many issues that need to be taken into consideration when building a predictive model from these partially refined materials: How complex does the structure of the predictive model need to be for a desired prediction? What is the minimal number of variables for marginal predictive power? What is the optimal number of variables for maximal predictive power? How statistically sound and generalisable is the model? In how far does the model reflect aspects of the internal structure of the biological system useful for therapeutic discovery? We will discuss selected aspects of these challenging and issues involved in the context of several examples. With respect to the question of model complexity and variable requirements, we will illustrate one approach based on the data mining results described above for drug response prediction in MS. Assuming that the advanced data mining search summarised in fig. 5 has yielded a highly informative set of genes, how could one best integrate the predictive power of these interacting variables? In terms of universal applicability, ANN (artificial neural network) computational models offer many degrees of freedom to fit a complex predictive problem. The parameters of ANNs can be fitted on a reasonably well-behaved training data set to provide a mapping from the input variables (genes) to the output variable (drug response). The left panel of fig. 6 shows the performance of a ‘‘committee of ANN’’ models built on the training data set based on the nine top genes from the nonlinear, two-dimensional IBISTM search (left panel, fig. 5). The committee of ANN model outputs a histogram of scores from 10 independent ANNs to compensate for the idiosyncratic and initial randomisation effects on neural network output (columns of rectangles in fig. 6). Each neural network produces a numerical score between 0 (‘‘no’’ or ‘‘bad’’) and 1 (‘‘yes’’ or ‘‘good’’) with respect to predicting a particular outcome. For example, most of the ANNs in the bottom part of the left graph scored close to 1 for ‘‘good’’ and therefore correctly predicted good outcomes. However, the rectangles outlined in red in the top part of
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Fig. 5. Advanced data mining identifies powerful predictive variables that would not have been brought to light using conventional methods. Many members of the most predictive 9-variable set (shaded in gray) from advanced data mining (left panel; IBISTM method – see text) would not have been rated as valuable based on p-values from a conventional ANOVA method (F-test; right panel). On the one hand, there is overlap between the top nine genes from advanced data mining (shaded in gray; prioritised according to minimal mean squared prediction error) and F-test (check-marked in right panel; prioritised according to minimal p-value); i.e. NFkB-60, IL-4Ra, and IL-10 are shared among both the lists. On the other hand, several genes that are selected as valuable and informative are below common scoring thresholds for the F-test. In the case of STAT1 (highlighted in cyan), found in five predictive variable pairs, we only observe a marginal p-value of 0.24, which does not suggest substantial statistical significance. Moreover, for MX1 (for details see fig. 4), we only observe a p-value of 0.54, which generally would be considered insignificant. The analysis and visualisation shown here were generated with the GeneLinkerTM Platinum software (Predictive Patterns Software, www.predictivepatterns.com).
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Fig. 6. Predictive modelling using ANNs (artificial neural network model) based on variables found by advanced data mining (IBISTM) or conventional methods (F-test). ANN models are an established computational tool for fitting complex, predictive problems covering many variables. ANNs were optimised to fit the training samples of the IFNbeta, good and poor responder MS patient datasets (see text). We evaluate above the performance of these models on the independent test datasets. Ten ANNs were independently trained on the top nine predictive variables shown in fig. 5, and the output of each ANNs is produced on a scale of 0 (‘‘no’’) to 1 (‘‘yes’’), in terms of predicting the bad or good responder class. The rectangles represent a histogram that counts how many of the ten ANNs ‘‘voted’’ for a particular good versus bad responder score; the majority of this vote is considered the overall output of the model. If a model prediction matches the sample class, the rectangle is outlined in black; if the prediction is incorrect, the rectangle is outlined in red. Left panel: 86% of the independent test samples are predicted correctly using a committee of ANN models based on nine gene expression variables from nonlinear, combinatorial search. Right panel: 73% of the test set samples are predicted correctly based on the nine genes with top p-value scores from an F-test. The analysis and visualisation shown here were generated with the GeneLinkerTM Platinum software (Predictive Patterns Software, www.predictivepatterns.com).
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the left graph show examples in which the ANNs voted for the ‘‘wrong’’ sample class, i.e. bad responders were classified as good responders in three cases. In one sense, these misclassifications suggest that the variables used in the prediction do not cover all biomedical factors that determine the outcome. In another sense these may highlight atypical forms of the disease for further investigation. Moreover, given the stochastic nature of diseases and therapeutic responses, the biomedical reality may never support a fully deterministic, 100% accurate model. For high-performance models, variables should be exploited in the best possible manner to maximise predictive power and reliability. Advanced data mining methods allow us to discover the variable sets that best reflect the biological complexity as we have shown. In comparison, by using variables found by a conventional F-test, and aggregating nine of these in the same type of ANN model, the predictive accuracy drops to 73 from 86% that we were able to achieve based on the nonlinear and combinatorial IBIS-selected variables. This highlights the subtle yet fundamental distinction between a multivariate model that is simply built on independent, linear predictive variables versus true combinatorial and nonlinear interactions. It is then not difficult to imagine the additional discoveries and value that could be generated from existing personalised medicine datasets by successfully exploring the space of nonlinear and combinatorial interactions. In addition to optimising challenging clinical predictive outcome tasks, how can we employ models to learn more about the causes and molecular interactions underlying disease and treatment response? The latter will be required for novel therapeutic discovery and design. Personalised medicine should not simply stop at better diagnosing diseases and prescribing currently available treatments, but should equally contribute to the discovery of new, individually targeted treatments. To provide an additional illustration of the valuable relationships that are hidden in the MS patient gene-expression dataset, we used algorithms for ‘‘genetic network reverse engineering’’ to reconstruct the molecular signalling interactions underlying therapeutic response (D’Haeseleer et al., 2000). In the examples above, we only considered expression measurements at time ¼ 0 for the prediction of drug outcome before treatment. However, the complete dataset covers a time series of responses at 0, 3, 6, 9, 12, 18, and 24 months after treatment. Essentially, the expression time series for each gene in each patient is the result of the molecular regulatory interactions in the disease and drug response process. Given that these time series are a result of a process we want to understand, would it be possible to infer key components of this process from the
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resulting activity profiles? The methods for accomplishing this task are referred to as ‘‘reverse engineering’’ of genetic regulatory networks. ‘‘Reverse engineering’’ is sufficiently universal to be applied to other data types within a general biosystemic network context. The results from reverse engineering of the IFNbeta response gene network are shown in fig. 7. The core of reverse engineering is based on co-fluctuation analysis of the time series of each gene with respect to each other gene over all the patients. The degree to which one expression profile over time is related to another is recorded as a numerical score. Genes that are linked by a high score are connected by a line in the signalling network graph in fig. 7 (genes in good and poor responders are connected by red and green lines, respectively). It must be emphasised that the gene interactions shown in the graph are mathematically inferred directly from numerical expression data in an unsupervised fashion (i.e. no domain knowledge of gene function was used in the analysis). Remarkably, several of the reverse engineered functional connections directly correspond to well-established signaling interactions and protein complexes. In four highlighted cases (fig. 7) we have direct evidence from the literature that reverse engineering has rediscovered important known interactions, i.e. 1. the Stat1–Stat2 heterodimer for the induction induces interferonstimulated genes (top left), 2. interferon signaling through phosphorylation of Stat1 by Jak2 (lower left), 3. Jak2 activation by IFN gamma receptor heterodimers, 4. Sos1 and Grb2 complexes in downstream Fos activation. In addition to discovering well-known components of protein interaction networks solely and directly from RNA expression data, many new pathway interactions are highlighted for which no specific literature exists yet. The model also allows us to distinguish interactions that are more prevalent in bad responders versus good responders. For example, the Jak2, Stat1 interaction is highlighted in poor responders; perhaps this pathway link may help explain why current IFNbeta treatment is not effective in these patients? A subnetwork linking MX1 to Stat6, Stat3 and Stat2 is highlighted in good responders; perhaps this illustrates effective components of the IFNbeta response pathway that could be further optimised? Along with the ability to predict which patients are indicated for what therapy and the ability to discover important mechanistic pathways for improved therapeutic interventions in personalised medicine, it is also very important and useful to be able to optimally customise dosing regimens for individual patients. The next section briefly describes a patient data-driven computational system that is available today that adaptively predicts successive drug doses for individual patients. We can foresee that
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linking genomic- and macromolecular-expression-based data mining and modelling approaches as described above with quasi-real time computational patient-customised dosing systems can become a powerful efficacious way to deliver personalised medicine.
6. PATIENT DATA-DERIVED PREDICTED DRUG DOSING FOR PERSONALISED MEDICINE The Intelligent Dosing System (IDS; US Patent 6,578,582) is a software suite that incorporates patient-specific dose–response data into a mathematical model that calculates the new dose of agent needed to achieve the next desired therapeutic goal. The IDS is a practical example of how data can be used to personalise medicine. The IDS was derived from dosing data that was mined from transplant patients taking immunosuppressants. These data were employed to create an expert system that utilises such patient-derived data in a predictive fashion. With the data loaded, the expert system was queried to determine response (level) changes that were occurring over the dosing range of the drug(s). Using these observations and rules an equation was created to fit the data. The IDS has been approved by the US FDA’s Center for Devices and Radiological Health (CDRH) as a Class II Medical Device. The model function is a fourvariable (previous dose, previous response, next dose, and next response) nonlinear equation and is designed to alter the degree of predictive responsiveness based on the value of the previous dose (McMichael et al., 1991, 1995). In general, for a given therapeutic agent, the dose/level relationship is linear at low doses, relative to the normal dosing range of the drug. However at high doses, the dose/level relationship is nonlinear and becomes increasingly nonlinear with higher doses. The basic function of the IDS is as follows: New Dose ¼ Current Dose þ ððNL CLÞ=CLÞ=ð1 þ ðCurrent Dose=RangeÞÞ Current Dose where CL ¼ Current Level and NL ¼ Next Level. As various factors can influence a subject’s markers, aside from dose alone (whether biological, pharmacological, physiological, or environmental), an additional equation has been incorporated that phenomenologically individualises dosing based on any influences acting on the subject. In order to accomplish this accurately in a universally standard manner, an adaptive stochastic open loop was added to the IDS equation.
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Fig. 7. Reverse engineering of gene network models of functional interactions. Network reverse engineering algorithms are designed to reconstruct functional interactions among variables from measurements of the activity output of the system. The network graph shown here was derived purely from co-fluctuation analysis of the gene expression time series from each of the 32 sample good responder and 20 sample bad responder datasets. No pathway domain knowledge was used to infer the connections. The four oval outlines and literature quotations highlight selected connections of RNA variables that directly correspond to known functional interactions in protein signalling networks. Some connections are found only in the good responder network (red lines), some only in the bad responder network (green lines), and some in both. Differentiating these connections may help us better identify genes that may be targeted for improving drug response in poor responders.
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This loop accounts for the individual variations that effect dosing, acts as a safety factor, and allows the equation to individualise the dosing. The loop looks like this: ð0:2 CDÞ ððEC AC Þ=EC=1:3ðCD=RangeÞ where CD ¼ Current Dose PD ¼ Previous Dose DL ¼ Desired Level CPL ¼ Current Predicted Level PL ¼ Previous Level EC ¼ Expected Change in Level AC ¼ Actual Change in Level CL ¼ Current Level CPL ¼ (CD PD)/PD (1 þ PD/Range) PL þ PL EC ¼ CPL PL AC ¼ CL PL The stochastic loop equation calculates how the patient responded in the last dosing cycle (percent response), thus allowing the system to ‘‘learn’’ as it operates for a specific patient. This proportional response is then multiplied by 20% of the patient’s total dose and is either added or subtracted as needed. Diabetic dosing data including insulin doses and blood glucose levels were collected on several hundred patients. These data were used to calibrate as well as validate the IDS system. Using retrospective data, the range of the drug was calculated where a 50% change in drug dose resulted in a 100% change in the response. This seed value was then used as the Range value in the dose calculation. The three-dimensional surface map of insulin generated by this function, describes the rates of change associated with different doses (fig. 8). With a glance at the equations, one can see that the function is linear at low doses and quickly becomes increasingly nonlinear at higher doses. This is consistent with our clinical observations as the model accurately predicted the next sequential best doses to achieve target responses (fig. 8), and is similar to what has been observed for immunosuppresive agents (McMichael et al., 1993, 1994). The IDS was applied to managing insulin therapy to determine if it could offer advantages over currently utilised dose adjustment protocols, which are empirically based and nonstandardised (Aubert et al., 1998; Scherbaum, 2002). We conducted a prospective observational study to examine if the IDS could be employed to titrate total daily insulin dose in a large urban outpatient diabetes clinic comprised mainly of patients with type 2 diabetes. Prescribed insulin doses were compared to amounts suggested by the IDS. Clinical observational data were used to validate the
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Fig. 8. Model-predicted and actual prescribed drug dosing in personalised medicine. This three-dimensional plot, from two different views, shows how actual clinical observations (red), closely map to the synthetically modelled surface area (white) of the IDS. The plane of fit represents ever increasing slopes or rates of change between the current dose, next dose, and the percent change in level.
insulin surface of fit. Changes in dose were correlated with resulting changes in effect (such as glucose level) and were compared to the predicted changes as defined by the surface of fit. We compared actual prescribed insulin doses with ones recommended by the IDS (fig. 8). Practitioners generally agreed with doses being calculated by the IDS, and the correlation between prescribed and IDS suggested doses was high (Pearson correlation coefficient r ¼ 0.99). The correlation between prescribed and IDS recommended doses was high regardless of whether patients were on insulin monotherapy (r ¼ 0.98), or when insulin was increased but oral agents were not (r ¼ 0.99). The high correlation between final prescribed total daily insulin dose and that recommended by the IDS suggested acceptance of the technology by the practitioners. The good correlations between values of expected glycemic targets calculated by the IDS model and actual levels observed at follow-up suggest that the system can be successfully employed to adjust total daily insulin doses. Moreover, the IDS resulted in high correlations between expected and observed follow-up markers regardless of which glycemic parameter (fasting glucose, random glucose, or A1c) was used, indicating that the system will provide the practitioner with great flexibility on the choice of data that can be utilised to modify insulin doses.
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The ability to apply patient data to the learning process through models allows us to quickly understand new processes and apply this new knowledge at the bedside.
REFERENCES Aubert, R.E., et al., 1998. Nurse case management to improve glycemic control in diabetic patients in a health maintenance organisation. A randomised, controlled trial. Ann. Intern. Med. 129(8), 605–612. Baranzini, S.E., et al., 2005. Transcription-based prediction of response to IFNbeta using supervised computational methods. PLoS. Biol. 3(1), e2. Brazma, A., et al., 2001. Minimum information about a microarray experiment (MIAME)toward standards for microarray data. Nat. Genet. 29(4), 365–371. D’Haeseleer, P., et al., 2000. Genetic network inference: from co-expression clustering to reverse engineering. Bioinformatics 16(8), 707–726. Jacobs, L., et al., 1981. Intrathecal interferon reduces exacerbations of multiple sclerosis. Science 214(4524), 1026–1028. Jacobs, L., et al., 1986. Multicentre double-blind study of effect of intrathecally administered natural human fibroblast interferon on exacerbations of multiple sclerosis. Lancet 2(8521–2), 1411–1413. Kaminski, N., Achiron, A., 2005. Can blood gene expression predict which patients with multiple sclerosis will respond to interferon? PLoS. Med. 2(2), e33. Kauffman, S. A., 1993. The Origins of Order: Self-Organisation and Selection in Evolution. Oxford University Press, New York. McMichael, J., et al., 1994. Three Dimensional Response Surface Comparison of FK506 and Cyclosporine (abstract). Western Multiconference Simulation in Health Science Conference, San Diego, SCS. McMichael, J., et al., 1991. Evaluation of a novel ‘‘intelligent’’ dosing system for optimizing FK 506 therapy. Transplant. Proc. 23(6), 2780–2782. McMichael, J., et al., 1993. Three dimensional surface mapping and simulation of FK506 dose-level relationships. Western Multiconference Simulation in Health Science Conference, San Diego, SCS. McMichael, J., et al., 1995. Physician Experience vs. Computer Learning: The Efficiency of Artificial Intelligence Learned Optimal Dosing of Cyclosporine and Tacrolimus in Transplantation. Western Multiconference Simulation in Health Science, San Diego, SCS. Oksenberg, J.R., et al., 2001. Multiple sclerosis: genomic rewards. J. Neuro. 113(2), 171–184. Roden, D.M., George, A.L., Jr., 2002. The genetic basis of variability in drug responses. Nat. Rev. Drug Discov. 1(1), 37–44. Roses, A.D., 2000. Pharmacogenetics and future drug development and delivery. Lancet 355(9212), 1358–1361. Scherbaum, W.A., 2002. Insulin therapy in Europe. Diabetes Metab. Res. Rev. 18(3), S50–S56. Somogyi, R., Greller, L.D., 2001. The dynamics of molecular networks: applications to therapeutic discovery. Drug Discov. Today 6(24), 1267–1277. Somogyi, R., Sniegoski, C., 1996. Modeling complexity of genetic networks. Complexity 1, 45–63.
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
11 Designs and therapies for stochastic neural systems Andre Longtin Department of Physics, University of Ottawa, Ontario, Canada
1. INTRODUCTION Noise is an unavoidable ingredient of neural behaviour that is receiving increasing attention from experimentalists and theorists alike. While it is often clear what the sources of neuronal noise are, we are just beginning to understand the potential computational functions these noise sources can accomplish. This paper reviews recent advances in our knowledge about the importance of noise in the design of neural systems. It also discusses new approaches to incorporate noise in therapies for the correction of defective neural function, both at the cellular and systems levels.
2. NEURONAL NOISE: BACKGROUND OR FOREGROUND? 2.1. Dissecting the deterministic from the stochastic Like many other metabolic systems, the nervous system is an intricate assembly of interacting cells. Descriptions of its function span a wide range of spatial and temporal scales, from the molecular to the systems level, and from the submillisecond to the circadian level and beyond (Koch, 1999). At every level, the observed behaviour is characterised by a regular ‘‘deterministic’’ component, as well as an irregular ‘‘noisy’’ component. The difference between these two components is usually revealed by repeating an identical experimental protocol a number of times, and assessing the deviations of the responses from the mean response.
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One such protocol at the single-cell level involves impaling a neuron and delivering a pulse of current for a given duration and intensity. Assuming that the cell’s behaviour is time-invariant and that its sources of noise are somewhat stationary, the regular component is reproducible across trials. However, only the statistics of the noisy component are reproducible: the individual time series, known as ‘‘realizations’’, are not. This simple picture of two components added to one another may be useful for pedagogical purposes, and applies indeed to systems where the noise is simply added to some deterministic observable. Yet this is usually an oversimplification, and one has to deal with a more intricate meshing of the deterministic and stochastic dynamics, where the noise is an intrinsic part of the dynamics. As we will review below, mathematically this translates into model descriptions involving stochastic differential equations. Another complication over this simplified picture is that the system may not be time-invariant. Various forms of adaptation or learning can occur, and the statistics and intensities of the noise sources may vary in time. It then becomes a significant challenge to experimentally and/or conceptually dissect out the deterministic and stochastic components.
2.2. Noise: averaged out or functional? It has been customary to ‘‘average’’ successive responses in order to extract the regular response, and neglect the noise manifested in deviations from this mean behaviour. Likewise, averaging across the responses of many cells does often occur in the nervous system, when, e.g. many cells project in parallel to a common postsynaptic cell. However, it is also clear that noise appears pretty much at every level of the nervous system, including such target-summing postsynaptic cells; and apart from a small subset of pacemaker cells, there is always a significant noisy component in neural behaviour. Thus, one question that has attracted much attention in recent years is: to what extent is this noise instrumental for neural function? A related paradoxical question is: in designing a therapy for restoring normal function to a defective neural system, how important is it to reproduce certain features of the original variability of the intact system? Specific answers to these questions will likely depend on the system of interest, but generalisations are also likely. Further, it is important to have a system whose function is partly known, and in which the noise level can somehow be altered to assess the impact of variability on this function. Cortical cells receive synaptic input from thousands of other cells, and this along with the complexity of the circuitry in which they are
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embedded, makes the determination of their function, let alone the role of noise, rather obscure. Accordingly, most studies of the effect of noise have been confined to primary sensory circuitry or to motor output activity, since for those cases, there is good knowledge supported by a strong intuition as to what the functions being implemented are. Finally, it is also crucial to have a clear theoretical model for what the cell (or system of cells) is doing and how noise affects the dynamics. One common approach toward this goal involves modelling the systems using nonlinear stochastic differential equations. This is a natural extension to the well-established literature on linear systems analysis that lies at the core of control theory and which can deal with noise, as well as the growing nonlinear dynamics literature that aims to model the genesis of oscillations of varying complexity, ranging from limit cycles to chaos, and qualitative changes in dynamics. This chapter will first review stochastic differential equations and common modelling assumptions about noise. Next we present a number of roles that have been recently suggested for noise. Finally, we give an outlook onto challenging theoretical questions surrounding these issues. Throughout, we try to emphasise the generality of the concepts, since indeed they are generalisable and relevant to non-neural physiological systems, such as genetic and biochemical regulatory systems.
3. MODELLING THE NOISE: STOCHASTIC DIFFERENTIAL EQUATIONS Noise as a random variable is a quantity that fluctuates aperiodically in time (Gardiner, 1985), and that takes on a different set of values every time we sample it. To be useful for modelling purposes, this random variable should have well-defined statistical properties such as a distribution of values (a density) with a mean and higher moments, and a correlation time. The latter quantity, which is well defined for a stationary process, is usually associated with the decay time of the two-point autocorrelation function of the noise (see below). A commonly used simple continuous-time noise process is the Gaussian white noise. Its distribution is Gaussian; ‘‘white’’ refers to the fact that the correlation time is a Dirac delta function at the origin, meaning that successive points have no correlation. Alternatively, this means that the Fourier transform of the autocorrelation function (the power spectral density, by the Wiener– Khintchine theorem) is flat. Specifically, the autocorrelation is hðtÞðt0 Þi ¼ 2Dðt t0 Þ
ðEq: 1Þ
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where D is the ‘‘noise amplitude’’, and the brackets denote an average over an ensemble of realisations of the noise process. This noise varies widely, and in fact is nowhere differentiable. It is the simplest to deal with from an analytical point of view, and is a good assumption when the time scale of noise fluctuations is shorter than all other system time scales. One of the difficulties with modelling noise is that we usually do not have access to the noise variable itself, but rather, to a state variable that is perturbed by one or more sources of noise. Thus, one may have to make assumptions about the nature of the noise and its coupling to the dynamical state variables. The accuracy of these assumptions can later be assessed by looking at the agreement between the predictions of the resulting model and the experimental data (see Longtin, 2003 for a review).
3.1. Observational, additive, or multiplicative? A first class of noise is observational noise. In this case, the dynamical system evolves deterministically, but the measurements on this system are contaminated by noise. For example, suppose a dynamical system described by one state variable x with the following time evolution: dx ¼ Fðx, Þ dt
ðEq: 2Þ
where is an external parameter coupling the system to its environment. Then observational noise corresponds to the measurement of yðtÞ ¼ xðtÞ þ ðtÞ
ðEq: 3Þ
where (t) is the noise process (the mean of (t) is zero). This form of noise does not lead to any new interesting dynamical behaviours, it simply blurs the state variable of the underlying process; nevertheless it may be important to model it to better understand data. Noise can also affect the parameter , thereby accounting for fluctuations in one of the system’s parameters. The source of noise then becomes coupled to the system via this parameter. Mathematically, we can simply set ðtÞ ¼ hi þ ðtÞ where hi denotes the average value of the coupling parameter. The deterministic evolution Equation (2) is now a stochastic differential equation (SDE). For technical reasons related to the nature of Gaussian white noise, the coupling parameter appears in a linear fashion in the evolution equation. If the coefficient of in the
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evolution equation is independent of the state x of the system, the noise is said to be additive: dx ¼ Fðx, hiÞ þ ðtÞ dt
ðEq: 4Þ
This kind of noise is a common assumption in neural modelling, as a first attempt at characterising dynamical effects of noise. For example, a simple model of the firing activity of a single neuron is the leaky integrate-and-fire model driven by Gaussian white noise (Koch, 1999): C
dV ¼ gVðtÞ þ I þ ðtÞ dt
ðEq: 5Þ
where V (a real number) is the transmembrane voltage, g is the total conductance for non-spiking currents, C is the membrane capacitance, and I is the bias current. A realisation to this equation evolves from a specified initial condition for the voltage. A firing event or ‘‘spike’’ occurs whenever V reaches the threshold for the activation of spiking currents; as the fast spiking currents are not included in this description (for simplicity), the voltage is reset to the initial condition after each spike. Alternatively, one can have multiplicative noise, for which the coefficient of the noise depends on the value of one or many state variables. In one-dimension, this looks like: dx ¼ Hðx, hiÞ þ ðtÞGðxÞ dt
ðEq: 6Þ
The important feature here is that the strength of the noise at any one time depends on the state variable at that time through the function G(x(t)). A given system may have one or more noise sources coupled in one or more of these ways. Furthermore, more than one state variable may be required to model the system. Multiplicative noise occurs typically in a more detailed model of neural firing, such as: C
dV ¼ gL ðV VL Þ ge ðV Ve Þ gi ðV Vi Þ þ I dt
ðEq: 7Þ
In this case, the leak conductance gL, the excitatory synaptic conductance ge, and the inhibitory conductance gi are each modelled by their mean value plus a Gaussian white noise, e.g. gi ¼ gi0 þ i ðtÞ: Usually one assumes that the noises on each conductance are uncorrelated. The infinite support for Gaussian white noise makes its physical interpretation challenging in
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this context, since the conductances are positive by definition. This leads to mathematical complications for computing physically relevant quantities such as the mean firing rate. Further, the Gaussian white noise is an approximation to synaptic input conductance, which more realistically is a point process (each point being associated with an incoming spike to the neuron) convolved with a response function of the synapse. There are still many challenges for the mathematical characterisation of the firing statistics of a neuron in response to incoming spike trains with a given temporal structure and mutual correlation.
4. THERAPIES FOR DEFECTIVE CELLULAR AND NETWORK DYNAMICS Much research is currently devoted to the repair of neural function, from deep brain stimulation treatment of Parkinson’s disease, to anti-epileptic drugs, to cochlear implants and artificial retinas. The degree to which modelling is involved in the design of the strategy for alleviating defective function varies with the neural system of interest. The mechanism by which deep brain stimulation provides beneficial effects is not understood, and modelling has suggested that it may involve changes in the synchronisation of neural assemblies (Terman, 2002). Cochlear implants bypass the organ of Corti and directly stimulate the cochlear nerve using a scheme based on good knowledge of the frequency separation performed by the organ of Corti, and modelling studies have been very helpful to guide these efforts (Hochmair-Desoyer et al., 1984). It is clear, however, that even a significantly successful device like a cochlear implant is rather rudimentary, given what is known about the auditory system. And we are still far from replacing visual cortices or thalamic areas, let alone short- or long-term memory. However, there has been significant progress for speech recognition by incorporating noise in a cochlear implant (Morse and Evans, 1996). One goal then is to understand (1) how information is coded and conveyed in the areas of interest, and (2) the biophysical rules that support this information transfer. The proper firing responses to the spatial and temporal aspects of stimuli have to be reproduced in some measure by devices, so that they perform their task with high fidelity and transparency. This ‘‘proper’’ response may have to go beyond first and second order statistics of the spike train or its derived firing interval density, to encompass perhaps even the temporal patterning of spike trains on the millisecond time scale. Such patterning can arise from intrinsic cellular dynamics, such as bursting phenomena where spikes are fired in clusters, or from neural network properties
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(Latham et al., 2000). Patterning has been suggested to be important for the proper activation of post-synaptic cells (via time-dependent synaptic properties). Modelling has revealed that deterministic and stochastic components are part of the equation that relates input stimuli to output firing patterns. The rest of this paper is devoted to the discussion of a subset of stochastic effects that may be of importance for therapies. There are two main aspects to noise in neural system. One is the variability in the design of components, which makes the neural networks heterogeneous. The other is dynamical noise, which is the one we focus on throughout.
4.1. Noise in the sensory periphery To set the stage, we focus on the sensory periphery, for which we have a clearer idea of the input and output to each population of neurons (in comparison e.g. to cortex). The basic circuitry for the processing of sensory input can be represented schematically as follows: Physical stimuli ! Receptor cell ! 2nd order neuron $ 3rd order neurons (Feedforward)
(Feedforward)
(Feedforward and Feedback)
In many senses, the information is relayed in a feedforward manner from receptor cell to second order neuron. For example, there are no known feedback projections from the thalamus to the retinal circuitry. There are however feedback projections at this level in the vestibular system (also in certain auditory systems, although another cell type is involved). Where then should we be concerned with stochastic effects if replication of original function is to be achieved by an implant? Most likely at every stage. The importance of noise is also anticipated purely from information theory, which is now commonly applied in a black-box manner to sensory peripheries in different animals (Rieke et al., 1997). Information theory deals with entropies, which can be greatly affected by noise (Chacron et al., 2003).
5. STOCHASTIC INPUT–OUTPUT RELATIONS 5.1. The frequency–input characteristic A basic property of a neuron is the relation between its mean firing rate and the mean current it receives from different channels. The deterministic
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Fig. 1. (a) Firing rate R aspaffiffiffi function of bias input current for three noise strengths (see Equation (5)). Here ¼ 2D. Note that the abrupt onset of firing for zero noise is smoothed out (‘‘linearised’’) by noise. (b) Rate of change of firing rate with input current as a function of noise strength. This derivative of the input–output relationship is taken at I ¼ 15 in (a), which is the subthreshold regime. The sensitivity thus exhibits a maximum as a function of noise.
component of this frequency–input ( f – I ) property is often caricatured as an ‘‘all-or-none’’ behaviour: a mean current I below the firing threshold produces no spikes, while a mean current above threshold produces periodic firing. This relation can be simply written down analytically for Equation (5) when the noise intensity is zero; a more involved first passage time calculation also yields an analytic expression for the mean rate for nonzero noise (fig. 1; see Gardiner, 1985). One sees from fig. 1 that without noise, currents less than 20 (for the parameters used) produce no output: they are subthreshold. However, this is not the case with noise. One sees a linearisation of the ‘‘all-or-none’’ behaviour by noise (note that the deterministic curve is not a Heaviside function, as all-or-none suggests, and its levelling off at the right has been truncated for our purposes here).
5.2. Gain Control In the context of a single neuron, gain control refers to the ability of the cell to modify its f–I characteristics. This ability may arise from intrinsic currents in the cell which can be modified by firing activity, of inputs from other cells. The f–I curve can be modified in two basic ways: (1) the threshold can be shifted, but the slope remains unchanged, i.e. subtractive gain control; or (2) the threshold remains the same, but the slope decreases, i.e. divisive gain control (Holt and Koch, 1997). Together, these two kinds of gain control (which may both be present, depending on the model details) allow the cell to alter (1) the range of inputs to which it responds, and (2) the rate of change of output with input, i.e. to scale the input by modifying the dynamic range of response.
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Biophysically plausible mechanisms for computationally very desirable ‘‘divisive’’ property have remained elusive (see however the suggestion in Gabbiani et al., 2003). However, this quest has been mostly confined to the context of deterministic firing. Further, f–I curves are often sigmoidal like the noisy ones in fig. 1. How does this noise affect gain control? Two recent studies have shown theoretically (Doiron et al., 2001) and experimentally (Chance et al., 2002) that the noise can actually produce a divisive effect at lower firing rates. This is similar to the behaviour of the three curves in fig. 1 in the range below the deterministic firing threshold (I ¼ 20). The zero-noise case has infinite slope when firing begins; the corresponding mean slope near firing onset decreases as noise intensity increases. However, the curves in fig. 1 were obtained only by increasing noise, without changing any other parameter; gain control usually also involves shifting a parameter such as the bias I. For example, inhibitory gain control will lower the bias level, thus raising the threshold. This moves the f–I curves to the right; increasing noise makes them more sigmoidal, expanding them to the left. If the noise level increases concomitantly with the inhibitory level (this is so for synaptic input), one obtains divisive gain control.
5.3. Noise expresses subthreshold signals: stochastic resonance It is clear from fig. 1 that variations in input below threshold always produce no output in a noiseless neuron. However, increasing noise intensity produces non-zero firing rates below threshold for a fixed bias current I. Can variations in this bias, due, e.g. to an input stimulus, produce variations in firing rate? The answer is yes, and for sufficiently slow signals, the input and output variations are simply related by the mean slope of the f–I characteristic. For a given bias, the slope of the f–I curve in this subthreshold domain actually goes through a maximum as noise is increased (see fig. 1b). Also, the noise will produce firings that tend to occur preferentially near peaks of the stimulus. Too much noise will destroy any correlations between stimulus and firings. Hence, an intermediate noise intensity best conveys stimulus information. This effect, whereby noise allows subthreshold signals to be expressed in the neurons’ output firings, is known as stochastic resonance. Many sensory neurons appear to be set-up in a manner that allows them to benefit from this effect. A comprehensive review can be found in Gammaitoni et al. (1998). Recent developments include demonstration of the effect in single cortical cells (Stacey and Durand, 2001), and of noise-enhanced balance control (Priplata et al., 2003).
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5.4. Noise as a necessary desynchronising agent We now shift our attention to the suprathreshold signal regime (this would correspond to I 4 20 in fig. 1a). Here, a neuron fires repetitively even without any stimulus. When such neurons communicate with one another, synchrony may arise. Synchrony has been proposed as a useful method by which the signaling of special events can occur (Hopfield and Brody, 2001; Gray and Singer, 1989). For this to be true, there must exist an asynchronous state which can be transiently synchronised by a special event. Given that synaptic connections can by themselves induce synchrony, other desynchronising factors may be required, and noise may be such a factor. Replacement circuitry may then require noise to counterbalance the tendency to synchronise. The importance of this desynchronisation is illustrated by recent work in weakly electric fish (Doiron et al., 2003). There, feedback from third to second order neurons has been shown to cause network oscillations (in the 30–50 Hz ‘‘gamma’’ frequency range) when the fish are stimulated by stimuli that extend spatially over their body. These band-limited random stimuli correspond to electrocommunication signals between the fish. However, for localised inputs, such as prey stimuli, no such oscillations occur. In this system, the second order neurons send signals to one another foremost indirectly, via the third order cells that summate all these inputs, and send their own output back to all second order cells. Our modelling of this network involves a system of equations like Equation (7), except that each one has an extra term that accounts for the current received as a result of feedback from the third order neurons. This feedback activity is also delayed by about 20 ms, due to the time lag for the activity to propagate around the loop. The best match of the model to experimental data occurs when each second order neuron is ascribed its own intrinsic noise source. Without this noise, which mimics synaptic noise, each neuron could not fire randomly (around 20 Hz) in the absence of a stimulus, as observed experimentally. Because the system has delayed negative feedback, it has a natural tendency to oscillate autonomously in the gamma frequency range. This oscillation is however suppressed by the noise in the second order neurons. A localised input has insufficient strength to overcome the noise and induce network oscillations. However, an extended stimulus drives many more neurons in parallel, and the feedback of their combined output can now overcome the intrinsic noise, causing an oscillation. Without the desynchronising effect of noise in this system, discrimination between signals relating to prey and to conspecifics would be impaired.
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5.5. Noise can affect frequency tuning Another important property of a neuron, especially one receiving direct oscillatory physical stimuli (such as an auditory hair cell), is its sensitivity to the frequency of its input. This is commonly measured as the minimal stimulus amplitude that causes a particular firing pattern (such as one firing per stimulus period, i.e. one-to-one firing). This minimum amplitude is then plotted as a function of stimulus frequency. For many neurons, the resulting curve displays a minimum at the ‘‘best frequency’’ of the cell. This best frequency is usually thought to be related to a deterministic resonance in the cell and/or its adjoining structures. Receptor neurons are often classified according to the width and best frequency of this tuning characteristic. There is often a significant stochastic component to the activity of these cells. What then is the effect of noise on this curve? Modelling studies have shown that noise can alter it not only quantitatively (HochmairDesoyer et al., 1984) but also qualitatively (Longtin, 2000). For example, the width increases with noise intensity; and if the tuning curve initially had a minimum, this best frequency can even disappear for sufficiently high noise. These results thus raise the possibility that, besides the resonance, the intrinsic receptor noise can shape the experimentally observed curve, while also introducing variability in the firing pattern. Consequently, a device that replicates the properties of, for example a receptor neuron may have to incorporate noise to tailor both tuning and firing variability, both of which influence the firing of the target postsynaptic cells.
5.6. Control on many time scales with parametric noise Neural control systems involve a sensory–motor pathway and also operate with noise. Delays for propagation around feedback loops (as discussed above) are another important feature of their design. This delay sets a minimal time before which a corrective action can be taken following a perturbation. It has been recently suggested (Cabrera and Milton, 2002) that noise can actually enhance the control involved in stick balancing. This skill involves not only proprioceptive feedback for hand/arm position and velocity, but also for visual feedback. The analysis of movement fluctuations during this task, combined with mathematical modelling with stochastic delay-differential equations, has led to the proposal that noise can actually enable control on many time scales, and in particular, on time scales shorter than the loop delays. This requires that the
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underlying deterministic system operates in the vicinity of a bifurcation point, i.e. of a point where there is an exchange of dynamical stability. This result, which begs to be investigated in other tasks, argues for combining noise with marginally stable dynamics to enable ‘‘control’’ in a repair strategy for high-level sensori-motor tasks.
6. WORKING MEMORY We finally consider a level beyond the sensory periphery, but which is closely related to it. Working memory is a high-level function that refers to the ability of neural systems to acquire and maintain information about a stimulus. Up to now, we have been discussing mainly the acquisition and relaying of sensory input. A simple working memory protocol involves a monkey fixating his eyes on a point in space. A light then goes on briefly somewhere in the visual field. The monkey has to move the fixation point to this new position after a time delay which can last many seconds. During this delay, the information about the position to which the eyes must move is stored in working memory. It is generally thought that noise is detrimental to working memory (see e.g. Brody et al., 2003). The localised bump of activity undergoes a kind of random walk over space at a rate proportional to the noise. Also, a decrease in firing rate following the onset of a stimulus, a very common property of neurons known as adaptation, is thought to affect certain neurons involved in working memory. This adaptation can destabilise a bump of activity, especially when the neurons are connected via short-range inhibitory connections and long-range excitatory connections, a common configuration. How can working memory operate under such circumstances where noise causes diffusion and adaptation causes deterministic movement? It has been shown that for such systems, noise can actually cause a stabilisation of the bump (Laing and Longtin, 2001). Specifically, the noise causes changes in the sign of the bump velocity; it starts moving, e.g. to the left, then to the right, then left, and the sign changes follow a simple random process giving rise to a persistent random walk. For a given time interval, the mean distance from the original position is smaller with than without noise. This prediction has yet to be verified experimentally, but it is reasonable, although counter-intuitive, given that noise has been invoked to explain a variety of high-level functions such as perceptual switching in binocular rivalry (Laing and Chow, 2002). What the stabilisation of bumps by noise further suggests is that any attempt to emulate the behaviour of neurons involved in working
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memory should pay close attention to the noise; and too much noise will destroy the bump!
7. CONCLUSIONS Noise is ubiquitous in the nervous system. Through a variety of examples relating to sensory processing and working memory, we illustrated its potential constructive roles, and discussed how to include it in models. These studies help predict what can happen when noise is absent, and provide insight into designing noise into technologies that repair or enhance neural function. One key outstanding problem is the analysis of situations where noise intensity depends on firing activity. For spike trains, this situation has been described briefly in our section on gain control. Noisy spike trains contribute a current to the cell, the variance of which increases with the mean. Such problems are beginning to receive attention (Lansky and Sacerdote, 2001), usually by simplifying them to multiplicative Gaussian white noise problems. It is likely that many new interesting effects lie ahead in this area. Another key outstanding problem involves the characterisation of the effect of noise on delayed feedback problems. There is no theory to describe the properties of such non-Markovian dynamical systems, and this problem constitutes a major stumbling block in our analyses of real neural loops. Finally, the influence of spatial correlations between inputs to a cell, and of temporal correlations between successive firings of a cell are receiving much attention. Correlations between noise processes increase the variance of the summed process. Thus, increases in correlation can produce effects similar to increases in noise intensity discussed throughout this paper (for example, stochastic resonance – see Rudolph and Destexhe, 2001). Many of the properties of single cells and networks discussed in our paper, such as response versus input strength characteristics, delayed feedback, tuning, and state-dependent noise are also of relevance to nonneural control systems. The distinct advantage of studying noise in the nervous system is that activity runs on a faster time scale, allowing more data to be gathered. Thus, the analysis and repair of genetic, immunological, and other networks are likely to benefit greatly from our understanding of neural dynamics, even though they may be slower and noisier.
REFERENCES Brody, C.D., Romo, R., Kepecs, A., 2003. Basic mechanisms for graded persistent activity: Discrete attractors, continuous attractors, and dynamic representations. Curr. Op. Neurobiol. 13, 204–211.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
12 Mining scenarios for hepatitis B and C Yukio Ohsawaa, Naoaki Okazakib, Naohiro Matsumurab, Akio Saiurac and Hajime Fujied a
School of Engineering, The University of Tokyo, Tokyo, Japan Faculty of Engineering, The University of Tokyo, Tokyo, Japan c Department of Digestive Surgery, Cancer Institute Hospital, Tokyo, Japan d Department of Gastroenterology, University of Tokyo Hospital, Tokyo, Japan b
1. INTRODUCTION: SCENARIOS IN THE BASIS OF CRITICAL DECISIONS Scenarios form a basis of decision making in domains where the choice of a sequence of events in the near future affects the long-term future significantly. Let us take the position of a surgeon, for example, looking at a time series of symptoms during the progress of an individual patient’s disease. At appropriate times, the surgeon must take appropriate actions to effect the patient’s recovery. If he does so, the patient’s disease may be cured; otherwise, the patient’s health might be worsened radically. The problem in this situation can be described as choosing one course of events from multiple possible sequence of events. For example, suppose states 4 and 5 in Equation (1) indicate outcomes of two similar sequences of events i.e. in state 4 the disease is cured, and in state 5 the disease is worsened. Sequence 1 ¼ fstate 1 ! state 2 ! state 3 ! state 4g: Sequence 2 ¼ fstate 1 ! state 2 ! state 5g:
ðEq: 1Þ
The surgeon must take effective action at the time of state 2, in order to ensure the patient’s progress through states 3 and 4, rather than his direct decline to state 5. 209
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A state like state 2, one that is essential for making a decision, has been called a chance (Ohsawa and McBurney, 2003). As we discuss later, methods to improve the discovery and recognition of chances are making important contributions in both science and business domains. Each event-sequence in Equation (1) is called a scenario if the events in it share some common context. Here, a context is the coherent meaning of an event-sequence. For example, Sequence 1 is a scenario of the context of cure, and Sequence 2 is a scenario of the context of worsening of the disease. Detecting an event at a crossover point among multiple scenarios, such as state 2 above, and understanding the values of all such scenarios is what we refer to as the discovery of a chance, or ‘‘chance discovery’’. An event is regarded as a valuable chance if there is a significant difference between the two scenarios that both include that event, but that end in different states. A scenario with an explanatory context is easier to understand than an event shown alone. For example, suppose you are a patient and you have just been diagnosed that a polyp is growing in your stomach. Lacking any other information, deciding to resect the polyp or leave it in place would be a difficult decision. However, suppose the doctor tells that you are at the turning point between two future scenarios – in one, the polyp will grow and the disease will worsen. In the other, the doctor resects the polyp and you have a high possibility of complete cure. With this additional information about the scenarios and their possible end points, it is easy to make the choice for surgery Recognising a chance and taking it into consideration is required for developing and narrating useful scenarios, and having access to useful scenarios helps decision makers recognise the existence of a chance.
2. SCENARIO ‘‘EMERGENCE’’ IN THE MIND OF EXPERTS In the term ‘‘scenario development’’, a scenario may sound like something to be ‘‘developed’’ by human(s) who consciously rules the process of making a scenario. However, scenarios really ‘‘emerge’’ in the (partially) unconscious interaction of human(s) and their environment. Researchers who develop planning and forecasting methodologies have recognised this quality of emergence and designed strategies to encourage the process. One example in which this tacit process is made explicit is that of the scenario workshop, as developed in Denmark by the Danish Board of Technology (2003). The Danish process begins with thought-provoking scenarios that are presented to experts in the knowledge domains of interest for decision makers. Over the course of the workshop,
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participants engage in discussion to improve the scenarios. The discussants write down their opinions during the workshop discussions, but rarely consciously recognise why certain opinions emerge, or why the expert discussants converge on a final scenario. For example, school teachers, students, publishers, etc., participated in a scenario workshop discussing the future of elementary education. They focussed on computer-aided education, but the scenarios about students’ use of computers were divergent, since scenarios were often presented without contextual continuation. Sometimes, a suitable number of scenarios should be selected compulsorily by the moderator in order to keep the workshop meaningful. This process of scenario creation in a workshop discussion is similar to the KJ method of idea generation (Kawakita, 2000), in which participants write down their initial ideas on cards and arrange the cards in a 2D-space as a way of collectively generating new plans. Here, the idea on each card reflects the future scenario in a participant’s mind. The new combination of proposed scenarios, generated during the arrangement and the rearrangement of KJ cards, helps the emergence of new valuable scenarios in our terminology. In a design process, by contrast, it has been pointed out that ambiguous information can trigger new creations (Gaver et al., 2003). The common points among the scenario ‘‘workshop’’, the ‘‘combination’’ of ideas in KJ method, and the ‘‘ambiguity’’ of the information to a designer is that scenarios, presented from the viewpoint of each participant’s environment, are bridged via ambiguous pieces of information about different mental worlds they inhabit. From these bridges, each participant recognises situations or events in their own scenarios that function as ‘‘chances’’ to import aspects of others’ scenarios and combine them with his or her own. Returning to the example of Equation (1), a surgeon who is incapable of imagining anything more than the sad outcome of Sequence 2 would be given new hope when Sequence 1 is proposed by his colleague. However, the surgeon would have to recognise that state 2 – the chance – is common to both the scenarios and that it presents an opportunity for action. Moreover, he would have to recognise before or during state 2, so that he is able to take appropriate action. In this chapter, we apply and describe a method for supporting the emergence of helpful scenarios by means of interaction with real data, using two tools for chance discovery: KeyGraph (Ohsawa, 2003b) and TextDrop. Using the blood-test data of hepatitis patients as a test case, we add information about causal directions in the co-occurrence relationships between values of variables to KeyGraph (let us call this a scenario map). In a complimentary fashion, TextDrop helps in extracting the expert knowledge of a surgeon and a physician.
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These tools support the development of useful scenarios of the disease’s progress and cure, reasonably restricted to understandable types of patients, from the complex real data taken from the mixture of various scenarios. The results obtained as possible scenarios for the progress of hepatitis were evaluated by two hepatologists, i.e. a hepatic surgeon and a hepatic physician, and were found to be useful for identifying the chances to optimise the treatment of both hepatitis B and C. This evaluation is still subjective in the sense that only a small number of the patient population was observed to follow any of the scenarios from beginning to end. A scenario corresponding to only ten patients should be carefully questioned. Nevertheless, we believe that the evaluation was appropriate, merging the subjective perspectives of experienced hepatologists with the objective information in the data. This represents an extension of traditional data mining, in which the experts engage in mining their own experience to make explicit their recognition of chances in real-world reactive behaviours.
3. MINING THE SCENARIOS OF HEPATITIS CASES 3.1. The Double Helix (DH) process of chance discovery A state of the art chance discovery process follows the Double Helix (DH) model of chance discovery (Ohsawa, 2003a) depicted in fig. 1. In the DH model, the discovery process begins when individuals decide to search for a chance. Their concern (which we define as an interest in finding a target, without knowing if the target really exists) dictates priorities for acquiring the data to be analysed by data-mining tools designed for chance discovery. In studying the results of the analysis, the user can identify various potential scenarios and assess differences among them. If multiple users collaborate and share their results, the visualised bridges may allow users to link different event-sequences and compose novel scenarios. In other words, participants in the process may locate chances in bridges they find in the visualised result. With these chances, the user may choose to take action in the real world or may do more research – for example, by choosing to simulate actions in a virtual (imagined/computed) environment. In the process of discovery, participants may generate a new concern and with finding new chances, the iterative helical process returns to the initial step. DH is discussed in this chapter as a framework for the development of hepatitis scenarios. Users watch and co-manipulate KeyGraph, thinking and talking with other users about the scenarios the diagram offers. Here, to ‘‘co-manipulate’’ means to cut/move/unify the components
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Fig. 1. The DH Model: A process model of chance discovery.
(i.e. nodes and links) in KeyGraph. Co-manipulations build bridges among the participants, because the process builds a common base of understanding as participants interact with each other in manipulating the real-world components depicted in KeyGraph. Co-manipulation urges users to ask questions, e.g. ‘‘why is this node here?’’ or ‘‘why is there no link between these two nodes?’’, while responses from co-participants spurs users to think of alternative scenarios they may not have considered.
3.2. KeyGraph and TextDrop for accelerating DH In the case of marketing of textile products, the Nittobo Corporation of Japan was successful in developing and selling a product to which they had added value, through developing a scenario of the lifestyle of consumers in their market. The market researchers of Nittobo visualised the map of their market using KeyGraph (Usui and Ohsawa, 2003), with nodes corresponding to products and links corresponding to co-occurrences between the products in the basket data of buyers. In this map, the researchers found a valuable new scenario that described the lifestyles of customers who buy textiles across a wider sector of the market. In contrast, previous methods of data-based marketing helped in identifying the customers, but the scenarios obtained in this process were restricted to customers in specific local segments. By combining scenarios from different customers in different market segments, the company realised that it could develop new and desirable products to appeal to multiple segments of consumers.
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However, following the process of DH using only KeyGraph is inefficient, because the user cannot easily extract interesting areas of data that might be useful in investigating a recently conceived concern with chances. For example, a user might develop a concern with the customer who buys product A or product B and also buys product C, but does not buy product D. To explore this concern, the user would need to quickly locate data about the customers who follow this purchasing pattern. To do so, the user can apply TextDrop, a simple tool for Boolean selection of the part of data corresponding to users’ concern described in a Boolean formula, e.g. concern ¼ ‘‘ðproduct Ajproduct BÞ & product C & !product D’’ ðEq: 2Þ TextDrop identifies data baskets that include product A or product B, and product C, but exclude product D. The output from TextDrop becomes a revised input to KeyGraph. This simple usage of TextDrop is particularly convenient when the user can express his/her own concern in Boolean formula as in Equation (2). However, we recognise that the concerns of users might be more ambiguous, especially in the beginning of the DH process. In this case, the user can approximate the concern in Boolean terms. An integrated toolbox that includes KeyGraph and TextDrop allows users to speed up the DH process.
3.3. DH process supported by KeyGraph and TextDrop Summarised below are the steps in the DH process using Key Graph and TextDrop: Step (1) Extract a portion of the data with TextDrop, corresponding to the user’s concern with combinations of events as expressed in the Boolean formula. Step (2) Apply KeyGraph to the data in Step (1), to visually map relationships among events, and to attach causal arrows (in the procedure explained later). Step (3) Co-manipulate KeyGraph with co-workers as follows: (3-1) Move nodes and links to the positions in the 2D output of KeyGraph, or remove nodes and links that users agree to be meaningless in the target domain. (3-2) Imagine, discuss, and document participants’ comments about scenarios, from KeyGraph. Step (4) Display participants’ comments obtained in (3-2) using KeyGraph, or read the comments, and choose noteworthy and realistic
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scenarios. Discuss and identify new concerns that have emerged from the discussions. Step (5) Simulate or execute the scenarios identified in Step (4), and, based on this experience, refine the understanding of the concern and document clearly. Step (6) Return to Step (1) and iterate the process.
4. DISCUSSION: THE PROCESS APPLIED TO DIAGNOSIS DATA FOR HEPATITIS 4.1. The hepatitis data We display the type of data obtained from blood tests of hepatitis cases here. Each event represents a pair consisting of a variable and its observed value. That is, an event written as ‘‘a_b’’ indicates that the value of a variable a was b. For example, T-CHO_high (T-CHO_low) means T-CHO (total cholesterol) was higher (lower) than a predetermined upper (lower) bound of normal range. For each name of blood attribute, uppercase letters are used in the text and lower cases in figures, for not hiding the links in the figures. Each line delimited by ‘‘.’’ represents the sequence of blood-test results for a single patient case. See Equation (3). Case 1 ¼ fevent 1, event 2, . . . , event m1g: Case 2 ¼ fevent 2, event 3, . . . , event m2g:
ðEq: 3Þ
Case 3 ¼ fevent 1, event 5, . . . , event m3g: As shown in Equation (3), we can regard one patient as a unit of co-occurrence of events, i.e. there are various cases of patients and the sequence of one patient’s events describes his/her scenario of progression through the larger universe of symptom events. For example, let us suppose we have data in which each event is described by a value for a particular attribute of blood. For example, GPT_high indicates a patient whose value for GPT exceeded the upper bound of the normal range. Values of the upper and the lower bounds for each attribute are pre-set, depending on the hospital in which the data is obtained. Each period (‘‘.’’) represents the end of one patient’s case. If the doctor becomes interested in patients having experiences of both GTP_high and TP_low, then s/he can enter ‘‘GTP_high & TP_low’’ to TextDrop in Step (1). TextDrop provides the italicised lines, in the form of Equation (3), that the user will enter into KeyGraph in Step (2). GPThigh TPlow TPlow GPThigh TPlow GPThigh TPlow:
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ALP_low F-ALB_low GOT_high GPThigh HBD_low LAP_high LDH_low TTT_high ZTT_high ALP_low CHE_high D-BIL_high F-ALB_low F-B_GL_low. GOT_high GPThigh LAP_high LDH_low TTT_high ZTT_high F-ALB_low F-B_GL_low G_GL_high GOT_high GPThigh I-BIL_high LAP_high LDH_low TTT_high ZTT_high GOT_high GPThigh LAP_high LDH_low TPlow TTT_high ZTT_high B-type CAH2A D-BIL_high F-CHO_high GOT_high GPThigh K_high LAP_high LDH_low T-CHO_high TPlow UN_high T-BIL_high ALP_high D-BIL_high GOT_high GPThigh I-BIL_high LDH_high T-BIL_high TTT_high UN_low ZTT_high T-BIL_high B-type CAH2B. When the user applies KeyGraph to the data as in Equation (3), s/he obtains the following components: Islands of events, where an island is a group of frequent events co-occurring frequently; i.e. events in an event-sequence that was common to many patients. The doctor is expected to know what kind of patients each island corresponds to, because a doctor should be familiar with a frequent sequence of symptoms. Bridges across islands: A patient may move from one event island to another during their experience with the disease. The data used in this example consists of 771 cases collected between 1981 and 2001. Figure 2 is the KeyGraph obtained first for all cases of
Fig. 2. The scenario map, at an intermediate step of manipulations for hepatitis B.
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hepatitis B in the data. The causal arrows in Step (2) of the DH Process, which do not appear in the original KeyGraph (Ohsawa, 2003b), depict approximate causations. That is, ‘‘X ! Y’’ means event X precedes Y in the scenario, indicating the causal explanation of event occurrences. Even if there are relationships in which the order of causality and time are in opposition (i.e. if X is the cause of Y but was observed after Y due to the delay of observation, or due to a high upper bound or a low lower bound of the variable in the blood test which makes it hard to detect symptom X), we should express a scenario including ‘‘X ! Y’’. For each arrow, we compare the strength of the statement ‘‘if event X appears, then event Y follows’’ and its opposite ‘‘if event Y appears, then event X follows’’ subjectively i.e. if a domain expert indicates that the former seems to be truer than the latter, we take this to mean that X is likely to be tied to the cause (rather than the result) of Y. We represent this with an arrow drawn from X to Y on the basis of a comparison between the two results of KeyGraph, one that represents data including X and the other that represents data including Y. If the expert is quite certain that the former includes more causal events than the latter and if the latter includes more consequent events than the former, X is regarded as a preceding event of Y in the scenario. If the order of causality and the order of occurrence time are opposite, we can infer that X exceeds Y using subjective but trustworthy judgment of an expert. For example, the upper threshold of ZTT may be set too low, making it easier to exceed than that of G_GL. This makes ZTT_high appear before G_GL_high, even though ZTT_high is a result of G_GL_high. In this case, we compare the results of KeyGraph, one for data including G_GL_high and the other for data including ZTT_high. Then, if the latter includes F1, an early stage of fibrosis, and the former includes F2, a later stage, we can understand G_GL_high really did precede ZTT_high. We refer to KeyGraph with the arrows drawn as described above a scenario map.
4.2. Results for hepatitis B The scenario map in fig. 2, for all the data of hepatitis B extracted by TextDrop entering query ‘‘type-B’’, was shown to a hepatic surgeon and a hepatic physician at Step (2) above, in the first cycle. This scenario map was co-manipulated by a KeyGraph expert and these hepatologists at Step (3), as part of a discussion about scenarios of hepatitis cases. Each cycle was executed similarly, presenting a scenario map for the data
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extracted according to the newest concern of the hepatologists. For example, in fig. 2, the dotted links show the bridges between events co-occurring more often than a given threshold of frequency. If there is a group of three or more events which co-occur often, they will be visualised as an island in the overall map shown by KeyGraph. See (Ohsawa, 2003b) for details of KeyGraph. During the co-manipulation of Step (3-1), the hepatologists and the KeyGraph expert grouped the nodes in the circles as in fig. 2, removed inessential nodes from the drawing, and eliminated redundancies that indicated the same symptom (e.g. displaying both ‘‘jaundice’’ and ‘‘T-BIL_high’’ (high total bilirubin)). We took note of the comments the participants made during Step (3-2), as they studied KeyGraph and discussed scenarios for the progression of hepatitis, both deterioration and cure. Each ‘‘?’’ in fig. 2 indicates a portion of the graph that the hepatologists did not understand clearly enough to narrate in the form of a scenario, but indicated as an interesting phenomenon. In figures hereafter, the dotted frames and their interpretations were drawn manually reflecting the hepatologists’ comments. Scenarios obtained by this step reflected common sense understanding about the progress of hepatitis B. The following short scenarios are some examples of those derived from the experts: (Scenario B1) Transition from/to types of hepatitis, e.g. CPH (chronic persistent hepatitis) to CAH (chronic aggressive hepatitis), CAH2A (nonsevere CAH) to CAH2B (severe CAH), and so on. (Scenario B2) Biliary blocks (ALP_high, LAP_high, and G-GTP_high) lead to jaundice i.e. increase in the T-BIL. So D-BIL increases more rapidly than I-BIL, which is from the activation of lien, due to the critical illness of liver. (Scenario B3) Increase in immunoglobulin (G_GL) leads to the increase in ZTT. At Step (4), we applied KeyGraph to the memo of comments obtained in Step (3-2), and obtained fig. 3. According to fig. 3, the hepatologists’ comments can be summarised as: For treatment, diagnosis based on ‘‘bad’’ scenarios in which hepatitis worsens is essential. However, this figure shows a complicated mixture of scenarios of various contexts, i.e. acute, fulminant, and other types of hepatitis. We can learn from this figure that a biliary trouble triggers the worsening of liver, to be observed with jaundice represented by high T-BIL (total bilirubin). An important new concern obtained here is that the scenario map illustrates a mixture of various scenarios, so it should be sorted into
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Fig. 3. KeyGraph to the memo of comments by hepatologists looking at fig. 2.
scenarios representing different contexts – for example, AH (acute hepatitis), CAH2B, CAH2A, etc. – by highlighting events that are common to each scenario. To extract acute hepatitis, we entered ‘‘AH’’ to TextDrop and obtained a scenario map for the extracted data, as shown in fig. 4. This simple output corresponded precisely to the physician’s and surgeon’s experience and knowledge. The increase in gamma globulin (IG_GL) is not seen here, and this absence is a typical pattern for the cases of acute hepatitis. Multiple paths to the cure of disease are displayed in this figure, and in fact AH is more easily cured than other kinds of hepatitis. We next entered ‘‘CAH2B’’ to TextDrop and obtained fig. 5. The early steps progress from symptoms common to most cases of hepatitis, e.g. GOT_high and GPT_high (corresponding to AST_high and ALT_high, in the current European and US terminologies), to more serious symptoms, such as jaundice as represented by I-BIL, D-BIL, and T-BIL. Later steps appearing in the lower left of the figure represent a complex mixture of the cure and the progress of hepatitis, difficult to understand even for hepatologists. However, we acquired a new concern for hepatologists from the partial feature of fig. 5, i.e. we could see that a quick sub-process from LDH_high to LDH_low (LDH: lactate dehydrogenase) can be a significant bridge from a weak hepatitis to a critical state shown by the high value of T-BIL and the low value of CHE (choline esterase). A sudden increase in the value of LDH is sometimes observed in the introductory steps of fulminant hepatitis B, but this is ambiguous
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Fig. 4. The scenario map for acute hepatitis B.
information for treatment because the high value of LDH is common to diseases of internal organs. However, according to the surgeon, the lower LDH is a rare event to appear in the two cases below: 1. A short time in the recovery from CAH and AH 2. The rapid progress (worsening) of fibrosis in fulminant hepatitis. Especially, scenario (2) was in the surgeon’s tacit experience, but not published yet as a medical research paper. The implications of fig. 5 drove us to separate the data that included progressive scenarios from the others, so we extracted the stepwise progress of fibrosis as denoted by F1, F2, F3, and F4 (or LC: liver cirrhosis). Figure 6 is the scenario map for hepatitis B, corresponding to the spotlights of F1, F2, F3, and F4 (LC), i.e. for data extracted by TextDrop with entry ‘‘type-B & (F1 | F2 | F3 | F4 | LC)’’. This figure matched with hepatic experiences, as itemised below. A chronic active hepatitis sometimes changes into a severe progressive hepatitis and then to cirrhosis or cancer in hepatitis B. The final state of critical cirrhosis co-occurs with kidney troubles, and become malignant tumours (cancer) characterised by deficiencies of white blood cells. Recoveries are possible in the earlier stages of fibrosis.
The destruction of liver cells
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Fig. 5. The scenario map for the severe chronic aggressive hepatitis denoted by CAH2B.
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The scenario map for hepatitis B, for the spotlights of F1, F2, F3, and F4.
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The destruction of liver cells, biliary block, jaundice
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The low LDH that appears after high LDH can be an early sign of fulminant hepatitis (see item 2 above). The decrease in Fe can be a turning point from acute illness to recovery from cirrhosis. This matches with preliminary results (Rubin et al., 1995) suggesting iron reduction may improve the response of chronic hepatitis B or C to interferon. However, it has not yet been clarified how iron reduction works over long-term hepatitis progress and recovery. These results are useful for understanding the state of a patient at a given time of observation in the transition process of symptoms, and for finding a suitable time and identifying actions that may improve outcomes in the treatment of hepatitis B.
4.3. Results for hepatitis C For the cases of hepatitis C, as in fig. 7, we also found a mixture of scenarios, e.g. (Scenario C1) Transition from CPH to CAH. (Scenario C2) Transition to critical stages, e.g. cancer, jaundice. These common-sense scenarios are similar to the scenarios in the cases of hepatitis B, but in the hepatitis C scenarios, we also found ‘‘interferon’’ and located a path to the region of cure indicated in fig. 7 with a dotted ellipse. GOT and GPT can be low for two reasons: after the fatal progress of severe hepatitis, as well as when the disease is cured. The latter case is rare because, when the liver is in a normal state, GOT and GPT are expected to take ‘‘normal’’ value (i.e. between the lower and the upper threshold), rather than being ‘‘low’’ (i.e. lower than the lower threshold). However, due to the oscillation of the values of GOT and GPT, we tend to find moments these variables take ‘‘low’’ values in normal states more often than we find them in critical states. Moreover, given the low value of ZTT in this region, it is probable that the case is progressing towards a cure. This suggested an important new concern: that data that included ‘‘interferon & ZTT_low’’ (i.e. interferon has been used, and the value of ZTT recovered) may clarify the role of interferon; namely, how giving interferon to the patient may influence the process of curing hepatitis. For the data that corresponded to this concern, we used TextDrop to create fig. 8, in which, we find features as follows: The values of GPT and GOT are lessened with the treatment using interferon, and then ZTT decreased. Both the scenarios of complete recovery (cure) and worsening disease are found after a fall in ZTT. In the worst scenarios, typically poor symptoms, such as jaundice and low values of CHE and ALB (albumin)
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Recovery hemolytic Critical progress of hepatitis
Changes in proteins
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The scenario map for all the cases of hepatitis C.
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Interferon, and its prompt effects (the recovery indicated by the decrease in ZTT)
Jaundice, cirrhosis, the deficiency in coagulation/ fibrinolysis hemolytic
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Fig. 8. Scenario map for cases with interferon and low values of ZTT.
appear in a set. In the better scenarios, the recovery of various factors such as blood platelets (PL_high) is obvious. In the worst (former) scenario, blood components such as PL are lessened. In the better (latter) scenario, the changes in the quantity of proteins are remarkable. Among these, F-A2_GL (a2 globulin, known to be composed of haptoglobin, which prevents critical decrease in iron by being coupled with haemoglobin before haemoglobin gets destroyed to make isolated iron) and F-B_GL (beta globulin, composed mostly of transferring, which carries iron for reusing it to make new haemoglobin) are relevant to the metabolism of iron (FE). In the dotted circle of ‘‘recovery’’, F-B_GL is consumed for carrying iron.
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The physician and the surgeon both supported the plausibility about the significance of these scenarios. To summarise them briefly, the effect of interferon is to support the patient cure only if the recycling mechanism of iron is active. In fact, the relevance of iron in hepatitis has been a rising concern of hepatologists, since (Hayashi et al., 1994) verified the effect of iron reduction in curing hepatitis C. We assumed that the change in F-A2_GL is relevant to the role of interferon in curing hepatitis C and we obtained the scenario map in fig. 9, showing that cases treated with interferon, in which there was a change in value of F-A2_GL (i.e. taken by TextDrop for the entry ‘‘F-A2_GL_low & F-A2_GL_high & interferon & type-C’’) experienced a significant turning point towards recovery with the increase in the value of TP (total protein). Furthermore, the event TP_high is linked with F-B_GL, mentioned above. These features correspond to fig. 7, in which the region of high globulins and high total protein (TP_high) appear in the process of curing hepatitis C. In the region framed by the dotted line in fig. 9, the decrease in GOT and GPT, followed by low ZTT, matches
Fig. 9. Scenario map for cases with F-A2_GL_high and F-A2_GL_low, and interferon. The effect of interferon is clarified at the top of the map.
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the scenarios depicted in fig. 7, as well as the results reported in (Tsumoto et al., 2003). Moreover, levels of the antibody HCV-AB of HCV (virus of hepatitis C) fell as well.
5. DISCUSSION: SUBJECTIVE BUT TRUSTWORTHY In the work reported here, we obtained some new qualitative, but significant, findings. For example, the low value as well as the high value of LDH seems to be relevant to the turning point of fulminant hepatitis B as it shifts to critical stages. This means a doctor should not be relieved when the value of LDH decreases simply because the opposite symptom, i.e. the increase in LDH, is understood as a sign of worsening hepatitis. Second, the effect of interferon is relevant to the change in the quantity of protein, especially ones relevant to iron metabolism (e.g. F-A2_GL and F-B_GL). The effect of interferon, as a result, appears to begin with the recovery of TP. These tendencies are apparent in both figs. 7 and 9. However, it remains unknown whether interferon is affected by such proteins as globulins, or if iron metabolism and interferon are two co-operating factors in the cure of hepatitis. Over all, the physician and the surgeon agreed that the process produced ‘‘reasonable, and sometimes novel and useful’’ scenarios of hepatitis progression and cure. Although not covered here, we also found other scenarios that seemed to indicate significant situations. For example, the increase in AMY (amylase) in figs. 1, 4–6 may be relevant to surgical operations or liver cancers. The relevance of amylase corresponds to (Miyagawa et al., 1996), and its relevance to cancer has been pointed out in a number of references such as (Chougle et al., 1992). These are the benefits of the double helix (DH) framework that focusses on the concerns of a user in interaction with target data. It is true that the subjective bias of the hepatologists’ concern influenced the results obtained in this manner. Moreover, this subjectivity may be used by scientists in discounting the merits of results obtained by DH. However, we believe the results are trustworthy, because they represent a summary of objective facts as selected through the lens of the hepatologists’ concerns. We believe that a positive aspect of this combination of subjectivity and objectivity is a broad range of knowledge, expressed in the form of scenarios, that can be useful in real-world decisions. We say this because a sense of importance and recognition, experienced subjectively, is an important form of cognition that enables humans to identify and study interesting parts of their wider environment. This subjective feeling of interestedness is a basic requirement for the production of useful knowledge.
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6. CONCLUSIONS As a tool for chance discovery, scenario emergence is useful for realworld decisions. In the real world, events are dynamic and unpredictable, and decision makers are required to make decisions promptly when they believe that a chance – a significant event – may be taking place. Here we have demonstrated an application of scenario emergence involving the discovery and representation of triggering events of essential scenarios in the domain of hepatitis progress and treatment. Subject matter experts indicated that the process we have described resulted in scenarios that were both novel and realistic. In the method presented here, the widening of user’s views was aided by the projection of users’ personal experiences on an objective scenario map that displayed a selection of contexts in the wider real-world. The process of narrowing the data involved focusing the users’ concerns and employing the TextDrop tool. Like a human wandering through unfamiliar terrain, a doctor wondering how a patient’s illness will progress might be helped with an overall scenario map that corresponds to the objective facts in the environment, as well as a more focussed range of the map that corresponds to his current concern with the patient. The newer the symptoms, and the more ambiguous the future, the more useful will be the map described here. We are currently developing tools to make the double helix process of discovery more efficient by combining the functions of KeyGraph and TextDrop, and further integrating with visual interfaces to enable the emerging concerns of users to feedback into new cycles of the spiral discovery process.
ACKNOWLEDGMENT The study was conducted by Scientific Research in the Priority Area ‘‘Active Mining’’. We are grateful to Chiba University Hospital for providing us valuable data under the convenient contract of its use for research.
REFERENCES Chougle, A., Hussain, S., Singh, P.P., Shrimali, R., 1992. Estimation of serum amylase levels in patients of cancer head and neck and cervix treated by radiotherapy. J. Clin. Radiother. Oncol. 7(2), 24–26. Gaver, W.W., Beaver, J., Benford, S., 2003. Ambiguity as a resource for design, Proceedings of Computer Human Interactions 2003.
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Hayashi, H., Takikawa, T., Nishimura, N., Yano, M., Isomura, T., Sakamoto, N., 1994. Improvement of serum aminotransferase levels after phlebotomy in patients with chronic active hepatitis C and excess hepatic iron. Am. J. Gastroenterol. 89, 986–988. Kawakita, J., 2000. KJ Method: A Scientific Approach to Problem Solving. Kawakita Research Insitute, Tokyo. Miyagawa, S., Makuuchi, M., Kawasaki, S., Kakazu, T., Hayashi, K., Kasai, H., 1996. Serum Amylase elevation following hepatic resection in patients with chronic liver disease. Am. J. Surg. 171(2), 235–238. Ohsawa, Y., 2003a. Modeling the process of chance discovery. In: Ohsawa, Y., McBurney, P. (Eds.), Chance Discovery, Springer-Verlag, pp. 2–15. Ohsawa, Y., 2003b. KeyGraph: visualised structure among event clusters. In: Ohsawa, Y., McBurney, P. (Eds.), Chance Discovery, Springer Verlag, pp. 262–275. Ohsawa, Y., McBurney, P., 2003. Chance Discovery. Springer-Verlag, Heidelberg. Rubin, R.B., Barton, A.L., Banner, B.F., Bonkovsky, H.L., 1995. Iron and chronic viral hepatitis: emerging evidence for an important interaction. Dig. Dis. 13(4), 223–238. The Danish Board of Technology, 2003. European participatory technology assessment: participatory methods in technology assessment and technology decision-making. Taken from the world wide web at page http://www.tekno.dk/europta on 6 April 2005. Tsumoto, S., Takabayashi, K., Nagira, N., Hirano, S., 2003. Trend-evaluating multiscale analysis of the hepatitis dataset, Annual Report of Active Mining, Scientific Research on Priority Areas, pp. 191–198. Usui, M., Ohsawa, Y., 2003. Chance Discovery in Textile Market by Group Meeting with Touchable Key Graph. On-line proceedings of social intelligence design international conference. Taken from the world wide web at page http://www.rhul.ac.uk/Management/ News-and-events/conferences/SID2003/tracks.html on April 6, 2005.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
13 Modelling the in vivo growth rate of HIV: implications for vaccination Ruy M. Ribeiroa, Narendra M. Dixitb and Alan S. Perelsona a
Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, USA b Department of Chemical Engineering, Indian Institute of Science, Bangalore, India
1. INTRODUCTION According to the UNAIDS2003 report, more than 40 million people are currently living with human immunodeficiency virus (HIV) infection worldwide. Despite the efforts on educational campaigns and the development of potent antiretroviral drugs, the acquired immunodeficiency syndrome (AIDS) epidemic continues to spread. In 2003, 3 million people died and about 5 million people were newly infected (UNAIDS, 2003). It now appears that only a truly preventive vaccine can control the HIV/AIDS pandemic. However, whether the development of a preventive vaccine for HIV infection is possible still remains uncertain. HIV infection occurs mainly through contact of bodily fluids, especially contaminated blood, through needle sharing, and by sexual transmission. Once the virus crosses the protective mucosal barrier it infects a variety of cells of the immune system, in particular CD4þ T-helper cells, macrophages, and dendritic cells. By subverting these important components of the immune system, the infection eventually leads to a general state of immune deficiency, known as AIDS. Certain characteristics of the virus, such as its ability to remain silent in latently infected cells or viral reservoirs for long periods, make treatment and viral eradication very difficult (for details on HIV/AIDS see for instance (Wormser, 2004). An effective HIV vaccine would equip the immune system with the ability to elicit sufficiently rapid, powerful, and specific anti-HIV responses when faced with an infection so that the virus is eradicated before it can establish 231
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long-lived infection. Of critical interest to vaccine design therefore is an understanding of how rapidly HIV multiplies and spreads in an infected individual and whether it can establish long-lived infection given the strength of the host-immune response. Whether a virus can establish infection can be determined by a quantity called the ‘‘basic reproductive ratio’’, R0 (Anderson and May, 1991; Heesterbeek and Dietz, 1996; Nowak and May, 2000). Consider a single host cell infected by HIV. HIV multiplies within the cell releasing progeny virions, which are either cleared, neutralised, or infect new host cells. R0 is the number of new host cells infected by the progeny virions. If R041, it follows that the infected cell transmits infection to more than one uninfected cell during its lifetime. The virus thus grows and successfully establishes infection within the host. If, on the other hand, R051, one infected cell transmits infection to less than one uninfected cell during its lifetime and the infection will eventually die out. Thus, R0, defined more precisely as the number of secondary infections originated by an infected cell in a wholly susceptible population, is a yardstick to measure the success of infectious viral growth. Clearly, R041 for HIV since long-term infection is established in most infected individuals. The aim in vaccine development is to boost the immune response and drive R0 below 1. In principle, R0 can be determined from the initial growth of the virus in an infected individual and the lifespan of an infected cell. However, this is usually very difficult, because very few patients are detected at the very early stages of infection when these measurements would have to be taken. Alternatively, if we have an explicit model of infection spread, we can calculate R0 from first principles in terms of the parameters of the model, which can be estimated by comparisons of model predictions with data, for instance the evolution of viral load under antiretroviral therapy. In this chapter, we describe standard models of HIV infection, for which we estimate parameters by data analysis and calculate R0. At the same time, we calculate R0 from the limited data available on the initial growth rate of HIV in humans and macaques. Based on comparisons of these calculations, we discuss implications for vaccine design.
2. A MODEL OF HIV INFECTION We begin by considering an ordinary differential equation model of the viral lifecycle (Nowak and May, 2000; Perelson, 2002; Di Mascio et al., 2004). Ordinary differential equations are commonly used in biological
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modeling to describe the rates of change of various quantities. Here we will focus on the changes in the quantity of cells that HIV infects and the quantity of virus. Although HIV infects different types of cells, with variable replication rates, there is a consensus that the bulk of HIV production occurs in CD4þ T-cells (Finzi and Siliciano, 1998). Thus a basic model of HIV infection only includes target CD4þ T-cells (T ), productively infected cells (T*), and free virus (V ). Target cells are assumed to be produced at constant rate l, and die at rate d per cell. In an uninfected individual, a steady state concentration of CD4þ T-cells is established at T ¼ l=d. However, in infected patients, HIV infects target cells at a rate proportional to the numbers of uninfected cells and free virus, with second order rate constant k. In other words, cells are assumed to become infected at rate kVT. Infected cells die at rate per cell, which is higher than the death rate of uninfected cells (d ). Finally, virus is produced from infected cells at rate p per cell, and is cleared at rate c. Figure 1 represents this system in schematic form, and the corresponding equations are: dT ¼ l dT kVT dt
ðEq: 1Þ
dT ¼ kVT T dt
ðEq: 2Þ
dV ¼ pT cV dt
ðEq: 3Þ
This basic model assumes that an infected cell begins producing virus immediately upon infection. In general, however, there is a delay ( )
λ
k T*
T V
p
d
δ
c
Fig. 1. Schematic representation of the model in Equations (1)–(3). Target cells (T ) are produced at rate l, and die at rate d per cell. HIV infects target cells at a rate proportional to k and infected cells die at rate per cell. Finally, virus is produced from infected cells at rate p per cell, and is cleared at rate c.
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between infection and the time a cell begins producing virus. If the delay is assumed to be constant, it could be incorporated in the above equations by replacing the first term in Equation (2) by kV(t )T(t )em , where m is the death rate of infected cells not yet producing virus, reflecting the fact that the number of infected cells that survive (the exponential factor) to become productively infected in the present depends on the number of virions and uninfected cells existing time units before (Herz et al., 1996; Mittler et al., 1998; Nelson et al., 2000, 2001; Nelson and Perelson, 2002). As we will show, taking this delay into account is crucial for the determination of R0 from the initial viral growth curve. To derive an expression for R0 based on the above model, we consider T0 productively infected cells introduced at time t ¼ 0 in a unit volume of a population of target cells with a number density equal to that in the uninfected steady state, T ¼ l=d. Since productively infected cells die with a first order rate constant , the number density of the introduced cells at a later time, t, is given by T ðtÞ ¼ T0 et . The number density of virions produced by these cells evolves according to Equation (3). Substituting for T *(t) in Equation (3) and integrating, we find VðtÞ ¼ pT0 ðet ect Þ= ðc Þ, where we have employed the initial condition, V(0) ¼ 0, as no free virions exist at time t ¼ 0. The rate at which virions infect target cells is kVT, Ð 1 so that the total number of target cells infected by these virions is 0 kVðtÞTdt ¼ kpT0 l=cd, where we have assumed that target cells remain at their steady state value. Thus, from one productively infected cell, T0 ¼ 1, we obtain R0 ¼
kpl cd
ðEq: 4Þ
new infected cells. In models where we include a constant intracellular delay, , the expression of R0 above is multiplied by em . R0 in Equation (4) is expressed in terms of model parameters, which we estimate below by comparing different types of data to the predictions of the model in Equations (1)–(3) and its variations.
3. HIGHLY ACTIVE ANTIRETROVIRAL TREATMENT (HAART) AND DATA ANALYSIS In 1995–96 potent drugs against HIV infection were introduced. Many people treated with these drugs experienced a sharp decline of virus measured in their blood in the first few weeks of treatment (Ho et al., 1995;
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Start of treatment
Log10 viral load
Delay
Initial phase of decay, corresponding to c and δ
“First” phase of decay, corresponding to δ Steady state
Subsequent phases of decay
Years
Hours/Days
Days/Weeks Months/years Time
Fig. 2. Schematic representation of the viral load decline upon initiation of treatment. Before treatment virus is at a quasi-steady state, which can last for years. After initiation of treatment, there is a delay before the virus starts declining, corresponding to a pharmacological and physiological delay (see text). The initial phase of the decline reflects the rate constants of free virion clearance, c, and infected cell removal, . These two phases can last from hours to a couple of days. A fast decline, commonly designated ‘‘first phase decline’’, ensues reflecting and can last a couple of weeks. Subsequent phases of decline require more complicated models to be analysed (Di Mascio et al., 2004) and can last months or years.
Wei et al., 1995). In fig. 2, we present the schematics of a typical profile of viral load change upon initiation of this highly active antiretroviral treatment (HAART). The drugs used fall into two main classes, according to which step of the viral life cycle they inhibit. Reverse transcriptase inhibitors disrupt the reverse transcription of the viral RNA into DNA, which is necessary after cell infection but before the viral genome can be integrated into the cell’s genome. Thus, these drugs prevent infection of new cells. The other class of drugs, called protease inhibitors, inhibits the function of the viral protease. This enzyme is necessary to cut the viral polyprotein formed by transcription of the integrated proviral DNA into smaller functional proteins. If this cutting does not occur, non-infectious virus particles, which are still quantified by our measuring assays, are formed. The effects of these drugs can be incorporated into the basic viral dynamics model of Equations (1)–(3). Reverse transcriptase inhibitors reduce the infection rate of virus, and hence k in Equation (2). Protease inhibitors reduce the production of infectious viruses (VI), and originate
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new non-infectious virus (VNI). We then rewrite the equations for viral dynamics as dT ¼ l dT ð1 "RT ÞkVT dt dT ¼ ð1 "RT ÞkVT T dt dVI ¼ ð1 "PI ÞpT cVI dt dVNI ¼ "PI pT cVNI dt
ðEq: 5Þ ðEq: 6Þ ðEq: 7Þ ðEq: 8Þ
where 0 "RT, "PI 1 are parameters that quantify the efficacies of reverse transcriptase inhibitors and protease inhibitors, respectively. Here, we assume that infectious and non-infectious virions have the same clearance rate, c. If we assume that the total number of uninfected cells (T ) remains approximately constant, which is usually true for short periods on therapy, Equation (5) can be decoupled from the other equations. The resulting linear system can be solved for the number of infectious and non-infectious virions (Perelson and Nelson, 1999). Assuming the system is at the infected equilibrium before the start of treatment, the time evolution of viral load V(t) ¼ VNI(t) þ VI(t) can be determined. By fitting the solution to measurements of viral load data, and (usually) assuming "RT, "PI ¼ 1, estimates of and c are obtained (Perelson, 2002). Over the years, increased frequency and accuracy of measurements of viral loads have led to increasingly refined estimates of and c. The best estimates currently available set and c at 1 day1 and 23 day1, respectively (Ramratnam et al., 1999; Markowitz et al., 2003). We note that these current best estimates are in great measure independent of the inclusion or not of the intracellular delay, . Indeed, Herz et al. (1996) show that the estimate of from treatment data, as presented above, is quite insensitive to the intracellular delay; whereas the estimate of c does depend on this delay. However, the c ¼ 23 day1 estimate comes from a set of independent experiments based on plasma apheresis, which again are independent of the intracellular delay (Ramratnam et al., 1999).
4. PHARMACODYNAMIC ANALYSES AND VIRAL DYNAMICS ESTIMATES Estimates of k and p are more difficult to obtain. We have recently reported on pharmacodynamic analyses of HIV drug treatment that lead
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to estimates of these parameters (Dixit et al., 2004; Dixit and Perelson, 2004). Here, we describe this analysis for monotherapy with the potent protease inhibitor ritonavir. Explicit incorporation of drug pharmacokinetics allows us to relax the simplifying assumption employed above that "PI ¼ 1. Instead, a two-compartment pharmacokinetic model consisting of blood and cells is employed to determine the drug concentration in blood, Cb, the intracellular drug concentration, Cc, and the time-dependent drug efficacy of ritonavir according to the following equations (Dixit et al., 2004; Dixit and Perelson, 2004): ke t FD ka e Cb ðtÞ ¼ k Vd ke ka e a Id 1 2 3 1 eðke ka Þt 1 eNd ka Id 6 7 ðNd 1Þke Id 7 6 4 kI 5 e 1 ððNd 1Þke þka ÞId ka Id e d e þ e e k I e d e 1 Cc ðtÞ ¼ ð1 fb ÞHCb ðtÞ "PI ðtÞ ¼
Cc ðtÞ : IC50 þ Cc ðtÞ
ðEq: 9Þ
ðEq: 10Þ ðEq: 11Þ
Ritonavir, administered orally, is absorbed into blood with the first order rate constant ka and eliminated from blood with the first order rate constant ke. Equation (9) describes the time evolution of Cb, with t ¼ 0 marking the administration of the first dose. F is the bioavailability of the drug, and Vd is the volume of distribution dependent on W, the body weight in kilograms, such that Vd/F ¼ (410 250)W ml, where we have taken into consideration the observed patient-to-patient variability in these parameters. D ¼ 600 mg is the dosage, Id ¼ 0.5 day is the dosing interval, and Nd is the number of doses administered until time t. For a patient with W 70 kg, independent pharmacokinetic studies yield ka ¼ 19 day1 and ke ¼ 8.2 day1 with uncertainties of 50–100% in either quantity (see (Dixit et al., 2004), for the estimation of parameter values). From blood, the drug enters cells, where it performs its therapeutic function. In vitro experiments indicate that ritonavir equilibrates rapidly across the cell membrane so that Equation (10) yields the time dependent intracellular concentration of ritonavir, Cc. In this equation, fb ¼ 0.99 is the fraction of ritonavir bound to plasma proteins and hence incapable of entry into cells, and H ¼ 0.052 is the partition coefficient giving the ratio of the equilibrium concentrations of ritonavir on either
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side of the cell membrane (Dixit and Perelson, 2004). Following standard pharmacodynamic descriptions, the function in Equation (11) is then employed to determine the time dependent efficacy of ritonavir, where IC50 is that value of Cc at which the drug is 50% efficacious. Setting "RT ¼ 0 and using "PI as input in Equations (5)–(8) above yields a model of viral dynamics that explicitly incorporates the effects of drug pharmacokinetics. With the aforementioned modifications to Equation (6) to account for the intracellular delay, the above equations can be integrated to predict the time evolution of plasma viral load under ritonavir monotherapy. Model predictions were compared with data from five patients under ritonavir monotherapy to obtain best-fit estimates of the production rate p, the intracellular delay, , and the IC50 (Dixit et al., 2004). In these comparisons, c and were set at 23 day1and 1 day1 respectively, and the second order infection rate constant k was set at 2% of its diffusion limited value, 2.4 108 ml day1. The average parameter estimates obtained were ¼ 1 0.5 day, IC50 ¼ 8 107 mg/ml, and p 1200 200 cell1 day1. While uncertainties exist in the above estimate of k, it can be shown that variation in k results in a variation in the best-fit estimates of p such that the product pk remains approximately constant. Thus, uncertainties in k will not affect our estimate of R0. Below, we therefore employ these estimates of k and p to determine R0.
5. PARAMETER ESTIMATES FROM T-CELL NUMBER DENSITIES IN VIVO The ratio of the final two parameters, l and d, can be estimated from the equilibrium value of CD4 þ T-cells in an uninfected individual. An uninfected individual has about 1000 CD4 þ T-cells/ml in the blood. Thus, l/d ¼ 106 cells/ml. Although this is the average number of CD4 þ T-cells in a healthy individual, it is unlikely that all of them are available for HIV infection. HIV preferentially infects cells that are dividing. In an uninfected individual, about 1% of CD4 þ T cells are dividing (Sachsenberg et al., 1998; Ribeiro et al., 2002), indicating that l/d may only be about 104 cells/ml. In lymph nodes, or mucosa, where infection primarily spreads and cell densities are intrinsically higher, the numbers of dividing CD4 þ T-cells could be higher than 106 cells/ml (Haase, 1999; Schacker et al., 2001). Further, more recent studies have shown that HIV can infect resting cells (Zhang et al., 1999), thus bringing l/d to some value between 104 and 4106 cells/ml. Here, we let l/d ¼ 106 cells/ml for our calculations of R0.
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6. ESTIMATES OF R0 FROM DYNAMIC MODELING Putting together the best estimates obtained from the different data analyses, we can estimate R0. With l/d ¼ 106 cell/ml, p ¼ 1200 cell1 day1, k ¼ 2.4 108 ml/day, c ¼ 23 day1, ¼ 1 day1, we find R0 1.25. However, if we consider the intracellular delay, this estimate is reduced slightly since em ¼ 0.9, if we assume m ¼ 0.1 day1 and ¼ 1 day (Dixit et al., 2004). Thus with the intracellular delay R0 1.13. While obtaining viral load measurements early in the infection process is rare, we did have the opportunity to analyse data from 10 patients detected during primary HIV-infection (Stafford et al., 2000). These patients were followed from presentation with acute infection syndrome, to a couple of months (and in eight cases up to a year) post-infection. We fitted the viral load data during this early period to the model defined by Equations (1)–(3), and obtained estimates for all the relevant parameters. Estimation of R0 showed that it varied between 2.8 and 11, with an average of 6 (Stafford et al., 2000).
7. CALCULATING R0 FROM THE INITIAL GROWTH CURVE In a population of wholly susceptible cells, if the virus has R041, the initial growth of the virus is roughly exponential, with a rate dependent on R0. This can be demonstrated for the simple model given by Equations (1)–(3). If we assume that initially the target cell population remains approximately constant at its pre-infection equilibrium value (l/d ), the initial growth rate r is given by the largest eigenvalue of the linear system (Lloyd, 2001; Nowak et al., 1997) dT ¼ kV T T dt dV ¼ pT cV: dt
ðEq: 12Þ
This eigenvalue corresponds to the dominant solution of the characteristic equation r2 þ ð þ cÞr þ cð1 R0 Þ ¼ 0,
ðEq: 13Þ
where we used T ¼ l=d and R0 is given by Equation (4). Thus, we have a relationship between r and R0 given by r r r 1þ 1þ , ðEq: 14Þ R0 ¼ 1 þ c
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where R0 is given by Equation (4) and the latter approximation follows from c and c r, as suggested by current estimates. If patients are identified early enough following infection, we can measure the virus growth rate, r, and use this formula to calculate R0, with the available estimates for (and c). The link between R0 and the initial growth rate, r, depends on the model employed. For example, if there is a delay between infection of a cell and production of virus, this will change Equation (14) and affect the prediction of R0 from r. For a detailed exposition of these issues see (Anderson and Watson, 1980; Lloyd, 2001). Here, we restrict our discussion to the case where the delay is modeled as a series of intermediate states, the so-called ‘‘method of stages’’ (Cox and Miller, 1965; Grossman et al., 1998; Mittler et al., 1998; Nelson et al., 2000; Lloyd, 2001). These states may or may not have biological significance, but mathematically they allow for the consideration of a distributed delay between cell infection and virus production that has a gamma probability distribution. The equations defining the system are dS1 ¼ kVT n!S1 jmS1 dt .. . dSn ¼ n!Sn1 n!Sn jmSn dt dT ¼ n!Sn T dt dV ¼ pT cV dt
ðEq: 15Þ
Upon infection, a cell goes through n non-productive stages, Si, until it becomes productively infected, T*. At each stage jm is the death rate of a cell in that stage, if j ¼ 0 non-productive cells do not die, and if j ¼ 1 we guarantee that the average lifespan of an infected cell, not yet productive, is 1/m. Likewise, the factor n! keeps the average delay at ¼ 1/!, independently of the number of stages, n. In the special case of n ¼ 1, the delay is exponentially distributed, and for n ! 1 it corresponds to a fixed delay of 1/!. Again, the initial growth rate r is the dominant solution of the characteristic equation for this linear system l ð1Þn1 pk ðn!Þn þ ð1Þn ðc þ rÞð þ rÞðn! þ jm þ rÞn ¼ 0 d
ðEq: 16Þ
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which can be re-arranged to r r jm þ r n 1þ 1þ R0 ¼ 1 þ : c n!
ðEq: 17Þ
When n goes to zero, and there is no delay, we recover expression (14). In the two special cases of exponential delay, when n ¼ 1, and fixed delay, when n goes to infinity, we obtain, respectively, with j ¼ 1 lpk ! r r ¼ 1þ 1 þ ð1 þ ðm þ rÞ Þ cd m þ ! c lpk m r r R0 jn!1 ¼ e 1 þ eðmþrÞ : ¼ 1þ cd c
R0 jn¼1 ¼
ðEq: 18Þ
where we also show the corresponding expressions obtained from the parameter formulation of R0 with an exponential and a fixed delay, respectively. To determine R0, we therefore need to know with some precision the magnitude of the delay and its distribution. For instance, with c ¼ 23 day1, ¼ 1 day1, and m ¼ 0.1 day1 as before, and a growth rate of about 2 day1, observed both in humans infected with HIV-1 (Little et al., 1999) and macaques infected with SIV isolates E660 and E543-3 (Nowak et al., 1997), we estimate R0 ¼ 3.3 with no delay, and R0 ¼ 10.1 or R0 ¼ 26.3, if the delay is exponentially distributed with average one day or if it is fixed at one day, respectively. In table 1 (see appendix), we reproduce the values estimated for the early growth rate of viral load found in HIV infected humans and SIV infected macaques (Nowak et al., 1997; Little et al., 1999). From these, we calculate R0, using Equations (14) and (18), with c ¼ 23 day1, ¼ 1 day1, and m ¼ 0.1 day1. With an average ¼ 1 day, we find R0 ¼ 8 4.2 for an exponentially distributed delay and R0 ¼ 17 44 for a fixed delay. Higher values are obtained if ¼ 1.5 day is assumed. Also, R0 is consistently higher for macaques infected with SIV isolates E660 and E543-3 than humans infected with HIV-1. However, different isolates of SIV or HIV-1 may have different growth properties and hence different R0 values.
8. COMPARISONS AND LIMITATIONS In table 2 (see Appendix), we summarise the values obtained for R0 by the different methods described above. There are obvious differences in the calculated values of R0, especially when we consider intracellular delay.
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Yet, independent estimates from different experiments and model fits suggest that R0 may be as low as 1.1–8. This indeed would give an optimistic view in terms of the target for vaccine efficacy, where the aim is to reduce R0 below unity. Vaccines can be designed to lower R0 via several routes (Ho and Huang, 2002). For instance, a vaccine that elicits an antibody mediated response will lower R0 by increasing the clearance rate c and/or decreasing the infection rate k by opsonizing and/or neutralizing free HIV virions, respectively. Similarly, a vaccine that induces a cell mediated response will lower R0 by enhancing the death rate of productive cells, , and perhaps through the secretion of antiviral factors lowering the production rate p. Ho and Huang (2002) present a detailed discussion of the current status of vaccine research together with the impending challenges. There the importance of accurately estimating R0 is further emphasised in order to establish the magnitude of the impact sought from a vaccine. The above estimates show that a better understanding of the intracellular delay is crucial for an accurate estimate of R0 from the initial growth rate of the virus. Realistic models must include this delay. Recent studies indicate the delay to be 1–1.5 days (Perelson et al., 1996; Reddy and Yin, 1999; Tomaras et al., 2000; van’t Wout et al., 2003), but the distribution of this delay remains poorly understood. As shown in table 1, estimates of R0 are sensitive to this distribution. In general, data on the initial growth rate of the virus seem to indicate that R0 is larger than what is calculated by parameter estimation, with values between 6 and 30 for an exponentially distributed delay.
9. CONCLUSIONS Developing a vaccine to prevent HIV infection is a priority, especially in developing countries where treatment costs are prohibitive. Here we combined theory with data analysis to understand the rapid initial growth of virus in an infected individual. This approach is based on the estimation of the basic reproductive ratio, R0. In untreated individuals, HIV spreads establishing infection, so that R041. Here, we find R0 to lie between 1.2 and 30 depending on the method of estimation. The goal of a vaccine is to boost the immune response and drive R0 below 1 so that the virus can be eradicated following infection. Refining estimates of R0, for instance by measuring more accurately the key parameters, will quantify the impact a vaccine must have in terms of the drop in R0 necessary to successfully combat infection. At the same time, comparisons of estimates of R0 will establish the relative efficacies of different vaccines and protocols.
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ACKNOWLEDGEMENTS Portions of this work were performed under the auspices of the U.S. Department of Energy and supported by contract W-7405-ENG-36. In addition, we acknowledge support from NIH grants AI28433 and RR06555 (ASP); and from a Marie Curie Fellowship of the European Community program ‘‘Quality of Life’’, contract number QLK2-CT-2002-51691 (RMR).
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van’t Wout, A.B., Lehrman, G.K., Mikheeva, S.A., O’Keeffe, G.C., Katze, M.G., Bumgarner, R.E., Geiss, G.K., Mullins, J.I., 2003. Cellular gene expression upon human immunodeficiency virus type 1 infection of CD4(þ)-T-cell lines. J. Virol. 77, 1392–1402. Wei, X., Ghosh, S.K., Taylor, M.E., Johnson, V.A., Emini, E.A., Deutsch, P., Lifson, J.D., Bonhoeffer, S., Nowak, M.A., Hahn, B.H., et al., 1995. Viral dynamics in human immunodeficiency virus type 1 infection [see comments]. Nature 373, 117–122. Wormser, G.P. (Ed.), 2004, AIDS and Other Manifestations of HIV Infection. Elsevier, Amsterdam. Zhang, Z., Schuler, T., Zupancic, M., Wietgrefe, S., Staskus, K.A., Reimann, K.A., Reinhart, T.A., Rogan, M., Cavert, W., Miller, C.J., Veazey, R.S., Notermans, D., Little, S., Danner, S.A., Richman, D.D., Havlir, D., Wong, J., Jordan, H.L., Schacker, T.W., Racz, P., Tenner-Racz, K., Letvin, N.L., Wolinsky, S., Haase, A.T., 1999. Sexual transmission and propagation of SIV and HIV in resting and activated CD4þ T cells. Science 286, 1353–1357.
APPENDIX: TABLES OF VALUES Table 1 Estimates of the basic reproductive ratio from the early growth rate of virus (data from Nowak et al., 1997 and Little et al., 1999) Basic reproductive ratio (R0) Delay 1 day
Humans A B C D Mean1 Std. Err. Macaques A B C D E F G H I J K L Mean1 Std. Err. 1
1.5 days
Growth rate
No delay
Exponential
Fixed
Exponential
Fixed
1.5 3.5 1.4 1.6 1.8 0.5
2.7 5.2 2.5 2.8 3.0 0.6
6.9 23.9 6.4 7.5 8.4 4.2
13.2 189.8 11.4 15.2 17.1 44.1
9.1 33.2 8.3 9.9 11.0 6.0
29.4 1147.9 24.2 35.6 38.3 279.6
1.7 1.8 2.0 2.2 2.3 1.7 1.7 2.0 2.1 2.2 2.7 2.7 2.0 0.1
2.9 3.0 3.2 3.4 3.6 2.9 2.9 3.2 3.4 3.5 4.1 4.1 3.3 0.1
7.9 8.8 9.8 11.2 12.3 7.9 8.2 9.9 11.1 11.3 15.6 15.6 10.3 0.8
16.6 20.2 25.2 32.7 40.0 16.8 17.8 25.6 32.2 33.1 67.1 67.1 26.6 5.1
10.4 11.6 13.1 15.1 16.7 10.5 10.8 13.2 15.0 15.2 21.4 21.4 13.7 1.1
40.0 52.2 70.6 100.7 132.9 40.7 44.0 71.9 98.8 102.5 270.8 270.8 73.1 23.5
Harmonic means.
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Table 2 Estimates of the basic reproductive ratio (R0) Basic reproductive ratio1 – R0 Exponential delay
Parameter estimation Stafford et al. (2000) Little et al. (1999) Nowak et al. (1997) 1
1.2 5.4 3.0 3.3
Due to large variations we used harmonic means.
1 day
1.5 days
1.09 4.9 8.4 10
1.04 4.7 11 14
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
14 A flexible, iterative approach to physiological modelling Murad Banajia,1 and Stephen Baigentb a
Department of Medical Physics and Bioengineering, University College London, London, UK b Department of Mathematics, University College London, London, UK
1. INTRODUCTION We explore some of the issues that arise when modelling physiology with a view to constructing medically useful models. Although some of the issues we discuss are fairly abstract, they all arise from concrete work on a specific system – the cerebral circulation – aimed at creating mathematical models to help understand cerebrovascular disorders. The ultimate aim has been to produce a computational model able to assist in the real-time interpretation of clinical signals and even to guide clinical decisions. Progress in this direction is described in Banaji et al. (2005), while an early version of the model is available on the web (Banaji, 2004). During the modelling work, a number of questions have arisen which go well beyond the details of the cerebral circulation. They include for example: Where should the boundaries of a model lie – what do we choose to exclude from the model? How can one deal with incomplete knowledge? What interplay should there be between experimental data and model construction? How can such models be tested?
1
Funded by an EPSRC/MRC grant to the MIAS IRC (Grant Refs: GR/N14248/01 and D2025/31).
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We will illustrate these questions with particular examples. None of them have simple answers applicable to every situation – what we hope to outline here instead are some guiding principles. Our most important general conclusions are about the modelling process itself. In particular, the reality that models are forced to have artificial boundaries suggests that we should construct them in ways which allow easy communication/combination with other models. Further, the fact that we are often faced with situations of incomplete knowledge suggests that models should be easy to update in response to new physiological knowledge. Both of these requirements lead naturally to modular structures, a theme we explore in some detail.
2. CEREBRAL AUTOREGULATION: DEFINING THE PROBLEM Our research started with the task of understanding cerebral autoregulation, broadly defined as the ability of the brain circulation to maintain certain physiologically important quantities within fairly narrow bounds despite wide variation in other quantities. We were interested in how this ability manifests normally, and how it can be affected by pathologies. The most frequently cited example of a quantity which is autoregulated is cerebral blood flow (CBF), which normally responds to significant changes in arterial blood pressure (ABP) with only slight variation. If the circulatory system were just a system of elastic pipes, then changing pressure would rapidly change blood flow, with potentially disastrous consequences. Thus for autoregulation to occur, there must be blood vessels whose diameter is actively controlled in such a way as to maintain blood flow. Understanding how this process fails, for example during stroke or haemorrhage, is of key clinical importance. There are a number of approaches to explain autoregulation. To understand them, it is helpful first of all to examine autoregulation more abstractly. Very generally, some quantity T is autoregulated with respect to a stimulus S if it is insensitive to S when the simplest arguments would suggest that it should not be.2 Autoregulation as thus defined is ubiquitous, if often unnamed, in nature: the pH of a buffer solution is autoregulated in response to the addition of acids or alkalis; homeothermic organisms autoregulate their temperature in response to changing 2
This caveat is important to avoid trivial cases: The rate of rotation of the earth is insensitive to changes in an individual’s blood pressure, but this cannot be called autoregulation!
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T
stimulus S
So
Fig. 1. A typical autoregulation curve. T is well autoregulated in a region around S ¼ So, i.e. its steady state value changes only gradually in response to the changes in S. Often however, there are limits beyond which autoregulation breaks down. In the example shown, autoregulation eventually fails on both sides of a central region.
ambient temperatures; if some enzyme-mediated reaction is running near saturation, then the rate of reaction is insensitive to changes in the concentrations of the reactants, and can be said to be autoregulated. Autoregulation is typically represented graphically by plotting steady state values of the autoregulated variable against values of the stimulus. A typical autoregulation curve is shown in fig. 1. Implicit in the definition we have presented is that autoregulation is a local phenomenon, and may break down globally – for example, if we push the ambient temperature high or low enough, eventually our body temperature will start to change. This observation provides an apparently trivial insight that is often missed in clinical comments on cerebral blood flow autoregulation: That it can break down either because the stimulus is out of the autoregulatory range, or because the shape of the curve is altered by some pathology. Figure 2 illustrates the fundamental difference between these scenarios. As the global picture is hard or impossible to access in clinical settings, these situations are often conflated, even though they may imply different treatment alternatives. Autoregulation curves, although useful, tell only part of the story. Generally, they represent steady state behaviour of some dynamical (i.e. time-dependent) system. For example when blood pressure is altered, the changes which stabilise blood flow do not take place instantaneously. So we take a step back from autoregulation curves to the underlying dynamical systems. The autoregulated variable T is usually only one variable among many which make up the ‘‘system’’ in question. If we term the remainder of the variables in the system X, assume that there are
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a
b
T
T
So
So
Fig. 2. Two scenarios for autoregulatory failure. (a) The autoregulation curve is normal, but the stimulus is out of the normal range. (b) The stimulus is in the normal range, but autoregulatory mechanisms are impaired.
parameters P which do not change rapidly, (but which have presumably evolved to take values which make T insensitive to changes in the stimulus S), and further assume that we wish to model in continuous time, we get a dynamical system of the form: dT ¼ f1 ðT, X; S, PÞ, dt
dX ¼ f2 ðT, X; S, PÞ dt
ðEq: 1Þ
for some functions f1 and f2. Assume that at normal, steady, parameter values the system evolves to a state G, in other words, that some function G ¼ (G1(t, S ), G2(t, S )) solves the above system for these parameter values, and is stable. The simplest case is when we have constant (i.e. time-independent) solutions, but periodic or chaotic solutions are also possible.3 Then T is autoregulated with respect to S near S ¼ So if the function G1(t, S) is insensitive to small changes in S near S ¼ So. In the steady-state case, G1(t, S ) ¼ K(S ) for some function K depending only on S, and we can identify the autoregulation curves described above as plots of K(S ) against S. Then we could locally define the slope of this curve:
dK
dS S¼So
ðEq: 2Þ
to be a measure of (static) autoregulation at S ¼ So, with a small value indicating that T is well autoregulated at this point. 3
Depending on the nature of the solution, the most useful definition of stable might need careful thought.
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3. PHYSIOLOGICAL VERSUS DATA-DRIVEN APPROACHES Starting with a very intuitive defnition of autoregulation we have been led to an underlying dynamical system – Equation (1). That this system exists and what we see are simply manifestations of its behaviour are undeniable. But what, if anything, do we do with it? We could: try to reconstruct the true dynamical system by exploring the physiology and hope that it reproduces experimental results such as the autoregulation curve try to construct some system of equations (dynamical or otherwise) from the experimental results, ignoring the underlying physiology Actually these possibilities – the physiological approach and the datadriven approach – are two ends of a continuum, with lots of possibilities in between. In modelling individual aspects of a system, the process of translating physiology into mathematics can be done with different degrees of detail, and in this sense can be more or less ‘‘physiological’’. This is wonderfully illustrated in the work of Bezanilla (2000) on the voltage sensor in voltage-dependent ion channels where a variety of models of one phenomenon are explored. Further, in a large model, it is quite possible to have some submodels which derive from the physiology, combined with others which are empirically determined. Of each function in a large model, one can ask the question: to what extent does it, like the law of mass action in chemistry, derive from underlying scientific assumptions, and to what extent does it, like the transfer functions in engineering, derive from the manipulation of experimental data? Data-driven approaches to cerebral autoregulation outnumber physiological ones. Some authors (e.g. Gao et al., 1998) use data to choose functional forms for autoregulation curves. An alternative which does not ignore time-dependent behaviour, but which is local, is transfer function analysis (e.g. Panerai et al., 2002 or Zhang et al., 1998). A limitation of this approach is the assumption that the underlying dynamical system is linear about some operating point, rendering it of little use in situations where there is significant variation in the stimulus. There are further possibilities such as that in Liu and Allen (2002), interesting because it is in discrete time, and is stochastic. There are no doubt, more complicated possibilities involving the elegant mathematical tools of nonlinear time-series analysis (Kantz and Schreiber, 1997). When it comes to physiological approaches, to our knowledge there are no integrated physiological models of the brain circulation, equivalent to those for the heart (see for example Kohl et al., 2000). Models such as those of Ursino and Lodi (1998) and Aubert and Costalat (2002) are steps in this direction, which we have taken as our starting point.
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Data-driven approaches come into their own in situations where physiological knowledge is very limited. However, there are certain problems with ignoring the underlying physiology. Paradoxically, physiology can be needed either to increase or limit the complexity required to construct a useful model. The first of these points is illustrated via questions like ‘‘Is autoregulation failing in Patient A because her vascular smooth muscle is damaged, or because of the presence of some vasoactive substance in the extracellular space’’? In general, data-driven models cannot answer questions concerning reasons for some event, because they are unlikely to have suffcient internal structure to do so. To illustrate the second point – that physiology can be needed to limit model complexity – consider a few of the large variety of experiments routinely used to challenge the cerebral circulation – blood pressure can be altered by various means (tilt tests, lower body negative pressure tests, etc.); cerebral pH can be changed (CO2 inhalation, acetazolamide injection); CSF volume can be altered (CSF injection, injection of hypertonic saline); local cerebral metabolic rate can be altered (functional activation experiments), etc. If we are using data-driven models and are interested in all of these situations, we are forced either to use a different model for each situation, or to try and construct multivariate models which can require a prohibitive amount of data for their construction. In situations like this, physiology provides constraints on the model structure by telling us about how different stimuli might interact.
4. MOVING IN A PHYSIOLOGICAL DIRECTION In response to the limitations of data-driven approaches, we decided to take our work in a more physiological direction. Exploring the physiology rapidly revealed a surprising degree of complexity.4 Taking just one stimulus, ABP, there are a messy set of interlocking pathways by which a change in ABP can cause a change in CBF, pathways which sometimes work in unison and sometimes counteract each other (see for example Bevan and Bevan, 1994; Mraovitch and Sercombe, 1996; Edvinsson and Krause, 2002). An incomplete set of pathways, which nevertheless conveys some of the complexity of the situation, is presented in fig. 3. It is no surprise that different pathologies interfere with these pathways at different points and in different ways. Clearly, creating a model 4
Perhaps the complexity surprised us, because we unwittingly made the teleological assumption that the system would have been ‘‘designed’’ to be as simple as possible.
A flexible, iterative approach to physiological modelling
blood flow
transmural pressure
gKCa
adenosine
gKATP
oxygen extracellular potassium
gKIR
extracellular pH
gKV
lactate
carbon dioxide
shear stress
NO
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membrane potential
calcium
VSM tension
Fig. 3. Some well-documented pathways involved in the regulation of cerebral blood flow. gKCa, gKATP , gKIR and gKV are conductivities of calcium sensitive, ATP sensitive, inward rectifier and voltage-dependent potassium channels respectively. VSM tension is the tension in vascular smooth muscle which acts to control vessel diameter and hence, cerebral blood flow. NO is nitric oxide, a potent endogenous vasodilator.
which incorporates all these feedback pathways is not a straightforward process. First steps often involve caricaturing processes – replacing complex mechanisms with simpler ones which reproduce gross behaviour reasonably well. For example, pathways of several chemical reactions can sometimes be represented as a single reaction. Sometimes a process is fast, and a dynamical equation can be replaced with an algebraic one. The current version of our model is broadly divisible into three components: a model of vascular biophysics; a model of metabolic biochemistry; and a model of smooth muscle function. The model can qualitatively reproduce results recorded in the physiological and medical literature. Data from a variety of clinical studies, including from normals and patients with primary autonomic failure undergoing tilt tests (see section 6.3), have been fed into it with promising results. Components of the model have been taken from a great variety of sources. For example, the model of vascular biophysics is largely taken from Ursino and Lodi (1998), while aspects of a number of existing biochemical models have been incorporated into the model of metabolic biochemistry. This process of piecing together a model led to the development of a methodology which has proven very useful, and which we now describe.
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5. MODULARITY AND THE LOGICAL STRUCTURE OF MODELS Flow diagrams such as that in fig. 3 provide some important insights into a system’s behaviour even without a detailed model. They are in general, objects which can be viewed at different scales – an individual arrow often itself hides much complicated physiology. For example, lying between oxygen and lactate in fig. 3 is the entire machinery of metabolism. But most importantly, what they highlight is the fact that every model has an underlying logical structure more abstract than its mathematical details. This structure represents the directions of causality in the model and exists regardless of whether the model is constructed in continuous or discrete time and space, or even of whether it is a dynamic model at all. There are two reasons why the logical model underlying a more detailed model is worthy of exploration. First of all, at a practical level it allows us to answer useful qualitative questions such as ‘‘by what routes does A influence B’’? Much of the clinical and experimental physiology literature is about answering such questions, and the understanding of pathways thus gained can have implications for drug and therapy research. It is not uncommon for the pathways to be many and complex, and in these situations, mathematical tools such as graph theory can prove helpful in analysing the system and suggesting useful experiments, without the need for numerical information. Secondly, an understanding of the logical structure helps us implement models in a modular computational way. To understand why, first of all we need to put some flesh on the notion of a process – a bite-sized chunk of physiology such as a chemical reaction, or an equation describing how membrane potential depends on ion-channel conductivities for example. These too, have both a mathematical structure and a deeper logical structure. We can illustrate this concept with a simple chemical reaction in which two substrates combine irreversibly to form two products (fig. 4). Since the logical structure merely captures causality, it is independent of different choices of the dynamics (e.g. mass– action dynamics or Michaelis–Menten dynamics). C
D
A
B
Fig. 4. Diagram representing causality in an irreversible chemical reaction A þ B ! C þ D in which substrates A and B combine to form products C and D. Mathematically such diagrams represent the structure of the jacobian of the dynamical system.
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F
B
F D
E
E B
B G
D
D A
A C
C
C
G
Fig. 5. Putting together processes. If the final product is a full model, then G is a parameter and F is an output variable. B, which is a parameter in one of the original processes, is a variable in the full system.
If we only address which quantities affect each other’s evolution, and ignore the details of how they do so, then we get diagrams like this, which are directed graphs, or ‘‘digraphs’’. Such digraphs can naturally be put together into larger structures as illustrated in fig. 5. Thus at their most abstract level, physiological models can be seen as digraphs pieced together from smaller digraphs. The digraph picture of a model gives us a handle on the notion of modularity. We can regard individual processes or combinations of processes as modules. The process of putting together modules to make a model can be visualised as the putting together of digraphs to make larger digraphs. There are some important subtleties to bear in mind. When we use digraphs to represent processes or groups of processes, we should remember that the quantities involved will in general be shared – will participate in other processes. Thus a process is generally an incomplete object. In fact, we do not know a priori whether a given quantity which appears to be a parameter in a process (i.e. is itself unaffected by the process) will turn out to be a parameter or a variable in the whole model. On the other hand, if a graph represents an entire model, then a parameter will be easily identifiable because it should have arrows emanating from it, but not leading to it while variables in general will have arrows leading both to and from them.5 5 A quantity which only has arrows leading to it, but not from it, is an ‘‘output variable’’ – something we are interested in, but whose evolution does not affect the rest of the model, and can hence be excised from the model without affecting its behaviour.
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symbolic model
parameter values
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Fig. 6. The natural order of the modelling process.
Constructing models computationally in a modular way is non-trivial, but the digraph analogy is the first step. In our work, a module is a datafile containing physiological information encoded symbolically. A model description consists of instructions about which modules are to form part of the model. The appropriate modules are then put together, and code for simulation is automatically constructed. The encoding of modules is carried out in a way such that the identity of a quantity as a parameter or variable is not fixed. Only when the whole model has been put together do various routines come into play to decide on the identity of the various quantities, and, if necessary, on how to set their values/initial values. This process of assigning numerical values to quantities is needed for simulation, but is separate from the construction of the model as a symbolic object. Thus a natural order arises in the modelling process as sketched in fig. 6. Apart from allowing easy building, modification, and combination of models, one further advantage of encoding models in a modular way is that it gives us two useful and complementary ways of looking at the model: focusing on the nodes of the graph (parameters and variables), or on subgraphs (processes). The difference between the two approaches is illustrated by the two alternative questions: What quantities are affected by process A and how? What are all the processes which affect the evolution of variable B? Such questions are central to understanding not only what a model does in a given situation, but why. When models are large, understanding why a particular variable responds to a stimulus the way that it does can become non-trivial.
6. SOME PROBLEMS ALONG THE WAY Having outlined an intuitive and useful way of visualising and encoding the modelling process, we are now in a stronger position to deal with some of the important issues which we highlighted at the start.
6.1. Choosing which processes to include When it comes to model building, choosing which processes to include and to exclude can be a difficult task. First, one has to examine the experimental
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physiology literature in some detail to work out if there is consensus about what is important. If, for example, experiments involving the blocking of a particular kind of potassium channel in vascular smooth muscle show significant effects on the membrane potential of these cells, we might choose to include these channels in the model. But interpreting the literature is often hard: The significance of certain processes might be very species-specific with no available human data, or no data available for the tissue type of interest. Second, thinking in terms of useful outputs is crucial. For example, if there is an instrument which can measure the value of variable X then we might want to include X to increase the possibility of future model validation. For example, we model an experimentally measurable variable called the ‘‘Tissue Oxygenation Index’’ (TOI) – the average oxygen saturation of cerebral blood expressed as a percentage – because it is a quantity measured in a number of patients and volunteers monitored during clinical studies of interest to us. Finally – and this is a point with wide implications – we are often forced to include processes by extension: if some process included so far involves chemical A, then in theory we should include all other processes which significantly affect the concentration of A. Models should, in this sense, be ‘‘closed’’. Such closure is of course always an approximation – biological systems, as we know, are not closed. Consider arterial blood pressure for example. This currently features as a parameter in our model – a quantity whose evolution is independent of the model. But it is known that ABP can be affected by quantities in the brain: the carotid body chemoreceptor provides a means by which changes in brain O2/CO2 levels have an effect on the cardiovascular and respiratory systems (see Marshall, 1994; Ursino and Magasso, 2002). We have chosen not to include these feedback pathways at this stage, but such choices can easily be criticised. As setting the boundaries of a model is a necessary but fairly arbitrary process, it is important to encode models in such a way as to allow for easy future communication/combination with other models. Treating models in a modular way makes this considerably simpler both conceptually and computationally. Looking at the logical structure, one can quickly decide on the points of contact between models and whether they have competing descriptions of the same phenomena.
6.2. Dealing with incomplete knowledge Central to model building is the task of representing biological processes mathematically. Sometimes this is relatively simple, and a variety of models
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of different physiological situations exist in the literature (Keener and Sneyd, 1998, provides a good introduction to this subject). But what do we do when a process seems to be important, but is incompletely understood at a physiological level? And how do we approach the frequent situation where there are heuristic descriptions of mechanism, but no experimentally derived numerical data? We have tended to take a pragmatic approach in these situations. Where a mechanism is lacking, but there is some experimental data, one can construct data-derived functions. Alternatively, we sometimes resort to modelling the process based on analogous physiological situations. We would consider such inaccuracies to be considerably greater shortcomings in our model if not for the fact that our approach is modular, and as new information comes in, the modules in question can be refined.
6.3. Issues connected with parameters and clinical data There are a number of issues concerning parameters which arise during modelling. Several of these issues are discussed in a biochemical context in Neves and Iyengar (2002). For a start, even when a parameter has a clear physiological meaning, it is often hard to get reliable values for it, and some educated guesswork might be required. In this context, what is important is to have a mechanism for assessing the sensitivity of models to the values of various parameters, especially those whose values are unreliable. A second set of questions arises when we consider interaction with clinical data. A feature of clinical data is that the quantities measured usually reflect only very indirectly the underlying processes. A typical clinical study involves some intervention with (mostly noninvasive) monitoring of a number of variables. In a tilt test, for example, subjects are tilted up and down again, while a set of quantities, such as ABP, blood velocity in some cerebral vessel, average cerebral blood oxygenation, heart rate, etc. are monitored. In such experiments, we can take measured arterial blood pressure as the stimulus, and attempt to compare model predictions of various variables to the monitored values. The way that such data can be used to inform the model in principle is shown in fig. 7. But in practice, things are not so simple. Our model, and large models in general, have a great number of parameters (in our case running into several hundred) and of course a great number of variables whose values are not measured during the experiment. So how many parameters do we try to optimise using the experimental data and which ones do we choose? There are no simple answers to these questions, but physiological knowledge, experience, and intuition are essential here. We have to ask
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questions like ‘‘Which variables seem likely to influence the outcome of a given experiment?’’ and ‘‘Which variables are known to show considerable inter-individual variability?’’ Whether stated explicitly or not, it is implicit in much of the literature that parameters for optimisation have to be chosen on heuristic bases (e.g. Ursino et al., 2000). A practical conclusion is that it is worth storing some estimate of the reliability/likely variability of a parameter as part of its definition in the computational structure where parameter values are stored. Apart from the difficulty of choosing parameters to optimise, the simplistic scheme in fig. 7 raises the question of what exactly it means to compare model outputs with experimental data. In our circumstances, the data is often a set of several noisy traces. Typical patient and modelled data-sets are shown in fig. 8. It usually makes considerably more sense first to process the modelled and measured data – to extract a few key features from them – before comparing the two. There is also a subtler issue involving parameters, connected with the fact that in order to be clinically useful, models are liable to have constraints. We return to this theme when we discuss evolving models.
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6.4. Model testing and validation An issue closely connected with that of how a model might interact with clinical data is how one tests large and unwieldy models. The word ‘‘validation’’ needs to be used with caution, but loosely speaking, how do we come to a point where we can trust the model? At the level of the whole model, one might set free parameters using one set of data (as described above) and then test the model on another data-set, with some criteria to judge how closely model output and experimental data match. However, we have already mentioned that one is forced to limit (in an extreme way) the number of parameters which are set in this way. Moreover, it is quite possible that fundamentally flawed models can reproduce particular clinical data-sets while failing in other situations. So there needs to be an entirely different level of testing, via an approach that is implicit or explicit in much of the biochemical literature (see for example Cortassa et al., 2003). This involves isolating and analysing the behaviour of submodels independently of the whole model, say by comparing their outputs to in vitro data, or checking the sensitivity of submodel behaviour to parameter values. Constructing submodels involves putting together subsets of the processes which make up the full model, which, given a modular structure, is relatively simple. As mentioned earlier, we need to bear in mind that the identities of quantities as variables or parameters (and hence how their values are set) depends on the structure of the model as a whole. We frequently run a model of mitochondrial metabolism independently of the rest of the model, with the stipulation that all extra-mitochondrial quantities are now controlled in ways which mimic typical experimental set-ups. Similarly we run models which simulate the behaviour of isolated blood vessels because of the large experimental literature on this (Ngai and Winn, 1995 for example). The values of quantities such as transmural pressure, shear stress, and metabolite concentrations become controlled parameters for this submodel, and we examine how quantities like channel conductivities, membrane potential, smooth muscle tension, and ultimately vessel radius vary in response to changes in these quantities.
7. EVOLVING MODELS We have discussed the advantages of a modular approach in the context of a large system about which we are partially ignorant. We now flesh out the notion of model flexibility, which, for large models at least,
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should be centre stage, rather than being seen as something which only happens at the development stage and hence is not worthy of much attention. How might we modify a model? In the light of new information, we might wish to: refine some process within the model by altering its mathematical but not its logical structure refine a process in a way which involves altering its logical structure add/remove processes. As detailed earlier, a modular structure makes the modification, insertion, or removal of particular modules simple enough. But parameter setting can be problematic, even with a modular approach. To illustrate a key problem, assume a process where variable S affects variable T. Now assume that at a later date, we take a closer look at the process and decide to incorporate more physiology which tells us that part of the mechanism by which S affects T is via some other variable A (see fig. 9). Clearly, the original arrow connecting S and T has changed its meaning. Prior to modification it represented all processes by which S affects T, but after modification, it represents all processes by which S affects T not involving A. Now the reality is that there might be quantities we wish to conserve despite the refinement. For example when we move between a more or less detailed model of glycolysis, we might want the normal rate of conversion of glucose to pyruvate to remain the same. Constraints of this kind differentiate models designed for clinical use from other physiological models. They arise because the modeller has expectations of model behaviour which are so fundamental as to warrant building into the model itself. In a clinical context, a highly detailed model of glycolysis is likely to be of little use, if the normal steady state flux through it is not comparable with normal clinical data. The issue of why constraints pose some difficulties is best illustrated with an example. In an initial model, lactate transport out of cells might be treated as diffusive, and the normal (known) rate of lactate efflux, along with the normal intra- and extra-cellular concentrations of lactate, used to set the effective diffusion constant. However, if a later
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modification adds a further active transport mechanism, the situation changes. Now the normal rate of lactate efflux provides an algebraic relationship between parameters in the diffusive and active processes (see fig. 10). Thus although a constraint may have a very simple physiological meaning, its mathematical form may be model-dependent. Evolving a model while keeping certain quantities stable adds a layer of complication to the modular, process-centred approach. Although processes as symbolic objects can exist in isolation and be put together easily, the values of the parameters involved in them are not necessarily independent of the rest of the model. If this is not acknowledged in the parameter-setting process, refining can become a tedious and complicated process, and the benefits of a modular approach can be lost. It can be argued with some justification that as a model becomes more and more ‘‘physiological’’ – i.e. has fewer and fewer caricatures in it – the number of parameters which need to be set with reference to the model structure should diminish because more and more parameters acquire precise biological meanings and hence should be measurable. But in our experience, it is not realistic to posit biological realism as an alternative to constraints on model behaviour. In any case, it is usually impossible to measure quantities like enzyme concentrations in a living human subject. Fortunately, despite the practical complications, the fact that in order to set parameter values in an individual process we might need global constraints whose form depends on more than one process, does not imply any logical contradiction, because we only need to access the ‘‘structure’’ of the model as a whole, something which is independent of the parameter values. It is compatible with the natural order sketched in fig. 6.
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8. CONCLUSIONS We have raised a number of questions in this chapter while providing only the shadows of answers. At the level of model testing, methodologies need to be developed for identifying parameters which show considerable inter-individual variability or to which the model is very sensitive, allowing them to be set using clinical data. But clinical data cannot be sufficient to validate large physiological models. It is important to be able to extract and test submodels against appropriate – often in vitro – data. Our most important conclusion is that a modular, computationally flexible, approach is central to building large models, and that such an approach involves understanding and manipulating the logical structures which underlie physiological models. Issues of inadequate information and arbitrary model boundaries cannot be circumvented, but they can be planned for by building models which are capable of easy evolution. Finally, clarity about the logical structure of a given model also makes later interaction between, and combination of, different models considerably easier. A modular approach puts physiology, rather than mathematical equations, centre stage. Hiding the mathematics behind a more understandable structure makes such models accessible to a much wider community, including doctors and experimentalists. As the increasing size of physiological modelling problems makes them necessarily more and more collective and multi-disciplinary endeavours this becomes a necessity, not an option.
REFERENCES Aubert, A., Costalat, R., 2002. A model of the coupling between brain electrical activity, metabolism, and hemodynamics: application to the interpretation of functional neuroimaging. NeuroImage 17(3), 1162–1181. Banaji, M., 2004. BRAINCIRC model and detailed documentation, Available online at http://www.medphys.ucl.ac.uk/braincirc/. Banaji, M., Tachtsidis, I., Delpy, D., Baigent, S., 2005. A physiological model of cerebral blood flow control. Math. Biosci. 194(2), 125–173. Bevan, R.D., Bevan, J.A. (Eds.), 1994. The Human Brain Circulation. Humana Press. Bezanilla, F., 2000. The voltage sensor in voltage-dependent ion channels. Physiol. Rev. 80(2), 555–592. Cortassa, S., Aon, M.A., Marba´n, E., Winslow, R.L., O’Rourke, B., 2003. An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics. Biophys. J. 84, 2734–2755. Edvinsson, L., Krause, D.N. (Eds.), 2002. Cerebral Blood Flow and Metabolism. Lippincott Williams and Wilkins.
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Gao, E., Young, W.L., Pile-Spellman, J., Ornstein, E., Ma, Q., 1998. Mathematical considerations for modelling cerebral blood flow autoregulation to systemic arterial pressure. Am. J. Physiol. Heart. Circ. Physiol. 274, H1023–H1031. Kantz, H., Schreiber, T., 1997. Nonlinear time series analysis. Vol. 7 of Cambridge Nonlinear Science. Cambridge University Press. Keener, J., Sneyd, J., 1998. Mathematical Physiology. Vol. 8 of Interdisciplinary Applied Mathematics. Springer. Kohl, P., Noble, D., Winslow, R.L., Hunter, P.J., 2000. Computational modelling of biological systems: tools and visions. Phil. Trans. R. Soc. A 358, 579–610. Liu, Y., Allen, R., 2002. Analysis of dynamic cerebral autoregulation using an ARX model based on arterial blood pressure and middle cerebral artery velocity simulation. Med. Biol. Eng. Comput. 40, 600–605. Marshall, J., 1994. Peripheral chemoreceptors and cardiovascular regulation. Physiol. Rev. 74, 543–594. Mraovitch, S., Sercombe, R. (Eds.), 1996. Neurophysiological Basis of Cerebral Blood Flow Control: An Introduction. John Libbey. Neves, S.R., Iyengar, R., 2002. Modeling of signaling networks. BioEssays. 24(12), 1110–1117. Ngai, A.C., Winn, H.R., 1995. Modulation of cerebral arteriolar diameter by intraluminal flow and pressure. Circ. Res. 77(4), 832–840. Panerai, R.B., Hudson, V., Fan, L., Yeoman, P., Hope, T., Events, D., 2002. Assessment of dynamic cerebral autoregulation based on spontaneous fluctuations in arterial blood pressure and intracranial pressure. Physiol. Meas. 23, 59–72. Ursino, M., Lodi, C.A., 1998. Interaction among autoregulation, CO2 reactivity, and intracranial pressure: a mathematical model. Am. J. Physiol. Heart. Circ. Physiol. 274(5), H1715–H1728. Ursino, M., Magosso, E., 2002. A theoretical analysis of the carotid body chemoreceptor response to O2 and CO2 changes. Respir. Physiol. Neurobiol. 130, 99–110. Ursino, M., Ter Minassian, A., Lodi, C.A., Beydon, L., 2000. Cerebral hemodynamics during arterial and CO2 pressure changes: in vivo prediction by a mathematical model. Am. J. Physiol. Heart. Circ. Physiol. 279(5), H2439–H2455. Zhang, R., Zuckerman, J.H., Giller, C.A., Levine, B.D., 1998. Transfer function analysis of dynamic cerebral autoregulation in humans. Am. J. Physiol. Heart. Circ. Physiol. 274(1), H233–H241.
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
15 Systems biology, cell specificity, and physiology Vincent Detours, Jacques E. Dumont and Carine Maenhaut Institute of Interdisciplinary Research, Free University of Brussels, Campus Erasme (CP602), 808 route de Lennik, B-1070 Brussels, Belgium
1. INTRODUCTION The sequences of whole genomes published in the literature open up the possibility of knowing all the RNA and protein molecular actors involved in the physiology of various organisms and their cells and, possibly, to find the relations among these actors. Thus, the whole network of information transfer within an organism or within a cell could be defined. Simulation of such a network could then theoretically predict the behaviour of the system and its alterations in disease. Examples of such constructs flourish in the literature as general maps of the various signal transduction pathways. With regard to such general schemes, the human mind is confronted with two opposite tendencies: (1) it rejects complexity and tends to simplify relations so as to keep schemes interpretable, e.g. it is difficult to get a feeling for the role of hundreds of proteins induced by a transcription factor and for their general effect; (2) a desire for completeness encourages the extrapolation of concepts and relations from one system to another so as to obtain an all-encompassing general picture. Both tendencies influence the picture of the proposed networks. Following the network concept, advocates of the new ‘‘systems biology’’ have begun to exhibit, in various systems, linkages maps, and controls of signal transduction proteins deduced from genetic, gene expression, and protein interaction data (Vidal, 2001; Ge et al., 2003). Such interaction networks have helped to shape concepts of great general interest (Aldana and Cluzel, 2003), which suggest striking analogies with other non-biological networks such as the Internet. In the present short review, we argue that these specific network structures are not applicable at the 265
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level of a single cell at a definite time. We first briefly outline the systems biology approach and then focus on its limits when it comes to investigating the multiple mechanisms through which rather general signal transduction pathways are accommodated to create the exquisite specificity of physiological cells.
2. THE EXPERIMENTAL METHODS OF SYSTEMS BIOLOGY 2.1. High-throughput methods and computational methods Genes or protein interrelations can be studied at the level of the genome, the transcriptome, and the proteome, a.k.a. genomics, transcriptomics, and proteomics in trendy scientific jargon. These involve a range of approaches. Comparative genomics reveals consistent association between genes during evolution, which suggests potential functional relationships. The methods are based on common phylogenetic distribution, conserved gene neighbourhood, and observed gene fusions (von Mering et al., 2003). This is pure in silico biology on available sequenced genomes. Coexpression of the same RNAs or proteins in the same organisms, tissues, cell types or cell compartments (the ‘‘localisome’’) may also suggest a relation. Conversely, lack of coexpression in one system will tend to exclude a relation (Stuart et al., 2003). Because 6% of interrogated genes are ubiquitously expressed, and because each tissue expresses 30 to 40% of the whole transcriptome, the number of potential coexpression events is enormous. Some coexpression events may just reflect colocalisation on chromosomes, and have no functional significance (Dillon, 2003). However, a coexpression event observed in many different biological contexts is more likely to be biologically important, and to convey high information value (Su et al., 2002). Large scale coexpression studies have been conducted in yeast (Kemmeren et al., 2002), mouse (Zhang et al., 2004) and human (Lee et al., 2004). Identical regulation of mRNA expression in the response of the cell to different agents, again, may reflect functional relationships. Similarly, coexpression with coordinated kinetics in response to various agents suggests functional relations. Similar morphologic responses to the suppression of genes – for instance, by the systematic use of RNA interference – has established such functional relations in Drosophila (Kiger et al., 2003). Finally, the potential for physical interactions between proteins (the ‘‘interactome’’) may be suggested by protein structures, domain
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composition, and also by their interactions in reconstituted systems, acellular preparations, or model systems such as yeast in the double hybrid methodology (Vidal, 2001; Pawson and Nash, 2003). The occurrence of such interactions in physiological cells is testable by co-immunuprecipitations. A systematic survey of proteins binding to individual tagged proteins uncovered thousands of protein complexes and protein interactions occurring in situ in yeast (Kumar and Snyder, 2002). The estimated false positive rate for high-throughput two-hybrid assays is 50% (Sprinzak et al., 2003). Nevertheless, new functional protein–protein interactions involving previously uncharacterised bacterial proteins have been uncovered and validated despite such a large error rate (Butland et al., 2005).
2.2. Successes In theory, the roads outlined above to the discovery of protein–protein interactions should converge. For example, ribosomal protein genes evolved together and are expressed concomitantly whenever cells require new ribosomes. The proteins of these organelles are bound and cosegregate in the cells, and presumably such interactions should be demonstrated in acellular or in double hybrid experiments. Network structures are emerging from protein interaction research. They already make it possible to draw very general conclusions about network structures (Alon, 2003). For instance, protein interaction networks – like metabolic pathways networks or the Internet – are scale-free. As a result, they are composed of relatively few nodes with many connections, and many nodes with few connections, constituting subsystems (modules) around the former. In such systems, the path from one node to any other is short (Bray, 2003; van Noort et al., 2004). These networks are robust. They survive massive losses of peripheral nodes. However, loss of a few highly connected nodes is lethal (Aldana and Cluzel, 2003). Such a predicted behaviour fits in well with many whole-or-nothing results of gene-knockout models. The network models generate general and even specific predictions that can be tested (von Mering et al., 2003). For example, in yeast, systematic inactivation of each gene and study of the corresponding phenotype allowed researchers to test the validity of the network connectivity. Essential genes are thought to be highly connected hubs in the network, whereas less connected genes are thought to be less essential. By identifying similar essential/secondary phenotypes for thousands of genes, von Mering et al. (2003) confirm parts of the proposed network.
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However, in vertebrates, and in yeast under certain conditions, the redundancy of signal transduction proteins will often ensure the absence of a distinctive phenotype for the knockouts. One pathway may complement another for a given function. Loss of function may require concomitant suppression of all network paths for that function. Predicted network structures will incrementally improve as attempts to validate them accumulate. This exercise will be most fruitful if conducted in specific types of cells, under many well-defined sets of conditions. This research agenda is being carried out both in yeast by several groups, and in vertebrate cells by the Alliance Consortium (Gilman et al., 2002). As evolution increases complexity, the application of systems biology will certainly bring its first reliable results in evolutionary simple systems such as yeast and C. elegans. Data on protein expression and localisation are becoming available in both models (Huh et al., 2003; Li et al., 2004). The modest aim of proposing testable protein interactions hypotheses and of narrowing the possibilities is already a great benefit of such efforts.
2.3. Shortcomings However, the prediction of the behaviour of a particular system in defined conditions, on the basis of protein network structure, is fraught with error. Each of the ‘‘omic’’ approaches will yield its lot of false positive and false negative results. One may wonder whether significant new molecular interactions will emerge from the background noise. The high-throughput nature of systems biology-related technologies implies that thousands of hypotheses are tested at once. Very stringent statistical significance thresholds are required. A recent study combining several high-throughput methods and selecting the interactions revealed by all of them yielded conceptually sound conclusions that were subsequently validated by tandem affinity purification tagging experiments in yeast (Jansen et al., 2003). Such success in the infancy of the field is comforting (Spirin and Mirny, 2003; Tyson et al., 2003). Cross-technology validation is increasingly applied to reduce the large number of false positives produced by noisy high-throughput methods (Detours et al., 2003). The proposed network structures are incomplete. They do not account for the absence of some molecular actors in particular cell types. They do not account for differences in kinetics and their consequences. They do not account for concentration–action relations (which might be biphasic), nor do they account for inter- and intracellular compartmentalisation, and other essential features of cell signalling presented in the
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next sections. In fact, published general signal transduction protein interaction networks are rarely applicable to the precise situation of a given cell type in a given set of circumstances. The scale-free character of the network implies that highly connected protein nodes may be linked to dozens of other proteins which, for steric reasons, will exclude each other or interfere with each other, thus suggesting the existence of a range of different complexes whose relative importance will presumably differ among cell types. The compliance of a theoretical model with experimental observation does not necessarily imply its validity, because variables can often be tuned to fit virtually any desired result. It is interesting to remember at this stage that in the 1970s, simulations of the glycolysis pathway on the basis of the known properties of the involved enzymes seemed to account fully for observed behaviours (Garfinkel et al., 1970; Hess and Boiteux, 1971; Goldbeter, 1976). Later however, the discovery of fructose 2, 6 biphosphate revealed an entirely different and unforeseen regulation network of this pathway which explained its true physiological regulation (Van Schaftingen, 1987, 1993). The systems biology approach should therefore be pursued and combined at different levels, down to the protein complexes and functional modules, and down to individual proteins in individual systems if possible. Combining the information from horizontal approaches (‘‘omes’’) and vertical approaches (one gene, several proteins, several effects for each isoform) will generate huge amounts of data that will have to be treated and integrated in comprehensive databases (‘‘Biological Atlases’’) (Vidal, 2001; Ge et al., 2003).
3. COMPLEX MOLECULAR INTERACTIONS UNDERLYING CELL SIGNALLING SPECIFICITY Network structures published in the recent systems biology literature give a general view of the potential interactions among molecular actors. These are useful in reducing the number of biological hypotheses to be investigated, and in generating useful predictions on the overall structure of the network. However, their ability to predict the behaviour of individual pathways is limited. As a matter of fact, the molecular mechanisms used in cell differentiation to ensure specific cell regulation by the common signalling pathways are precisely the mechanisms which preclude the strict application in a given cell of general protein-interactionbased networks.
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3.1. Posttranslational control of protein synthesis Each protein is regulated quantitatively or qualitatively at transcription, translation, or posttranslation. The response of a given cell to the activation of, for instance, one specific kinase or phosphatase depends on the nature of the available substrates of these enzymes. Within one category of enzymes, the existence of different isoforms may result from the existence of different genes or from the alternative splicing of each gene, from RNA editing, or from processing of each protein. Use of different promoters for the same genes will entail differences in gene expression. Different splicings, RNA editings, or protein posttranslational processing will generate distinct protein isoforms (Cichy and Pure, 2003). Isoforms differing by only one small segment may result in opposite responses to the same signal, e.g. a phosphorylation by cAMP on one optional segment of a protein may produce an effect inverse of that of phosphorylation on another segment. TERP, a truncated estrogen receptor expressed in the pituitary, does not affect the receptor transcriptional activity, but does inhibit its repressors (Lin et al., 2003). Similarly, the truncated MDM2 inhibits MDM2 (Bartel et al., 2002). Assuming a similarity of recognition from a similarity of domain structure is dangerous. Although they lack structural similarity with the insulin receptor, LGRs of the family of glycoprotein hormone receptors are activated by insulin-like hormones (relaxin) (Hsu et al., 2002). The number of isoforms increases with evolution. It is estimated that the 25,000 genes in the human genome may generate more than 100,000 different proteins (Brentani et al., 2003). Many of these proteins may have different, sometimes unrelated, cell distributions, functions, affinities for ligands, and controls of expression (Pandini et al., 2003). This diversity is illustrated by cyclic nucleotide phosphodiesterases which are grouped in 12 families, sometimes with multiple genes for each family and/or multiple isoforms for each gene (Wang et al., 2003). This diversity is further compounded by the fact that a single protein may have entirely independent functions (moonlighting) (Jeffery, 2003; McKnight, 2003), and tertiary structures. For example, superoxide dismutase exists in two forms. Each one has a distinctive disulfide bridge pattern and therefore, a unique tertiary structure (Petersen et al., 2003).
3.2. A given signal may have opposite effects depending on the overall molecular state of the cell There are countless examples of opposite results obtained by the activation of any given pathway in different cell types, or even in the same
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cell in different conditions (Dumont et al., 2002). One example is the essential ambivalence of many signal transduction proteins which either promote or inhibit cell proliferation and apoptosis depending on the cell type (Sporn, 1988; Vermeulen et al., 2003). Other well-established examples are the opposite roles of TGF at different stages of carcinogenesis (Roberts and Wakefield, 2003) and of E2F3 on tumorigenesis of different cell types (Ziebold et al., 2003). The same cAMP signal may either be an inducer, or a repressor, depending on the state of chromatin in the promoter region (Mulholland et al., 2003). Besides the influence of intracellular protein content, the same cell may respond differently, depending on the architecture of its extracellular support (Abbott, 2003). As our knowledge of gene expression develops, the number of possible subcategories of cell types, and therefore cell-regulation characteristics, increases rapidly. For example, Purkinje cells, i.e. neurons with the same histology as conventional neurons, express a specific protein pattern (Zoghbi, 2003). Histologically similar endothelia in different tissues are also differentiated (Chi et al., 2003).
3.3. Proteins are localised in specific intra-cellular compartments Compartmentalisation of proteins and signal molecules is an inherent correlate of subcellular organisation and cell polarity. The latter may be very dynamic as in chemotaxis, in which cell polarity changes with the orientation of the gradient of chemoattractants (Meili and Firtel, 2003). The same signal may be localised or diffuse depending on the location of the synthesising and catabolising enzymes. One example is the cAMP adenylate cyclase and phosphodiesterase system (Swillens et al., 1974). If both enzymes are located on the plasma membrane, cAMP concentration is uniform in the cell. If the cyclase is on the membrane and the phosphodiesterase is in the cytosol, a decreasing gradient from the membrane to the centre of the cell is observed. The same signal may operate differently at different distances from its emission site. For example, the EGF receptor induces a very localised actin polymerisation during chemotaxis. This local activity contrasts with the body-wide EGF receptor-mediated activation of ERK (Kempiak et al., 2003). Location of the same protein in different cell compartments or different supramolecular complexes may result in entirely distinct responses to stimulus. For example, nuclei located at the neuromuscular junction respond to stimuli by inducing genes of synaptic proteins, whereas nuclei located elsewhere in muscles respond by repressing acetylcholine receptors
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(Schaeffer et al., 2001). Compartmentalisation of a protein greatly reduces the number of possible interactions. For example, scaffolding proteins JIP1 and ksr, involved in MAPK signalling, hold in a distinct supramolecular complex all the enzymes of a cascade in which each enzyme modulates its successor (Douziech et al., 2003). Compartmentalisation must be postulated to explain how the same molecule can be used in one cell as a signal at very low concentrations, and as a metabolite at much higher concentrations. (e.g. H2O2 in macrophages or thyrocytes). Compartmentalisation also explains the important roles of scaffolding or anchor proteins. For instance, AKAP proteins localise cAMP-dependent protein kinase, which allows a spatially restricted interaction of cAMP and this kinase (Hulme et al., 2003), and thus of protein substrate phosphorylation. Compartmentalisation is also a dynamically regulated process in which a protein is segregated, and consequently inactivated, in one compartment and activated after translocation in another compartment. For example, p53 is inactive in the cytoplasm, but activated in the nucleus (Nikolaev et al., 2003).
3.4. The combinatorial complexity of protein–protein interactions is huge The response of a cell may result from the specific combination of the actors involved, which may be missed when networks are considered out of a precise physiological context. This has been especially well analysed in the control of transcription where only specific combinations of transcription factors will elicit a response. The sophistication of this combinatorial logic increases with evolution to higher living forms. It seems that the increasingly more elaborate regulation of gene expression accounts for organismal complexity (Levine and Tjian, 2003). Combinatorial variations involve the following: The specific combination of existing actors such as receptors, transcriptional factors, kinases, etc. may combine with an and control (each factors is necessary), or an or control (either factor is sufficient). Such regulations have been demonstrated in physiology for odour discrimination by the olfactory system. Each odour activates a specific combination of receptors, and thus of olfactory cells (Malnic et al., 1999). Similarly, different combinations of transcription factors are necessary to obtain different gene expression patterns (Ghazi and VijayRaghavan, 2000). Such combinations may partially overlap. A special case in the category is the specific addition of one factor acting as a switch to the existing
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combination of factors, e.g. one general transcription factor complementing various existing combinations is necessary and sufficient to trigger an outcome specific of this combination. Induced Egr1 combined with different other transcription factors in gonadotrophs or Sertoli cells triggers the induction of different genes (Tremblay and Drouin, 1999). LH and GSU, two genes needed for luteinising hormone (LH) synthesis, are activated by distinct, but partially overlapping, combinations of transcription factors (Jorgensen et al., 2004). The specific combination of posttranslational modifications on a given protein may determine activity or location. For example, the regulation of p53 expression is controlled by a phosphorylation code, each phosphorylation site having a functional meaning (Webley et al., 2000). The sequence of the molecular events is essential. The expression of a gene depends successively on the nature of its responsive element (RE), on the transcription factor(s), on the opening or closing of the chromatin, DNA methylation, specific histone phosphorylation, methylation, or acetylation, etc. (Schreiber and Bernstein, 2002). Expression also depends on the qualitative or quantitative modulation of the transcription factor by posttranslational modification or on allosteric agent binding, on their complement of coactivators and corepressors, etc. (Holstege et al., 1998; Yamamoto et al., 1998). Studies on estrogen receptor- targets have revealed a sequential and combinatorial assembly of dozens of transcription factors controlling the timing of promoter activation, supporting the concept of a ‘‘transcriptional clock’’ (Metivier et al., 2003).
3.5. Effects of signals depend on their timing In addition to the sequence of molecular events, the duration and/or rhythmicity of the signal may specify qualitatively the response. Bimodalsignal processing characteristics with respect to stimulus duration have been demonstrated for NFkB, the main transcription factor involved in inflammation (Hoffmann et al., 2002). With regard to rhythmicity, high-frequency calcium pulses account for cardiac rhythmic contractions while sustained intracellular calcium concentrations and calcineurin activation are responsible for heart hypertrophy (Vega et al., 2003). Egg to embryo transition is driven by differential responses to Caþþ oscillation frequency (Ducibella et al., 2002) Other phenomena typically overlooked by systems biology approaches include: The quantitative variations of stimulus strength, which may result in the activation of distinct cascades, sometimes with opposite effects.
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An example is the opposite effects of the same MCSF signal but at different concentrations in cell proliferation and ERK activation (Rovida et al., 2002). The TNF receptor activates both an apoptotic and a survival cascade (Micheau and Tschopp, 2003). Estrogen receptors or have opposite effects in response to estrogen (Weihua et al., 2003). The final effect reflects the balance between the responses of both receptors to estrogen. The quantitative differences of expression by quantitative or qualitative modulation of synthesis or degradation: cyclin, which trigger cell cycle and DNA synthesis, are regulated both at the transcriptional level, and at the level of their degradation following ubiquitinylation (Reed, 2003). Both positive and negative specific modulators, which may act on the expression of proteins at various levels, on the synthesis or degradation of mRNAs, on proteins intracellular signal molecules, on posttranslocational control of proteins, or directly on the activity of proteins. (Dumont et al., 2002).
4. CONCLUDING REMARKS Evolution increases complexity. The number of protein isoforms increases considerably from simple organisms like C. Elegans to man. If different isoforms have evolved to carry on specific functions, one would expect specificity to increase also with complexity, possibly at the price of a loss of efficiency. In the case of the duplication of follicle stimulating hormone (FSH) and thyroid stimulating hormone (TSH), and of their receptors from their common ancestral genes, a great increase in specificity allowing a complete separation of the function of the two signalling systems entails a decreased affinity (Smits et al., 2003). Similarly, analysis of protein domain interactions in yeast suggests system-wide negative selection optimising specificity in a network (Zarrinpar et al., 2003). Thus, evolution increases both the number of possible actors at many steps of signal transduction cascades and also confers them with interaction specificity, which allows the same cascades to produce different regulation patterns in different cell types. Systems biology and physiology are not antagonistic, but complementary. The former will allow the formulation of general concepts of regulation and provide the catalogue of possible molecular interactions to be considered in the study of any given model. Physiology and cell biology will define what makes any cell type at a given time in its history
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specific, and allow detailed predictions on behaviour in normal or pathological conditions.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
16 Modelling T cell activation, proliferation, and homeostasis Andrew J. Yatesa, Cliburn C. T. Chanb and Robin E. Callard c a
Biology Department, Emory University, 1510 Clifton Road, Atlanta, GA 30322, USA b Department of Biostatistics and Bioinformatics, Duke University Laboratory of Computational Immunology, Centre for Bioinformatics and Computational Biology, 106 North Building, Research Drive, Box 90090, Durham, NC 27708, USA c Immunobiology Unit, Infection and Immunity, Institute of Child Health, University College London, London, UK
1. INTRODUCTION T cells are thymus-derived lymphocytes with clonally distributed surface receptors that recognise and respond to antigen in association with self major histocompatibility antigens (MHC) expressed on antigen-presenting cells. Depending on the nature of the signals they receive following antigen recognition they can differentiate into effector cells with cytotoxic (Tc), helper (Th), or regulatory (Treg) functions. Since they were first identified as a separate lymphocyte lineage from B lymphocytes (Miller and Mitchell, 1968), they have been found to be involved in almost every aspect of the immune system and an enormous effort has been directed at understanding the molecular and cellular interactions that determine their differentiation and function. The picture that has emerged is more complex than was ever imagined even ten years ago and hundreds of different molecules including cell surface receptors and soluble cytokines that determine T cell responses have now been identified. Indeed, the picture is so complex that it is now clear that a complete understanding of T cell responses cannot be fully understood by present experimental methods alone. Rather, experimental investigations often need to be combined with mathematical modelling if understanding T cell responses is 281
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to progress beyond the purely descriptive. The need for a mathematical approach is exemplified by the increasing number of mathematical models published in recent years dealing with all aspects of T cell biology. However, mathematical modelling has a bad name amongst many immunologists because of the failure in many cases of the mathematicians to take into account the detailed experimental information available and/or to produce a model that gives any deeper understanding of the biology. It is important that models do not simply reproduce a biological response in silico. To be useful they must give a deeper insight into how the biology works. Moreover, good models should not aim to reproduce all the biological components or interactions. Apart from the fact that this is practically impossible because a complete description of the biology is rarely if ever available, the essence of a good model is to understand and make predictions of biological behaviour in the simplest way possible. In biology, this can mean finding the minimum number of key components and interactions required for a particular function, which is often a difficult task. In this chapter, the biology of T cell receptor (TCR) activation, proliferation, and homeostasis, and how mathematical approaches have enhanced the understanding of these processes will be considered.
2. BIOLOGY OF THE IMMUNE SYSTEM The immune system is an extraordinarily complex network of cells and signalling molecules that is able to recognise foreign molecules and invading microorganisms as different from self and mount an appropriate response to eliminate the invader. In vertebrates, two systems work together to afford protection against infections. The innate immune system is the first line of defence. It depends on recognition of molecules found on microorganisms but not on the host by a relatively small number of genetically encoded receptors known as pattern-recognition receptors. The response is fast but not adaptive and does not have memory. The adaptive system, on the other hand, depends on B and T lymphocytes which express clonally distributed receptors that are not genetically encoded but are generated by random rearrangement of the receptor genes during development. The adaptive response is slower than the innate response but it has the advantage of being able to adapt and respond to changes in the antigens expressed by infecting microorganisms and of generating memory to previous infections that allow faster and more effective responses on subsequent exposure. The two main lymphocyte lineages of the adaptive immune system are B cells and T cells. B cells are derived from multipotent precursor cells in
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the bone marrow. They have only one effector function, which is to make antibodies. During B cell ontogeny, the genes coding for the immunoglobulins (antibody) are rearranged in a random fashion to generate a huge diversity of antibodies with different antigen-recognition specificities. These are expressed on the B cell surface with any one B cell making antibody of only one specificity. On meeting an antigen, B cells proliferate and differentiate to secrete large number of antibody molecules of the same specificity that will inactivate or kill the invading microorganism. T lymphocytes, on the other hand, are derived from the precursor cells that come originally from the bone marrow and differentiate into T cells in the thymus. At an early stage of T cell differentiation, the T cell receptor (TCR) is expressed on the T cell surface. As a result of random rearrangement of the TCR gene during differentiation, each T cell will express a unique receptor with a particular affinity for self MHC. Differentiating T cells with high affinity for self are eliminated, as are cells with low affinity. As a result, most T cells differentiating in the thymus die and only those with intermediate affinity for self MHC are released into the periphery. This is one mechanism of guarding against producing autoreactive T cell clones that can give rise to autoimmune disease but it is an imperfect mechanism and other safeguards such as Treg cells are present to prevent autoreactivity. The selection process in the thymus is still not well understood, particularly at the molecular level of TCR activation and signalling for survival or death, and this is an area of active research for mathematical modelling. Two major classes of T cells are produced in the thymus: CD8 T cells and CD4 T cells. CD8 T cells differentiate into effector cells called cytotoxic T cells or Tc, which are responsible for killing (virally) infected cells. CD4 T cells are important for inflammatory responses and helping B cells make antibody (T helper cells or Th) or regulating other T cell responses (T regulatory cells or Treg). CD4 T helper cells can be further subdivided into Th1 and Th2 according to the cytokines they make and the type of antibody they help B cells to produce. Th1 cells secrete interferon-g (IFNg) and promote IgG production whereas Th2 secrete interleukin 4 (IL4) and promote IgE production. T cells released from the thymus are known as naı¨ ve T cells and can be distinguished from memory T cells (i.e. those that have encountered antigen) both functionally and phenotypically. Naı¨ ve T cells respond to antigen by undergoing a pre-programmed number of cell divisions and then differentiation into effector T cells that work to eliminate the foreign antigen/pathogen. The rapid burst of proliferation and clonal expansion is followed by programmed cell death (apoptosis) to reduce the number of T cells back to the homeostatic level but leaving an
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increased number of specific memory T cells (Grayson et al., 2002). Here again, the homeostatic processes that balance the need for increased number of effector cells to eliminate the infection and for expanded clones of memory cells for long-term protection against infection with mechanisms that keep the overall size of the T cell pool approximately constant are not well understood and make a fruitful area for mathematical investigations. Whereas the B cell antigen receptor (immunoglobulin) recognises foreign antigens directly, the T cell receptor (TCR) does not. Rather, the TCR binds to a small fragment of protein antigen (peptide) bound to the MHC. During an infection, the foreign antigens are digested into small peptide fragments, which are then picked up by MHC molecules and expressed on the cell surface. CD4 T cells respond to antigen taken up by professional antigen-presenting cells (monocytes, B cells, and dendritic cells) and expressed in association with MHC Class II whereas CD8 T cells respond to antigen in association with MHC Class I found on almost every cell in the body. Binding of the TCR to the antigen MHC I/II complex, sets of a series of signalling events that results in T cell proliferation and differentiation into an effector Th, Tc, or T reg cell. In both the cases, the antigen-presenting cells also provide additional cell surface and cytokine signals that combine to determine which differentiation pathway the T cell will embark on. The nature of an immune response to any particular pathogen will depend mainly on the signals, a T cell receives when it recognises antigen. These signals come from the affinity of T cell receptor binding to antigen, cell surface interactions with the antigen-presenting cell, and/or cytokines produced both by the antigen-presenting cell, and other cells in the local microenvironment. The exact nature and combination of these signals will determine which subset of T cells (CD4 or CD8) is activated and which differentiation pathway into Tc, Th1, Th2 or Treg results. Understanding how the complex signals interact to govern T activation is a major area of research for both experimentalists and theoretical immunologists. In this chapter, we will look at how mathematical models have been derived and used to gain a better understanding of TCR activation, proliferation, and homeostasis.
3. MODELLING T CELL RECEPTOR BINDING AND ACTIVATION Antigens recognised by the TCR are short peptides of about 8–12 amino acids held in the groove of the MHC (fig. 1). MHC Class I is present on
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all nucleated cells and presents peptides derived from cytoplasmic proteins to CD8 T cells. MHC Class II is present only on specialised antigenpresenting cells (APCs) including dendritic cells (DC), macrophages, and B cells and binds peptides from antigens taken up by the APC for presentation to CD4 T cells. While all the TCRs of any particular T cell are identical, there is great diversity in the peptides presented by MHC on the surface of an antigen-presenting cell, with most of the peptides being derived from self-proteins. It has been estimated that the T cell can recognise and respond to as few as 10–200 foreign peptide–MHC complexes (Demotz et al., 1990; Harding and Unanue, 1990). In general, previously activated T (memory) cells require fewer peptide–MHC complexes for activation (Kimachi et al., 1997 Kersh et al., 2003). Since mature DCs may present up to 105–106 peptide–MHC complexes, this implies that each individual TCR must have a false positive rate of lower than 1 in 103 to 105 if it is to distinguish pathogen signals from self-antigens. How T cells respond selectively to such low number of peptide–MHC complexes is poorly understood. Another feature of T cell recognition is the relatively low affinity of TCR for the activating peptide–MHC complex (about 5–50 mM or 1000fold lower than typical antibody–antigen interactions). Most experiments suggest that the critical parameter for peptide–MHC recognition is not the affinity per se, but the dissociation rate (koff). For example, peptides mutated at a single amino acid residue may have different binding times to the same TCR as compared with the wild-type peptide. In general, experiments with these altered peptide ligands (APL) suggest that the longer the duration of binding, the more efficacious the ligand, although there is also data supporting an optimal duration of binding (Hudrisier et al., 1998; Kalergis et al., 2001). Finally, it has been shown that as little as 30–50% difference in the ligand half-life can result in large differences in biological potency (Williams et al., 1999), suggesting the presence of a kinetic threshold for TCR activation. The process of T cell activation begins when a T cell ‘‘scans’’ the surface of an APC. When it recognises a peptide ligand, the movement of the T cell is arrested and the formation of an immunological synapse is initiated and the TCR is triggered (fig. 1). The immunological synapse is a spatial arrangement of receptor ligand pairs, which evolves over several minutes into the distinct zones of peripheral and central supramolecular activation clusters (pSMAC and cSMAC) (Monks et al., 1998; Grakoui et al., 1999). Providing a mechanistic basis for understanding the formation of the immune synapse has been one of the notable successes of immune modelling. Using reaction diffusion equations and realistic kinetic and structural parameters, two groups have shown that the mature
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Fig. 1. T cell receptor signalling: A possible sequence of events involved in proximal T cell signalling. Ligand induces TCR clustering or cross-linking and/or association with lipid rafts (1), which results in ITAM phosphorylation by src-family kinases (Lck and Fyn) (2). Phosphorylated ITAMs act as docking sites for ZAP-70 (3), which activates other proteins such as the transmembrane adaptor LAT and triggers further downstream signals (4).
synapse pattern can be explained on the basis of extracellular domain sizes alone (Qi et al., 2001; Burroughs and Wulfing, 2002; Wulfing et al., 2002). Recently, a Monte Carlo simulation of TCR signalling in the immune synapse coupled with experimental results on CD2AP (necessary for receptor segregation in the cSMAC) deficient T cells strongly suggested that the immune synapse functions as an adaptive controller, boosting weak signals by concentrating TCRs, peptide–MHCs and signalling molecules, while attenuating strong signals over a longer time course by enhancing the rate of TCR degradation (Lee et al., 2003). Whereas the formation of the immune synapse takes several minutes, TCR signalling can be observed seconds after peptide–MHC binding. In addition, transport of peptide–MHC complexes into the APC cSMAC is strongly correlated with the dissociation rate of the peptide–MHC complex (Grakoui et al., 1999), suggesting that ligand discrimination has occurred prior to immune synapse formation. This suggests that while the immune synapse may have an important role in the modulation
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Modelling T cell activation, proliferation, and homeostasis k-1 k-1 k-1 k-1
k-1 TCR + pMHC
k1
C0
kp
C1
kp
C2
... kp
kp
Ci
... kp
kp
CN
SIGNAL
Fig. 2. The kinetic proofreading model. k1 is the association rate constant, k1 is the dissociation rate constant, and kp is the rate constant for each modification in the proofreading chain. While peptide–MHC remains engaged with the TCR, the peptide MHC–TCR complex undergoes a series of modifications. Only when the final complex CN is formed does the TCR signal. This enhances specificity since ligands with short dissociation times are exponentially more likely dissociate before CN is formed and so do not signal. After fig. 1 from (McKeithan, 1995).
of TCR signalling, it cannot explain the selectivity of individual TCRs, and is probably insufficient by itself to explain the extreme sensitivity of the T cell. The kinetic proofreading hypothesis was proposed by McKeithan in 1995 to explain the selectivity of TCR activation (McKeithan, 1995). Essentially, the model proposes that each TCR requires a series of modifications or biochemical events to be completed before activation (fig. 2). These events, in turn, only occur while the TCR is bound to a peptide– MHC complex. Peptide–MHC complexes that bind for a short period fail to complete the sequence and the TCR does not signal, while peptide–MHC complexes that bind for a longer time lead to T cell activation. Variants of this model allow for negative signalling by peptide–MHC complexes that dissociate before full TCR activation, and show that this enhances the ability to discriminate between ligands (Rabinowitz et al., 1996; Lord et al., 1999). We have recently proposed that TCR discrimination may arise from the nonlinear feedback of kinase and phosphatase molecules, resulting in a threshold for TCR activation (Chan et al., 2004). As with kinetic proofreading, this model provides a possible explanation for the ability of the T cell receptor to discriminate between ligands with high specificity and sensitivity, as well as a mechanism for sustained signalling. The model also explains the recent counter-intuitive observation that endogenous ‘‘null’’ ligands can significantly enhance T cell signalling. The leading model to explain the sensitivity of T cell activation is serial triggering, which suggests that a few peptide–MHC molecules could potentially activate or ‘‘trigger’’ a large number of TCRs by sequential binding (Valitutti et al., 1995; Valitutti and Lanzavecchia, 1997). Together with the kinetic proofreading model, this makes the clear prediction that there is an optimal half-life for peptide–MHC binding to the TCR.
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While there is experimental support for this prediction (Hudrisier et al., 1998; Kalergis et al., 2001), the model has been challenged by studies with in vitro engineered TCRs with extremely high affinities where this effect was not seen (Holler et al., 2001; Holler and Kranz, 2003). In addition to the potential role of kinetic proofreading as a sensitivity amplifier, mathematical models combining kinetic proofreading and serial triggering have been used to understand the effectiveness of thymic selection (van Den Berg et al., 2001), provide insight into the mechanism of ligand antagonism (van Den Berg et al., 2002), predict the existence of activated TCRs that were no longer associated with the peptide–MHC but still marked for internalisation, and suggest a possible explanation for the different activation requirements of naı¨ ve and memory T cells (Coombs et al., 2002). It is unlikely, however, that even a combination of kinetic proofreading and serial triggering can fully account for the observed sensitivity and specificity of T cells (Chan et al., 2003). One possible limitation of these models is that individual TCR triggering events are considered to be independent. Cross talk between TCRs can, however, significantly enhance the overall T cell specificity (Chan et al., 2001). In the E. coli chemotaxis model, it has similarly been shown that receptor cooperativity can improve sensitivity and maintain signal gain over a wide range of ligand concentrations (Bray et al., 1998; Duke et al., 2001). Currently, most mathematical models of T cell activation focus on TCR and peptide–MHC interactions. In reality, however, there are a host of other factors that modulate the effect of a T cell–APC encounter, including co-receptors (CD4 and CD8), a diverse and growing collection of co-stimulatory and co-inhibitory molecules, as well as cytokines and chemokines in the local microenvironment. While it is nice to contemplate a ‘‘complete’’ model of T cell activation that integrates these factors and provides a mechanistic linkage of cell-surface events including immune synapse formation to the intracellular signalling cascades leading to gene expression, cellular proliferation, and gain of effector function, the challenges facing such a goal are formidable, not least how to estimate the multiple parameters necessary to characterise such a system. It therefore seems most likely that near term successes in modelling T cell activation will come from relatively narrowly focused projects much like the work described above, with the modest aim of providing insight into some aspect of T cell activation rather than the building of a ‘‘complete’’ and ‘‘true’’ model. With the rapid advances in imaging and high-throughput techniques (e.g. microarray analysis, proteomics), the amount of data being collected is rapidly outstripping the ability of immunologists to integrate into informal models. It therefore seems likely that the marriage between
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experiment, modelling, and simulation will become ever more common, so much so that it may be the norm for future immunological research.
4. MODELLING T CELL PROLIFERATION The parallels between the growth and death of populations of T cells and other ecological or population growth scenarios has led to many attempts to explore T cell biology using imported modelling techniques. Associated terminology has also crept into the language of T cell population dynamics; competition for resources, occupation of ecological ‘‘niches’’, competitive exclusion. Although some of these concepts persist, perhaps most strongly in the context of memory maintenance and homeostasis, our knowledge of T cell proliferation at the single cell and population levels has grown in recent years and so modellers are now faced with the problem of how best to represent the unique features of T cell biology. For example, it now appears that antigen-specific T cell responses are characterised by a programmed series of divisions that is modulated by the ‘‘quality’’ of the initial contact with antigen (a combination of binding affinity, duration of signaling, and costimulation) (Gett et al., 2003) and dependent to a limited extent on the presence of antigen once the response has started (Bajenoff et al., 2002; Lee et al., 2002). A simple consequence of this is that predator–prey type models may not be appropriate for modelling T cell kinetics. This highlights one of the key problems faced in any sort of biological modelling – how to choose a model most appropriate to the properties of the underlying system, as well as the form that the experimental data takes. At the same time, modellers strive to obtain conclusions that are as insensitive as possible to their assumptions. In this section, we do not attempt to review comprehensively the literature relating to modelling T cell proliferation, but rather to illustrate these issues. Modelling of T cell proliferation has addressed two distinct areas. The first is the antigen-driven T cell response, in which (either in vivo or in vitro) T cells with receptors that are specific or sufficiently cross-reactive with antigenic peptides presented in the context of MHC and with costimulatory signals are driven to divide rapidly and acquire effector status. This can also be mimicked by the use of mitogens to induce polyclonal activation and proliferation, although it is not clear how well this relates to a normal antigen-specific response. The other is homeostatic division (Antia et al., 1998; Callard et al., 2003), which does not appear to result in acquisition of effector phenotype and contributes to the maintenance of peripheral T cell numbers.
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De Boer and Perelson (1994, 1997) developed a model to address the first issue. They have described the initiation of an immune response in which T cells compete for a finite quantity of antigenic sites (the resource) and divide once when they successfully bind and dissociate. A common limitation of ODE models of cell growth is that proliferation rates do not accurately reflect the fact that the division rate of cells is limited by the time taken to transit the cell cycle. This problem occurs with simple predator–prey-type models in which per capita growth rates grow without bound as resource availability increases. De Boer and Perelson showed how a limit to T cell division rates can emerge naturally in their reaction kinetic approach through a modification of the usual steady state assumption for the number of intermediate agent–resource complexes (in this case, the number of T cell/Antigen-presenting cell complexes). Borghans et al. (1999) extend this approach significantly using in vitro proliferation data from T cell lines and Ag-loaded antigen-presenting cells to distinguish between competition for a resource (such as non-specific growth factors), competition for activation signals from APCs and inhibitory T–T interactions. They conclude that T cells compete for access to antigenic sites on APCs, such that APC number rather than MHC–peptide density on the APC surface is a limiting factor. Modelling the T cell population as a homogenous cohort of cells in this way necessarily introduces approximations and assumptions that conflict with our knowledge of the biology (for example, the requirement for continuous access to antigen to drive proliferation, as mentioned above). It also necessarily provides averaged estimates of parameters such as division and death rates that may be functions of division history, or correlated; for instance, dividing cells may be more susceptible to apoptosis than quiescent cells. Here, we discuss modelling approaches to this heterogeneity.
5. LABELLING APPROACHES TO MODELLING T CELL PROLIFERATION For many years, experimental assessment of T cell proliferation in vitro has provided estimates of bulk kinetic parameters such as average rates of cell division or apoptosis by measuring the frequency of cells that incorporate labels such as BrdU, tritiated thymidine or (more recently) deuterated glucose during mitosis. Bromodeoxyuridine (BrdU) is an analogue of the nucleoside thymidine that is incorporated into newly synthesised DNA and can be detected by flow cytometry. Deuterium is incorporated into the pentose sugar of synthesised nucleosides and the
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frequency of labelled base pairs can be measured by mass spectroscopy of extracted DNA. The non-toxicity of deuterium allows it to be given to humans, typically as deuterated glucose. With all these labelling techniques, estimating kinetic parameters requires fitting to models of cell division and death (Hellerstein et al., 1999; Bonhoeffer et al., 2000; Mohri et al., 2001; Asquith et al., 2002; De Boer et al., 2003) and has been a valuable and accessible application of mathematics to experimental biology. A potential pitfall however is that while the overall uptake of label is indeed a measure of the total number of divisions undergone by the T cell population, caution is needed when using the data to infer net proliferation and death rates. Typically, cells are observed during and after a labelling period. While the label is being infused, its rate of uptake reflects the mean proliferation rate of all cells; when absent, its decline reflects only the death rate of recently divided cells, which may differ from that of resting cells. Essentially, the labelling process preferentially samples the dividing population (Asquith et al., 2002). To obtain robust estimates of average rates of division and death one must average correctly over resting and dividing subpopulations. Ribeiro et al. deal carefully with the mathematical interpretation of deuterated glucose labelling data and consider the heterogeneity of the population with a two-compartment model (Ribeiro et al., 2002). This approach is similar to the homeostatic model (Yates and Callard, 2001) in which resting and dividing cells have different kinetics. They model the number of labelled DNA strands rather than cells themselves. This is an efficient method, which suits the manner in which data is obtained from D-glucose studies. De Boer et al. (2003) discuss the use of BrdU and D-glucose labelling to study homeostatic turnover of T cells in macaques, and find that only quantities such as the average proliferation and death rates averaged over all populations can be estimated in a robust (model-independent) manner with these labelling techniques. The predictions that can be made from modelling are limited to some extent by our prior knowledge of the heterogeneity of the T cell pool. Reconstructing the replicative history of a cell population requires accounting of multiple cell divisions, which has been difficult experimentally as the labelling methods described above are essentially binary – that is, either present in divided cells or not. As interest in the processes underlying T cell activation and proliferation has increased, new techniques for following division at a single-cell level have been exploited. In particular, (5- and 6-) carboxyfluorescein diacetate succinimidyl ester (CFSE) is a dye that can be used to label resting cells and is shared equally between daughters when a cell divides (Lyons and Parish, 1994; Hasbold et al., 1999). Using flow cytometry to
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Fig. 3. Flow cytometry of CFSE labelled dividing T cells showing cells that have not divided (0) and number of cells that have divided once, twice . . . five times. Figure adapted from Oostendorp, R.A., Audet, J., Eaves, C.J., 2000. High-resolution tracking of cell division suggests similar cell cycle kinetics of hematopoietic stem cells stimulated in vitro and in vivo. Blood 95(3), 855–862.
sort cells according to their CFSE content, the division profile of the cell population can be monitored (fig. 3). Studies of T cell activation and division using this technique have provided insights into the biology of the initiation and progression of the cell cycle. (Gett and Hodgkin, 2000). CFSE labelling is a complementary approach to BrdU or D-Glucose labelling and provides a generational snapshot of the cells that have divided, whether resting or currently dividing, whereas the time course of the proportion of BrdU-positive cells provides information about the net rate of uptake (division versus death) across the whole population at any time. CFSE data invites the application of generation- or age-structured models. A good basis for this is, perhaps, the stochastic/deterministic model of the cell cycle put forward by Smith and Martin (Smith and Martin, 1973). In their model, resting cells in state A, corresponding to the G0/G1 phase of cell-cycle arrest, are activated with a constant probability per unit time (l) – that is, activation is a Poisson process – and take a fixed time to complete a cell cycle (denoted the B phase) before returning to the A state in the next division generation. Cells die at rates dA and dB, respectively in each phase. If Ai and Bi are, respectively the number of resting and dividing cells in generation i, their expectation values are given by dA0 ðtÞ ¼ ðl þ dA ÞA0 , dt
dAi ðtÞ ¼ 2lAi1 ðt ÞedB ðl þ dA ÞAi ðtÞ dt
and Z Bi ðtÞ ¼ 0
Ai ðt sÞedB s ds:
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Variations of the above model lend themselves naturally to modelling CFSE-labelled T cell proliferation. Cell cycle times and division and death probabilities can be allowed to vary with generation number, appropriate to the amount of data available and the knowledge of the underlying biology. In the simple version above, the presence of the finite delay ensures that there is zero probability of cells appearing in the nth generation before a time n, although the time delay makes the full model difficult to work with analytically. In the limiting case ¼ 0, a class of ODE models is obtained with simple exponentially distributed probabilities of transiting from one generation to the next, which populate all generations arbitrarily quickly. Although less biologically realistic, these models are commonly encountered (see below) and are more analytically tractable. A goal of modelling is to obtain conclusions that are insensitive to the details of the model or our lack of knowledge of the system. An elegant example of this in T cell proliferation studies is provided by a structured population model in which cells have rates of division l or death that vary with the time (s) since their last division, so that if xn(t, s) is the density of cells in the nth generation at time t that divided time s ago (Pilyugin et al., 2003). @ xn @ xn þ ¼ ðlðsÞ þ ðsÞÞxn @t @s with Z1 xn ðt, s ¼ 0Þ ¼ 2
lðrÞxn1 ðt, rÞdr, x0 ðt, 0Þ ¼ 0: 0
Allowing these rates to be arbitrary functions makes this an attractive model, but one wants to extract useful information by fitting it to data. The authors describe a method of estimating the mean division time and death rates by fitting a rescaled version of the model to CFSE time series, without knowledge of the precise form of the functions l(s) and (s). A similar structured model in which cells are labelled with time since their last division, but with constant rates of death and division, has been used to follow the resting and dividing subpopulations (Bernard et al., 2003). This is equivalent to the Pilyugin model with constant l and and zero transit time ( ) through the dividing compartment. A different method is used by Gett and Hodgkin (2000), who developed an approach appropriate to modelling CFSE data from T cell activation with mitogens in vitro in which cells enter their first division after a time drawn from a normal distribution, and divide at a constant rate thereafter.
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This model was developed further to allow for a non-proliferating subpopulation and a death rate of proliferating cells (Deenick et al., 2003). The assumption of the normally distributed time to first division provides an explanation for the approximately log-normal profile observed in their CFSE labelling experiments. However, this illustrates the sensitivity of the interpretation of the data to the details of the model. This division profile can also arise from a conceptually very different one parameter model in which cells divide with probability p per day. Let xi(n) be the number of cells that have divided i times on day n in culture. If one starts with X viable cells, we have the initial conditions ð0Þ xð0Þ 0 ¼ X, xi ¼ 0 8i41
The proportions of cells that have divided i times in n days, where i n, have expectation values given by the binomial distribution, such that ni i i xðnÞ i ¼ X2 p ð1 pÞ
n! i!ðn iÞ!
Following Gett and Hodgkin (2000), one can define the mean division number on day n, m(n), to be the average number of divisions undergone by the precursor population, obtained by weighting xi(n) by a factor 2i, Pn i 2i xðnÞ i ¼ np, mðnÞ ¼ Pi¼0 ðnÞ n i i¼0 2 xi which is simply the mean of the binomial distribution, as expected. Alternatively, if the mean division number is calculated using the raw CFSE peak heights (i.e. using absolute rather than rescaled ‘‘precursor’’ cell numbers), then Pn
m~ ðnÞ Pi¼0 n
i xðnÞ i
ðnÞ i¼0 xi
¼
2np : 1þp
An ODE model in which cells divide at rate p can also be proposed. This is equivalent to taking the Poisson limit of the discrete time (binomial) model above. It is also equivalent to the Smith–Martin model in the limit of zero transit time through the B-phase (Pilyugin et al., 2003). If xi(t) denotes the number of cells that have divided i times at time t, then dx0 ¼ px0 , dt
dxi ¼ 2pxi1 pxi , dt
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with solution x0 ðtÞ ¼ Xept, xi ðtÞ ¼ X
ð2ptÞi pt e : i!
Then the mean division number is P1 i 2i xi ðtÞ mðtÞ ¼ Pi¼0 ¼ pt, 1 i i¼0 2 xi ðtÞ and m~ ðtÞ ¼ 2pt if absolute rather than rescaled cell counts are used. All the models and definitions above predict a linear increase in mean division number with time, as observed by Gett and Hodgkin. In the limit of large cell numbers and n (in the case of the binomial model) or large values of pt in the ODE model, the division profile will tend to the observed Gaussian. This illustrates the non-uniqueness of interpretations of data. Again, it is important to choose the model most appropriate to the underlying biology. Another example illustrates how estimates of biological parameters are sensitive to the model assumptions. For example the ODE model above can be extended to include a death rate d of resting cells (Pilyugin and Antia, 2000; Pilyugin et al., 2003) such that dx0 ¼ ð p þ d Þx0 , dt
dxi ¼ 2pxi1 ð p þ d Þxi , dt
ðEq: 1Þ
then x0 ðtÞ ¼ Xe ð pþd Þt , xi ðtÞ ¼ X
ð2ptÞ ð pþd Þt e : i!
Alternatively, if death is confined to the dividing (B-phase) cells, so that a fraction f die, then dxi ¼ 2pð1 f Þxi1 pxi , dt and xi ðtÞ ¼ X
ð2pð1 f ÞtÞi pð12f Þt e : i!
ðEq: 2Þ
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In the first model, the rate of increase in the mean division number is independent of the death rate, where in the second it is a function of f. Depending on whether model (1) or (2) is used, different estimates of mean division time 1/p can be obtained. Given the possibility that many models may describe a certain set of data, and the difficulty in avoiding artefacts, it is often more instructive to discover which models cannot fit the observations. This is the approach taken by Allan et al. (2004) who proposed a general structured framework of ODEs similar to Equation (1) above. Little is known about the mechanisms that regulate clonal expansion of T cells and reduce the size of the expanded population once the immune response is over. The aim of the study by Allan et al. was to rule out mechanisms for limiting the T cell response by fitting several variations of a division-structured ODE model to published data. Fits were assessed by eye and potential regulatory mechanisms ruled out if the fitted parameters were not deemed to be biologically realistic. Models here are ruled out, rather than mechanisms. Note that there is often the possibility that a given mechanism could be recast in a new mathematical way and achieve a fit to data. We have emphasised here that the choice of model has to be motivated by the biology if meaningful parameter estimates are to be extracted. However, despite the successes of many modelling approaches to labelling studies, a number of fundamental issues in T cell proliferation remain unresolved. Are dividing cells more susceptible to apoptosis than resting cells, and at what point of their division programme? In a population of cells with a range of division rates, are these rates inherited by the daughter cells? Answering these questions and understanding the kinetics of heterogeneous cell populations may well require modelling a combination of these labelling methods, allowing us to go beyond the measurement of bulk kinetic parameters and explore the details of cell-cycle progression.
6. T CELL MEMORY AND HOMEOSTASIS One of the defining features of the adaptive immune system is its ability to respond more rapidly and with greater vigour on re-exposure to an antigen or pathogen. This feature of adaptive immunity is known as memory and is due to increased numbers of antigen-specific T and B memory cells that remain after proliferation and differentiation in response to antigen. Long-term immunological memory depends on a self-renewing pool of antigen-specific T memory (Tm) cells but the homeostatic mechanisms that maintain the size and diversity of the pool are largely unknown. Reconstitution experiments in athymic and intact mice have shown that the
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T memory cell (Tm) compartment is regulated independently from the naı¨ ve compartment and that the homeostatic mechanism concerned is very stable, maintaining constant number of cells over time (Tanchot and Rocha, 1998). CD4 and CD8 memory cells also appear to be maintained independently (Varga et al., 2001) with approximately constant number throughout adult life (Cossarizza et al., 1996). It has been suggested that the Tm compartment is maintained by low-level reactivation with persistent or cross-reacting antigens but there is now persuasive evidence for the maintenance of specific memory in the absence of T cell receptor (TCR) stimulation (Murali-Krishna et al., 1999; Swain et al., 1999). In vivo labelling experiments in mice and humans have shown that 1–5% of both CD4 and CD8 memory cells are in cycle at any one time (Hellerstein et al., 1999; Beverley and Maini, 2000; Mohri et al., 2001). Low-level proliferation has also been found for naı¨ ve T cells in lymphopenic hosts (Ge et al., 2002; Jaleco et al., 2003) and more recently B cells (Macallan et al., 2004). This background proliferation has been termed homeostatic proliferation and is required to maintain the Tm compartment (Goldrath et al., 2002; Prlic et al., 2002) and is probably also required for maintaining number of naı¨ ve T cells and B cells. Homeostatic proliferation of CD8 Tm cells occurs in response to interleukin-15 (IL-15) (Zhang et al., 1998; Prlic et al., 2002; Tan et al., 2002) and a similar (cytokine-driven) mechanism is thought to be responsible for CD4 memory T cell proliferation, probably in response to IL7 (Lantz et al., 2000; Tan et al., 2002; Seddon et al., 2003). Homeostasis of the T and B cell compartments clearly depends on balancing the number of cells that enter each compartment through antigen stimulation and/or homeostatic proliferation against the number that leave the pool by differentiation and/or cell death. Competition for space or growth factors has been suggested as a homeostatic mechanism but the molecular processes concerned have not been defined and there is as yet no direct experimental evidence to support this notion. We have recently suggested that Fas-mediated apoptosis (fratricide) within the small ( 1–5%) proliferating sub-compartment of the Tm pool would give rise to a T cell density-dependent death rate that can maintain a constant memory pool size. There is evidence that the rate of apoptosis in the homeostatic proliferating sub-compartment of T memory cells is higher than in the non-proliferating compartment, which is consistent with the fratricide model, but till date it is not possible experimentally to distinguish between these two ideas. The following discussion is concerned with Tm cells as more is known of the biological mechanisms involved, but the principles may well apply to the other T and B cell compartments as well as many or all the other haematopoietic lineages.
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OUTPUT
INPUT • Antigen activation (naïve and memory T cells) • Homeostatic proliferation
• Death • Differentiation • Fratricide
Fig. 4. Tm homeostasis requires that cells flowing into and out of the memory cell compartment are exactly balanced. Each colour represents a different T cell clone and the bifurcating arrows represent homeostatic or antigen driven proliferation (from Callard et al., 2003).
6.1. Fratricide: a model of nonlinear cell death To maintain a constant Tm cell pool size the rate of flow into the pool must equal the rate of cells leaving the pool (fig. 4). In the fratricide model, the dynamics of the Tm pool are represented with: dx ¼ a þ bx fx2 dx dt where a40 is the flow into the Tm compartment from antigen activation of naı¨ ve T cells, b is the homeostatic proliferation rate of Tm cells, d is the rate of loss from nonlinear death and/or differentiation, and f is the rate of fratricide due to Fas-mediated apoptosis (Gorak-Stolinska et al., 2002; Callard et al., 2003). From this it can easily be shown that there is a single positive stable fixed point given by 1
x ¼
c þ ðc2 þ 4af Þ2 , 2f
c ¼ d b:
This simple model is biologically plausible and shows that fratricide can provide a homeostatic mechanism for memory T cells. However, maintenance of long-term memory requires that there is proliferation within the memory pool otherwise the long-term memory cells would be rapidly diluted out by the influx of new cells. In vivo labelling experiments with BudR or 2H-glucose have shown unequivocally that a small proportion ( 1–5%) of both CD4 and CD8 memory cells are in cycle at any one time. A small proportion of memory B cells have also been found to be in cycle suggesting that homeostatic proliferation is also required for B cell memory (Macallan et al., 2004).
299
Modelling T cell activation, proliferation, and homeostasis (a) resting Tm
(r)
Proliferating Tm (yi)
(xi)
Non-specific loss (d)
(c)
(p)
antigen activation (s)
Fratricide (k)
Antigenactivated Tm (zi) Fratricide (k) Antigen-activated naïve T cells (v)
(c)
Fig. 5. Three-compartment model for Tm homeostasis.
This led us to propose a two-compartment model of Tm homeostasis (Yates and Callard, 2001), which was extended to a three-compartment multiclonal model. This more refined model takes into account homeostatic proliferation and antigen activation of individual Tm clones (Yates and Callard, 2001; Callard et al., 2003). A schematic representation of the model is shown in fig. 5. The equations describing this model are: dxi ¼ ryi axi dxi si xi þ pðsi ÞZi dt N X dyi ¼ 2axi þ cyi kyi yi ryi si yi dt i¼1 N X dzi ¼ si ðxi þ yi þ vÞ þ czi fðsi Þzi zi pðsi Þzi dt i¼1
In this refined model, the Tm pool was considered to consist of an arbitrary number (N ) of individual clones. Each clone of resting Tm cells is represented by xi, cycling Tm cells by yi, and antigen-activated T cells as zi, where i ¼ 1, 2, . . . .N. Proliferation within compartments ( y) and (z) occurs at a rate c. Fratricide of the proliferating Tm cells occurs at rate (k) and of antigen-activated Tm cells at rate ( f ). The flow of cells between the various compartments is shown. An infection was simulated by introducing a quantity si , which represented the activating capacity of
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a particular antigen/pathogen. During infection, pre-existing memory cells of clone (specificity) i are recruited into the effector pool zi from memory at rate si. Recruitment also occurs from naı¨ ve cells (v). The effector cells die by fratricide at a rate k, which is small (klow) while the infection is present (si 6¼ 0) and high when the infection is cleared. Cells are also ‘‘rescued’’ back into memory at a constant per capita rate p, which is zero during the infection. Pathogen clearance by the immune system is not included here. Rather, antigen stimulation (si) is set to be non-zero over a finite time interval, usually several days. Parameter values were estimated from experiment as described elsewhere (Yates and Callard, 2001). Fratricide (apoptotic cell death) was restricted to the proliferating compartments. This was justified by evidence that apoptosis of Tm shown by Annexin V staining is largely confined to recently divided cells (P.C.L. Beverley, pers. commun.) The enhanced model showed that the total T-memory-cell pool is maintained at a constant level by a single positive fixed point that is inversely proportional to the rate of apoptosis and independent of antigen (Yates and Callard, 2001). The pool size was also independent of its clonal constitution. Moreover, because homeostatic proliferation and apoptosis rates were taken to be the same for each clone, the proportion of the memory pool occupied by any given clone was preserved over time. This is an entirely reasonable assumption because expression of different TCR ab chains should not affect intrinsic cell cycle or apoptosis rates. The absence of competition between clones implied by this assumption is an important property that allows clonal diversity to be maintained over time. It is less clear how this diversity can be maintained in the face of intermittent entry of new clones from naı¨ ve cells and/or selective expansion of pre-existing Tm clones in response to antigen. It is also unclear what factors are responsible for the very large number of individual clones that are known from TCR analysis to be present in the CD4 compartment compared to the smaller number of large clones in the CD8 compartment (Beverley and Maini, 2000). To see how clonal diversity could be maintained, we analysed the behaviour of CD4 and CD8 Tm cells following antigen activation of selected clones and entry into a memory pool was investigated. When antigen stimulation was ignored, pre-existing clones expanded to fill the pool to its homeostatic level, which then remained constant. Infection was incorporated into the model in two ways. To mimic entry from the naı¨ ve pool, Tm cells were introduced rapidly into the memory compartment. Resolution of the infection resulted in a gradual reduction in Tm cell numbers until the total (sum of all the clones) returned to the normal equilibrium. Infection was also modelled by antigen stimulation of
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pre-existing Tm cells. At first, this resulted in rapid loss of the responding clone from the memory pool as it differentiated into effector cells. After the removal of antigen, a rapid introduction of new Tm cells from this clone was observed, which at first increased the total size of the memory pool before returning to the normal homeostatic level. Similar effects have been shown previously by experiment (Selin et al., 1996). The lower apoptosis rate and larger burst size for CD8 cells resulted in larger numbers of cells attempting to enter the memory pool after each infection. This diluted the CD8 memory population and rapidly decreased the relative size of any pre-existing clone that had not been stimulated with antigen. As a result, those clones most recently or repeatedly activated with antigen dominated the memory population, which became ‘‘oligoclonal’’. It should be noted, however, that those clones not recently stimulated by antigen were still present, albeit with lower cell numbers. By contrast, the CD4 Tm population remained ‘‘polyclonal’’ with all the clones having approximately the same number of cells whether they had been recently stimulated with antigen or not (fig. 6). This difference in diversity was due to the larger number of CD8 compared to CD4 effectors at the peak of the response and to the lower rate of apoptosis within the CD8 population. Both these differences are consistent with experimental evidence (Whitmire et al., 2000).
7. COMPETITION MODELS The fratricide model described above shows that density dependent cell death from Fas-mediated apoptosis can give rise to a stable Tm population with the known experimental characteristics. Such a model can be expressed in the form dx ¼ a þ bx cx2: dt
ðEq: 3Þ
However, contact-mediated cell death is unlikely to be bilinear in cell number in this way for all population sizes; at large pool sizes, the underlying ‘‘well-mixed’’ approximation that may break down and the death rate becomes linear in cell number. A more biologically realistic model is then perhaps dx x ¼ a þ bx cx , dt kþx
ðEq: 4Þ
where k is now the population size at which cell crowding in lymph nodes means that cells are restricted to contact with nearest neighbours.
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Fig. 6. Effect of introducing new clones on the clonal distribution of the CD4 and CD8 T-memory-cell (Tm) pools. Two clones were introduced into the CD4 and CD8 memory pool at time zero. Both CD8 and CD4 Tm populations were treated in the same way except that CD8 cells were taken to have a greater burst size on activation and a lower rate of apoptosis amongst effector cells during the resolution phase of the response. These differences introduced into the model were based on published experimental data showing that clonal expansion of CD8 cells is greater than CD4 T cells (Homann et al., 2001) and that their susceptibility to Fas-mediated apoptosis is lower during the resolution phase of the response (Grayson et al., 2000; Whitmire et al., 2000; Homann et al., 2001). The introduced clones proliferated rapidly to fill the pool until the numbers reached the homeostatic level. To mimic infection to a new pathogen, clones shown in blue, mauve, and turquoise derived from the naı¨ ve pool were added at different times. Following resolution of the infection, the size of each new clone was reduced so that the overall memory pool size returned to its homeostatic level. Antigen stimulation of pre-existing memory clones at days 900, 1000, and 1200 at first caused their removal from the Tm pool as they differentiated into effector cells, resulting in a small homeostatic expansion of the remaining clones. At the resolution of the infection, memory cells derived from these clones were reintroduced into the pool in high numbers. The homeostatic mechanism then reduced the size of all the clones so that the total memory-cell compartment returned to equilibrium. Note that the introduction of new clones into the CD8 pool gradually diluted the unstimulated clones giving rise to a reduced heterogeneity. In contrast, all the clones in the CD4 pool whether stimulated or unstimulated were approximately evenly distributed and clonal heterogeneity was maintained. The different effect on clonal distribution in the CD8 and CD4 pools was entirely due to the larger number of CD8 cells entering the pool compared to CD4 cells in response to infection (clonal expansion) and the lower rate of apoptosis (from Callard et al., 2003).
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T cell response to IL15 2.5
2
1.5
1
0.5
0
Fig. 7. Typical dose–response curve for T cell proliferation to IL15.
One may test this hypothesis by observing the rate of decline of cell numbers as a function of pool size in animals overpopulated with T cells. However, this does not guarantee that the mechanism described above actually operates! Competition for ‘‘space’’ or ‘‘resources’’, particularly growth or survival factors (cytokines) or peptide–MHC complexes, is often suggested as a mechanism for T cell homeostasis. These models express rates of proliferation or death as functions of the concentration of a resource that is consumed by the cells themselves. Experimentally, dose–responses for growth and survival factors are roughly sigmoidal in shape (fig. 7). These can be represented mathematically by a Hill function of the form: fðrÞ ¼
krn xn0 þ rn
where k is a constant, r is the concentration of a resource, r0 is the concentration of resource that gives half maximal response, n ¼ 0 .. 1 .. 2 . . . n. Typically, for experimentally observed responses of T cells to cytokines r0 100 pg/ml and n 1. The simplest form for a competition model of this type would be dx ¼ f ðrÞx dx: dt
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Without consumption of the resource r, this leads to simple exponential growth or decay of the population, depending on the relative sizes of f ( r) and d. A more biologically plausible model can be made by considering equations for both the resource r and the Tm cells that consume it. Let us suppose that a resource is produced at a rate constant rate and is degraded at a rate . It is also consumed by the T cells, and we assume that its rate of uptake is simply proportional to its proliferative effect on a cell. Then dr rn ¼ n x r dt r0 þ rn dx rn ¼þl n x x dt r0 þ rn
ðEq: 5Þ
Choose n ¼ 1 and assume that the resource is in a quasi-steady state (i.e. its rates of production and removal are much higher than the rates governing T cell dynamics). This gives
r¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " ðxÞ þ " ðxÞ2 þ 4r0 2
where " ðxÞ ¼ x þ r0 : This can be substituted into the equation for dx/dt to generate a one-dimensional dynamical system, which exhibits a single stable fixed point (we do not present its analytic expression here). Our point is that in the vicinity of the homeostatic fixed point, or indeed at large cell numbers, the dynamics of this model – and indeed any of a number of plausible models of homeostasis – are effectively indistinguishable from those of fratricide. To say any more about how, for example, the steady state pool size depends on the biological parameters requires further experimental work to assess which model is most appropriate. The converse, however, is that the conclusions of the T memory model are relatively independent of the precise homeostatic mechanism. For its conclusions to hold, it is sufficient that growth of the T cell pool is self-limiting and that death or competition for resources is independent of TCR specificity.
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Rabinowitz, J.D., Beeson, C., Lyons, D.S., Davis, M.M., Mcconnell, H.M., 1996. Kinetic discrimination in T-cell activation. Proc. Natl. Acad. Sci. USA 93, 1401–1405. Ribeiro, R.M., Mohri, H., Ho, D.D., Perelson, A.S., 2002. Modeling deuterated glucose labeling of T-lymphocytes. Bull. Math. Biol. 64, 385–405. Seddon, B., Tomlinson, P., Zamoyska, R., 2003. Interleukin 7 and T cell receptor signals regulate homeostasis of CD4 memory cells. Nat. Immunol. Selin, L.K., Vergilis, K., Welsh, R.M., Nahill, S.R., 1996. Reduction of otherwise remarkably stable virus-specific cytotoxic T lymphocyte memory by heterologous viral infections. J. Exp. Med. 183, 2489–2499. Smith, J.A., Martin, L., 1973. Do cells cycle? Proc. Natl. Acad. Sci. USA 70, 1263–1267. Swain, S.L., Hu, H., Huston, G., 1999. Class II-independent generation of CD4 memory T cells from effectors. Science 286, 1381–1383. Tan, J.T., Ernst, B., Kieper, W.C., Leroy, E., Sprent, J., Surh, C.D. 2002. Interleukin (IL)-15 and IL-7 jointly regulate homeostatic proliferation of memory phenotype CD8(þ) cells but are not required for memory phenotype CD4(þ) cells. J. Exp. Med. 195, 1523–1532. Tanchot, C., Rocha, B., 1998. The organisation of mature T-cell pools. Immunol. Today 19, 575–579. Valitutti, S., Lanzavecchia, A., 1997. Serial triggering of TCRs: a basis for the sensitivity and specificity of antigen recognition. Immunol. Today 18, 299–304. Valitutti, S., Muller, S., Cella, M., Padovan, E., Lanzavecchia, A., 1995. Serial triggering of many T-cell receptors by a few peptide-MHC complexes. Nature 375, 148–151. van Den Berg, H.A., Burroughs, N.J., Rand, D.A., 2002. Quantifying the strength of ligand antagonism in TCR triggering. Bull. Math. Biol. 64, 781–808. van Den Berg, H.A., Rand, D.A., Burroughs, N.J., 2001. A reliable and safe T cell repertoire based on low-affinity T cell receptors. J. Theor. Biol. 209, 465–486. Varga, S.M., Selin, L.K., Welsh, R.M., 2001. Independent regulation of lymphocytic choriomeningitis virus-specific T cell memory pools: relative stability of CD4 memory under conditions of CD8 memory T cell loss. J. Immunol. 166, 1554–1561. Whitmire, J.K., Murali-krishna, K., Altman, J., Ahmed, R., 2000. Antiviral CD4 and CD8 T-cell memory: differences in the size of the response and activation requirements. Philos. Trans. R. Soc. Lond. B. Biol. Sci. 355, 373–379. Williams, C.B., Engle, D.L., Kersh, G.J., Michael White, J., Allen, P.M., 1999. A kinetic threshold between negative and positive selection based on the longevity of the T cell receptor-ligand complex. J. Exp. Med. 189, 1531–1544. Wulfing, C., Tskvitaria-Fuller, I., Burroughs, N., Sjaastad, M.D., Klem, J., Schatzle, D., 2002. Interface accumulation of receptor/ligand couples in lymphocyte activation: methods, mechanisms, and significance. Immunol. Rev. 189, 64–83. Yates, A.J., Callard, R.E., 2001. Cell death and the maintenance of immunological memory. Discr. Cont. Dynam. Sys. B. 1, 43–60. Zhang, X., Sun, S., Hwang, I., Tough, D.F., Sprent, J., 1998. Potent and selective stimulation of memory-phenotype CD8þ T cells in vivo by IL-15. Immunity 8, 591–599.
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
17 A theory for complex systems: reactive animation Sol Efroni a,c, David Harelb and Irun R. Cohenb a
National Cancer Institute Center for Bioinformatics, Rockville, MD, USA b The Department of Immunology, The Weizmann Institute of Science, Rehovot, Israel c The Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, Israel
1. SYNAPSES ‘‘Multidisciplinary Approaches to Theory in Medicine’’ is the name of this book. Multidisciplinary is easy to understand; medicine encompasses different academic disciplines that investigate the organism at many scales of enquiry: genetic, molecular, cellular, systemic, pathological, behavioural, social, and historical. The use of the term multidisciplinary here, however, refers specifically to the synapse between bio-medical scientists and applied mathematicians and physicists aimed at understanding the complexity of the organism. This multidisciplinarity is characterised by the use of mathematics and computer science to explicate biology. Here, we discuss concepts of theory, complexity, and understanding, and describe a visually dynamic way to represent and study complex biologic data: Reactive Animation (RA).
2. THEORY What is the meaning of theory in medicine? The Oxford English Dictionary provides various definitions of theory, including this one: 4. a. A scheme or system of ideas or statements held as an explanation or account of a group of facts or phenomena . . . the general laws, principles, or causes of something known or observed. So a theory is an explanation based on laws, principles, or causes. 309
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The word theory, however, does not derive from law, principle or cause; theory is derived from the Greek "! , which means to look at or view (Oxford English Dictionary, 1989). The etymology of theory makes the point that a theory is basically a way of looking at the world. Usually we make theories about things that we cannot actually see with our bare eyes; despite its etymology, a theory usually aims to explain a reality behind appearances. A theory is a way a mind eyes the world. A theory, from this point of view, is a representation of what cannot be seen, but only surmised. (Parenthetically, note that the word representation, like the word theory, is a paradox; just as a theory visualises the invisible, a representation presents the absent.) So, ‘‘Theory in Medicine’’ refers to what our view of the organism – in health, disease, and experiment – can teach us about the core laws, principles, or causes that form and animate the organism. Theory thus contributes to understanding: We look at a complex piece of the world and our theory expresses the way our minds understand the spectacle.
3. COMPLEXITY A complex system, such as an organism, is a system composed of many different interacting parts. The attribute we call emergence distinguishes a complex system from a simple system (Cohen, 2000). The solar system is a simple system because, however complicated, the solar system boils down to the bodies in the system (sun, planets, moons, etc.) and the laws of gravity that connect their masses. For example, knowledge of the masses of the earth and the moon (and the sun too) and the law of gravity is good enough to put a man on the moon (provided you have a proper rocket ship). Understanding the component parts of a simple system is sufficient to understand the system, viewed as a whole system. Just as the solar system is formed by a fundamental interaction between masses (the laws of gravity and motion), the organism is formed by the fundamental interactions of its component molecules (the laws of chemical reactions). However, the organism is more complex than is the solar system because cataloguing the chemistry of all the individual molecules that make up the body does not suffice for understanding the organism as a whole. We cannot readily see how the component parts of the body generate the behaviour of the organism, so we need theory; we need a representation of the inside – the microscopic components – of the organism that will account for the emergence of the visible – macroscopic – properties of the organism.
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4. PARTS CATALOGUE An automobile is composed of thousands of parts, many of which move and mutually interact, while they also interact with the road and the driver. But an automobile, compared to a cell, is not really a complex system because a good mechanic can fix one or even build one using the parts and the parts catalogue; quite simply, each part of an automobile has a defined place and a defined function. Your living body differs fundamentally from your automobile in relation to its component parts: body parts, unlike automobile parts, are pleiotropic, redundant, degenerate, and apt to learn new tricks. Many (probably most) biologically important molecules perform more than one function (bio-molecules are pleiotropic); different molecules can perform similar functions (important cells and molecules are redundant); interacting ligands and receptors are hardly ever exclusively specific (molecular interactions are degenerate); and a molecule’s structure and function (allosteric effects, posttranslational modifications, and the like) are responsive to the environment and the history of past interactions (Cohen, 2000). One cannot predict the behaviour of an organism based on a list of its component molecules and their possible interactions. The structure – function relationship of your automobile has a simple one-to-one arrangement between parts and performance: not so your body. Consider, for example, the role of interferon gamma (IFN) in autoimmune diseases. IFN is the prototypic Th1-type cytokine responsible for destructive inflammation in autoimmune diseases, clinically and experimentally (Liblau et al., 1995). Any treatment that down-regulates the expression of IFN will turn off the disease (Cohen, 1997; Elias et al., 1997). So, IFN is an undisputedly essential agent in the disease process. But it is very difficult to visualise exactly what IFN does that is so essential; IFN is a molecule that, among its own many direct activities, activates at least 220 other genes (Boehm et al., 1997); IFN is very pleiotropic (but probably not more so than other cytokines). Strangely, some of the effects of IFN can be carried out by a molecule called tumor necrosis factor alpha (TNF) (Sullivan, 2003). Thus IFN and TNF are somewhat redundant. IFN is also degenerate; it can interact as a ligand for more than one receptor (Dinarello, 2002). How frustrating to knock out key genes in a mouse, only to discover that the knock-out mouse manifests an unpredicted phenotype, or no noticeable change in its wild-type phenotype. IFN is a frustrating example; mice with their IFN gene knocked out still can develop autoimmune diabetes (Serreze et al., 2000) or experimental autoimmune
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encephalomyelitis (Glabinski et al., 1999). But remember, treatments that inactivate IFN do block these diseases (Liblau et al., 1995; Cohen, 1997; Elias et al., 1997). So how can knocking out the gene itself leave the disease phenotype intact? We may suppose that the mammalian immune system is sufficiently complex to self-organise an effective immune response in the absence of IFN by implementing other programmes. Your automobile, unfortunately or not, simply cannot learn to make do.
5. SIMPLICITY BELIED Classically it was assumed that the organism, however complicated, could be reduced, like an automobile, to a collection of individually simple functional sequences, each sequence characterised by a one-to-one relationship between a gene, its encoded protein, and a specific function (Mayr, 1961). Immunologists, like other biologists, have attempted, and attempt even today, to represent the immune system using the simplest theory imaginable – not without controversy (Efroni and Cohen, 2002; Langman and Cohn, 2002; Cohn, 2003; Efroni and Cohen, 2003). The genome was thought to be the body’s blueprint; knowing the genome, it was hoped, would allow us to understand the organism. But now we realise that the genes are not enough (Cohen and Atlan, 2002); we have to catalogue all the proteins too and decipher the proteome. And that too, be assured, will not suffice. Pleiotropism, redundancy, ligand-receptor degeneracy and epigenetic and post-translational modifications of the organism’s component molecular and cellular parts thwart understanding (Cohen, 2000). Indeed, the living organism is generated, not by parts, but by process – a dynamic web of interactions generates the system; the component cells and molecules and the laws of chemistry are mere infrastructure. Life emerges. The organism and its states of being cannot be reduced to the laws of chemistry and physics in the way that the solar system can be reduced to the laws of chemistry and physics, or the automobile to its parts.
6. UNDERSTANDING COMPLEXITY Science grounds understanding on observation, measurement, and repeatability. So understanding in biology (and in any science) is not merely a state of mind; biological understanding must be a proficiency, a competence (Cohen, 2000). Understanding the world amounts to dealing well with the world. Understanding is active. Understanding is
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manifested by how we respond to what we see. Medicine illustrates this well: The degree to which the doctor understands the patient’s illness is demonstrated by the ability of the doctor to restore the patient to better health. The patient, in fact, does not care much about the theories the physician might have had in mind when he or she started the treatment; the patient rightfully judges the physician’s understanding by the physician’s performance: ‘‘Am I getting better’’? What specific rules of competence demonstrate scientific understanding? The doctor, for example, understands the illness by making a correct diagnosis. The proper diagnosis allows the doctor to predict the patient’s clinical course, and so make a prognosis. Diagnosis and prognosis are abstractions, merely words; classifications of illnesses are merely representations of reality. Nevertheless, these representations can be translated into significant actions. A diagnosis, for example, rests on a regularity of nature. All cases of type 1 diabetes emerge from a lack of insulin. A diagnosis of type 1 diabetes tells the doctor that the patient needs insulin. Thus, the abstract nosological representation we call diabetes allows the physician to predict the course of the illness, based on professional knowledge. The abstract representations we call diagnosis and prognosis allow the doctor to institute successful therapy. Correct therapy makes the patient healthier – changes the world. Science too measures understanding by performance: A scientist understands his or her field to the degree to which he or she carries out (or teaches others to carry out) productive research. Productive research requires three proficiencies. Similar to diagnosis, prognosis, and therapy in medicine, scientific understanding is tested by successful representation, prediction, and utility.
7. REPRESENTATION A complex system is complex precisely because we cannot reduce the data to a simple basic law or single cause that can account for all the details we have learned about the system through observation and experimentation. We are confounded by the limitations of memory and mental computation. In former days, when we had relatively little data, it was easy to formulate theories that included all we knew. At the present state of biology, however, we have learned too much; we suffer from a flood of information. Now only the computer can supplement our weak memories and help us compensate for our limited mental computation. The database is too heavy for the mind alone to bear; we are confounded by the organism’s basic pleiotropism, redundancy, degeneracy, and functional adaptation.
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Of course, an experimenter does not need a comprehensive and integrated understanding of the field to continue with the reductionist agenda of isolating and characterising each molecule, cell, connection, and process in a system of study. Normal biologic science can go on and on successfully accumulating data about the parts catalogue. But a more comprehensive and integrated understanding of living systems seems to be on the agenda. The present proliferation of ‘‘systems biology’’ programmes arises from a general perception that reductionism alone (a completed parts catalogue) will not suffice for understanding. At least some people will have to keep track of the whole system, and inform the rest. Interdisciplinary efforts will be needed to make good biological theory. Thus, the impact of theory on biology and medicine will depend to some degree (probably to a great degree) on how intelligently we use computers to represent in comprehensible format the complexity of biological data. Apt representation is the key to comprehension. But when is a representation ‘‘apt’’? How can we tell an appropriate representation from an inappropriate representation? Is there, in fact, only one true representation of a complex system? A representation, like any idea, can be judged by its performance. As we shall now discuss, a good representation will usefully engage our minds to formulate predictions, think new thoughts, and undertake new experiments. Obviously, then, there is no one true representation of a complex system. Different presentations of the data can suit different purposes. In fact, different presentations of the data constitute different theories about the meaning of the data.
8. PREDICTION The value of prediction in science needs no elaboration. Science aims to detect and characterise the regularities of nature, and prediction is a functional test of regularity. If you cannot foresee the outcome of the experiment, then your theory might be wrong. Fortunately, even complex systems are predictable. In fact, a living system survives through its ability to predict what its environment has to offer. A living system survives by mining information and energy from its niche in the environment (Cohen, 2000). A theory or a representation of a living system, like the living system itself, survives by the success of its predictions.
9. UTILITY Clearly, a most important feature of a theory is its usefulness. A theory is manifestly useful when it solves a problem – achieves a goal, provides a
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technique, leads to a cure. But, a good theory not only solves a problem; but also should engage minds to think new thoughts and undertake new experiments. James B. Conant (1951 p.25) has defined science as ‘‘an interconnected series of concepts and conceptual schemes that have developed as a result of experimentation and observation and are fruitful of further experimentation and observation’’. Science, according to Conant, is a chain reaction: theory leads to experiments that produce new data, and the new data, in turn, stimulate new theories that trigger new experiments, that generate new data, and on to more useful models of understanding.
10. THEORY FOR COMPLEXITY The distinction between simple systems and complex systems suggests that each type of system needs its own type of theory. A scientific theory for a simple system boils down to a timeless list of immutable laws or standing principles that explain the workings of the system of interest. As we have discussed above, we can understand the solar system by reducing the system to the unchanging laws of gravity and motion. Discovering a fundamental law that governs the behaviour of a simple system puts one’s mind to rest; the problem of understanding the data seems to be solved. The data can be replaced by the fundamental law that accounts for them. The laws behind a simple system supersede the noisy details of the data. The fundamental laws of a simple system represent the system as neatly and as efficiently as possible. Complex systems, in contrast to simple, can never get away from the noisy details. The noisy details are the essence. Consider two well-studied species: the round worm, C. elegans and the human, H. sapiens. A physicist would note that both the creatures obey precisely the same basic laws of matter, are composed essentially of the same molecules, and house the same spectrum of chemical reactions. In fact, both creatures realise very similar, if not identical principles of organisation. There is no essential difference between the person and the worm, when we view both with the tools of physical theory. The differences, for the mathematician and physicist, and for the chemist too, between worm and us are in the noisy details. But the noisy details between the species are exactly what we want to understand as biologists, physicians, and citisens. Reduction to fundamental laws fails to explain what we want to understand. Theory
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for a complex system cannot do away with the noisy details. A simple theory for a complex system misses the system. Actually, there is one simple theory that has proved to be of continuous usefulness in biology, and in complexity generally: the theory of evolution. The theory of evolution is the best – perhaps the one-and-only – basic law in biology. The theory of evolution tells us to mind the noisy details; evolution says nothing about any of the particular details that comprise and distinguish species, only that they are likely to be essential.
11. REACTIVE ANIMATION: A PROTOTYPE FOR COMPLEXITY So, a theory for a complex system must live with the data; the theory does not supersede the data. Complex system theory amounts to organising the data and representing it in a way that engages the mind to see the data anew and undertake new experiments. A theory for a complex system, then, must pass two tests: the theory must simplify and compress the data to the point where the system is rendered comprehensible, but the simplification and compression must not go beyond the point at which the essence of the complexity is lost. This principle sounds simple enough, but it would require a book or two to present a full theory of complexity theory, and we have only this brief chapter. Let us close then by describing reactive animation (RA for short), our initial approach to organising the data so as to engage the mind without over-simplifying the system.
12. ORGANISING THE DATA We have used the visual formalism of Statecharts to capture and model data related to the immune system. The Statecharts language was developed originally as a language for aiding in the design and specification of computerised, man-made systems (Harel, 1987). Statecharts captures the states of a system and the transitions between them. Its most popular version is applied within an object-oriented framework, where the system is described as a collection of interacting objects and each object is provided with a Statechart that captures its behaviour. Statecharts has become widely used in system design in computer science and engineering (Harel and Gery, 1997), and we have only recently begun to apply Statecharts to the immune system. Our first piece of work was a pilot project on the activation of T cells (Kam et al., 2001). Now we have applied Statecharts to the development of T cells in the thymus (Efroni et al., 2003).
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A theory for complex systems: reactive animation Thymocyte System Analysis DP Cells: •
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Cytokines, etc. Interactions: Organ:
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Fig. 1. Thymocyte system analysis. Here is a general overview of the data incorporated into the Statecharts analysis of thymocyte development. Note that the range of data covers scales from molecules to the developing organ.
The objects in the immune system are molecules, cells, and organs, individually and collectively; connections between objects include their relationships and their interactions. The object-oriented version of Statecharts suits biologists because biologists experiment with objects (genes, molecules, cells, organs, organisms, and societies) and study their connections (fig. 1). The visual formalism of Statecharts is also much less daunting than are mathematical equations, and are more convenient for most biologists who are used to representing data visually; open any biological text. Indeed, biologists are no strangers to the notions that objects exist in particular states and that the behaviour of a system may involve the transitions of component objects to new states. Figure 2 illustrates a Statecharts representation of some aspects of thymocyte development (Efroni et al., 2003). In a Statechart the boxes represent states, and may be nested to capture levels of detail. States can also be related to each other concurrently (depicted by dashed separator lines). The transitions between states are represented by arrows labelled with the triggering event and possible guarding conditions. The Statecharts themselves are used to represent the behaviour of each class of objects. The Statecharts language is described in detail in the literature (Harel, 1987; Harel and Gery, 1997; Harel and Politi, 1998); here we shall only mention its attractive features for biological complexity.
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Fig. 2.
Thymocyte cell phase. Here is an example of one of many hundreds of charts that comprise the Statecharts analysis.
Detailed data. The details of the database can all be included in the Statechart description. Statecharts makes possible a ‘‘bottom–up’’ representation of the data about experimental objects. Multi-scale. One can zoom out to look at cells and collectives of cells, or zoom in to look at molecules inside cells, or cells inside organs, or at combinations of scales, as long as these scales of the system have been modelled too. Mathematical precision. The visual formalism of Statecharts is mathematically precise and semantically legible to computers. Modular. Statecharts easily accommodates new data by allowing the user to add to an existing model new kinds of objects as they are discovered and to specify their behaviour using new Statecharts, or to add to, or modify the Statecharts of existing objects as new facts about behaviour are discovered. One does not have to redo all the equations when one wishes to integrate new information into the representation of the system.
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Concept of RA
Fig. 3. The concept of reactive animation (RA). RA is based on the general idea that any system has two functional components: the mechanisms that comprise the system and the appearance of the system to our minds. RA separates the precise specifications of the mechanisms that simulate the system from an animation of the simulation that engages our minds. In this way, the data create a semantically precise representation of the system’s behaviour that is translated into an interactive, moving representation that reveals emergent properties, excites curiosity, motivates experimentation, fosters creativity and strengthens understanding.
Executable and interactive. Systems represented in a Statecharts format can be ‘‘run’’ on computers. Statecharts simulations are feasible and are supported by powerful software tools, and so experiments can be performed in silico. The user can see the simulated effects of adding or removing molecules or cells, or of changing or manipulating interactions. Thus, Statecharts makes it possible to experiment with complex systems without simplifying or ignoring the known data. RA uses Statecharts to organise and run the data, but RA adds animation to organisation.
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Fig. 4. Motifs for making a T cell. In our present example of RA, we equip Flash with basic components for making T cells, thymic epithelial cells (not shown here), and other motifs, from which the animation is constructed.
Emergent Anatomy
Emergent anatomy of the thymic lobule. The circles are developing thymocytes. The figure is a snapshot of an animated simulation. Thymocytes are color-coded for each developmental stage.
Fig. 5. The emergence of thymus functional anatomy. The figure illustrates that a functioning, anatomically correct thymus can emerge from the entry of a few stem cells and their migration and differentiation according to molecular gradients and cell interactions.
13. ENGAGING THE MIND A theory for complexity, as we have discussed above, should motivate the mind to make new associations and propose new experiments. Statecharts, with its diagrammatic visual formalism, is not the customary way the minds of biologists (or of humans generally) represent systems.
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Cell Migration
Fig. 6. Migration of a single thymocyte. The blue line traces the cell’s migration from its entry to the cortico-medulary junction as a stem cell to the subcortical zone (SCZ). The red line traces the cell’s journey of differentiation to the medulla, from which it will exit to serve the immune system outside the thymus. Note the control panel at the foot of the thymus animation.
Zooming into the Thymus
Fig. 7. Zooming into the thymus. The thick blue line represents the extensions of the thymus epithelial cells upon which the thymocytes interact, differentiate, proliferate or die. Thymocytes are coded according to their state and expression profile.
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Fig. 8. Experimenting in silico. The RA format makes it possible to probe the animation and experiment with various functional components of the system. Here is an example of some of the things one can ask of a thymocyte, and see what happens to the cell.
Humans draw pictures and respond to pictures that ‘‘resemble’’ the prototypic objects they like to see, or have learned to see. We need not discuss here the meaning of visual ‘‘resemblance’’, or why humans tend to feel at home cognitively with visual objects. But it is clear that we are captivated by visual representations. In fact, we are most responsive to moving pictures. The cinema, TV, DVD, the computer screen, the world of advertising, all demonstrate that moving pictures move minds and generate returns. So we have built RA to connect the simulations of Statecharts to traditional (textbook-type) representations of cells and molecules in an animated format. The RA animation is created by connecting the Statecharts language and its support tool, Rhapsody, to the Flash system, a commonly used software package for programming animation (Efroni et al., 2003). We supply the Flash program with a repertoire of basic motifs representing cells and key molecules. The simulation produced by Statecharts then connects to Flash to create a moving picture of the simulation. Moving pictures of biological systems are not our innovation; turn on any educational TV channel and see moving cells, developing organs, bodies mending. The innovation of RA is that here the moving representation emerges from – indeed is driven by – the precise specification of the data run on Statecharts. The moving pictures seen in RA are generated by the
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data themselves, bottom–up, and not by our imagination or preference, top–down. The aim of RA is to represent the data in a way that does not over-simplify its complexity (recording the data and simulating it by Statecharts), but yet engineer the representation (by its connection to Flash) to stimulate the mind with a moving and interactive picture of the show. Seeing the cells move, differentiate, interact, proliferate, kill or die excites curiosity and triggers associations. Thus, the Statecharts arm of RA guarantees mathematical precision; the Flash arm of RA enhances creativity. RA, in other words, departs from the approaches to biological system modeling developed till now; traditionally, modeling has focused on neat concepts (top–down) rather than on messy data (bottom–up), or has abandoned the data entirely to construct artificial and synthetic computations aimed at ‘‘reproducing’’ in silico ersatz genomes, life-like patterns, or evolving biomorphs (see Kumar and Bently, 2003). RA encourages the user to experiment with the system, and not only to see it in action; is that not the aim of any theory for biological complexity?
REFERENCES Boehm, U., Klamp, T., Groot, M., Howard, J.C., 1997. Cellular responses to interferon – Annu. Rev. Immunol. 15, 749–795. Cohen, I.R., 1997. The Th1/Th2 dichotomy, hsp60 autoimmunity, and type I diabetes. Clin. Immunol. Immunopathol. 84(2), 103–106. Cohen, I.R., 2000. Tending Adam’s Garden: Evolving the Cognitive Immune Self. Academic Press, San Diego. Cohen, I.R., Atlan, H., 2002. Limits to genetic explanations impose limits on the human genome project. In Encyclopedia of the Human Genome, Nature Publishing Group, Macmillan, London. Cohn, M., 2003. Does complexity belie a simple decision – on the Efroni and Cohen critique of the minimal model for a self-nonself discrimination. Cell Immunol. 221(2), 138–142. Conant, J.B., 1951. Science and Common Sense. Yale University Press, New Haven, p. 25. Dinarello, C.A., 2002. The IL – 1 family and inflammatory diseases. Clin. Exp. Rheumatol. 5(Suppl. 27), S1–S13. Efroni, S., Cohen, I.R., 2002. Simplicity belies a complex system: a response to the minimal model of immunity of Langman and Cohn. Cell. Immunol. 216, 22–30. Efroni, S., Cohen, I.R., 2003. The heuristics of biologic theory: the case of self – nonself discrimination. Cell Immunol. 223(1), 87–89. Efroni, S., Harel, D., Cohen, I.R., 2003. Toward rigorous comprehension of biological complexity: modeling, execution, and visualisation of thymic T-cell maturation. Genome. Res. 13(11), 2485–2497. Elias, D., Melin, A., Ablamuntis, V., Birk, O.S., Carmi, P., Konen-Waisman, S., Cohen, I.R., 1997. Hsp60 peptide therapy of NOD mouse diabetes induces a Th2 cytokine burst and downregulates autoimmunity to various beta-cell antigens. Diabetes 46(5), 758–764.
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Glabinski, A.R., Krakowski, M., Han, Y., Owens, T., Ransohoff, R.M., 1999. Chemokine expression in GKO mice (lacking interferon-gamma) with experimental autoimmune encephalomyelitis. J. Neurovirol. 5(1), 95–101. Harel, D., 1987. Statecharts: A visual formalism for complex systems. Sci. Comput. Programming 8, 231–274. Harel, D., Gery, E., 1997. Executable Object Modeling with Statecharts. Computer. Vol. 30, no. 7, IEEE Press, pp. 31–42. Harel, D., Politi, M., 1998. Modeling Reactive Systems with Statecharts: The STATEMATE Approach. McGraw-Hill, NY. Kam, N., Cohen, I.R., Harel, D., 2001. The immune system as a reactive system: Modeling T cell activation with Statecharts. Proc. Visual Languages and Formal Methods (VLFM), IEEE. Kumar, S., Bently, P.J., 2003. (Eds.), On Growth, Form and Computers. Elsevier Ltd., Amsterdam. Langman, R.E., Cohn, M., 2002. If the immune repertoire evolved to be large, random, and somatically generated, then . . . Cell. Immunol. 216(1–2), 15–22. Liblau, R.S., Singer, S.M., McDevitt, H.O., 1995. Th1 and Th2 CD4þ T cells in the pathogenesis of organ-specific autoimmune diseases. Immunol. Today 16, 34–38. Mayr, E., 1961. Cause and effect in biology. Science 134, 1501–1506. Oxford English Dictionary, 1989. 2nd Edition. Oxford University Press, Oxford, UK. Serreze, D.V., Post, C.M., Chapman, H.D., Johnson, E.A., Lu, B., Rothman, P.B., 2000. Interferon-gamma receptor signaling is dispensable in the development of autoimmune type 1 diabetes in NOD mice. Diabetes 49(12), 2007–2011. Sullivan, K.E., 2003. Regulation of inflammation. Immunol. Res. 27(2–3), 529–538.
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
18 Modelling of haemodynamics in the cardiovascular system by integrating medical imaging techniques and computer modelling tools Nigel Bruce Wood and Xiao Yun Xu Department of Chemical Engineering and Chemical Technology, Imperial College, London, UK
1. INTRODUCTION Research on the combination of medical imaging and computational fluid dynamics (CFD) began nearly ten years ago and the first image-based CFD models of realistic arterial geometries were derived from clinical X-ray angiograms. A year or two later, magnetic resonance imaging (MRI) (Underwood and Firmin, 1991; Mohiaddin and Pennell, 1998) was successfully integrated with CFD for studies of large artery haemodynamics under physiologically realistic anatomical and flow conditions (Milner et al., 1998; Taylor et al., 1999; Long et al., 2000a,b). The use of conventional ultrasound imaging to acquire in vivo geometrical information for CFD analysis has only started very recently (Starmans-Kool et al., 2002; Augst et al., 2003). When the first publications appeared showing human in vivo velocity imaging in regions of the larger arteries (e.g. Bryant et al., 1984) it became clear that linking such results to the maturing methods of CFD might give valuable insights in understanding the measured flow structures, although some of the features seen were the result of imaging artefacts. CFD allows the simulation of complete flow fields within a specified domain, in space and time, via the numerical solution of the equations of motion. The domain in this application is the imaged region of the cardiovascular system, such as part of the aorta, the carotid or iliac bifurcation, or the left ventricle. Details are discussed later, but the flow solution is specific to the geometry of the domain (fixed or moving), in this 325
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case a segment of the vessel, and conditions at a boundary, e.g. the velocity distribution at the inlet to the domain. Thus, it depends both on the local geometry and the geometry and cardiovascular characteristics of the regions contiguous with the domain. Hence, anatomy and velocity imaging have close synergy with CFD. With the advancement of high-resolution imaging and image-processing techniques, the combination of in vivo imaging and CFD now allows patient-specific flow simulations and paves the way to patho-physiological and clinical utility. It was quickly realised that an important focus of image-based computer modelling should be its use to simulate parameters that could not be measured, or derived directly from imaging measurements, with acceptable resolution (e.g. Wood et al., 2001). Research on the development of atherosclerosis had begun to support early suggestions (Fry, 1968; Caro et al., 1971) that arterial wall shear stress was an important determinant of the observed patterns of arterial disease (Ku et al., 1985; Giddens et al., 1993). Moreover, related research in fields such as cell biology was showing that endothelial shear stress is a signalling parameter for blood flow, both in short-term control of haemodynamics and longer term responses of the arterial system to blood flow variations (Davies, 1995; Wootton and Ku, 1999). The induced responses generally involve gene expression (Resnick and Gimbrone, 1995; Davies et al., 1999; Dai, 2004), giving additional potential importance to these methods. Therefore, research has focused on the computation of the spatial and temporal distributions of wall shear stress (Friedman and Fry, 1993) and related parameters (Steinman et al., 2002; Glor et al., 2003a). As has been made clear, in vivo image-based modelling gives subject-specific or patient-specific results (Steinman et al., 2002; Zhao et al., 2002; Saber et al., 2003). Another application of patient-specific image-based modelling is the possibility of clinical decision support via ‘‘virtual surgery’’, i.e. the predictive simulation of alternative vascular surgical interventions for optimising treatment, although its practice appears to be relatively limited at present. Early proponents of this application are Taylor et al. (1999) at Stanford, who have developed an interactive system where surgeons are able to simulate alternative femoral graft geometries. The system comprises an internet-based user interface with image segmentation, geometric reconstruction, automatic mesh generation, CFD and visualisation software. Outcomes are sought based mainly on achieving adequate flow to lower limb regions affected by arterial occlusions. Further, recent applications include fluid–structure interaction: the modelling of arterial wall mechanics in association with the flow field, particularly involving atherosclerotic plaques or stenoses (Bathe and Kamm, 1999; Tang et al., 2001; Lee and Xu, 2002; Lee et al., 2004).
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Here, a principal aim is to determine stress distributions in the plaques with a view of predicting rupture, an initiating factor in stroke or coronary events (Richardson et al., 1989). Again, in vivo image-based modelling allows patient-specific studies, paving the way to related clinical decision support. Simulations of laminar flow through severe stenoses have indicated the induction of very large negative pressures by very high velocities at the throat of the stenosis, although in reality, laminar-turbulent transition is likely to modify the flow field in such cases (Giddens et al., 1976). Moreover, the pulse-wave transmission, whose velocity would change through such a configuration, would bear investigation. Potentially linked to these studies is the tracking of emboli released from a plaque, and an associated field of study is the tracking of platelets and their fluid shear stress history, a determinant of their activation (Longest and Kleinstreuer, 2003). Consideration of the motion of formed elements in blood raises the question of their effects on fluid viscosity. Frequently, the viscosity is treated as Newtonian (independent of fluid shear), but non-newtonian effects may be readily modelled in computer simulations (Perktold et al., 1991). Until now, the arterial segments modelled have been largely restricted to the larger arteries and the heart. As the size of the vessel reduces, the relative effects of the formed elements on the flow become greater, including plasma skimming (Enden and Popel, 1994), until in the smallest vessels the distortion of the erythrocytes during their passage must be considered (Fitz-Gerald, 1969). In drug studies, it has been found that anti-hypertensive therapy may not only affect arterial wall thickness (Mayet et al., 1995), but that different agents can have different morphological, and hence fluid dynamic, outcomes (Ariff et al., 2002). Patient studies involving such agents have already been reported (Stanton et al., 2001) and could be potentially important in future clinical research. A few researchers have considered the mass transfer of substances between the flowing blood and the arterial wall, including large molecules like albumin and lipids, and small molecules such as oxygen and nitric oxide (Rappitsch and Perktold, 1996; Ma et al., 1997; Stangeby and Ethier, 2002). The wall boundary condition can be in the form of a wall concentration, set to reflect known clearance rates, or the dynamics of the arterial wall may be included (Stangeby and Ethier, 2002). Besides the transfer of natural substances, it is of interest to note that the substances could include drugs at their sites of action (pharmacokinetics or pharmacodynamics). In the present review, we will comment on a range of imaging modalities and methods, and computational simulation possibilities, but we will concentrate our discussion on MR and ultrasound imaging. Moreover, we will
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concentrate our examples on the exploration of flow structure and wall-shear-stress distributions, and the latter’s relationship with arterial disease patterns.
2. IMAGING METHODS An accurate description of 3D vessel geometry is a prerequisite for accurate modelling of blood flow using CFD. To date, X-ray angiography and magnetic resonance angiography (MRA) have been the most popular techniques for obtaining this information in vivo. However, for superficial vessels such as the carotid and femoral arteries, 3D extravascular ultrasound (3DUS) could be a cost-effective alternative to MRA. Multislice spiral CT has emerged recently as a high definition imaging modality, but involves high exposure to X-rays (Achenbach et al., 2001). Moreover, X-ray angiographic methods requiring injection of iodine-based radio-opaque dye or contrast-enhanced MR using gadolinium-based dyes may be considered quasi-invasive, with some subjects presenting adverse reactions (Nieman et al., 2001). Intra-vascular ultrasound (IVUS), a fully-invasive catheter technique, is also being used in some centres, particularly for coronary artery imaging and modelling (Krams et al., 1997). Nevertheless, regardless of which imaging techniques are used, the rationale remains the same, i.e. to construct a 3D volume of interest from a series of 2D cross-sectional slices. Here, we shall focus on the use of MRA and 3DUS for non-invasive acquisition of arterial geometries.
2.1. Image acquisition Time-of-flight (TOF) angiography is the most widely available method of MRA. It is performed with the gradient echo sequence enhanced by flow compensation. The detection of the high signal from the inflow of fresh spins in blood vessels and the suppression of background tissue signal enhances the lumenal image. The TOF sequence is versatile and robust, and has been applied to virtually every part of the body (Dumoulin et al., 1986, 1987). Although images acquired with TOF can be gated to the ECG in order to differentiate changes in arterial calibre from systole to diastole, it does not provide information about dynamic changes of the vessel throughout the cardiac cycle. Blood velocity profiles are often measured via phase contrast (PC) velocity mapping, which may give vessel wall movement if a sufficiently
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high spatial resolution can be achieved. It exploits the fact that motion through magnetic field gradients results in a phase shift in the net transverse magnetisation of moving material as compared to that of stationary material imaged at the same physical location. Transverse magnetisation is a vector quantity having both magnitude and phase, and each MR experiment produces an image which portrays the transverse magnetisation in each voxel. In order to resolve changes throughout the cardiac cycle, flow measurements are obtained at multiple time points during each RR interval of the ECG signal, and can be made in all three coordinate directions. For highest accuracy the scan plane needs to be orthogonal to the vessel axis. PC angiography benefits from signal enhancement provided by the velocity sensitivity. An alternative to conventional MRA is black-blood MRI, which uses a modified sequence with dark-blood preparation at the end of the preceding cardiac cycle. It allows both the vessel lumen and outer wall to be imaged at relatively high resolution, hence providing information for not only the lumen shape but also wall thickness; the latter is required for wall-stress analysis and is potentially important for studies of atherosclerosis development. However, it is insensitive to calcium, and may fail to detect stenoses. For 3D ultrasound acquisition, the system usually consists of a standard 2D ultrasound scanner and an electromagnetic position and orientation measurement (EPOM) device (Barratt et al., 2001). During a 3D scan, the EPOM sensor mounted on the scan-probe tracks its position and orientation. An image and the corresponding position/ orientation are captured simultaneously when an R-wave trigger is detected. By sweeping the probe through the vessel of interest, a set of non-parallel transverse slices along with position/orientation of each slice are recorded and stored on a PC for off-line analysis. Examples of images acquired using TOF MRA, black-blood MRI, and 3DUS are given in fig. 1.
(a) 3DUS
Fig. 1.
(b) Black-blood MRI
(c) 2D TOF MRA
Examples of carotid artery images acquired using (a) 3DUS, (b) black-blood MRI and (c) 2D TOF MRA, from healthy human subjects.
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2.2. Image segmentation and 3D reconstruction The resulting 2D transverse images are often segmented manually or semi-automatically to delineate the lumen contours. This may take a number of steps including pre-processing, edge detection, and smoothing. Numerous image-processing algorithms have been developed to accomplish these tasks, e.g. the adaptive local contrast enhancement method (Ji et al., 1994), the Prewitt edge detection algorithm and the active contour model (Kass et al., 1988). A number of commercial medical image-processing packages is also available, such as MIMICS, IDL, and CMRTools. One of the key issues here is to obtain a continuous and smooth contour while preserving as much original geometry as possible. By stacking the segmented lumen contours according to their spatial relationships (parallel with MRA but angled with 3D ultrasound), a 3D object can be constructed. At this stage, smoothing of the image data is required in order to minimise imaging artefacts, random errors due to subject movement, and beat-to-beat variation during the scan. Smoothing may also take a number of stages, such as contour smoothing in its transverse plane, centreline smoothing and 3D surface smoothing. Moore et al. (1998) employed a three-phase smoothing procedure based on Woltring’s (1986) smoothing spline algorithm GCVSPL, while Long et al. (1998a) used a twostep procedure. A comprehensive review of the image segmentation and smoothing techniques suitable for handling MRA images was given by Long et al. (1998b).
2.3. Comparison of MRI and 3DUS for geometry reconstruction In a recent in vivo study carried out by our group, comparison was made between the reconstructions from black-blood MRI and 3DUS of carotid bifurcations (Glor et al., 2003b). Nine healthy volunteers, aged between 24 and 56, were scanned while lying supine with head held in a straight position. For each subject, two sets of MR images (1.5 T Siemens Magnetom Sonata) were acquired which corresponded to mid-to-late diastole and end-systole. For these volume selective Turbo Spin Echo (TSE) images, a true resolution of 0.47 0.47 mm in plane and a FOV of 120 24 mm were typical with 28 slices (2 mm thick). Each scan lasted 3–5 minutes, depending on the subject’s heart rate. For systolic TSE imaging, a modified sequence with dark-blood preparation at the end of the preceding cardiac cycle was used. Black-blood MR images were segmented
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and reconstructed semi-automatically using the region growing method together with the snake model. However, it was necessary to check the semi-automatically segmented images and make some manual adjustment where appropriate, due to acquisition errors inherent to black-blood MRI. The serial 2D contours were then aligned to produce a 3D vessel surface geometry. Smoothing was performed on the vessel centrelines and surface. The 3DUS scanner (Ascension Technology Inc., Vermont, USA), equipped with a conventional 12/5 MHz broadband linear array transducer (HDI 5000, ATL-Philips Ltd., Bothell, MA, USA) was used to acquire ECG gated transverse images of the carotid bifurcation (Barratt et al., 2001). An electromagnetic position orientation measurement (EPOM) device, mounted on the probe, recorded the position and orientation of the probe in 3D space. A series of transverse images, captured at mid-to-late diastole as the transducer probe was swept slowly over the subject’s neck, was stored digitally on the scanner and later downloaded to a PC to be analysed off-line. Acquired images were segmented using purpose-built software, which required at least 6 boundary points to be selected manually on the vessel wall and a smooth cubic spline or ellipse would be fitted to these points. The delineated contour usually represents the media–adventitia border rather than the lumen, hence needs to be readjusted by subtracting the intima–media thickness from it. From the resulting lumen contours, combined with the positioning information from the EPOM device, the 3D geometry of the carotid bifurcation can be reconstructed. (There are 3 principal layers, or tunicae, in the structure of the arterial wall, the intima, media, and adventitia being respectively the inner, middle, and outer layers.) Lumen areas were calculated along each of the arteries for all carotid bifurcations reconstructed. The average area was evaluated for each artery generated from the systolic and diastolic black-blood MR images and 3DUS images (diastolic). Comparisons of average lumen areas derived from these three sets of images are given in fig. 2, representing a good and an average case. It was found that areas estimated from diastolic black-blood MR images were generally larger than those from 3DUS (also at mid-to-late diastole). Comparisons of vessel centrelines were made between diastolic black-blood MRI and 3DUS for all subjects. By performing single value decomposition on the matrix formed by all points on the centreline, a quantitative measure of bifurcation non-planarity can be derived. Large differences in non-planarity between the two imaging methods were noticed.
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Fig. 2. Average lumen area in the common carotid (CCA), internal carotid (ICA), and external carotid arteries (ECA), derived from 3DUS (diastolic), diastolic black-blood MRI, and systolic black-blood MRI for two representative subjects.
Results suggest that there is a good agreement in lumen areas derived from the black-blood MRI and 3DUS images, but significant differences in centreline exist. When making these comparisons, it is important to note that image-segmentation and geometric-reconstruction were performed differently with the two different types of images. It would be impractical to adopt a unified approach, owing to differences in image quality and data format. Moreover, it is almost impossible to scan a subject in exactly the same head and neck position during MRI and 3DUS sessions. Especially in a 3DUS scan, the operator might have to reposition the subject’s neck in order to gain more coverage of the carotid branches and/or better ultrasound images. This will inevitably change the vessel curvature, hence the shape and non-planarity of the centrelines. Overall, 3DUS has proved to be able to generate 3D in vivo carotid geometries which are suitable for CFD simulations and are comparable to those reconstructed from MRI. However, 3DUS still has a number of limitations, such as limited field of view owing to the presence of the jaw bone and relatively high operator dependence as a result of manual image segmentation. Nevertheless, with the current level of accuracy and reproducibility achieved and with further improvement in imaging and automation of the segmentation/reconstruction procedures, 3DUS has considerable potential to become a relatively inexpensive, fast and accurate alternative to MRI for CFD-based haemodynamics studies of superficial arteries.
3. COMPUTER MODELLING TOOLS As discussed in the Introduction, computer modelling of cardiovascular mechanics can be carried out at a number of levels. The dynamics of the
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flow, the wall mechanics, the motion of formed elements in the blood, and the transport of substances can all be simulated. In the case of wall-motion, it may be possible to measure it, particularly if the excursions are large (Saber et al., 2001, 2003), so that the flow equations can be solved on a domain with moving boundaries. The modelling of the interaction of the fluid and wall is far more challenging and requires knowledge of the wall material properties, wall thickness as well as an efficient numerical algorithm to solve the coupled set of fluid and solid equations (Zhao et al., 1998, 2000). However, considerable insights can be gained in many cases where the walls are assumed to be rigid, and we will give examples of both rigid and elastic wall simulations. The description that follows is intended as a brief overview; for a more comprehensive review, see Steinman (2002). A concise treatment of CFD is given in the book by Ferziger and Peric (1996).
3.1. Flow equations and their solution The equations of fluid motion for a homogeneous medium are known as the Navier–Stokes (NS) equations, after the nineteenth century mathematicians M. Navier in France and Sir G. G. Stokes in England, who derived them, and they are exact for laminar flows of simple fluids. They express Newton’s law of the conservation of momentum in the fluid as it passes through a ‘‘control volume’’, and are combined with the equation of continuity, or conservation of mass. The equations may be expressed in various forms, such as in partial differential Cartesian coordinate form or integro-differential form. They are written below as vectorial statements, in incompressible form, for an arbitrary fluid volume V:
@ @t
Z V
@ @t
Z dV þ
ðU US Þ ndS ¼ 0 S
Z
Z UdV þ
V
ðEq: 1Þ Z
UðU US Þ ndS ¼ S
½p þ rU þ ðrUÞT ndS
S
ðEq: 2Þ U is the instantaneous fluid velocity at time t, p is the instantaneous static pressure relative to a datum level, n is the unit vector orthogonal to and directed outward from a surface S of the volume, and and are respectively the fluid density and viscosity. The former is constant under the incompressible assumption and the second is assumed constant since
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we shall be assuming blood to be a Newtonian fluid in the examples considered. The surface S is here moving locally at velocity US. The superscript ‘‘T ’’ represents the transpose of the quantity (remembering that we shall be dealing with a set, expressed in matrix form, of numerical values of the terms in the equation for each cell of a computational mesh). The equations cannot be solved analytically, except in certain special cases, when they may be approximated (Schlichting, 1979; Wood, 1999). Therefore, for most flows of practical interest, we use numerical solution methods, which have become more important as computers have become faster and able to store a large amount of data. The form of Equations (1) and (2) is appropriate for ‘‘finite volume’’ numerical analysis, used in many CFD codes, where V is the volume of a cell of the mesh on which the computation is carried out. If the boundaries are rigid, the velocity of the boundary US ¼ 0. Alternatives to finite volume codes are finite difference, where a differential form of the NS equations is used, and finite element codes, developed from structural analysis methods.
3.2. Coupled fluid/wall interactions Arterial walls are compliant and exhibit non-linear viscoelastic behaviour. The basic equations to describe the wall motion can be written as:
w
@2 di @ij ¼ þ w Fi @t2 @xj
ði ¼ 1, 2, 3Þ
ðEq: 3Þ
where di and ij are the components of wall displacement vector and the components of the wall stress tensor, respectively; w is the wall density and Fi are the components of body force acting on the wall (Lee et al., 2004). The relationships between stress–strain and strain–displacement depend on the assumptions made on the wall material behaviour (Lee and Xu, 2002). Modelling of coupled fluid/wall interactions requires solutions of the equations of motion for both the flow and the wall, and has become a specific topic in computational mechanics in recent years. A comprehensive review on fluid/solid coupling in the context of blood flow in arterial structures was given by Zhao et al. (1998). Briefly, there are essentially 3 coupling methods: simultaneous, iterative, and hybrid. In simultaneous and hybrid approaches, the equations governing the flow and the wall are solved wholly or partly simultaneously, limiting the use
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of existing CFD, and structural analysis packages. However, the iterative approach treats the fluid and solid equations separately, and couples them externally in an iterative manner. This is a ‘‘weak’’ coupling approach and can be implemented by transferring the pressure loads computed by the CFD solver to the structural solver, and feeding the newly predicted wall velocity and displacement back to the fluid solver. In doing so, a wide range of commercial CFD and structural analysis codes can be utilised. A practical problem in coupled fluid/wall modelling of blood flow is the difficulty in acquiring in vivo data about the arterial wall compliance and wall thickness, which are required by the structural solver. Wall thickness can be measured using B-mode ultrasound or B-mode tissue Doppler techniques at selected 2D longitudinal and transverse planes, whereas determination of wall mechanical properties requires simultaneous recording of wall motion and local pressure at, preferably, a number of different sites along the vessel. This requires a high-resolution wall tracking device as well as a non-invasive (external) pressure transducer (applanation tonometry; Nichols and O’Rourke, 1998).
3.3. Boundary conditions The solution of such equations, whether analytical or numerical, requires a solution domain and boundary conditions, as outlined in the Introduction. The domain is the chosen region of the (cardio)vascular system in this case and the boundary conditions include the ‘‘no-slip’’ condition at the blood-endothelium boundary, imposed by the frictional action of the fluid viscosity, and the impervious and rigid wall conditions, meaning all velocity components are zero at the wall. These are complemented by a definition of the flow conditions through the domain for the specific case, set by velocities and/or pressures at the inlet and outlet(s) to the domain (see below). In a typical case where the domain is a simple arterial region, with no branches, then we should normally expect to provide a known time-varying velocity profile at the proximal (inlet) boundary and uniform static pressure at the distal (outlet) boundary. The known velocity distribution might be obtained from magnetic resonance velocity imaging, but the measurement uncertainty needs to be noted (Weston et al., 1998; Wood et al., 2001). If the pressure level is unimportant, as is usual in rigid wall cases, the distal pressure may be set to zero at each time step, so that it represents a relative pressure floating in time. The pressure differences throughout the domain at each time-step will be correctly determined,
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but if the absolute pressure distribution is required, as when arterial elasticity is being simulated, they must be related to the current value of the time-varying absolute pressure at some point (Zhao et al., 2002). Where the domain includes a branch, say a bifurcation, the flow division between the two branches must be specified, either in absolute or relative terms. This may generally be based on measurements, but if absolute velocities are specified at both proximal and distal boundaries, the measurement uncertainty means that scaling between measured inlet and outlet flows will be required to maintain mass flow continuity between inlet and outlet (Long et al., 2000b). The application of measured velocity boundary conditions gives rise to the question whether all velocity components, or just the axial component should be incorporated. When the geometry of the adjoining regime is complex and/or the modelled region is relatively short, inclusion of all the velocity components would be recommended (Wood et al., 2001). However, in many cases, it is not feasible or practicable to measure the required velocity profiles in vivo. An alternative is to measure the flow waveforms in the vessels concerned and derive the time-varying velocity profiles using the Womersley solution (Nichols and O’Rourke, 1998). At its simplest this is based on the Navier–Stokes equations for the pulsatile flow in an axially symmetrical long, straight circular pipe. Formally, they are solved with the time-varying pressure gradient as boundary condition, decomposed into its Fourier frequency components. In this case, we have the pulsatile flow wave as boundary condition, which is treated in a similar way (Holdsworth et al., 1999). However, if the adjoining arterial anatomy, particularly proximal, includes curvature and branches, the true velocity profiles may differ significantly from the axisymmetric ones derived via Womersley.
3.4. Numerical mesh or grid Having made a ‘‘virtual’’ reconstruction of the imaged domain ( previous section), the numerical solution requires a grid on which the solution variables are calculated. Generally, the grids are said to be ‘‘structured’’ (hexahedral cells) or ‘‘unstructured’’ (including tetrahedral cells); both may be divided into blocks to fit different parts of the domain, but unstructured meshes can more readily fit into a complex geometry. In general, the distal boundary should be extended well beyond the region of interest to reduce the effects of any errors propagated into the domain from the site where boundary conditions are applied. Moreover, it is usually advised that the flow should be directed out of
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the domain over the entire cross section (Ferziger and Peric, 1996). This, of course, cannot be adhered to in all arterial flows, where retrograde flow is not uncommon, at least over part of the lumen, and the extended outlet boundary becomes even more important in these cases. Where assumed boundary conditions are applied at the proximal boundary, there is a case also for extending the mesh ‘‘upstream’’ from the true inlet, to reduce the effects of the entry geometry of the domain on the applied conditions, and giving space for the flow to develop under its influence.
3.5. Discretisation and solution methods The exact equations of motion have to be set in a form which is amenable to numerical solution, requiring algebraic approximations to the differential and integral terms in the equations. The earliest examples were developed for hand calculation of finite difference methods by the eighteenth century Swiss mathematician, Leonhard Euler, who replaced the terms in differential equations by approximate difference formulae, also since adopted for finite difference computer methods. In finite volume methods, the surface and volume integrals have to be approximated by algebraic quadrature formulae applied to the flow variables residing in the cells of the computation mesh. Familiar examples of quadrature are the Trapezium rule and Simpson’s rule, but there are more accurate variations. The temporal differential term in Equation (2) is often represented in CFD codes by methods originally developed by Euler. The discretised equations need numerical values of variables that are different in each cell, so that there is a large system of simultaneous non-linear algebraic equations that has to be solved. Initial values are needed to start the computation, and when the system has ‘‘converged’’ the equations contain the solution values of the variables. The initial values are required in addition to the boundary conditions, but would generally be related to them. For unsteady flows, the solutions advance in time step by step (‘‘time marching’’). There are many solution methods and there is an extensive literature on them, usefully summarised in various textbooks (e.g. Hirsch, 1988; Ferziger and Peric, 1996).
3.6. Accuracy We have said that the NS equations are exact for laminar flows in simple fluids, but it will have been noted that we have referred to the necessity
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of using algebraic approximations to the exact equations in order to obtain numerical solutions. The selection of the algebraic discretisation method is an element in the control of accuracy as is the numerical solution method, mentioned above. The resolution and accuracy of the solution depends also on the size and form of the mesh cells, and the time step for unsteady flows. Since numerical solutions require iterative methods at some stage in the process, setting or finding the number of iterations required to obtain adequate convergence is a further criterion. Moreover, for complex flows, experimental confirmation of some aspect of the solution may be required, such as the re-attachment point or zone of a separated flow, particularly if laminar-turbulent transition is involved (Bluestein et al., 1997; Mittal et al., 2001). This is where the combination with velocity imaging can include the verification or validation of the solution, as well as the provision of boundary conditions.
3.7. Parameters simulated The computed solution comprises numerical values of flow field parameters on the computational mesh, at the nodes or on the faces of the cells. The principal parameters are the fluid velocity vectors, which may be resolved into orthogonal coordinate directions, and the static pressure distribution. Other variables might be the temperature, the velocities of particular particles in the fluid and the concentration distributions of particular species, but additional equations would have had to be solved for these parameters to be included. Concentrating on the velocity and pressure, the best method of interrogating a three-dimensional, time-varying solution is via a graphical display, and there are numerous commercial packages available, including those supplied with commercial CFD packages. From these graphical images a good impression may emerge of the flow structure and pressure distribution, but it is important to look at a sufficient variety of views, possibly including animations, both to be certain that one has the full picture and that there are no unphysical features. From the details of the velocity field near the wall, provided the mesh is sufficiently fine to give adequate resolution, the wall shear, @U=@y may be evaluated as well as the wall shear stress (WSS), @U=@y, where is the dynamic viscosity coefficient and @U=@y is the gradient normal to the wall of the velocity parallel with it. This would be an instantaneous value averaged over each wall cell of the mesh, but it could also be integrated over the pulse period and divided by the same period to give
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a spatially varying time average. Other WSS related parameters can also be derived, such as the oscillatory shear index, WSS gradient, and WSS angle deviation (e.g. Glor et al., 2003a). These and the pressure distribution may be displayed as surface contours or as variations in chosen directions or planes.
4. EXAMPLES AND APPLICATIONS 4.1. Aorto-iliac bifurcation An example of flow in the human aorto-iliac bifurcation is used to demonstrate the application of the image-based modelling approach (Long et al., 2000b). A healthy male adult was examined using MRI to obtain measurements of both arterial geometry and blood velocity for a complete set of subject-specific input conditions. In this case the arterial wall was assumed rigid and just the flow structure was simulated. Nevertheless, the results confirm that in vivo flow patterns may differ substantially from those observed in simplified aortic bifurcation models. This study was undertaken on a 1.5T whole body MR imager (Signa HiSpeed Advantage, GE Medical Systems) using the body coil and software release 5.6. Firstly, 2D TOF angiography (gradient echo sequence) was utilised to provide the anatomical information necessary for defining the geometry of the aortic bifurcation (FOV 28 cm, slice thickness 1.5 mm and matrix of 256 128 pixels). Secondly, 2D cardiac gated cine phase contrast velocity mapping (Twenty-four cardiac phases, FOV 28 cm., slice thickness 7 mm, and matrix 256 128) was performed at four separate locations to provide 3D velocity-encoded information within the vascular region of interest. Velocity data were obtained in the abdominal aorta across two planes located between the renal artery origins and the bifurcation, and in each common iliac artery proximal to the origin of the internal iliac artery. The aortic velocity profile obtained closest to the bifurcation was used to validate the flow simulations with the other measurements providing boundary conditions. Specific software was designed to extract time-dependent velocity profiles from the phase contrast acquisitions. The 3D geometry of the aortic bifurcation was generated from a stack of 2D MR angiograms. In this application it is required that not only the image intensity distribution, but also the smoothness of the contour should be considered. An active contour model was therefore used to segment the 2D images and produce a smooth representation of
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A
Fig. 3.
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Surface rendering of the aorto-iliac bifurcation model reconstructed from MR scans of a healthy human adult.
the cross-sectional vascular anatomy (Long et al., 1996). Alignment of the contours in the axial direction yields the 3D structure of the arterial bifurcation. Figure 3 shows the surface rendering of the reconstructed aortic bifurcation after centreline and surface smoothing. It was noted that for the subject examined, the distances between the aortic and common iliac bifurcations were short (about 50 mm, less than 6 diameters long). As a result, the iliac arteries included in the model were only about 3.5 diameters long, implying that the outlet flow could not be assumed to be fully developed. For this reason, the time-varying velocity data extracted from MR velocity images of the downstream planes in the iliac arteries were specified at the two outlets of the bifurcation model. To maintain conservation of mass in the CFD calculation, measured velocities at the proximal aortic inlet were then scaled using mass conservation, while preserving the shape of the velocity profiles. Maps of time-averaged WSS obtained from the CFD simulation are presented in fig. 4. It can be noticed that the average WSS level is low on the posterior wall in the abdominal aorta and at the outer wall of the left iliac where the low WSS region spirals along the left-anterior wall. High average WSS appears in the flow divider. Generally, the right iliac artery has higher values of WSS than the left iliac, and in the abdominal aorta WSS on the anterior wall is higher than on the posterior wall. Since atheroma localises to sites of low endothelial shear stress and/or disorganised flow, such as at the outer wall of bifurcations and the inner walls of curved arterial segments, combined MRI/CFD approaches may provide unique insights into these factors in individual subjects.
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WSSt 4.1828e+00 3.1371e+00 R
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2.0914e+00 1.0457e+00 0.0000e+00
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Anterior view
Fig. 4. Whole cycle time-averaged WSS (N/m2) maps obtained using a combined MRI/CFD approach. (In figs. 4, 6, 7 each colour represents a range of colours, and the value defined for ‘‘red’’ is the minimum of that range).
4.2. Carotid bifurcation A further example is the flow in the human carotid bifurcation, in which elastic walls and fluid-structure interaction were modelled (Zhao et al., 2000). The carotid arteries are of special interest since the ‘‘bulb’’ in the bifurcation is a frequent focal site for atherosclerosis, the principal cause of stroke (carotids) and heart attack (coronaries). Results presented here are based on anatomical images acquired using 2D TOF angiography with a 1.5T MR scanner (Signa, GE Medical System), and flow data measured by pulsed Doppler using an HDI 3000 ultrasound system (Advanced Technology Laboratories, Bothel, Washington). Continuous carotid pulse pressure was obtained non-invasively using a highfidelity external pressure transducer (model SPT-301, Millar Instruments, Texas, USA) applied to the skin overlaying the pulse of the common carotid artery, based on the principle of applanation tonometry (Nichols and O’Rourke, 1998). Measurement of intima-media thickness was made by means of B-mode ultrasound at selected locations in the common, internal and external carotid arteries. Wall mechanical properties were determined from wall tracking data recorded using M-mode ultrasound. The anatomical images along with the flow and pressure data were processed and incorporated into a weakly-coupled fluid/wall model, which solves the fluid and wall equations in an iterative manner
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(Zhao et al., 2000). Blood was assumed to be a newtonian fluid with constant viscosity. The Navier–Stokes equations governing the fluid flow were solved with specified time-varying velocities at the proximal end of the common carotid artery and the distal end of the internal carotid, together with a pressure boundary at the exit of the external carotid. For the wall equations, constraints were placed at all inlet and outlets in order to avoid translation or rotation of the bifurcation, but circumferential expansion was permitted. Figure 5 shows the surface rendering of the carotid bifurcation models reconstructed from MR scans of 4 subjects. It clearly demonstrates considerable individual variations in the anatomy of the carotid arteries. Differences in anatomy would inevitably result in variations in flow patterns as well as wall shear–stress distributions. Topological maps of the predicted time-averaged wall shear stress for one of the carotid bifurcation models are given in fig. 6 which shows a very strong anterior–posterior asymmetric feature. Given in fig. 7 are the corresponding wall mechanical stress contours at peak pressure phase in the same model. It was found that within this model the patterns of principal stress distribution changed very little with time during the cycle, although the magnitude varied. The maximum principal stress was found at the bifurcation point, while relatively high stresses occurred in the region of the carotid bulb. By comparing the time-averaged wall shear stress maps with the corresponding principal stress maps, it can be noticed that
Fig. 5. Surface rendering of the carotid artery bifurcation models reconstructed from MR scans of 4 healthy human adults.
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Shear Stress (N/m2) 1.3873e+00 1.0405e+00 6.9364e-01 3.4682e-01 0.0000e+00
Fig. 6. Time-averaged wall shear stress in one of the carotid bifurcation models.
Mechanical Stress (N/m2) 6.5056e+04 5.0884e+04 3.6703e+04 2.2522e+04 8.3145e+03
Fig. 7.
Maximum principal stress at peak pressure phase in the carotid bifurcation model shown in fig. 6.
the high mechanical stress regions show some overlap with the areas of low shear stress in all models. Detailed results for the time-varying flow patterns and wall shear, stress in the carotid bifurcation were given by Zhao et al. (2002).
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5. DISCUSSION Methods and techniques needed to compute blood flows in realistic arterial models constructed from in vivo imaging data have been summarised, and examples given of the modelling of the flow in arterial bifurcations using anatomical images obtained from MRA. Like any other modelling tools, the combined imaging/CFD modelling approach involves a number of approximations and uncertainties; hence, solutions to new problems must always be validated, or at the very least verified. Since different kinds of errors are introduced throughout the whole process starting from image acquisition, image segmentation, and geometric reconstruction, to CFD or coupled fluid/solid simulations, a thorough validation of the approach becomes extremely difficult. Due to the absence of a ‘‘gold standard’’ (neither MRA nor CFD data could be regarded as the gold standard) for an in vivo system, in vitro flow phantoms and casts may be very useful in the early stages of the validation exercise. There have been a number of studies concerned with validations or verifications of CFD predictions using simple as well as complex flow phantoms (e.g. Weston et al., 1998; Long et al., 2000). Related to accuracy and uncertainty is reproducibility of, for example, wall shear–stress distribution, and there have been several studies of this aspect in our group and elsewhere (Augst et al., 2003; Glor et al., 2003a; Thomas et al., 2003). A recurrent problem in this type of modelling is the lack of reliable in vivo data for the specification of boundary conditions and estimation of wall elastic properties. Although MR phase-contrast velocity imaging is capable of measuring 3D velocities, the time required to obtain such images still presents a major difficulty. Given the sensitivity of solutions to boundary conditions, the validity of using a fully developed flow assumption in association with the pulsed Doppler acquired flow waveforms should be examined carefully (Wood, 2003). More accurate and detailed measurement of wall thickness and properties will also improve the predictions. Nevertheless, these problems will be largely overcome through the parallel development of novel imaging techniques and system hardware in the foreseeable future. New MR imaging sequences are emerging. The volume selective technique, where the signal is enhanced by restricting the magnetisation to a limited region around the target vessel, has already been mentioned. For example, high-resolution imaging of a carotid artery has been enabled within an acquisition time of a few minutes (Crowe et al., 2003). Moreover, the volume selective approach is also giving improvements in MR velocity imaging, where it has been shown that it is practical to
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perform high-resolution real-time quantification of the haemodynamic response to femoral artery occlusion (Mohiaddin et al., 1999). ‘‘Real-time’’ imaging includes both capturing data in a time that is short relative to cardiac motion, and real-time feedback and control of a longer acquisition to remove problems of cardiac and respiratory motion, with high spatial resolution. It promises high efficiency imaging of the coronary arteries and, therefore, will offer benefits also for less demanding sites. Although intravascular ultrasound, which is invasive, has already been used for image-based coronary flow simulations, the emergence of the methods mentioned above will allow high-resolution non-invasive image acquisition for such simulations. MR is already allowing cerebral artery imaging (Cebral et al., 2003), and trans-cranial Doppler ultrasound is being used for detection of emboli (see below) and its application may be extended to image-based flow simulations (IBFS). Retinal vessels, part of the cerebral circulation, are already being imaged optically for IBFS, although, as with other parts of the cerebral circulation, the development of outflow boundary conditions for the vessels capable of resolution, and the representation of sub-resolution scale vessels, is a research issue (Traub et al., 2004). As flow simulations progress to such smaller vessels, so the range of application expands, for example, also to include organs. The question of decision support for vascular surgery has been mentioned, and its use is expected to expand as confidence is gained. Improvements are likely with the introduction of multi-scale methods, where the CFD boundary conditions for the 3D region of interest are provided by lower-dimensional treatments, giving better modelling of, for example, effects of peripheral resistance and wave reflection. Research is already proceeding in this area, involving the combination of CFD with one-dimensional wave mechanics and zero-dimensional lumped parameter ‘‘Windkessel’’ methods (Lagana et al., 2002). The combined imaging/CFD modelling approach is still at its early stage and needs to be further improved in a number of ways. New commercial software is becoming available that incorporates full coupling for fluidstructure interactions, and it is already being used, for example, in simulations of arterial stenoses (Bathe and Kamm, 1999). This example immediately brings into focus the question of laminar-turbulent transition, which occurs in severe stenoses (Giddens et al., 1976) and is an issue for computational modelling. Transition has been explored in some detail for normal arteries, e.g. canine (Nerem et al., 1972) and the human aorta with both normal and diseased aortic valves (Stein and Sabbah, 1976). Bluestein and Einav (1995) analysed their own laboratory measurements and published data relevant to transition in the mitral and aortic valves, but
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the mechanisms of transition in arterial stenoses remain relatively unexplored. There have been some simulations of flow through stenoses using semi-empirical turbulence transport models (Ryval et al., 2004; Wood and Xu, 2004) but, because of doubts about their handling of the flow separations distal to most stenoses, turbulence simulation methods (Akhavan et al., 1991; Mittal et al., 2001) probably represent surer means to success. Mass transfer of solutes between the flowing blood and the endothelium has been mentioned and it is likely that research in this area will grow, aimed at better understanding of blood flow regulation and arterial pathology. The simulation of solute transport leads naturally to consideration of the motion of formed elements, including platelets and monocytes and their activation (Wurzinger and Schmid-Schoenbein, 1990; Bluestein et al., 1999; Wootton et al., 2001; Longest and Kleinstreuer, 2003), plaques and the release of emboli, and plaque rupture. Finally, in vivo image-based flow simulation is becoming a useful tool not only for physiological studies aimed at gaining more insight into the complex flow phenomena in the cardiovascular system, but also to aid the design of interventional diagnostic, measuring and treatment devices. The ultimate goal is to develop it into a clinical tool suitable for multi-scale patient-specific studies. Clinical applications, in addition to the clinical decision support for vascular graft surgery already mentioned, might be expected to include aneurysm repair, treatment regimes, and monitoring drug treatment outcomes, whilst aids to development of treatments might include pharmacokinetics and thermal modelling to aid plaque detection and treatment (Verheye et al., 2002).
ACKNOWLEDGEMENT The following people have contributed to the data used here: Drs. B. Ariff, A. D. Augst, D. C. Barratt, M. Bourne, P. L. Cheong, L. Crowe, Prof. D. N. Firmin, Dr. F. P. Glor, Profs. T. M. Griffith, A. D. Hughes, Dr. Q. Long, Prof. S. A. Thom, Dr. S. Z. Zhao.
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Underwood, S.R., Firmin, D.N., 1991. Magnetic Resonance of the Cardiovascular System. Blackwell Scientific Publications. Oxford. Verheye, S., De Meyer, G.R., van Langenhove, G., Knaapen, M.W., Kockx, M.M., 2002. In vivo temperature heterogeneity of atherosclerotic plaques is determined by plaque composition. Circulation 105, 1596–1601. Weston, S.J., Wood, N.B., Tabor, G., Gosman, A.D., Firmin, D.N., 1998. Combined MRI and CFD analysis of fully developed steady and pulsatile laminar flow through a bend. J. Magn. Reson. Imaging 8, 1158–1171. Woltring, H., 1986. A Fortran package for generalised, cross-validatory spline smoothing and differentiation. Advances Eng. Software 8, 104–107. Wood, N.B., 1999. Aspects of Fluid Dynamics Applied to the Larger Arteries. J. Theor. Biol. 199, 137–161. Wood, N.B., Weston, S.J., Kilner, P.J., Gosman, A.D., Firmin, D.N., 2001. Combined MR imaging and CFD simulation of flow in the human descending aorta. J. Magn. Reson. Imaging 13, 699–713. Wood, N.B., 2003. Velocity boundary conditions for subject-specific arterial flow simulations. (Abstract). ASME, Proc. 2003 Summer Bioeng. Conf. Key Biscayne FL. Wood, N.B., Xu, X.Y., 2004. Turbulence in stenoses: survey & early numerical results. Proc. Fourth Int. Conference Fluid Mech, July 20–23, Dalian, China, Tsinghua Univ. Press & Springer-Verlag. 641–644. Wootton, D.M., Ku, D.N., 1999. Fluid mechanics of vascular systems, diseases, and thrombosis. Ann. Rev. Biomed. Eng. 1, 299–329. Wootton, D.M., Markou, C.P., Hanson, S.R., Ku, D.N., 2001. A mechanistic model of acute platelet accumulation in thrombogenic stenoses. Ann. Biomed. Eng. 29, 321–329. Wurzinger, L.J., Schmid-Schoenbein, H., 1990. The role of fluid dynamics in triggering and amplifying hemostatic reactions in thrombogenesis. Blood flow in large arteries: Application to Atherogenesis and Clinical Medicine. In: Monogr. Atheroscler, Vol. 15, (Ed.), Liepsch, D., Basle, Karger, pp. 215–226. Xu, X.Y., Collins, M.W., 1990. A review of the numerical analysis of blood flow in arterial bifurcations. Proc. Instn. Mech. Eng. 204, 205–216. Zhao, S.Z., Xu, X.Y., Collins, M.W., 1998. The numerical analysis of fluid-solid interactions for blood flow in arterial structures Part 2: development of coupled fluid-solid algorithms. Proc. Instn. Mech. Engrs. Part H. 212, 241–251. Zhao, S.Z., Xu, X.Y., Hughes, A.D., Thom, S.A., Stanton, A.V., Ariff, B., Long, Q., 2000. Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation. J. Biomech. 33, 975–984. Zhao, S.Z., Ariff, B., Long, Q., Hughes, A.D., Thom, S.A., Stanton, A.V., Xu, X.Y., 2002. Inter-individual variations in wall shear stress and mechanical stress distributions at the carotid artery bifurcation of healthy humans. J. Biomech. 35, 1367–1377.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
19 Vasopressin and homeostasis – running hard to stay in the same place Nancy Sabatier and Gareth Leng Centre for Integrative Physiology, College of Medical and Veterinary Sciences, The University of Edinburgh, George Square, Edinburgh, Scotland, UK
1. INTRODUCTION 1.1. Fluid and electrolyte homeostasis in mammals Plasma volume and electrolyte composition are interdependent – both must be maintained within narrow limits, but the answer to a threat to either of these is in itself a threat to the other. The most common threat to plasma sodium concentration ([Naþ]) comes whenever we eat, in the sodium that we ingest – and the natural response to this threat is thirst. We drink water to dilute electrolytes when they are present in excess, but drinking in turn threatens our control of plasma volume. Conversely, when we exercise on a hot day, to cool our bodies we sweat and thereby lose fluid – but by sweating we lose an excess of salt, so drinking to restore plasma volume now becomes a threat to plasma electrolyte balance. Thirst is a first line of defence against the threat of reduced plasma volume, signalled mainly by low venous pressure, or against the threat of raised plasma [Naþ]. However, there must be equally prompt regulation of water and electrolyte excretion, and this is achieved by the kidney. Water resorption is achieved through a single antidiuretic hormone, vasopressin, and electrolyte balance is additionally maintained through active control of sodium excretion – natriuresis. We will focus on vasopressin, and a closely related hormone, oxytocin. Apart from its functions as the hormone that regulates milk letdown and parturition, oxytocin is a natriuretic hormone in many animals, including the rat.
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The issues that we will consider here are: how is the set point for electrolyte homeostasis determined; how does the vasopressin system act in defence of this set point; and how does this system maintain its function throughout life despite degradation through ageing?
2. VASOPRESSIN – HOMEOSTATIC REGULATOR OF FLUID AND ELECTROLYTE BALANCE The Brattleboro rat suffers congenital hypothalamic diabetes insipidus as a result of a complete absence of vasopressin. To maintain fluid balance, it relies on thirst; the Brattleboro rat drinks about its own weight of water every day, and excretes a similar volume of dilute urine. For normal rats and normal humans exposed to varying degrees of osmotic challenge through dehydration or infusions of hypertonic fluid, the plasma vasopressin concentration is linearly related to plasma [Naþ] above an apparent threshold value, which lies close to the normal plasma [Naþ]. Thus, the set point for sodium homeostasis is the plasma [Naþ] above which vasopressin secretion rises above basal levels. In response to hyperosmotic challenge, vasopressin secretion is proportionate to the degree of imbalance. In this respect, vasopressin is like a passenger who chides you with increasing agitation the faster you drive, and is unlike the passenger who becomes hysterical whenever you creep above the speed limit. It might be that the second type of passenger is a more effective check on a driver’s speed, so why does the vasopressin system respond so ‘‘reasonably’’ to challenge? Perhaps the vasopressin system simply needs to conserve its energy. In normal circumstances, the pituitary gland holds a large store of vasopressin, and probably there is a cost to synthesis and a cost for storage. Large though the stores are, it takes only about two days of dehydration to exhaust them almost completely. By this time, the synthesis of vasopressin will have been escalated, and so secretion does not collapse; but because it takes time to increase synthesis, and to transport the hormone to its site of release, the margin for error is narrow. Another explanation might be that there are lags in the control system: an imbalance in electrolyte concentration cannot be corrected rapidly, and so the control system must make an implicit estimate of the minimal necessary response for correction. A proportionate response is thus appropriate, but here we note one point to which we will return. For a proportionate response to be effective, the slope, or ‘‘gain’’ of the response must be right. The gain of the response reflects the amount of vasopressin released in response to a given stimulus – how is the gain preserved when
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the system starts to degrade, when for instance vasopressin cells die through ageing?
3. PHYSIOLOGICAL ANATOMY OF THE MAGNOCELLULAR SYSTEMS Vasopressin and oxytocin are made in large ‘‘magnocellular’’ neurons in two bilaterally paired hypothalamic nuclei – the supraoptic nucleus and the paraventricular nucleus. The paraventricular nucleus contains several different neuronal populations, but the supraoptic nucleus contains only magnocellular vasopressin and oxytocin cells, and most of what we know of magnocellular neurons comes from studies of the supraoptic nucleus. Every supraoptic neuron has just one axon, with few if any collateral branches are present. Each axon projects into the neural lobe of the pituitary gland, where it gives rise to numerous axonal swellings and about 10,000 neurosecretory nerve endings. The neural lobe lacks a blood–brain barrier; the capillary endothelium at this site is fenestrated, so vasopressin released from these nerve endings can freely enter the blood. However, there is a blood–brain barrier to vasopressin, so vasopressin released into the blood does not re-enter the brain. Blood-borne vasopressin cannot act directly at the supraoptic or paraventricular nuclei, nor, as far as we know, does it act at any sites in the brain. Action potentials (spikes) that are generated in the cell body of a vasopressin cell are propagated down the axon to the neurosecretory endings, where depolarisation triggers Ca2þ entry through voltage-dependent Ca2þ channels, which in turn triggers secretion by exocytosis of large neurosecretory granules. Thus the secretion of vasopressin (and oxytocin) into the blood is regulated by the electrical activity of the magnocellular neurons.
4. CELLULAR BASIS OF OSMOSENSITIVITY Magnocellular neurons are osmosensitive (Leng et al., 1982). The cell membranes contain stretch-sensitive channels; to be specific, they contain non-inactivating, stretch-inactivated non-selective cation channels. In response to a decrease (or increase) in the osmotic pressure of the extracellular fluid, all cells will swell (shrink) as water enters (leaves) them, but most cells respond promptly with a cell volume regulatory mechanism. Vasopressin (and oxytocin) cells do not show this prompt cell volume regulation, and, when they shrink in response to hyperosmotic challenge,
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the sustained change in membrane tension leads to a sustained depolarisation. This mechanism is responsible for the acute response to osmotic challenge. During sustained osmotic activation, the magnocellular neurons hypertrophy, accompanying an elevated rate of synthesis of secretory products. How signalling through membrane stretch receptors is sustained in chronic conditions, or whether other mechanisms take over, is not known. The appearance of an ‘‘osmotic threshold’’ does not reflect a distinct threshold that is evident in the behaviour of the osmoreceptors. Vasopressin cells are hyperpolarised by a decrease in osmotic pressure just as they are depolarised by an increase in osmotic pressure. However because ‘‘normal’’ rates of electrical activity and secretion from vasopressin cells are low, hyperpolarisation has little effect on basal secretion. While vasopressin cells are osmoreceptors rather than sodium receptors, in practice, sodium is nearly always the relevant osmolyte. This is because most circulating factors that influence osmoreceptive mechanisms do not cross the blood– brain barrier, but have the effect of osmototically withdrawing water from extracellular fluid into the blood, hence indirectly causing an increase in extracellular [Naþ]. In response to an increase in extracellular osmotic pressure, magnocellular neurons are depolarised, but only by a few millivolts at the most. The normal resting potential of these neurons (about 70 mV) is well below the threshold for activation of spikes (about 55 mV), and the direct osmotic depolarisation is of the same order of magnitude as the synaptic noise. However, this slight depolarisation is highly effective in modulating the rate of spike discharge. This is because the resting potential is normally not stable, but rapidly fluctuating, as a result of perturbation by synaptic input. This input is approximately balanced; it comprises a similar amount of transient hyperpolarisations as a result of inhibitory input (inhibitory post-synaptic potentials, IPSPs, mainly exerted by the release of GABA from impinging nerve endings) and transient depolarisations (excitatory post-synaptic potentials, EPSPs, mainly exerted by glutamate release). In effect, a small osmotically induced depolarisation changes the probability that membrane fluctuation (EPSPs) will reach spike threshold. The set point for sodium homeostasis is determined by the vasopressin/ oxytocin systems, but its value depends upon environmental factors. This dependence is visible in two well-characterised conditions, namely one pathological and one physiological. In the Syndrome of Inappropriate Antidiuretic Hormone Secretion (SIADH), circulating concentrations of vasopressin are inappropriately high, usually as a result of ectopic production of vasopressin. This condition is characterised by vasopressindependent hypertension resulting from expanded blood volume, and by
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hyponatraemia. In SIADH, the imbalance is pathological. However, in pregnancy there is also a shift in the set point for sodium homeostasis, and in this case the shift seems to be a physiological adaptation that is necessary to allow plasma volume expansion, to serve the needs of the placenta and foetus. In mid-pregnancy, the uterus and/or corpus luteum (depending upon species) secrete large amounts of a peptide hormone, relaxin. Relaxin acts via anterior regions of the brain to activate vasopressin cells, resulting in an expansion of plasma volume and a reduction in plasma [Naþ] that feeds back on vasopressin cells to offset the increased drive from relaxin. Pregnancy is characterised by normal levels of vasopressin secretion, but these co-exist with an abnormally low plasma [Naþ] and high plasma volume, and the set point for sodium homeostasis (and vasopressin secretion) is thus apparently re-set. In fact, these changes are predictable consequences of a sustained additional excitatory drive to the vasopressin cells.
5. THEORETICAL ANALYSIS OF OSMORECEPTIVE MECHANISMS Vasopressin cells, although osmosensitive, require tonic synaptic input for them to translate this osmotic signal into an increased spike frequency. This mechanism was recognised in 1982, when it was noted that this was an instance where synaptic input might serve a physiologically important function even if the input did not itself carry any relevant information, but merely provided neural ‘‘noise’’. In fact, one source of input to vasopressin cells, from neurons located in circumventricular regions of the anterior hypothalamus, does carry osmotic information. Interestingly, this input is not purely excitatory, but appears to be a balanced mix of inhibition and excitation. The nature of the osmotic input was first predicted from a theoretical analysis, and subsequently confirmed by experiments (Leng et al., 2001). While recording from vasopressin cells and oxytocin cells, we had recognised that the response of both cell types to a slow increase in systemic osmotic pressure was linear. The characteristics of the stretchsensitive channels mean that the direct depolarisation is linearly related to osmotic pressure, but since the mechanisms of spike generation in neurons are highly non-linear, the linear firing rate response was nevertheless unexpected. To interrogate this, we built a computational model. The oxytocin cell is relatively simple computationally; its activity can be described by a modified leaky integrate-and-fire model neuron which assumes that spikes arise from random (Poissonian) inputs,
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subject only to a refractory period after spiking. This refractoriness could be identified as the consequence of a post-spike hyperpolarising afterpotential (HAP) that has been extensively studied in these cells. As anticipated, such model neurons respond to increasing depolarisation or to increasing excitatory input with a non-linear increase in firing rate. In consequence, their dynamic range is very narrow – once a cell is activated, it takes only a small increase in excitatory drive to cause a large increase in firing rate, to the point when the cell’s ability to generate spikes is saturated. However, the response of model cells was different when they were challenged with a balanced input, comprising equal average numbers of EPSPs and IPSPs. The model cell still increased its firing rate when exposed to a combination of direct depolarisation and increasing balanced input, but now the response curve was very linear, with a shallow slope reflecting a wide dynamic range. We hypothesised that the input to magnocellular neurons from osmoreceptors in the anterior hypothalamus is not purely excitatory, but comprises an equal mixture of excitation and inhibition. We tested this in several ways, but most directly by measuring the release of GABA and glutamate in the supraoptic nucleus in response to osmotic stimulation, finding that both were increased similarly. Osmoreception is one of the clearest examples of stochastic resonance in a neural network. Stochastic resonance is a phenomenon that can occur in non-linear systems, whereby the presence of noise can enhance the detection of a signal (Douglass et al., 1993). For oxytocin and vasopressin cells, the direct effect of osmotic stimuli, in the absence of neural noise, is subthreshold to spike generation. However in the presence of neural noise – random fluctuations with no net average effect on resting potential – the cells can respond reliably and linearly to this otherwise subthreshold stimulus. Osmotic information is also transmitted in the form of modulation of the amplitude of the noise, because, as explained above, afferent inputs from the anterior hypothalamus are the source of a mixed input that is activated by osmotic stimuli. However, the conclusion that signal transduction utilises stochastic resonance remains sound if the afferent input remains balanced in response to osmotic stimulation. This system is an example of a physiological signal being encoded by variance: increased input from osmoreceptors results in an increased output of neuroendocrine neurons, not by causing a net depolarisation but by increasing the irregularity of the membrane potential. The above analysis was directed at oxytocin cells. The same principles probably apply to vasopressin cells, but there are features of their behaviour which make them much more difficult to model. Oxytocin cells
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Fig. 1. Schematic representation of the magnocellular vasopressin system. Vasopressin cells discharge spikes in a phasic pattern, consisting of bursts of activity separated by periods of silence (top right panel). Phasic bursts typically show high initial firing rate followed by a ‘‘plateau’’. This activity pattern is the most efficient stimulation for vasopressin secretion into blood, because vasopressin bursts without silence periods, or stimulation at constant frequency with or without silence, induce less total evoked secretion (bottom left panel). Vasopressin cells are autoregulated by dynorphin and by vasopressin released from dendrites. In isolated cells, vasopressin increases intracellular calcium by activating vasopressin receptors, which probably induce further vasopressin dendritic release (top left panel). Dynorphin acts back on the vasopressin cell of origin to inactivate the burst mechanism; vasopressin is much more long lasting and acts as a weak population signal, with bidirectional effects; it is excitatory to slow firing cells and inhibitory to active cells.
during activation by hyperosmotic stimuli, discharge spikes continuously. However vasopressin cells, when activated by osmotic stimuli, discharge phasically.
6. VASOPRESSIN CELLS AND PHASIC FIRING In the rat, in response to increases in osmotic pressure, vasopressin cells discharge spikes in a phasic pattern, comprising ‘‘bursts’’ that last for between 10 and 90 s or more, separated by silent periods of 15–40 s in duration. As the osmotic pressure is raised, bursts become more intense and, at least in the short term, more prolonged.
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6.1. Physiological significance of phasic firing Vasopressin cells fire bursts asynchronously, so this activity does not give rise to a similarly phasic secretion of vasopressin into the blood. So, why do vasopressin cells fire phasically? This question has been resolved by studies of stimulus-secretion coupling. The neural lobe of the pituitary gland, which contains only axons and nerve endings of magnocellular neurons, can be maintained in vitro. The isolated lobe releases large amounts of vasopressin and oxytocin in response to electrical stimulation (which triggers spikes in the axons), and the dynamics of stimulus-secretion coupling can be resolved well. It turns out that the efficiency of stimulussecretion coupling depends critically on the pattern of stimulation. At high frequencies of stimulation, secretion is potentiated for at least two reasons; first, Ca2þ entry evoked by spikes summates temporally, and because Ca2þ entry facilitates exocytosis non-linearly; second, at higher frequencies of stimulation, spike invasion of the arborising axon is more complete, mainly because of the residual depolarising effect of raised extracellular Kþ following the passage of a spike, which leads to a reduced ‘‘failure rate’’ of propagation for subsequent spikes. Frequency facilitation saturates in efficiency at a stimulation rate of about 13 Hz, and within a few seconds of stimulation. In addition to frequency facilitation, there is a converse process of secretory fatigue. The mechanisms that underlie fatigue are not clear, but might involve either Ca2þ-induced inactivation of Ca2þ entry, or Ca2þ-activated opening of Kþ channels resulting in terminal hyperpolarisation. The effect of fatigue is that high rates of secretion cannot be maintained for more than about 20 s. However, a silent period of about 20 s is sufficient to reverse fatigue. Thus, the most efficient pattern of stimulation alternates activation at up to 13 Hz for about 20 s, with silent periods of similar duration. Because these parameters closely match the discharge characteristics of vasopressin cells, it seems natural to conclude that vasopressin cells fire phasically because this pattern results in a given level of hormone release for the least number of spikes. This is important for two reasons. First, it demonstrates that the pattern of spike activity, not just the quantity, is important in information transfer. Second, here is evidence of an optimisation principle. From this, we might infer that there are adaptive benefits to minimising the generation of spikes, or at least that there is a significant penalty associated with excess excitation, that is independent of waste associated with excess secretion. The most likely costs are (1) the risk of cell damage and (2) the risk of seizures.
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Seizures – epileptiform activity – can arise through positive-feedback effects of excessive neuronal excitation. When a spike is generated, there is an efflux of Kþ and an influx of Naþ. The increase in extracellular [Kþ] will tend to depolarise neighbouring cells, and accordingly, there are efficient mechanisms for removing this excess; in particular, glial cells, whose processes are interleaved between neurons to limit such ‘‘crosstalk’’ – subsequently clear the excess Kþ into the blood. However, these mechanisms can be overwhelmed by excessive activation, leading to uncontrolled spread of excitation. Seizures can be generated particularly when the actions of GABA are blocked, since activation of inhibitory neurons would otherwise tend to suppress the seizure activity. Seizures can result in neuronal death, and at the least, destroy any concurrent information processing by the affected neurons. Although glutamate is the most abundant excitatory transmitter in the CNS, glutamate agonists, through inducing hyperactivation, can induce neuronal death. Excitotoxic neuronal death seems to be associated with excessive Ca2þ intake through voltage-dependent Ca2þ channels. However, this is not the only threat. Increased electrical activity also entails up-regulation of electrolyte pump activity. In addition, elevated secretion must be balanced by elevated synthesis. For vasopressin and oxytocin cells, which must produce enough peptide to act at distant peripheral targets, the synthetic load is considerable, and in chronic conditions of activation, there are marked morphological changes, including cell volume hypertrophy and proliferation of nucleoli. Hypertrophy changes the electrical properties of nerve cells, entails changes in expression of membrane receptors to maintain normal function, and entails the promotion of reactive synaptogenesis. All these require increased oxygen and metabolite utilisation. These changes might be considered as representing the sort of accommodations that any neuron must make when hyperactivated. However, most neurons are protected from chronic activation by negative-feedback mechanisms. For most receptors, continued activation by agonists results in down-regulation of receptor expression or function (desensitisation). Excitation in many neurons results in activity-dependent hyperpolarisation, restoring normal activity. In many networks, excitation is limited synaptically, by recurrent inhibition. As a consequence of negative-feedback mechanisms, operating at different timescales and through multiple mechanisms, activity in neurons is generally transient even in response to sustained stimuli – neurons detect dynamic information well; they register changes promptly, and then return to normal activity levels. However, dehydration poses a threat to body homeostasis that must be met by a sustained response, sustained over several days if necessary, and
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requiring a continuous, high secretion of vasopressin and oxytocin. In these circumstances, if elevated electrical activity poses a threat to cell survival, then there will be strong adaptive pressure favouring optimal efficiency of stimulus-secretion coupling.
7. MECHANISMS UNDERLYING PHASIC FIRING Phasic bursts in vasopressin cells have a characteristic shape (see Leng et al., 1999) – initial firing rates are high, and within about 4 s, the mean firing rate settles down to a relatively stable ‘‘plateau level’’ that is proportional to the peak early firing rate. The plateau rate might be anything from 4 to 12 spikes/s, and the plateau might be maintained anywhere from 15 s to several minutes. When a burst ends, the cell enters a period of ‘‘burst refractoriness’’ that typically lasts about 20 s, during which only a few spikes at most are discharged. Both the onset and termination of bursts are activity-dependent. At the beginning of each burst, spontaneous spikes are followed by a depolarising afterpotential (DAP) which means that a second spike is likely to be triggered soon after the first, generating a further DAP. As the DAPs summate, a ‘‘plateau potential’’ is formed. Activity during a burst is moderated by a second spike-dependent potential – a slow afterhyperpolarisation (AHP), which slows the initial rate of firing of the cell; the AHP and DAP reach an approximate equilibrium underlying a steady rate of firing within the burst. However there are further activity-dependent feedbacks, and one important feedback results from dendritic secretion. Although vasopressin and oxytocin cells only have one axon, which projects to the neural lobe, each cell also has 2–3 large dendrites. Dendrites are neuronal processes that receive information – most afferent synapses end on the dendrite – but in very many neurons, spikes are also propagated along dendrites and can result in dendritic secretion. The dendrites of vasopressin cells contain large numbers of neurosecretory granules, and so there is considerable activity-dependent secretion of vasopressin within the supraoptic nucleus. Here, concentrations of vasopressin might be 100–1000 times higher than those in the circulation. The bursts of vasopressin cells are ultimately terminated by inactivation of the mechanisms that underlie the DAP. This inactivation is the result of activity-dependent dendritic secretion of another peptide, dynorphin. Dynorphin is an endogenous opioid that is co-packaged with vasopressin in the neurosecretory granules. The levels of dynorphin in granules are about 300 times lower than those of vasopressin, nevertheless, the vasopressin cells contain the highest concentrations of dynorphin found anywhere in
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the brain, and the amount released is considerable. Dynorphin acts on kappa opioid receptors which are expressed by the vasopressin cells themselves, and the most important action of dynorphin appears to be a selective inactivation of the DAP (Brown et al., 1999). Thus bursts are activity-dependent in both their initiation and their termination – and the vasopressin cell acts as a bistable oscillator. In particular, brief activation of a vasopressin cell might either trigger a burst (if applied during the silent period between spontaneous bursts) or stop a burst (if applied during a burst). Vasopressin itself also has important feedback actions within the supraoptic nucleus, but before we discuss these, we will mention one other activity-dependent negative-feedback mechanism. Vasopressin cells have the highest concentration of nitric oxide synthase (NOS) of any neurons in the brain, closely followed by oxytocin cells (Sanchez et al., 1994). This enzyme, whose activity is induced by increases in intracellular [Ca2þ], results in production of nitric oxide (NO) – a short-lived gaseous neuromodulator with powerful, but very local actions both on the vasopressin and oxytocin cells themselves and on afferent nerve endings. The direct effects of activity-dependent production of NO are inhibitory to oxytocin and vasopressin cells, and the indirect effects are also inhibitory, for presynaptically, NO stimulates the release of the inhibitory neurotransmitter GABA (Stern and Ludwig, 2001). The NO system in vasopressin and oxytocin cells is apparently inactive at normal basal levels of activity, but is increasingly active at higher levels of neuronal activity (Kadowaki et al., 1994). In effect, the NO system serves as a brake on neuronal excitation in both these cell types. We have described three mechanisms intrinsic to vasopressin cells which each have a different, negative-feedback role in regulating cell activity. The afterhyperpolarisation is an intrinsic mechanism that etches the profile of bursts. Dendritic secretion of dynorphin has a role that is probably also mainly confined to the cell of origin, and dynorphin determines burst duration. Thirdly, NO production has a strong restraining influence at high levels of activity. There is a fourth local feedback mechanism that is in many ways the most interesting, for this feedback is bi-directional, and operates at a population level; this feedback is exerted by dendritic secretion of vasopressin itself.
8. AUTOREGULATORY ACTIONS OF VASOPRESSIN Vasopressin cells express specific receptors for vasopressin, and oxytocin cells express specific receptors for oxytocin, thus the activity of both cell
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types is regulated by their own secretory product. These receptors are functional, as has been demonstrated most directly by experiments monitoring intracellular [Ca2þ] in single, isolated cells in vitro. These studies have shown that vasopressin cells express at least two classes of receptors that are sensitive to physiological concentrations of vasopressin; the receptors can be distinguished by studying the effects of synthetic agonists and antagonists with differing pharmacological profiles of affinity for different receptor classes. Classically, there are three characterised subtypes of the vasopressin receptor, classed as V1a, V1b, and V2 subtype receptors. To date, the V2 subtype has not been clearly shown to be expressed anywhere in the brain. However mRNA expression for both the V1a and the V1b receptor has been reported in the supraoptic nucleus (Hurbin et al., 1998). Vasopressin cells when exposed to vasopressin show a large increase in intracellular [Ca2þ] that is mediated in part by entry through voltage-gated channels and in part arises from mobilisation of Ca2þ from intracellular, thapsigargin-sensitive stores (Sabatier et al., 1997). As a result of this increase in intracellular [Ca2þ], vasopressin stimulates further release of vasopressin from dendrites. The activation of voltage-gated Ca2þ entry suggests that vasopressin has a direct depolarising effect on vasopressin cells. However, the electrophysiological effects of vasopressin are complex. When active vasopressin cells are exposed to vasopressin, they are inhibited, but inactive vasopressin cells are excited (Ludwig and Leng, 1997; Gouze`nes et al., 1998). The mechanisms underlying these dual effects are not clear. One possibility is that when vasopressin cells are active, the additional effects of potentiating voltage-sensitive Ca2þ channels is minimal, but the enhancement of intracellular [Ca2þ] will lead to hyperpolarisation through Ca2þactivated Kþ conductances. In other words, the dual action might arise through non-linearities in the relationships between membrane potential and Ca2þ entry, and between intracellular [Ca2þ] and Kþ conductance. This might well be too simple, for vasopressin actions involve several intracellular signalling pathways. Vasopressin receptors are G protein-coupled receptors, classified by their pharmacology and the nature of their intracellular signalling. Activation of vasopressin receptors of V1a and V1b-type induces an increase in intracellular calcium resulting from the stimulation of phospholipase C and hydrolysis of phosphatidyl inositols (IP3); while activation of V2-type receptor increases cAMP via stimulation of adenylyl cyclase. The nature of vasopressin receptors expressed in supraoptic vasopressin neurons is still unclear. While various studies agree on the presence of V1a receptor, discrepancies arise about whether or not V1b and V2 receptors are functionally
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expressed. In isolated vasopressin neurons, vasopressin activates both the phospholipase C pathway and the adenylyl cyclase pathway (Sabatier et al., 1998). As mentioned above, the release of calcium from intracellular calcium stores might hyperpolarize the cells by activating Ca2þ-activated Kþ channels. On the other hand, cAMP-stimulated protein kinase A can modulate the opening of voltage-dependent Ca2þ channels on the cell membrane and induce depolarisation. It might be that in physiological conditions, vasopressin stimulates one or the other pathway depending on the activity of the cell, and this might result in the dual regulation of the electrical activity observed in vivo. If the effects of vasopressin upon inactive vasopressin cells are physiological, there must be circumstances in which inactive vasopressin cells are exposed to vasopressin – and probably therefore, inactive vasopressin cells are sensitive to vasopressin release from other, active vasopressin cells. Thus the neuronal actions of vasopressin might represent population signalling, not intrinsic autoregulation. The dendrites of vasopressin cells lie in close proximity to each other, and concentrations of vasopressin measured in dialysates of the supraoptic nucleus imply very high local concentrations, so we may assume that dendritic vasopressin release in the supraoptic nucleus does indeed function as a population signal that feeds back to influence the electrical activity of the population as a whole. This autoregulatory action of vasopressin will tend to equalise the level of activity throughout the population of vasopressin cells – to share the load. Clearly this might be important if electrical hyperactivation predisposes cells to damage. Let us consider the consequences of hyperactivation for a population of vasopressin cells whose responses to osmotic stimulation were very heterogeneous. The cells most sensitive to osmotic stimuli would be most strongly excited, and most likely to die. Their death would result in a loss of vasopressin secretion, leading to raised osmotic pressure, and enhanced excitatory drive to the surviving vasopressin cells, with risk of further damage to the most sensitive of the remainder – and so on. The vasopressin system would drift to a higher set point for osmoregulation, with progressively fewer cells surviving to share the demands of response to acute osmotic challenge. Interestingly, there might be pathological examples of exactly such a vicious circle in the vasopressin system.
9. DIABETES INSIPIDUS – THE CONSEQUENCES OF FAILURE OF VASOPRESSIN RELEASE Hypothalamic diabetes insipidus is rare in humans, but the most common heritable manifestation of this disease has some extraordinary features
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that might cast light on how this homeostatic system compensates for degradation with age. Typically, familial hypothalamic diabetes insipidus is expressed not from birth, as would be expected from a failure to produce vasopressin, but appears suddenly in adulthood, as an abrupt loss of detectable vasopressin. Familial hypothalamic diabetes insipidus has been identified in seventy kindreds for whom the genetic mutation has been identified. In most cases, and in every case of late onset disease, the mutation affects a single allele of the vasopressin gene, and the defect is in no cases autosomal dominant – meaning that the normal allele is expressed alongside the mutant allele. Thus, carriers of this gene are initially asymptomatic because the normal allele can produce enough vasopressin to sustain apparently normal water and electrolyte balance. So what goes wrong later? Vasopressin is synthesised from a larger prohormone, enzymatic cleavage of which yields vasopressin, a larger peptide – neurophysin I, a signal peptide, and a glycopeptide. The seventy characterised kindreds with familial hypothalamic diabetes insipidus exhibit many different mutations, but in every case, the mutation does not affects that part of the gene which codes for vasopressin. Instead, the mutations in most cases result in the production of a mutated neurophysin. Neurophysin is normally co-secreted with vasopressin, but appears to have no function after secretion. Instead it appears to be a ‘‘chaperone’’ for vasopressin; neurophysin associated with vasopressin folds in a way that facilitates aggregation of vasopressin–neurophysin complexes, and this facilitates packaging into neurosecretory granules. Aberrant forms of neurophysin do not enter the secretory pathway, but remain in the cell body. Here they are normally disposed of by autophagocytosis (see De Bree et al., 2003). However, the aberrant proteins can accumulate in the cell body with ultimately toxic effects to the cell. It seems most likely that, when the synthesis of vasopressin is increased, the synthesis of the aberrant peptide might exceed the cell’s capacity to dispose of it. Whether these accumulations of aberrant peptide result in cell death, or simply functional inactivation of the vasopressin cell is not clear. Strikingly, when the disease manifests itself, it does so abruptly rather than progressively. One likely explanation is that mutant peptide accumulates most in relatively active cells, causing these to be most likely to fail. As the most active cells die, the pressure on the remainder to sustain effective antidiuresis increases, causing others to fail. The more cells die, the greater the secretory stress on the remainder, resulting in a progressively escalating rate of cell death and the appearance of a sudden onset of symptoms.
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This is a particular example of what is probably a general threat to neurons: hyperactivity is dangerous for any neuron; and this has been exploited by the wide experimental use of so-called ‘‘excitotoxins’’ to induce focal experimental brain lesions in experimental animals. This propensity for overactive neurons in a network to die might be regarded as the converse of the opposite propensity seen during development especially – the propensity for inactive neurons to be eliminated through apoptosis. These two constraints therefore together will tend to force any neuronal network into distributed information processing.
10. SUMMARY Vasopressin neurons homeostatically regulate plasma volume and body fluid electrolyte composition in the face of (a) differential and variable loss of fluid and electrolytes through sweating and urine flow, and (b) perturbation by fluid and electrolyte intake. Correction of excessive electrolyte concentration by water intake threatens regulation of plasma volume; conversely, when plasma volume falls, restricting urine output threatens electrolyte balance. Vasopressin promotes water retention through antidiuresis, which restricts water loss and concentrates the urine, and vasopressin secretion is proportional to excess electrolyte concentration and inversely (non-linearly) proportional to fluid volume excess. The threshold and gain of this system are maintained in conditions that result in substantial depletion of secretory capacity; the system maintains its behaviour throughout our normal life, despite neuronal loss through ageing; and can compensate for abnormal cell loss following injury. The vasopressin system has several properties whose importance is poorly understood. (1) they function as asynchronous bistable oscillators. Vasopressin neurons are restrained by negative feedbacks operating on varying time scales, through dendritic generation of nitric oxide, cannabinoids, and dynorphin and the network is subject to weak population feedback through dendritic vasopressin release. Some features of the system might reflect general constraints on neuronal network architectures: (1) neurons are vulnerable to ‘‘burn-out’’ – overactive neurons are likely to die. (2) inactive neurons are eliminated early in development. Together, these constraints might force the emergence of highly distributed processing that is very robust against noise and damage. Other apparent constraints on the architecture include the cost of storage and synthesis of vasopressin, and the cost of generating electrical activity to stimulate secretion.
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REFERENCES Brown, C.H., Ghamouri-Langroudi, M., Leng, G., Bourque, C.W., 1999. k-opioid receptor activation inhibits post-spike depolarising after-potentials in rat supraoptic nucleus neurones in vitro. J. Neuroendocrinol. 11, 825–828. De Bree, F.M., Van der Kleij, A.A.M., Njenhuis, M., Zalm, R., Murphy, D., Burbach, J.P.H., 2003. The hormone domain of the vasopressin prohormone is reuired for the correct prohormone trafficking through the secretory pathway. J. Neuroendocrinol. 15, 1156–1163. Douglass, J.K., Wilkens, L., Pantazelou, E., Moss, F., 1993. Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature 365, 337–340. Gouze`nes, L., Desarme´nien, M., Hussy, N., Richard, Ph., Moos, F.C., 1998. Vasopressin regularises the phasic firing pattern of rat hypothalamic magnocellular neurons. J. Neurosci. 18, 1879–1885. Hurbin, A., Boissin-Agasse, L., Orcel, H., Rabie´, A., Joux, N., Desarme´nien, M., Richard, Ph., Moos, F.C., 1998. The V1a and V1b, but not V2, vasopressin receptor genes are expressed in the supraoptic nucleus of the rat hypothalamus, and the transcripts are essentially colocalised in the vasopressinergic magnocellular neurons. Endocrinology 139, 4701–4707. Kadowaki, K., Kishimoto, J., Leng, G., Emson, P.C., 1994. Upregulation of nitric oxide synthase messenger ribonucleic acid together with nitric oxide synthase activity in the rat hypothalamo-hypophysial system after chronic salt loading; evidence of neuromodulatory role of nitric oxide on arginine vasopressin and oxytocin secretion. Endocrinology 134, 1011–1017. Leng, G., Mason, W.T., Dyer, R.G., 1982. The supraoptic nucleus as an osmoreceptor. Neuroendocrinology 34, 75–82. Leng, G., Brown, C.H., Russell, J.A., 1999. Physiological pathways regulating the activity of magnocellular neurosecretory cells. Prog. Neurobiol. 56, 1–31. Leng, G., Ludwig, M., Scullion, S., Brown, C.H., Bull, P.M., Currie, J., Verbalis, J.G., Blackburn-Munro, R., Onaka, T., Feng, J., Russell J.A., 2001. Responses of magnocellular neurons to osmotic stimulation involves co-activation of excitatory and inhibitory input: an experimental and theoretical analysis. J. Neurosci. 21, 6967–6977. Ludwig, M., Leng, G., 1997. Autoinhibition of supraoptic nucleus vasopressin neurons in vivo: a combined retrodialysis/electrophysiological study in rats. Eur. J. Neurosci. 9, 2532–2540. Sabatier, N., Richard, Ph., Dayanithi, G., 1997. L-, N- and T- but neither P- nor Q-type Ca2þ channels control vasopressin-induced Ca2þ influx in magnocellular vasopressin neurones isolated from the rat supraoptic nucleus. J. Physiol. 503, 253–268. Sabatier, N., Richard, Ph., Dayanithi, G., 1998. Activation of multiple intracellular transduction signals by vasopressin in vasopressin-sensitive neurones of the rat supraoptic nucleus. J. Physiol. 513, 699–710. Sanchez, F., Alonso, J.R., Arevalo, R., Blanco, E., Aijon, J., Vazquez, R., 1994 Coexistence of NADPH-diaphorase with vasopressin and oxytocin in the hypothalamic magnocellular neurosecretory nuclei in the rat. Cell Tissue Res. 276, 31–34. Stern, J.E., Ludwig, M., 2001. NO inhibits supraoptic oxytocin and vasopressin neurons via activation of GABAergic synaptic inputs. Am. J. Physiol. 280, R1815–R1822.
Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
20 Mathematical modelling of angiogenesis and vascular adaptation1 Tomas Alarcona, Helen Byrneb, Philip Mainic and Jasmina Panovskac a
Bioinformatics Unit, Department of Computer Science, University College London, London, UK b Centre for Mathematical Medicine, Division of Applied Mathematics, University of Nottingham, Nottingham, UK c Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK
1. INTRODUCTION Angiogenesis, i.e. the process whereby new blood vessels are formed in order to supply nutrients and/or metabolites to starving tissue, plays a key role in the normal functions of many healthy organisms and also in pathological situations, such as wound healing or cancer. In the particular case of cancer, the study of tumour-induced angiogenesis was boosted by the research of Folkman and co-workers (Folkman, 1995). While the development of solid tumours is a rather complicated process, it can be assumed to occur in three different stages. During the first stage, solid tumours are avascular, i.e. they comprise a colony of cells that lacks its own blood supply. During this stage, there is typically a maximum, diffusion-limited size to which the tumour can grow (several millimetres) and it does not normally invade the host organ. Thus, avascular tumours are relatively harmless. The second stage of tumour growth starts when some of the cells within the avascular tumour secrete and release so-called tumour-angiogenic factors (TAFs). These substances diffuse towards the nearby vasculature, whereupon they degrade the basal membrane of the blood vessels and promote (chemotactic) migration 1
The authors would like to dedicate this paper to the memory of their friend and colleague, Ray Paton.
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towards the source of TAF and proliferation of the endothelial cells (ECs). Once the tumour has thus established its own blood supply, the third phase of vascular tumour growth starts. In this stage, the tumours may become lethal for two main reasons. First, they have access to a virtually endless supply of nutrients and, in consequence, may exhibit the uncontrolled growth typical of cancer. Second, the new vasculature can act as an escape route, enabling the tumour cells to migrate to other parts of the body (metastasis). Once a solid tumour has successfully established a blood supply, other issues related to blood flow through the vascular network become important in determining the tumour’s growth and response to treatment. The major factor here is probably blood flow heterogeneity which is recognised as one of the key physical barriers to drug delivery in tumour treatment (Jain, 2001). Drugs are usually blood-borne, and therefore heterogeneity in blood flow means that most of the injected drug will fail to reach the tumour and be eliminated or, even worse, assimilated by healthy tissue producing deleterious side effects. On the other hand, most nutrients are also blood-borne and therefore heterogeneity in blood flow induces heterogeneity in nutrient distribution within the tissue. This factor and its effects on tumour growth have been recently analysed (Alarcon et al., 2003). Both angiogenesis and blood flow through vascular networks are active fields of research in the theoretical and mathematical biology communities. In this chapter, we give a brief review of continuum models that have been proposed to describe tumour-induced angiogenesis. Then we present some recent results concerning the organisation of vascular networks and how this is coupled to blood flow and the behaviour of the surrounding tissue. Finally, we present our conclusions.
2. REVIEW OF CONTINUUM MODELS OF TUMOUR-INDUCED ANGIOGENESIS In this section, we describe briefly deterministic models of tumour-induced angiogenesis. Since there are several excellent and detailed reviews in the literature (see for example, Mantzaris et al., 2004, or Preziosi, 2003), we choose not to go into detail here. We simply summarise the general features of the various models and discuss their strengths and weaknesses. Some of the earliest continuum models of tumour angiogenesis are based on an analogy with fungal growth, both phenomena exhibiting interconnected, branched structures that evolve in response to environmental signals. For example, Balding and McElwain (1985) adapted a
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fungal growth model developed by Edelstein (1982). They focused on three key physical variables: a generic, diffusible chemical produced by the tumour and termed as tumour-angiogenesic factor (or TAF), capillary tips, and capillary sprouts. Their one-dimensional model consisted of three nonlinear partial differential equations that were derived by applying the principle of mass balance to each species. It was assumed that the capillary tips migrate via Chemotaxis towards the source of TAF, i.e. the tumour. New capillary tips emanated from existing vessels and/or tips at rates that increased with increasing TAF levels and were lost as a result of fusion with other tips and/or vessels (i.e. anastomosis). The production of capillary sprouts was assumed to be driven by migration of the capillary tips, the sprout density increasing at a rate that matched the flux of capillary tips – the so-called ‘‘snail trail’’. The TAF was modelled as a diffusible chemical that was produced by the tumour, underwent natural decay, and was consumed by the migrating capillary tips. Many modifications to Balding and McElwain’s model have been developed, in terms of different production and removal terms for the TAF and the capillary tips (see for example, Byrne and Chaplain, 1995; Orme and Chaplain, 1996). However, in each case, the results are similar and exhibit many of the characteristic features of angiogenesis that have been observed in vivo (Muthukkaruppan et al., 1982). Indeed, for parameter values that give rise to successful angiogenesis, typical numerical simulations show an accelerating front of capillary tips and sprouts propagating towards the tumour, the maximum capillary tip density preceding the maximum capillary sprout density. Recently it has been shown that enhanced migration together with tip production from the vessels via branching, rather than endothelial cell proliferation, can be an alternative to constant migration and additional proliferation of the endothelial cells in the tips for successful angiogenesis (Panovska, 2004). A similar approach has been used before (Anderson and Chaplain, 1998), but without branching, leading to vessels stopping at some distance from the tumour. Whilst it is straightforward to extend Balding and McElwain’ model to two and three space dimensions (Orme and Chaplain, 1997), the resulting models highlight some of the shortcomings of using a continuum framework to study angiogenesis. This is primarily because angiogenesis is a twoor three-dimensional process, with tips sprouting in directions other than that of the propagating vascular front, and it is not immediately clear how the snail trail should be generalised in higher space dimensions. In addition, because the dependent variables are densities, the models are unable to distinguish between different vascular morphologies (e.g. a region perfused by one, large vessel would be identical to a region perfused by many
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small vessels, even though their surface areas and, hence, nutrient delivery rates would differ). Moreover the models do not distinguish between anastomosis and capillary tip death, even though the former will increase nutrient supply to the tissue while the latter will not. Finally, no account is taken of vascular remodelling and, in particular, the impact of blood flow and haematocrit on the evolving vasculature. In spite of these weaknesses, the models do provide useful insights into the ways in which different physical mechanisms (e.g. the strength of the chemotactic response, the rate of TAF production, the rate of capillary tip formation) influence angiogenesis. In particular, the success of angiogenesis is tightly controlled by the balance between endothelial cell proliferation and migration: as the strength of the chemotactic response increases, the tips migrate towards the tumour more rapidly, thereby reducing both the time available for tip proliferation and the density of the vasculature when the tumour is reached. Anderson and Chaplain (1998) developed a continuum–discrete model in which the movement of the tips of the vessels was modelled by means of a biased random walk whose transition probabilities were derived by discretisation of a previously developed PDE model. In this work, the role of haptotaxis (migration upward gradient of adhesive molecules, in particular fibronectin) was examined and shown to be a key factor in successful angiogenesis. Since Balding and McElwain’s model of tumour angiogenesis was developed, detailed knowledge of the specific chemicals and biochemistry involved has been elucidated. Following Orme and Chaplain (1997), Levine et al. (2001) have developed highly complex models that account for much of this new detail and, as such, these represent an important step towards understanding angiogenesis using biochemically based rather than phenomenological arguments. For example, Levine et al. account for interactions between ECs, angiogenic factors and cells such as pericytes and macrophages that are also involved in angiogenesis. One important difference between Levine et al.’s model and that of Balding and McElwain is their treatment of the ECs cells. Levine et al. based their model on the theory of reinforced random walks developed by Othmer and Stevens (1997). The models of angiogenesis mentioned above do not account for nutrient delivery to the tissue by the developing vasculature and cease to apply once the capillary tips reach the tumour. Recently, Breward et al. (2003) have used a multiphase modelling framework to develop continuum models of vascular tumour growth that address these shortcomings. Possibly the main criticism of the above models of angiogenesis stems from their inability to track individual capillary tips and, hence,
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to reproduce accurately the patterns of vascular growth observed during tumour angiogenesis (but see the work of Chaplain and co-workers (Anderson and Chaplain, 1998)). In the next section, we explain how hybrid cellular automata models can be used to resolve these issues.
3. DESIGN PRINCIPLES AND STRUCTURAL ADAPTATION OF VASCULAR NETWORKS In the previous section, we focused on continuum modelling of tumourinduced angiogenesis, explaining how the evolution of the (continuous) density of capillary tips or ECs could be analysed. We now concentrate on interactions between blood flow, signalling cues from the surrounding tissue, and the structure of the vascular tree and show how they may be incorporated into a hybrid cellular automata modelling framework.
3.1. A design principle for vascular beds: role of complex blood rheology The idea that design principles govern the organisation of vascular systems has proved to be a fruitful approach (LaBarbera, 1990). Design principles are based on the hypothesis that the organisation of the vascular system comprises geometrical, physical, and physiological constraints that optimise overall function. Several design principles based on different hypotheses have been proposed. Gafiychuk and Lubashevsky (2001) based their design principle on the geometrical requirement of space filling. A different approach, based on fractal modelling and scaling concepts, was introduced by Gazit et al. (1995). They measured the fractal dimensions of capillary beds, normal arterial trees, and tumour vasculature. The resulting fractal dimensions were found to be compatible (within experimental errors) with the fractal dimensions of clusters generated by classical, non-equilibrium growth processes extensively studied in statistical mechanics (space filling, diffusion-limited aggregation, and invasion percolation, respectively). The third type of design principle is based on optimisation arguments, whereby some physical quantity (dissipated power (Murray, 1926), wall material (Kurz and Sandau, 1997), etc) is minimised so that the performance of the vascular system is maximised. The best known of these optimisation principles is Murray’s law. Murray’s law states that the vascular system is organised so that a balance exists between the metabolic energy of a given volume of blood and the energy required for blood flow. While resistance to blood flow
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diminishes when the radius of the vessel increases, the metabolic energy needed to maintain a larger volume of blood increases. Specifically, Murray’s law is based on a minimisation principle for the dissipated power, W. The blood is viewed as a Newtonian fluid of constant viscosity and the flow assumed to be Poiseuille. The vessels are considered rigid tubes and the pressure gradient is assumed to be constant. These assumptions lead to the following formulation of the design principle for a single vessel of length L and radius R: @W ¼ 0, @R W ¼ WH þ WM , 8Q2 0 L WH ¼ ,
R4
ðEq: 1Þ
WM ¼ b R2 L, where WH is the power dissipated by the flow, WM is the metabolic energy consumption rate of the blood, Q is the flow rate, 0 is the blood viscosity, and b is the metabolic rate per unit volume of blood. Using Equation (1) we deduce that the total dissipated power W is minimised if rffiffiffiffiffiffi
R3 b : ðEq: 2Þ Q¼ 4 0 Equation (2) shows how the vessel radius R and the flow rate Q are related when the optimisation principle is satisfied. Additionally, at a bifurcation in the vascular tree, conservation of mass implies: QP ¼ Q1 þ Q2 ,
ðEq: 3Þ;
where QP is the flow rate through the parent vessel, Q1 and Q2 are the flow rates through the daughter vessels. Taken together, Equations (2) and (3) imply that, at a bifurcation, the radius of the parent vessel, RP , and the radii of the daughter vessels, R1 and R2 , satisfy: R3P ¼ R31 þ R32 :
ðEq: 4Þ
This is Murray’s basic result concerning the architecture of the vascular tree. Furthermore, using the above result, it is easy to determine the wall shear stress (WSS) within a given vessel. For Poiseuille flow, the WSS is given by w ¼
40 Q pffiffiffiffiffiffiffiffiffiffi ¼ b 0
R3
ðEq: 5Þ
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using Equation (2). Thus we conclude that the WSS is constant throughout vascular networks constructed according to Murray’s principle. While the WSS is approximately constant in large arterial vessels, experimental work by Pries et al. (1995) shows that it depends on the transmural pressure in a sigmoidal manner, saturating to a constant value only for large pressures (i.e. large arteries and arterioles). Murray’s law neglects certain factors, such as rheology, which may play important roles in the organisation of the vascular tree. Blood is far from being a simple fluid with constant viscosity: it is a highly complex suspension of cells and molecules of a wide range of sizes. Consequently, treating blood as a Newtonian fluid is a very crude approximation. Red blood cells play a key role in the rheology of blood. The relative (non-dimensional) blood viscosity, rel ðR, H Þ, depends on R and also on the haematocrit, H, which is defined as the ratio between the total blood volume and the volume occupied by red blood cells. The relative viscosity exhibits a non-monotonic dependence on R, which can be subdivided into three different regions. If R is much greater than the typical size of a red blood cell, then the viscosity is independent of the vessel radius. As the radius of the vessel decreases, the viscosity also decreases (the Fahraeus–Lindqvist effect) until the viscosity attains a minimum. For smaller values of R the viscosity increases as R decreases. The dependence on H is easier to understand: the higher is H, the thicker the blood becomes, and therefore its viscosity increases (Pries et al., 1994). The question we pose concerns whether it is possible to generalise Murray’s law in order to obtain results that reproduce more realistically the behaviour of the wall shear stress and, in particular, the wall shear stress–pressure relationship observed by Pries et al. (1995). To this end we reformulate the design principle as follows: @W ¼ 0, @R W ¼ WH þ WM , 8Q2 0 rel ðR, HÞL WH ¼ ,
R4
ðEq: 6Þ
WM ¼ b R2 L, which predicts that Q and R are related as follows:
R3 Q¼ 40
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b : 4rel R@rel =@R
ðEq: 7Þ
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This equation needs to be solved numerically since the analytical expression for rel ðR, H Þ, i.e. " rel ðR, HÞ ¼ 1 þ
ð0:45
2 # 2 ð1 HÞC 1 2R 2R 1Þ , 2R 1:1 ð1 0:45ÞC 1 2R 1:1 0:645
0:45 ¼ 6e0:17R þ 3:2 2:44e0:06ð2RÞ , 1 1 0:15R C ¼ ð0:8 þ e Þ 1 þ , 12 11 11 1 þ 10 ð2RÞ 1 þ 10 ð2RÞ12 ðEq: 8Þ (see Pries at al., 1994) is very complicated. Even though its solution is of the same type as that obtained by Murray, i.e. Q ¼ CðR, H ÞRðR, H Þ . In the present case, however, the coefficient C and the branching exponent depend on R and H. This fact, together with mass conservation at a bifurcation, leads to the following equation relating the radii of the parent and daughter vessels: CðRP , HP ÞRPðRP , HP Þ ¼ CðR1 , H1 ÞR1ðR1 , H1 Þ þ CðR2 , H2 ÞR2ðR2 , H2 Þ
ðEq: 9Þ
(See Alarcon et al., 2005a for full details). The main difference between Equations (4) and (9) is that the last one is local, in the sense that it depends on the state of the vessels at a particular bifurcation. By contrast, Equation (4) is global. Later, we will see that the local nature of Equation (9) has important implications. In order to proceed further, we have used our design principle to construct simple branching vascular networks. A full analysis of these simulations is presented in Alarcon et al. (2005a), here we only summarise the main results. Concerning the behaviour of the wall shear stress, we have found that in our optimal branching network it varies with the pressure (see fig. 1a). Indeed, our results are in good quantitative agreement with experimental and simulation results reported in Pries et al. (1995) and Pries et al. (1998), respectively. Quantitative agreement with experimental results concerning other quantities such as the flow velocity is also obtained (see fig. 1b). Another interesting feature of this optimal branching network is the branching exponent ðR, H Þ. Experimentally, it is determined by averaging data collected from many junctions and many vascular generations (Frame and Sarelius, 1995). Doing this, for our optimal branching network, we obtain a figure very close to 3, i.e. Murray’s law. However, Murray’s law predicts a uniform value for the wall shear stress.
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Fig. 1. Wall shear stress as a function of the pressure (a) and flow velocity as a function of the radius (b) in an optimal branching network. Our results are in quantitative agreement with simulation results reported by Pries et al. (1998) and experimental results obtained in Pries et al. (1995). See text for details.
This apparent contradiction has its origin in the use of a local bifurcation law (Equation (9)), rather than a global one with an average branching exponent. Karau et al. (2001) obtained similar results when studying vascular trees with heterogeneous branching exponents: even when the mean value of the branching exponent was three, non-uniform wall shear stress was observed. Their conclusion was that the influence on the wall shear stress in determining vessel radius is not necessarily manifested in the mean value of the branching exponent. This result also reconciles the experimental observations of a non-uniform wall shear stress with the geometrical design principle of space filling (Gafiychuk and Lubashevsky, 2001) and the supporting experimental evidence (Gazit et al., 1995).
3.2. Vascular structural adaptation: coupling vascular structure to tissue metabolic demands The vasculature provides all the tissues in a particular organism with all the nutrients and metabolites they need to carry out their normal functions. As such, it cannot be a rigid, static structure. Rather, vascular networks are remarkably adaptable to local conditions, changing their structure in response to local increases in the demand for nutrients and other substances stimulated by increased activity. As has been proposed in the previous section, vascular trees may comply with a design principle. Pries et al. (1998) proposed an adaptation mechanism to describe how different competing effects modify the lumen radius. One of these factors can be viewed as a hydrodynamic stimulus. It effects changes in the vessel radii such that the wall shear stress–pressure curve
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within the network approaches that reported in Pries et al. (1995). The second stimulus is a metabolic stimulus. It will cause an increase in the radii of the vessels in response to increasing metabolic demands of the surrounding tissue. Pries et al. (1998) argued that when the flux of haematocrit (given by QH ) transported through a vessel falls below a threshold value (Qref), basically corresponding to the rate at which oxygen must be supplied to maintain homeostasis, its radius must be increased. The third, and last, stimulus that we consider is the so-called shrinking tendency. According to Pries et al. (1998), this stimulus corresponds to a natural tendency of the vessels to reduce their size in the absence of growth factors. This structural adaptation mechanism is mathematically implemented by: w Qref þ 1 ks , Rðt þ tÞ ¼ RðtÞ þ Rt log þ km log ðPÞ QH
ðEq: 10Þ
where t is the time step, (P) is the set-point value of the wall shear stress as a function of the pressure, km is a constant accounting for the strength of the metabolic stimulus. The first and second terms on the right-hand side of Equation (10) account for the hydrodynamic and metabolic stimuli, respectively. The constant ks accounts for the shrinking tendency. For details of the actual expression for (P) we refer the reader to Pries et al. (1998). We have incorporated complex blood rheology (by assuming that the viscosity depends on the radius and haematocrit in the manner described in the previous section) and structural adaptation in simulations of blood flow through a vascular network with a hexagonal structure (see fig. 2 and Alarcon et al., 2003). In these simulations, we assumed that initially all the vessels in the network had the same radii. We assumed further that the flow could be described by Poiseuille’s law. Since, this assumption implies a linear relationship between flow rate and pressure drop between the ends of each vessel, we can also use Kirchoff’s laws to calculate the flow rate and other hydrodynamic quantities of interest. The haematocrit in each vessel was calculated from an empirical law that states that at a bifurcation, the ratio of the haematocrits in each of the daughter vessels is proportional to the ratio of their flow rates. Furthermore, it has been found in model experiments with RBCshaped pellets that if the ratio of the flow rates exceeds some threshold value, then all the RBCs pass through the fastest branch (Fung, 1993). Once we know the haematocrit and the hydrodynamic quantities for each vessel, we apply the structural adaptation mechanism Equation (10). This procedure is repeated until the system reaches a stationary state (Alarcon et al., 2003).
Structure of the vascular network used in our blood flow simulations.
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Fig. 2.
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(a)
(b)
Fig. 3. Simulation results for the haematocrit distribution over a hexagonal vascular network. The results shown in (a) correspond to an uncoupled network (i.e. the structural adaptation of the vessels is carried out according to Equation (9), whereas (b) shows the results for a coupled network (vascular structural adaptation according to Equation (10)). The grey scale indicates the amount of haematocrit: lighter grey corresponds to higher haematocrit. See text for details.
The main result we obtain from our simulations (see fig. 3a) is that, as a result of the combination of complex blood rheology, structural adaptation, and uneven distribution of haematocrit at bifurcations, the distribution of both the blood flow and the haematocrit over the network are considerably heterogeneous. The non-uniform haematocrit distribution may have important consequences for the dynamics of the surrounding tissue, since blood-borne oxygen is carried by the red blood cells. This has been studied in Alarcon et al. (2003), where the evolution of colonies of normal and cancer cells growing in response to the extracellular oxygen produced by the (inhomogeneous) distribution of haematocrit was investigated. Our simulations suggest that there may be significant differences between the behaviour of colonies growing under homogeneous and heterogeneous conditions. The dynamics of the cell colony were modelled using a hybrid cellular automaton. Our two-dimensional model consisted of an array of N N automaton elements, which will eventually be identified with real cells. The state of each element was defined by a state vector, whose components correspond to features of interest. To start with, the state vector had three components: (i) occupation status, i.e. whether an element is occupied by a normal cell, a cancer cell, an empty space, or a vessel, (ii) cell status, i.e. whether the cell is in a proliferative or quiescent state, and (iii) the local oxygen concentration.
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The state vector evolved according to prescribed local rules that update a given element on the basis of its own state and those of its neighbours at the previous time step (Alarcon et al., 2003). While cells were considered as discrete entities, the oxygen concentration was treated as a continuous field, as the typical length of an oxygen molecule is very small compared to the characteristic size of a cell. The time evolution of the oxygen concentration was thus governed by a reaction–diffusion equation, with sinks, sources, and boundary conditions determined by the corresponding distribution of cells and haematocrit in the host vasculature. The rules of the automaton were inspired by generic features of tumour growth, such as the ability of cancer cells to elude the control mechanisms, which maintain stasis in normal tissues. They can also alter their local environment, providing themselves with better conditions for growth and, eventually, for invasion of the host organism (King, 1996). In our simulations, we allowed the cancer cells to survive under lower levels of oxygen than normal cells. A well-known, though not exclusive, characteristic of cancer cells is their ability to enter a quiescent state, in which they suspend all activities (including cell division) that are not essential for their survival (Royds et al., 1998). They can remain in this latent state for a period of time, before starving to death. Finally, we incorporated into our model, competition between cancer and normal cells for existing resources, as proposed by Gatenby (1996). Normal tissue is a noncompetitive cell community, since, under conditions such as overcrowding or starvation, feedback mechanisms act to maintain tissue stasis. However, when members of this community become cancerous, a new population, with its own dynamics is formed. For further progression of the transformed population to occur, the tumour cells must compete for space and resources with the normal cells. For further details of our automaton rules, we refer the reader to Alarcon et al. (2003). In simulations involving mixed colonies of normal and cancer cells (see fig. 4 for the initial conditions used in these simulations) we observed two distinct outcomes depending on whether we assumed the haematocrit distribution to be homogeneous or heterogeneous. When the haematocrit was distributed uniformly, the colony of cancer cells (which eventually eliminates the normal cell population) grew until it occupied all the available space (see fig. 5). Furthermore, the pattern of growth was isotropic. By contrast, when the haematocrit distribution was heterogeneous the colony saturated to a maximal size and its pattern of growth was anisotropic (see fig. 6). The above behaviour can be explained as follows. If a cell divides and the new cell is situated in a poorly oxygenated region, it will die within a few iterations of the automaton. Consequently, all viable cells are located
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Fig. 4. Initial conditions for our growth simulations. The white spaces are occupied by vessels, light grey elements are occupied by cancer cells, dark grey elements correspond to normal cells, and black elements to empty spaces.
in well-oxygenated regions of the domain. While the regions in which cells accumulate are rich in oxygen, the amount of oxygen being supplied is finite and can only sustain a certain number of cells. The combination of these two effects with a non-uniform haematocrit distribution leads to the stationary patterns observed in figs. 5 and 6 (see also Alarcon et al., 2003). One of the shortcomings of the model we have presented so far is that there is no feedback between the dynamics of the growing tissue and the adaptation of the vascular structure: the vasculature remains static while the colony develops. In practice, the vasculature remodels itself according to the local needs of the surrounding tissue either via dilation of the lumen (structural adaptation of the radius) as occurs, for example during the inflamatory response, or via angiogenesis, as in the cases of wound healing and tumour growth. As a first attempt at developing a more realistic model, we have introduced into our basic model (Alarcon et al., 2005b) internal dynamics for each of the automaton elements that may occupy a cell. These dynamics account for three different intracellular processes, namely the cell cycle, apoptosis, and secretion of vascular endothelial growth factor (VEGF), a potent angiogenic factor. For details, we refer the reader to Alarcon et al. (2005b). In brief, we assume that when subjected to oxygen starvation (i.e. hypoxia) both cancer and normal cells produce and then release VEGF. Released VEGF diffuses through the tissue and eventually reaches the vessels. There it activates the cells’ proteolytic machinery, causing the basal
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Fig. 5. Three snapshots of the time evolution of a colony of cancer cells under homogeneous conditions (see text for details). We can see that the pattern of growth is fairly isotropic and that the colony grows until it takes over the whole available space. The white elements are occupied by cancer cells. Black elements correspond to either vessels or empty spaces.
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384 T. Alarcon et al. Fig. 6. Three snapshots of the time evolution of a colony of cancer cells under inhomogeneous conditions (the corresponding haematocrit distribution is shown in fig. 2(a). We can see that the pattern of growth is highly anisotropic and that the colony reaches a saturating size. The right panel corresponds to the stationary pattern. The white elements are occupied by cancer cells. Black elements correspond to either vessels or empty spaces.
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membrane of the vessels to be degraded. This increases leakiness of the vessel and enables the endothelial cells to migrate towards the source of VEGF. Rather than modelling tumour-induced angiogenesis in all its complexity, we have assumed that the angiogenic response in a given region can be described in an effective manner by an increase in the radius of the vessels in that region. (Similar approximations are common in the Plant Sciences, where the complex branching structure of the roots is replaced by a cylindrical tube of an equivalent radius.) In our model, growth of a vessel radius is thus indirectly stimulated by hypoxia, and directly stimulated by VEGF. The model we propose to account for the interactions between the vasculature and the underlying tissue involves modifying Equation (10) in the following way: w Rðt þ tÞ ¼ RðtÞ þ Rt log ðPÞ V Qref þ km 1 þ log þ 1 ks , ðEq: 11Þ V0 þ V QH where V is the (local) concentration of VEGF. Equation (11) implies that the metabolic stimulus will be more intense for vessels in hypoxic regions, since in these regions rates of VEGF secretion will be higher. The effect that this modification to the structural adaptation algorithm has on the distribution of haematocrit is shown in fig. 3b. When the effect of VEGF is introduced, vessels in hypoxic regions tend to grow larger under the angiogenic stimulus of VEGF. As a result blood flow through those vessels increases, and therefore more haematocrit is supplied. The net effect of this is a more effective distribution of haematocrit: the red blood cells are more evenly distributed than when the evolution of the vasculature is independent of the surrounding tissue. This effect can be seen by comparing fig. 3a (uncoupled case) and fig. 3b (coupled case). As a consequence, we have shown in Alarcon et al. (2005b) that a colony that is perfused by a vasculature whose evolution is influenced by the colony grows to an equilibrium size that is bigger than that obtained when there is no coupling.
4. CONCLUSIONS The main aim of the research summarised in this chapter is to make clear that accounting for the properties of the vascular system and blood flow is necessary to develop realistic models of angiogenesis. Most of the models currently in the literature concentrate on endothelial cell migration in response to the chemotactic stimulus of the VEGF, and neglect most of
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the aforementioned issues (i.e. blood flow and haematocrit heterogeneity, coupling between metabolic needs of tissue and vascular structural adaptation). However, these phenomena must be taken into account when coupling models of angiogenesis to models of solid tumour growth. The usual assumption is that the local concentration of oxygen or other nutrients is proportional to the local concentration of endothelial cells. We have shown that this assumption may be overly simplistic due to blood flow heterogeneity. In particular, we have shown that when the nutrient concentration is proportional to the local endothelial cell concentration then the growth of the colony is markedly different from that for which blood flow heterogeneity is taken into account (compare figs. 5 and 6). A similar situation arises when modelling chemotherapy. If we assume that the blood-borne concentration of the drug is proportional to the local concentration of endothelial cells, we might overestimate the concentration of drug reaching regions in which blood flow is poor and underestimate the concentration in regions where blood flow is high. As a result, the intrinsic non-uniformity in the spatial structure of many solid tumours may be an important factor in predicting the efficacy of chemotherapy protocols (see Riba et al., 2003).
REFERENCES Alarcon, T., Byrne, H.M., Maini, P.K., 2003. A cellular automaton model for tumour growth in inhomogeneous environment. J. Theor. Biol. 225, 257–274. Alarcon, T., Byrne, H.M., Maini, P.K., 2005a. A design principle for vascular beds: the effects of complex blood rheology. Microvasc. Res. 69, 156–172. Alarcon, T., Byrne, H.M., Maini, P.K., 2005b. A multiple scale model of tumour growth. Multiscale Model Sim. 3, 440–475. Anderson, A.R.A., Chaplain, M.A.J., 1998. Continuous and discrete mathematical models of tumour-induced angiogenesis. Bull. Math. Biol. 60, 857–899. Anderson, A.R.A., Chaplain, M.A.J., 1998. A mathematical model for capillary network formation in the absence of endothelial cell proliferation. Appl. Math. Lett. 11, 109–114. Balding, D., McElwain, D.L.S., 1985. A mathematical model of tumour-induced capillary growth. J. Theor. Biol. 114, 53–73. Breward, C.J.W., Byrne, H.M., Lewis, C.E., 2003. A multiphase model describing vascular tumour growth. J. Math. Biol. 65, 609–640. Byrne, H.M., Chaplain, M.A.J., 1995. Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions. Bull. Math. Biol. 57, 461–486. Edelstein, L., 1982. The propagation of fungal colonies: a model of tissue growth. J. Theor. Biol. 98, 679–701. Folkman, J., 1995. Angiogenesis in cancer, vascular, rheumatoid, and other disease. Nature Med. 1, 27–31. Frame, M.D.S., Sarelius, I.H., 1995. Energy optimisation and bifurcation angles in the microcirculation. Microvasc. Res. 50, 301–310.
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Fung, Y.-C., 1993. Biomechanics. Springer, New York. Gafiychuk, V.V., Lubashevsky, I.A., 2001. On the principles of the vascular network branching. J. Theor. Biol. 212, 1–9. Gatenby, R.A., 1996. Application of competition theory to tumour growth: implications for tumour biology and treatment. Eur. J. Cancer. 32A, 722–726. Gazit, Y., Berk, D.A., Leunig, M., Baxter, L.T., Jain, R.K., 1995. Scale-invariant behaviour and vascular network formation in normal and tumour tissue. Phys. Rev. Lett. 75, 2428–2431. Jain, R.K., 2001. Delivery of molecular and cellular medicine to solid tumours. Adv. Drug Delivery Rev. 46, 146–168. Karau, K.L., Krenz, G.S., Dawson, C.A., 2001. Branching exponent heterogeneity and wall shear stress distribution in vascular trees. Am. J. Phisol. 280, H1256–H1263. King, R.J.B., 1996. Cancer Biology. Longman, Harlow. Kurz, H., Sandau, K., 1997. Modelling of blood vessel development – bifurcation pattern and hemodynamics, optimality and allometry. Comments Theor. Biol. 4, 261–291. LaBarbera, M., 1990. Principles of design of fluid-transport systems in Zoology. Science 249, 992. Levine, H., Pamuk, S., Sleeman, B.D., Nilsen-Hamilton, M., 2001. Mathematical modelling of capillary formation and development in tumour angiogenesis: penetration into the stroma. Bull. Math. Biol. 63, 801–863. Mantzaris, N., Webb, S., Othmer, H.G., 2004. Mathematical modelling of tumour-induced angiogenesis. J. Math. Biol. 49, 111–187. Murray, C.D., 1926. The physiological principle of minimum work, I: the vascular system and the cost of volume. Proc. Natl. Acad. Sci. USA 12, 207–214. Muthukkaruppan, V.R., Kubai, L., Auerbach, R., 1982. Tumour-induced neovascularisation in the mouse eye. J. Natl. Cancer Inst. 69, 699–705. Orme, M.E., Chaplain, M.A.J., 1996. A mathematical model of the first steps of tumour-related angiogenesis: capillary sprout formation and secondary branching. IMA J. Math. Appl. Med. Biol. 13, 73–98. Orme, M.E., Chaplain, M.A.J., 1997. Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. IMA J. Math. Appl. Med. Biol. 14, 189–205. Othmer, H.G., Stevens, A., 1997. Aggregation, blow-up and collapse: the ABC’s of taxis in reinforced random walks. SIAM J. Appl. Math. 57, 1044–1081. Panovska, J., 2004. Mathematical modelling of tumour growth and application to therapy. DPhil Thesis. Oxford. In preparation. Preziosi, L., 2003. Cancer modelling and simulation. Chapman and Hall/CRC. Pries, A.R., Secomb, T.W., Gessner, T., Sperandio, M.B., Gross, J.F., Gaehtgens, P., 1994. Resistance to blood flow in microvessels in vivo. Circ. Res. 75, 904–915. Pries, A.R., Secomb, T.W., Gaehtgens, P., 1995. Design principles of vascular beds. Circ. Res. 77, 1017–1023. Pries, A.R., Secomb, T.W., Gaehtgens, P., 1998. Structural adaptation and stability of microvascular networks: theory and simulations. Am. J. Physiol. 275, H349–H360. Riba, B., Marron, K., Agur, Z., Alarcon, T., Maini, P.K., 2003. A mathematical model of Doxorubicin treatment efficiency in non-Hodgkin’s lymphoma: investigation of the current protocol through theoretical modelling results. Bull. Math. Biol. 67, 79–99. Royds, J.A., Dower, S.K., Qwarnstrom, E.E., Lewis, C.E., 1998. Response of tumour cells to hypoxia: role of p53 and NFkB. J. Clin. Pathol. Mol. Pathol. 51, 55–61.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
21 Towards understanding the physical basis of re-entrant cardiac arrhythmias Oleg V. Aslanidia, Vadim N. Biktashevb, Irina V. Biktashevac, Richard H. Claytond and Arun V. Holdena a
Cardiovascular Research Institute, University of Leeds, Leeds, UK Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK c Department of Computer Science, The University of Liverpool, Liverpool, UK d Department of Computer Science, University of Sheffield, Sheffield, UK b
1. INTRODUCTION Cardiovascular disease causes globally over 5 million premature adult deaths, and in the US, cardiovascular disease is the single most common cause of death. The incidence is lower in less developed countries, but increases as infectious diseases are controlled, nutrition improves, and high-fat diets, smoking, and sedentary lifestyles become more prevalent. Over half of the mortality from cardiovascular disease is due to sudden cardiac deaths (SCD), occurring within 24 h of a cardiac event, usually outside any medical institution. In western developed economies, the annual incidence of premature (age 570 years) adult (age 420 years) SCD is 1 per 1000 inhabitants. Over 80% of SCD are associated with coronary artery disease (Yusuf et al., 2001; Huikuri et al., 2003; Naghavi et al., 2003; Priori et al., 2003). Ventricular fibrillation is recorded in about three-quarters of SCD victims reached promptly by emergency paramedics (Huikuri et al., 2003; Priori et al., 2003). The mechanisms by which heart disease leads to ventricular fibrillation and SCD are complex and varied. The sequence of thrombotic occlusion of a coronary artery, causing acute ischaemia and infarction, followed by the initiation of re-entry in or around regions of prior infarction, is well established, but not universal. An increased 389
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SCD risk also occurs in cardiomyopathies and valvular heart disease, and ventricular hypertrophy; all of which lead to a life-limiting impaired ventricular function, and a life-threatening increased risk of re-entrant arrhythmias. The commonest, immediate cause of SCD is the ventricular tachyarrhythmia or fibrillation that prevents the rhythmic pumping of blood and maintenance of circulation i.e. is an electrophysiological process. The most effective treatment is termination of ventricular fibrillation by electrical defibrillation. This must be within a few minutes, as survival rates from cardiac arrest decrease from 90% within the first minute to less than 5% beyond 12 min (Capucci et al., 2002). This intervention could be by emergency paramedics, or automatic external or implanted defibrillators. Paramedics reach few victims within this time in only a few communities. Automatic external defibrillators that can be operated by untrained bystanders are becoming increasingly available in public areas, such as airports or stations, in developed economies, but can only have a limited impact on overall SCD (Pell et al., 2002). The implantable cardioverter defibrillator (ICD) automatically detects and terminates ventricular tachycardia and ventricular fibrillation (Huikuri et al., 2001; Sanders et al., 2001), is effective but expensive, and only suitable for implantation in high risk patients, who have already survived episodes of VF, or who have depressed ventricular function associated with coronary artery disease. However, although it is possible to identify individual patient groups who have a SCD incidence approaching 10% per year, fewer than a third of all SCDs occur in this small subset of the general population. Most SCDs occur in the much larger, lower risk, population and in 40–50% of victims, SCD is the first sign of heart disease (Huikuri et al., 2001). There is little scope for reducing SCD by improvement in treatment, from the 90% survival from cardiac arrest for defibrillation applied within one minute. There is scope for reducing SCD by reducing the time to intervention, but positioning an automatic defibrillator within a few minutes of most of the population all of the time is clearly impractical even in wealthy societies. Prevention of the arrhythmia, rather than treating it after it occurs, is preferable. Life-style adjustments that reduce their risk factors associated with a sedentary, high cholesterol and obesity-favouring diet, and smoking, are highly effective but difficult to implement in commercially competitive open societies. They could range from education (teaching simple cooking in primary schools), through economic (punitive taxation of tobacco and high fat/sugar/salt processed food products, restrictions on advertising) and social (retain high school playing fields rather than convert them into parking lots, and the encouragement of active rather than spectator sports within the adult community) engineering. Just as much of
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the improvements in life expectancy in the late nineteenth century/early twentieth century Europe were due to public health and civic engineering, driven by economic development, and were not due to developments in medicine, major reductions in cardiac SCD rates require political will rather than medical advances. However, the need for effective and available medical interventions remains. Medical approaches to arrhythmia prevention would have the greatest impact if applied to the large population of perhaps asymptomatic patients at risk for coronary artery disease. They must have a very low incidence of toxic side effects because many more patients would receive preventive treatment than those who would actually benefit by prevention of SCD. Prevention can be targeted at preventing coronary disease and myocardial ischaemic attacks – in patients with coronary artery disease and prior myocardial infarction, beta-adrenergic blocking drugs, angiotensinconverting enzyme inhibitors, n-3 polyunsaturated fatty acids, and aspirin reduce sudden death and mortality: see table 1. Ward and Law (2003) have proposed the combination of a cholesterol-lowering statin, blood pressure lowering drugs (beta-adrenergic blocking drugs, angiotensin converting enzyme inhibitor, and a thiazide, with folic acid and aspirin in a single ‘‘Polypill’’ to be taken daily by all adults over 55 years, with the aim of reducing the incidence of heart disease by 80%. Taking aspirin after a heart attack reduces the likelihood subsequent death from arryhthmia by 23% and a subsequent nonlethal event by about 50% (ISIS-2, 1988): administering this is routine on admission to accident and emergency on suspicion of a heart attack. Many heart attacks that result in infarcts do not lead the victim to seek medical attention, because of denial, or the misconception that after symptoms subside, all must be well. SCD rates could fall by up to 20% if most adults carried soluble aspirin, and responded to the suspicion of a heart attack that may lead to an arrhythmia by taking it even if their symptoms did not convince them to seek emergency treatment. The results of rational antiarrhythmic drug therapies, targeted on the electrophysiology of arrhythmias, based on our understanding of cardiac ionic channel, membrane and cell electrophysiology, specifically targeting the prevention of VF by acting on membrane excitability has been Table 1 Drugs
SCD rates
Beta blockers n-3 fatty acids Ca2þ channel blocker
0.80 0.15 0.90 0.10 1.05 0.10
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SCD rates
Class IA Class IB Class IC (CAST) Dofetilide (DIAMOND) Amiodarone (EMIAT) Amiodarone (CAMIAT) D-Sotalol (SWORD)
1.25 0.25 1.10 0.20 2.35 0.90 0.90 0.10 1.00 0.30 0.80 0.30 1.90 0.80
pathetic – see table 2 (Members of the Sicilian Gambit, 2001a, b; Huikuri et al., 2003; Priori et al., 2003). Antiarrhythmics have been proposed based on their selectivity for membrane channels, e.g. in the Vaughan-Williams classification, class I antiarrhythmics block sodium channels, while class III prolong repolarisation by blocking potassium channels. However, sodium channel blockers and the potassium channel blocker D-sotalol lead to an increase in mortality. Amiodarone, which blocks multiple ionic currents reduces sudden death but has significant toxicities that preclude wide spread administration to a lower risk population. Antiarrhythmics that have sufficient efficacy combined with acceptable toxicity to allow use in large populations remains an important challenge for pharmacology. One of the core beliefs of post-genome biology is the idea that detailed knowledge of the genome will lead, one way or another, to more precise molecular targeting for drug design, giving an increased selectivity and reduced side effects. The current generation of antiarrhythmics provides an example where the most selective drugs are the least effective. Risk stratification, to identify people susceptible to VF can potentially allow application of available therapies to higher risk groups (Priori et al., 2003). Noninvasive electrophysiological methods assessing ambient arrhythmias and heart rate variability from ECG recordings are not effective in predicting arrhythmic death outside of some specific high risk populations (Sanders et al., 2001). Invasive methods, that require endocardial stimulation and recording, such as programmed stimulation, are not suitable for application to the general population. Genetic markers of susceptibility to SCD could allow a molecular approach to risk stratification (Spooner et al., 2001; Naghavi et al., 2003). Here we consider the electrophysiological mechanisms or re-entrant arryhthmias, using membrane and cellular electrophysiology, the histology and anatomy of the heart within virtual tissue engineering (Panfilov and Holden, 1997; Clayton and Holden, 2003), that is combined with the mathematics and physics of nonlinear wave processes in excitable media (Holden et al., 1991; Holden, 1995).
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2. CARDIAC EXCITATION There are a number of published and available models for ventricular excitation that summarise the results of voltage clamp experiments on ventricular tissue and cells (Noble and Rudy, 2001). None of these models are definitive, they all represents steps in an on-going process of modelling the behaviour of different types of ventricular cells by a description of membrane currents and pumps, and intracellular ion binding and concentration changes. Cm
dVm ¼ Iion dt
ðEq: 1Þ
3. CARDIAC PROPAGATION MODELS Cardiac tissue is electrically excitable and supports travelling waves of electrical activation. Propagating action potentials can be described by a non-linear reaction diffusion equation (Clayton, 2001): @Vm ¼ rðDrVm Þ C1 m Iion @t
ðEq: 2Þ
The left hand side of the equation gives the current that flows due to the capacitance of the cell membrane, and the two terms on the right hand side give current flow due to both gradients in transmembrane potential (diffusive term) and current flow through ion channels, pumps, and transporters in the cell membrane (reactive term). Vm is voltage across the cell membrane, Cm is the membrane capacitance per unit membrane area, and Iion is the membrane current flow per unit area. Cardiac tissue possesses a complex fibre-sheet structure (Nielsen et al., 1991), and electrical activation propagates more quickly along fibres than across fibres. The anisotropic diffusion of electrical activation can be modelled in this equation by setting the diffusion coefficient to be a tensor, denoted here by D.
4. 1D VIRTUAL CARDIAC TISSUES The reaction-diffusion Equation (2) in one dimension has a spatially uniform solution, corresponding to resting tissue, and can support solitary wave and wave train solutions. The solitary travelling wave solution has a propagation velocity proportional to the root of the diffusion coefficient,
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and so the diffusion coefficient can be chosen to give appropriate length and velocity scaling. At the higher rate, the action potential duration is shortened, and the action potential velocity is reduced, and the spatial extent (the ‘‘wavelength’’, say measured at 95% repolarisation) is shortened. Thus, although there may not be enough room in the heart for more than one action potential at low rates, as rate is increased by about ten-fold during re-entrant tachycardia, the shorter wavelength may allow more than one action potential. Two travelling wave solutions meeting head on collide and annihilate each other; this destructive interference results from the refractory period of the travelling waves. Supra-threshold stimulation at a point in a uniformly resting one-dimensional model produces a pair of travelling wave solutions that propagate away from the initiation site. The initiation of a single solitary wave in a one-dimensional ring provides a computationally simple model for re-entry; such unidirectional propagation can only be produced in a homogeneous one-dimensional medium if the symmetry is broken, say by a preceding action potential. Figure 2 illustrates the responses of a one-dimensional ventricular tissue model to stimulation at different times in the wake of an action potential. The vulnerable window is the period after a preceding action potential during which a unidirectional wave in a one-dimensional medium can be initiated; stimulation during the vulnerable period in the wake of a plane wave in a two-dimensional medium would initiate a pair of spiral waves. Thus the test pulse in fig. 2(middle) falls into the vulnerable window. Starmer et al. (1993) have characterised the vulnerable window for Beeler–Reuter and FitzHugh–Nagumo models. If the effects of pharmacological agents or pathological processes (ischaemia, acidosis) can be expressed as changes in the excitation system, then repeating the computations of fig. 2 and measuring the width of the vulnerable window 60
200 180
20
APD (ms)
voltage (mV)
40 0 -20 -40 DI
-60
APD
160 140 120
-80 -100 0
100
200
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time (ms)
400
500
100 50
100
150
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DI (ms)
Fig. 1. Action potentials (left) and action potential duration restitution curve (right) for normal (black) and LQT 2 (gray) syndrome modified virtual ventricular cells (Noble and Rudy, 2001; Aslanidi et al., 2002).
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Fig. 2. Response of a one-dimensional virtual ventricular tissue (Biktashev and Holden, 1998) to a stimulus (left) before the vulnerable window (middle) during the vulnerable window, giving retrograde unidirectional propagation and (right) after the vulnerable window.
provides a means of quantifying the pro- or anti-arrhythmogenic effects of these changes.
5. 2D VIRTUAL CARDIAC TISSUES 5.1. Re-entry as a spiral wave In a 2-dimensional excitable medium, the propagation velocity depends on curvature, as well as rate, and a simple idealisation for re-entry is a spiral wave. A spiral wave solution of (2) appears as a circulation of excitation, in the form of an Archimedean spiral, around the core, which acts as an organising centre that imposes its rhythm on the rest of the tissue by emitting propagating waves. In both experimental observations and in numerical investigations with homogeneous, isotropic media, spiral waves need not rotate rigidly around a circular core, but can meander. (Winfree, 1991) In meander, the tip of the spiral wave (defined in experiments by a phase singularity, or the point on a voltage isoline where the wavefront meets the waveback, and in numerical solutions by intersection of isolines of two state variables, say voltage and a gating variable) follows a complicated trajectory. This complicated motion can be classified as biperiodic meander (Barkley, 1990, 1994; Karma, 1990; Biktashev and Holden, 1995, 1996, 1998; Biktashev et al., 1996; Sandstede et al., 1997, 1999; Nichol et al., 2001) nþ1-periodic hypermeander (Winfree, 1991) or deterministic Brownian hypermeander (Biktashev and Holden, 1998; Nichol et al., 2001). We use meander to describe the motion of the tip trajectory for the particular excitable medium, including both rigid rotation and biperiodic motion. The transition from rigid rotation to biperiodic meander is by a supercritical Hopf bifurcation (Barkley, 1990; Karma, 1990) with some specific features due to the symmetry of (2) with respect to Euclidean
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motions of the plane. A method for studying meander patterns reduces Equation (1) by the Euclidean group SE(2) to a generic (without the symmetries of Equation (2)) ODE for tip motion, by moving over to a frame of reference attached to the tip of the spiral (Barkley, 1994; Biktashev et al., 1996; Sandstede et al., 1997, 1999). An equilibrium solution of the ODE generates rigid periodic rotation. Transition from the equilibrium to a limit cycle via a Hopf bifurcation generates the transition from rigid rotation to biperiodic motion; in the biperiodic regime, there are isolated co-dimension 1 resonant parameter sets, with unbounded linear drift of spirals. An invariant n-torus and a chaotic attractor for the ODE generate bounded n þ 1 periodic and unbounded deterministic Brownian hypermeander. This qualitative theory can be extended to consider motion of spiral waves produced by symmetry-breaking perturbations, such as spatial gradients in parameters corresponding to spatial tissue gradients in the expression of membrane channel proteins. For example, if there is a gradient in the parameters, the spiral wave will drift and the drift velocity in the first approximation is proportional to the gradient of parameter. The component of the drift orthogonal to the gradient depends on the chirality (direction of rotation) of the spiral whereas the component along the gradient does not. The theoretical explanation of that is based on the observation that the homogeneous and isotropic reaction-diffusion system is equivariant with respect to the group of Euclidean motions of the physical space. Since the isotropy subgroup of a rigidly rotating spiral wave is trivial, its orbit by the Euclidean group is a three-dimensional manifold of spiral waves with different rotation centres and phases. A small symmetry-breaking perturbation, such as a smooth spatial gradient of properties, then leads to a drift along this manifold with the periodaveraged position and phase described by response functions that are localised around the core of the spiral (Biktashev and Holden, 1995, 1998). Thus there is the outline of a theory for understanding the meander and drift of spiral wave solutions in homogenous and inhomogeneous media, that depends only on the symmetries of (2). Although mathematical analysis can account for the occurrence of meander and drift, to obtain quantitative information about its spatial extent and speed, we require numerical solutions of specific models. Spiral wave solutions for virtual ventricular tissue can demonstrate another kind of biperiodic meander. In these models, the tip trajectory is composed of almost linear segments and sharp turns, and the local wavefront velocity close to the tip of the spiral changes, with slower velocities as the trajectory curves around in sharp turns. This slowing down, with bunching of isochronal lines, appears as a functional partial
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conduction block produced by accumulated Naþ inactivation, leaving Caþþ current to sustain propagation (Biktashev and Holden, 1998). Thus the pattern of meander can be understood in terms of the balance between the kinetics of the two depolarising currents. The excitation wavefront propagates as fast as, and wherever, it can: in re-entry, this is determined not only by the spread of excitation (the depolarising currents and the effective diffusion coefficient), but also the degree of recovery in tissue ahead of the wavefront, i.e. the repolarising Kþ currents. The kinetics and magnitudes of the ionic currents underlying these excitatory and recovery processes differ in congenital syndromes that are characterised by abnormal ventricular action potentials, in different parts of the ventricle, in different species, and in different models of ventricular electrophysiology. The pattern of meander computed for these different virtual tissues can provide insight into the role of individual ionic conductances in meander, allowing the possibility of targeting conductances to change the pattern and extent of meander. Within the functional block or core the membrane potential remains between 45 and 5 mV; this persistent depolarisation means the inward INa is inactivated, blocking propagation into the core.
5.2. Resonant drift The tip of the spiral wave solutions presented in fig. 3 moves irregularly in a complicated trajectory, but does not move out of the medium: if the medium is large enough to contain the early transient motion produced by initiation from a broken wavefront the spiral wave remains in the medium. Small amplitude, spatially uniform repetitive stimulation can be used to produce directed movement of a rigidly rotating spiral, wave, if the period of stimulation is equal to the period of the spiral wave rotation (resonant drift). If the stimulation period is close but not equal to the rotation period of the spiral a circular drift is obtained (Agladze et al., 1987; Davydov et al., 1988; Biktashev and Holden, 1995). If the stimulation period is fixed, this drift is strongly influenced by medium inhomogeneities. In the ventricular virtual tissue model, even in the absence of inhomogeneities, the instantaneous frequency of the spiral is always changing, because of the meander and the slow change of the spiral wave period due to ageing and so a pure resonant drift is not observed at any constant frequency. A typical trajectory, produced by constant frequency perturbation of a meandering spiral, is shown in fig. 4(left). The resultant motion is a nonlinear interaction between the pattern of meander and the motion produced by the perturbations. The directed
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Fig. 3. A spiral wave in a homogeneous, isotropic 2-dimensional cardiac virtual tissue showing the distribution of potential, the tip (solid ball) obtained by the intersection of a voltage (Vm ¼ 10 mV) and calcium current activation variable ( f ¼ 0.5) and (right top) voltage isolines every 2 ms during one rotation and the tip trajectory over many rotations. The wavefront of the action potential is the sharp transition between light and dark shade, and far from the tip of the spiral the wavelength of the spiral (the distance between successive wavefronts) is about 40 mm. The trajectory of the tip of the spiral (right bottom) is not stationary, but meanders, and its motion is nonuniform, moving by a jump-like alternation between fast and very slow phases, with about 5 jumps per full rotation. This motion resembles an irregular, nearly biperiodic process, with the ratio of the two periods close to 1:5.
Fig. 4. Tip trajectories in ventricular virtual tissue (Biktashev and Holden, 1996) produced (left) by periodic perturbations at three different frequencies close to the rotation frequency of the meandering spiral–circular motion would be produced for a rigidly rotating spiral, interaction with meander distorts the circular pattern expected for Lamour drift (right) by repetitive stimulation under feedback control applied at four different fixed delays after the wavefront reached the bottom left corner. The delay determines the initial direction of drift. A repetitive perturbation of 15% the amplitude of the single shock defibrillation threshold produces a directed motion with a velocity of about 0.75 cm/s.
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motion of resonant drift is much more robust if instead of choosing a fixed frequency, some kind of feed-back is used to synchronise the stimulation with the spiral wave rotation (Biktashev and Holden, 1994, 1996). Such feedback control can provide the stable resonant drift, forcing the spiral to a boundary, and extinguishing it (Biktashev and Holden, 1996).
5.3. Self-terminating re-entry Self-terminating ventricular tachyarrhythmias are occasionally observed in clinical practice, and during Holter recording of the electro-cardiogram. Recordings of spontaneous ventricular tachyarrhythmias, including fibrillation, are rare even from patients in intensive or Coronary Care Units – for example, recording from 2462 patients showed 57 examples of spontaneous ventricular tachyarrhythmia, of which 12 self-terminated and 45 were terminated by prompt clinical intervention (Clayton et al., 1993). Idiopathic episodes of syncope are a common reason for referral for electrocardiographic investigation, and a possible cause could be a self-terminating arrhythmic episode. Self-terminating episodes of ventricular tachyarrhythmias may not be exceptional: a lethal episode may be considered as an episode that failed to self-terminate in time. Although they are encountered most commonly during clinical electrophysiology studies, when they have been induced, spontaneously occurring self-terminating tachyarrhythmias have also been recorded. Examples of two such events, recorded from Coronary Care Unit patients, are shown in fig. 5. Until they self-terminate, the electrocardiographic signals are virtually indistinguishable from those of tachyarrhythmias that are terminated by a defibrillating shock, or are lethal. Understanding the mechanisms that terminate these episodes is important since a pharmaceutical agent capable of encouraging self-termination would be of enormous clinical value. Although these episodes could be sustained by repetitive discharge of an ectopic focus, the rapid frequency of between 4 and 8 Hz suggests a re-entrant mechanism. Re-entry can terminate by different mechanisms. One is if the region of unidirectional conduction block at the center of the re-entrant circuit is enlarged. Oscillations of the period of re-entry in both 1-dimensional virtual tissues (Hund and Rudy, 2000) and patients (Frame and Rhee, 1991) have been observed, and this is a potential mechanism to explain self-termination. Alternatively, the propagation wavefront may slow down, stop and dissipate, or restart (Biktashev, 2003; Biktasheva et al., 2003).
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Spontaneous occurring episodes of self-terminating ventricular fibrillation (Clayton et al., 1993; Aslanidi et al., 2002).
Another mechanism, derived from the point of view of nonlinear wave propagation in excitable media, corresponds to either movement of the re-entrant core to an inexcitable boundary or movement of the cores of a pair of re-entrant waves so that they annihilate each other. Meander to an inexcitable boundary has been proposed as an explanation for the relative lethalities of the different inherited long QT (LQT) syndromes. These LQT syndromes are characterised by lengthening of the ventricular action potential (as seen in fig. 1), resulting in a prolonged QT interval in the electrocardiogram, and are associated with an increased risk of ventricular tachyarrhythmias, and of early, sudden death. They are rare but intensively studied syndromes, and mutations at loci that give rise to the syndrome have been identified. LQT1 results from mutations in the KVLQT1 gene encoding a subunit of the IKs potassium channel; LQT2 from mutations in the HERG gene encoding a subunit of the IKr potassium channel; and LQT3 from mutations in the SCN5A gene encoding the sodium channel (Splawski et al., 1998). Although different mutations have different effects on kinetics, the LQT1 and LQT2 mutations result in a loss of Kþ channel function and a reduction in the total maximal Kþ conductance, while LQT3 mutations result in failure to deactivate in a small fraction of Naþ channels, giving a persistent Naþ current. These mutations all produce similar increases in the action potential duration, but can have radically different outcomes: although the death rates for the syndromes are similar, an arrhythmic event of LQT3 is five times more likely to be lethal than an episode of LQT1 (Zareba et al., 1998). This implies that LQT1 episodes are five times more likely to self-terminate.
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A possible mechanism for this difference in the probability of selftermination of arrhythmic episodes in the LQT syndromes is (Clayton et al., 2001) that meander in LQT1 tissue is greater, and so more likely to reach an inexcitable boundary. In a slab of real tissue, the minimum distance between the initiation site of a re-entrant wave and the inexcitable boundaries enclosing it has effectively a random value, and the wave moves in effectively random direction. The larger the extent of meander, the more likely it is that the core will reach a boundary within a given time, in whatever direction it is, and extinguish the re-entrant wave. Spatial inhomogeneities also produce drift of the spiral – depending on its direction this drift could facilitate or retard motion towards a boundary. Thus, the spatial extent of meander (quantified by the radius of the smallest circle completely enclosing the tip trajectory during one second of rotation) provides a measure of the likelihood of the spiral wave being extinguished by reaching an inexcitable boundary within some given time. Virtual tissue modifications for LQT1, LQT2, and LQT3 showed that although the vulnerable window of homogeneous, isotropic, LQT virtual tissues were not greater than that of the normal tissues, the spatial extent of meander in LQT1 virtual tissue was 2–5 times greater than the spatial extent of meander in LQT2 and LQT3. In LQT1 tissue, the spatial extent of meander continued to increase with time. For both the Oxsoft and the Luo-Rudy ventricular cell models, the spatial extent of meander is greatest in LQT1 and least in LQT3. The repolarising Kþ currents in the Oxsoft and Luo-Rudy family of models for ventricular excitation have different magnitudes; in the standard Luo-Rudy model GKs 4 GKr, and so reduction of GKs has the larger effect on action potential duration. In the Oxsoft model GKs 5 GKr, and so reduction of GKr has the larger effect on action potential duration. In spite of the opposite effect on action potential duration in the Oxsoft and Luo-Rudy models, changes in GKs in LQT1 always produce the largest extent of meander. The spatial extent of meander does not simply reflect the action potential duration, but depends on the detailed kinetics of the repolarising currents. This suggests GKs as a target for producing changes in the extent of meander.
5.4. Pharmacologically enhanced self-termination In principle, it would be possible to selectively and differentially block both GKs and GKr, for example, the Kþ channel blocker Chlofilium is a proarrhythmic agent that is used to produce induced LQT syndrome and torsade de pointes in an in vivo rabbit model. Figure 6 presents the
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1 mm
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GKr (%) 75
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GKs (%) Fig. 6. Tip trajectories of spiral waves in LQT 1 and LQT 2 virtual ventricular tissues embedded in the parameter space of the conductances GKs and GKr (Aslanidi et al., 2002). Established rotation of a spiral wave initiated with the phase distribution method is followed over 1 s in a 3 mm square region of the virtual tissue. Numbers at the axis indicate the percentage of the respective conductances for each column and row of the trajectories.
meander during 0–1 s after initiation by the phase distribution method in an 8 cm square, two-dimensional virtual tissue obtained with separate and combined blocks of these two separate Kþ conductance systems. The largest increase in meander shown here is with 70% block of model GKs. For panels where no meander is displayed, it was not possible to initiate a sustained spiral wave in the 8 cm square medium. The spatial extent of the meander can be measured by the minimum radius of the circle that completely encloses the meander pattern: fig. 6 plots this measure for LQT1 and LQT2 Luo-Rudy virtual tissues, with different degrees of block of GKs and GKr: as in virtual tissues based on the Oxsoft model, the largest meander is produced by maximal block of GKs.
6. 3D MODELS 6.1. Ventricular wall as a slab Microelectrode recordings from cells and tissue isolated from endocardial, mid-myocardial, and epicardial regions of the ventricular wall of many
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species show marked differences in action potential shape (cells and tissue isolated from close to ventricular epicardium tend to have a pronounced notch following the upstroke of the action potential) and duration, as well as differential responses to changes in pacing cycle length, pharmacological intervention, and pathophysiology. The most prominent differences between endocardial, M, and epicardial cells are differences in the voltage dependent Ca2þ independent transient outward current (Ito), and the slowly activating delayed rectifier current (IKs). Multiple mechanisms can underlie breakup of re-entrant waves (Fenton et al., 2002), and these include intrinsic 3D instabilities (Biktashev et al., 1994), steepness of the APD restitution curve (Qu et al., 1999, 2000), and the effects of rotational anisotropy in the ventricular wall (Fenton and Karma, 1998). A transmural gradient in APD is able to destabilise a re-entrant wave with a filament that is oriented transmurally (Clayton and Holden, 2003). Re-entry had a different period in regions with different APD, and so the re-entrant wave became twisted and was pulled apart (Mikhailov et al., 1985).
6.2. Re-entry with an intramural filament The effects of transmural differences in cell properties on re-entry with a filament aligned intramurally within the virtual ventricular wall composed of uniform epicardial tissue, or endocardial and epicardial layers, and with endocardial, M cell and epicardial layers have been characterised (Clayton and Holden, 2003) The re-entrant wave in the homogeneous tissue was stable, and persisted throughout the duration of the simulation. The virtual tissue with layers of endocardial and epicardial tissue also supported re-entry, but the longer APD of the endocardial layer acted to push the tip of the clockwise re-entrant wave towards the bottom of the virtual tissue, corresponding to the ventricular apex where it was extinguished. This effect occurred before the simulation with a layer of M cells. The longer APD of the M cell region caused the wave to meander first towards the apex and then towards the base, where it was extinguished. These simulations are consistent with other computational and experimental studies that show how parameter gradients can impose motion and instability on re-entrant waves. The potentially powerful influence of an M cell region on the motion of intramural re-entrant waves revealed by our simulations could be exploited as a mechanism to encourage self termination of re-entrant arrhythmias (Aslanidi et al., 2002), and also suggest the Purkinje fibre–endocardial tissue interface can also provide a route to self-termination of intramural filaments.
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Fig. 7. Spiral waves 200 ms after initiation in a slab of virtual ventricular tissue (a) simple scroll in homogenous isotropic slab; twisted scrolls (b) in isotropic slab with transmural heterogeneity in APD (c) in homogeneous anisotropic slab and (d) in anisotropic slab with transmural heterogenity in APD.
6.3. 3D re-entry with a transmural filament To investigate the effect of transmural differences in APD and anisotropy on the behaviour of re-entry with a filament aligned transmurally, we initiated re-entry in isotropic and anisotropic 3D slabs with dimensions 40 40 10 mm. Each slab had layers of endocardial, M cell, and epicardial tissue of equal thickness. For the isotropic slab, we set D to be 0.1 mm2 ms1. In the anisotropic slab fibres rotated through an angle of 1208 between the endocardial and epicardial surfaces, and we set the transverse and longitudinal components of the diffusion tensor to be 0.05 mm2 ms1 and 0.2 mm2 ms1 respectively. We initiated re-entry by imposing an Archimedian spiral on the virtual tissue as an initial condition. Figure 7 shows snapshots of re-entry in the homogeneous and heterogeneous isotropic and anisotropic slabs. In the isotropic slabs, re-entry remained stable for the duration of the simulation, which was 1 s. Despite the stability of re-entry, the shape of the activation surface in the heterogeneous isotopic slab was not smooth. Sites in either the epicardial or endocardial layers activated first, and activation spread into the M cell layer. The overall effect was as if activation in the endocardial and epicardial was pulling activation in the M cell region around the filament. In the anisotropic slab, this effect was more pronounced, and a short period of transient breakup was observed between 300 and 600 ms after initiation. In this period, activation in the epicardial layer broke away from activation in the M cell layer. Breakup in the anisotropic model could have resulted from decreased transmural coupling, or from the effect of rotational anisotropy.
7. WHOLE VENTRICLE 7.1. Re-entry and fibrillation in whole ventricle The detailed canine ventricular anatomy and fibre orientation available from the University of Auckland (http://www.cmiss.org) provides a finite
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Fig. 8.
Voltage isosurface and filaments 1s after initaition of re-entry in right ventricular wall in canine virtual ventricle (Clayton and Holden, 2004).
Fig. 9.
Changes in the number of filaments with time, following initiation of re-entry as illustrated in fig. 8, in the right and left ventricular walls, and in the septum.
element description of both shape and fibre orientation that can be sampled on a regular Cartesian grid to give a ventricular geometry with 5 106 grid points (Clayton and Holden, 2002). To investigate the effect of VF originating in different locations, re-entry was initiated in the LV free wall, RV free wall, and septum by stimulating the base while maintaining a line of block running from base to apex for 120 ms. Filaments were identified from the intersection of Vm ¼ 20 mV and dVm/dt ¼ 0 isosurfaces, and constructed from connected voxels. The filament length, and the locations of each end (unless it was a closed ring) were also recorded. By comparing the overlap of filaments in two successive timesteps we can identify the birth, death, bifurcation, amalgamation, and continuation of filaments, and
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quantify filament dynamics (Clayton and Holden, 2002). Figure 9 presents a snapshot of the pattern of fibrillation 1 s after initiation in the septum, as a voltage isourface and as filaments. Following breakup of the initial; re-entrant wave, the number of filamants increased, and at any point in the ventricle the action potentials became shorter and more irregular. Figure 9 shows how the number of filaments increased during each simulation. Between 500 and 1000 ms after initiation in the LV free wall, the number of filaments increased at a rate of up to 70 s1. Following initiation in the thinner RV free wall and septum, the rate of breakup was about half of this value. All three simulations approached a steady state beyond 1500 msc where the number of filaments in each simulation fluctuated around a mean value of 36. The location at which VF is initiated effects the rate of breakup, but not the eventual number or the dynamics of filaments. The breakup of functional re-entry to multiple wavelet VF is rapid, and suggests that the number of filaments could increase from 1 to around 40 in less than 1 s during the early stages of VF. Breakup by other mechanisms may result (Karma, 1993; Holden et al., 2004) in different rates of filament multiplication. Nevertheless, experimental studies also suggest that the breakup of a single re-entrant wave into fibrillation can occur within a few cycles, and this has implications for any therapy that attempts to provide an early intervention. One of the main findings is that during breakup, the balance of filament creation and filament destruction could be extremely finely poised. Other large scale simulations of fibrillation in 3D using other models suggest that this type of dynamics is not dependent on the model that we have used (Panfilov, 1995, 1999) and that it is likely to be a generic feature of complex 3D re-entry. Several questions remain to be answered, including identifying which parameters are important in determining the balance of creation and destruction, and determining the influence of regional differences in both cell and tissue properties. Strategies that can alter this balance may be effective for antiarrhythmic and antifibrillatory therapy, and this balance may also be important in determining the success and failure of defibrillation shocks.
ACKNOWLEDGEMENTS Research in the Computational Biology Laboratory, University of Leeds, is funded by project and programme grants from the MRC, EPSRC, and British Heart Foundation.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
22 Reflections on the quantitative analysis of liver fibrosis in biopsy specimens Nicola Dioguardi Scientific Direction, Istituto Clinico Humanitas, IRCCS, Rozzano, Milan, Italy and ‘‘M. Rodriguez’’ Foundation – Scientific Institute for Quantitative Measures in Medicine, Milan, Italy
1. INTRODUCTION These reflections are based on some discussions that arose during our attempts to identify a quantitative method of analysis for the metric evaluation of the fibrosis characterising the histological picture of a liver biopsy during the course of chronic virus-related liver disease. The initial three-dimensional configuration of this newly formed structure appears as a dispersed set of collagen fibres. During the course of the disease, the newly formed collagen tends to evolve into a single collagen mass called fibrosis as a result of the splicing of the distal ends of the growing fibres fuelled by the chronic inflammatory process. The morphological irregularity that is part of the complexity of the collagen elements making up liver fibrosis, and the susceptibility of these elements to changes in shape and size depending on the scale at which they are observed, mean that the traditional metric methods based on Euclidean geometry and the additiveness of classical physics can only provide approximate measurements. The same properties also make it difficult to identify a suitable measure that would allow the discrimination of (numerical) differences in size and the recognition of relationships between objects and between evaluations. Due to its irregular shape, collagen tissue occupies a space whose dimension is different from the one-, two-, or three-dimensional nature of the objects typical of Euclidean geometry. This difference makes the spatial dimension the basic element of systems for measuring irregular objects insofar as the interaction between the object and the unit of measurement 411
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is a function of the law of additiveness, and therefore also of the dimensional equality between the object and the unit of measurement. In other words, the measurement of irregular objects requires the use of a metric unit whose dimension is the same (or as close as possible) as that of the object to which it is applied. Bearing in mind this principle of reciprocity between space and metre, as well as the rules of measurement theory suggested by the geometries of irregular bodies, we have devised a method of quantifying the objects whose complexity excludes them from the measures based on the canons of Euclidean geometry (Dioguardi et al., 2003). On the basis of these premises, and without wishing to write about the psychology of shape or topology, we have perceived (become aware of ) the ‘‘observable’’ using some concepts taken from the following points of scientific rationale: (1) Geometry and its subjective perceptions were used when we evaluated biopsies on the basis of purely qualitative and semi-quantitative concepts for diagnostic purposes, whereas we have used the objective perceptions of the purely quantitative concepts of metric measurement to evaluate the two-dimensional metric space occupied by the normal and pathological elements present in hepatic tissue. (2) Gestalt: Gestalt is useful in studying multi-part configurations that cannot be understood in their entirety as a simple summation of their parts. Such objects are characterised by an organisation of parts so that a change in one part brings about a fundamental change in the entire entity. This change cannot be attributed to the addition or subtraction of characteristics but involves the emergence of a new order in the object. (3) Topology by means of the properties that are conserved during the deformations of shape, led us to define the relationships between the parts, and between them and the system as a whole. (4) A phenomenological view allowed us to study the essence of the observable that cannot be revealed by an empirical approach or simple lists of data. It thus provided us with a logic for identifying the significance to be attributed to the shapes of the structures on the basis of (not only pathological) historical events and the general laws of physics (diffusion, dilation, compression, and infiltration) inducing their current configurations.
2. THE STATE OF THE ART OF EVALUATING FIBROSIS The first classification of the forms of chronic hepatitis was the canonical foundation stone of modern hepatology (De Groote et al., 1968). It fuelled the identification of endogenous and exogenous aetiological factors, a new
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understanding of their pathogenesis, the elucidation of their clinical and biochemical signs and symptoms, and the description of histological details for disease grading and staging. The need for rigorous verifications of the effects of new antiviral molecules has for some time required the replacement of semi-quantitative estimates (whose subjectivity has led to them being widely criticised) by purely quantitative (metric) concepts (Scheuer, 1991; Desmet et al., 1994; Feldmann, 1995; Hubsher, 1998; Rosenberg, 2003). The aim is to define statistically their therapeutic effects not only on aetiological agents and biochemical homeostasis, but also on the tissue lesions characterising the course of viral hepatitis. The key for this control during the course of chronic disease is to evaluate biopsy specimens of the scars due to chronic hepatocyte necro-inflammatory lesions (Desmet, 1996; Bravo, 2001; George, 2001; Imbert-Bismut et al., 2001; Oh and Afdhal, 2001; Rosenberg et al., 2002; Schuppan et al., 2001; Forns et al., 2002; Lagging et al., 2002). In (twodimensional) histological liver slices, fibrosis appears during its growth as highly wrinkled Sirius Red areas in liver tissue (fig. 1), which are evaluated using Knodell’s score (Knodell et al., 1981) or one of its subsequent modifications (Chevallier et al., 1994; Ishak et al., 1995; Bedossa and Poynard, 1996; Scheuer et al., 2002) on the basis of semi-quantitative concepts. Using this family of scores, hepatology has tried to give systematic order to the forms of chronic hepatitis by dividing the histological pictures of liver biopsies into classes labelled by ordinal numbers on the basis of the severity of the morphological lesion. The subjectivity characterising these methods makes it difficult to include in different classes, elements belonging to the same whole which, except for their diversity, are attributed a common morphological significance. Despite these limitations, semi-quantitative evaluations are widely used in hepatological disciplines to define therapeutic plans and decide on alternatives. The records of fibrosis provided by classical morphometry (Chevallier et al., 1994; Kage et al., 1997; Pilette et al., 1998; Masseroli et al., 2000; Wright et al., 2003) are also approximate because the wrinkledness of its pieces, i.e. the collagen islets (fig. 1), makes them incommensurable with the smoothness of standard metric tools. In geometrical terms, the intermediate non-integer spatial dimension of pieces of wrinkled collagen fibrosis impedes its interaction with the Euclidean topological integer spatial dimension of standard international measurements. Other attempts to quantify the elements of liver collagen have been made by defining the fractal dimension of collagen islets (Dioguardi et al., 1999, 2003; Grizzi and Dioguardi, 1999; Dioguardi and Grizzi, 2001; Moal, 2002),
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Fig. 1. Sorting of the collagen isles. Catalogue of all the collagen islets automatically recognised and ordered in terms of their magnitude.
but this is independent of magnitude and so the non-integer expressing the fractal dimension can only indicate the change in location between two Euclidean dimensions of the space filled by the irregularly shaped object as a function of the changes of its irregularity. In other words, the fractal dimension is the main property characterising the degree of irregularity of an object regardless of its magnitude. In conclusion, the quantitative study of new antiviral therapies is faced with the problem of the inadequacy of evaluating their effects on fibrosis
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on the basis of the histological pattern of a bioptic sample. This is due to the inconsistency of the inequalities identified by the current methods of evaluation, as semi-quantitative analyses can be considered descriptions that use numbers in the form of words; the fractal dimension is an index of complexity; and standard morphometrical measurements are little more than an attempt to simplify the complexity of the histological image of fibrosis using the razor of Occam.
3. THE NATURAL HISTORY OF MATURATION I believe the fact that the hepatological area clearly raised the need for quantitative concepts in order to evaluate the effects of new molecules (Scheuer, 1991; Feldmann, 1995; Hubsher, 1998; Rosenberg, 2003) goes beyond simple therapeutic requirements and has a much more general significance. This conclusion can be reached if it is accepted that the maturity of a discipline is represented by the quantitative concepts it uses, without the prejudice that this idea forms part of the legacy of eighteenth century physics (Rosenblueth, 1971). This thesis was sustained by Feigl (1956), who considered that the maturational course of a science is marked by a hierarchy going from purely qualitative or classificatory logical concepts, to semi-quantitative or ordering concepts, and finally, purely quantitative or metric concepts. Consideration of the evolution of the hepatological sciences during the end of the second half of the twentieth century suggests that it went through its initial phase of maturation in the second half of the 1960s, when it classified the forms of chronic hepatitis in purely qualitative terms (classifiers on the basis of the discrimination of differences) as persistent and aggressive, active and non-active, and subsequently added chronic lobular hepatitis. The second phase began in the 1980s with Knodell, who used semiquantitative concepts in the tendency to order and simplify the classified diversities. The discipline entered the third and more mature phase when it started using purely quantitative metric concepts, i.e. by considering only what could be measured as ‘‘observable’’ (Rosen, 1979), while recognising the existence of what cannot be measured. The third phase of the process of maturation coincided with the development of an awareness of two canonical factors: the first was the concept of quantity, according to which similar things can be intrinsically (quantitatively) different while preserving their similarity; the second was the concept of the quality of objects, or the set of (determinant) characteristics that can be evaluated using objective
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methods of measurement, such as their number, extent and type, their dynamic movement, and their Euclidean or fractal dimensions. In our case, we became aware that knowing fibrosis does not mean either admitting the existence of a large number of collagen islets in a liver affected by chronic hepatitis, or in seeking to reduce these pieces to a single whole, but above all identifying its concentration in the histological pattern on the basis of the number and metric parameters of the collagen islets making it up. Using metric methods of measurement, hepatology has discovered that complexity is not only a generic semantic term for defining the status of living matter when, among other things, it is wanted to indicate its incommensurability, but a concrete physical value that needs to be measured.
4. COMPLEXITY AND HOW TO DEFINE IT There is no definition of complexity because it does not have an epistemological statute (Morin, 1985), and is devoid of the norms and rules that would assimilate it to the notions considered, as belonging to scientific areas. It can only be said that, although not forming part of any theory, it belongs to the physical, biological, and medical sciences because it is capable of indicating the type of organisation of living and non-living matter (Dioguardi, 1992). The outline of a promontory or continent is complex, as is the profile of a mountain peak and the conformation of its rocks, the shape of a tree, or a collagen islet in inflamed liver tissue, or a mathematical fractal constructed using a computer (fig. 2). The concept of complexity is different from that of complication: a manmade machine is complicated, whereas all natural living and non-living objects are complex. The components of even the most complicated machines have smooth and even shapes that can be divided into identical fractions according to the statute of Euclidean geometry, which is based on the criteria of additiveness and divisibility of linear mathematics. The smoothness of these objects gives them that kind of invariance of scale that is a fundamental canon of Euclidean geometry and makes them measurable (quantifiable) using the same type of unit of measurement. However, studying collagen covered areas begins with the knowledge that they are objectively characterised by other properties dependent on the bizarre complexity of their configuration, which occupies a space whose characteristics cannot be expressed using the definitions, axioms, and unequivocal postulates of the geometry of Pythagoras, Plato, and Euclid.
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Fig. 2. Classical examples of natural fractal and mathematical objects (computer generated). a. tip of a mountain; b. isle; c. tree; d. hepatic collagen, pieces of the organ’s fibrosis; e. inflammatory cell cluster; f. mathematic fractal (computer-constructed with iterative procedure).
This complexity means that their metric study requires the consideration of more general invariance than those of classical metrics. As there is no definition of complexity, studying the space occupied by institutionally complex natural objects means that it is necessary to construct a statute capable of defining this characteristic and giving it a sense that can be used to abstract measurable properties. In the case of the metric study of collagen islets, their irregular shapes were extracted from their complexity. Scheme 1 shows the terms of the statute constructed in order to abstract measurable parameters of the irregularity of the areas of collagen making up the fibrosis found in a bioptic specimen, from its fractal dimension to its tectonics (Bogdanov, 1921), from its perimeter to its area and then to its wrinkledness, which is the canonical property of all irregular objects.
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irregularity
form
spatial
tectonics
distribution
fractal dimension
perimeter length
area extension
wrinkledness
Scheme 1
4.1. The fractal characteristics of a collagen islet A key problem in obtaining repeatable metric recordings of the liver fibrosis, which on the cut surface of a liver histological section, appears as numerous, irregular Sirius Red-stained areas (Junqueira et al., 1979), is to reduce the bias that is generated when the regular tools of the international systems of measurement (designed for topological or Euclidean dimensions) are confronted by the irregularity of fibrous objects. This can only be done using with an ad hoc metre capable of reflecting the specific irregularity of every collagen islet forming the fibrous mass (fig. 1). These elements of collagen are not pure but statistical fractals (Mandelbrot, 1982; Dioguardi et al., 2003). The non-integer dimension (also known as the fractal or Hausdorff dimension (Hausdorff, 1919)), is a property common to all fractal objects insofar as their physical (spatial) configuration is defined by the inequality D4D , where D is the fractal and D, the topological dimension (Mandelbrot, 1982; Hastings, 1993; Bassingthwaighte et al., 1994; Rigaud et al., 1998). When they are fracted, these objects produce pieces that are ‘‘kind of like’’ the whole (Mandelbrot, 1982; Hastings, 1993; Bassinghtwaighte et al., 1994), i.e. their irregularity is
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5.0 4.5 4.0
log(A1/2Dp)
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
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log(P)
Fig. 3. Self-similarity of the collagen islets. This property was evaluated using the geometrical parameters of all the collagen isles identified by means of the pattern recognition in a prototypical case. The patient was affected by cirrhosis. The points closer to the regression line have a higher self-similarity than those farther away.
statistically similar to the irregularity of the whole (in our case, the entire fibrous mass). This property is what fractal geometry calls self-similarity. The self-similarity of the collagen pieces was identified using the power law P ¼ x A1=2DP , where P is the perimeter and A the area of the examined object (both calculated on the same fixed scale), x the scaling factor, and DP the fractal dimension of the perimeter. In fig. 3, the points obtained using this power law indicate the collagen islets. Their distance from the straight line indicates the degree of their statistical self-similarity detected in a prototypical, with the points that are further from the straight line representing those that are less self-similar. Increasing the number of less self-similar elements creates patterns that express the changes in the state of the collagen caused by the dynamics of the pathological process, and was used to identify the collagen islets dispersed in the liver tissue belonging to the chronic inflammation scar system. Like all natural objects, collagen islets are characterised by the limited significance of their fractal condition due to their lost levels of meaningful self-similarity above and below a fixed-scale cut-off point. This kind of asymmetry makes them asymptotic fractals (see fig. 4).
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log(Nµ)
Fractal Dimension Window
∆µ,D
log(1/µ)
Fig. 4. Geometrical definition of the asymptoticity of a statistical fractal. The solid line describes asymptotic fractal behaviour (the asymptote is represented by the dashed line) and the dotted line geometrical fractal behaviour. indicates the difference between the asymptote of the perimeter function and the fractal contour function.
On the basis of the knowledge, collagen islets have been considered planar asymptotic fractals (Rigaud et al., 1998) whose perimeters tend to a finite value. The dimensions of these fractals are indicated by the symbol D. This allows irregular objects to be measured by constructing a real physical unit of measurement with dimensional characteristics very near to the dimension of the objects themselves. The scaling effect (Mandelbrot, 1982; Hastings, 1993; Bassingthwaighte et al., 1994; Dioguardi et al., 2003) is another fractal property of collagen islets insofar as the scale at which they are observed greatly influences their shape and size, i.e. at higher magnification they reveal details of their wrinkleness that would otherwise be hidden. The details of the contours and surfaces of irregular objects determine the stick length effect on the measurement on the basis of the principle that shorter the stick, longer the perimeter or broader the surface. Consequently, the only way to ensure the reproducibility of their measures is to define rigorously both the scale of observation and the length of the stick. Empirical observations have shown that, under our experimental conditions and the most adequate scale being 200 microscopic enlargements, the stick length is rectified for every single case.
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4.2. Construction of the ad hoc metre As explained above, the irregular shapes of liver collagen islets are excluded from the domain of Euclidean dimensions. The planar irregular islets fill intermediate spaces that can be discriminated using fractal dimensions expressed by non-integer numbers. This condition makes them incommensurable with the standard metre defined by Euclidean dimension 1, and so they can only be rigorously measured using units of measurement adapted to their intermediate non-integer dimension. For this purpose, the wrinkled line was viewed as an expression of a straight line over dimension 1 that does not reach dimension 2 and the corrugations of the irregular planes as an expression of the regular plane over dimension 2 that does not reach dimension 3. The formalisation of this concept, which considers the length of an irregular object as a dilation of a regular straight line, was made using the general dilation formula: 1: S ¼ sð1 þ ltÞ where s and S are respectively the length before and after dilation, l the dilation coefficient when the object has the form of a line, and t is the temperature. The expression in brackets is called the binomial linear dilation factor. Formula 1 was adapted to a geometrical form, as shown in 2: 2: L ¼ l 1 þ ð m,DÞ where l and L are respectively the morphometrical and the rectified length of the perimeter, and is a factor that is dependent on the fractal dimension D and m is the stick length used for the measurement. Some of the physical parameters of liver fibrosis were measured using this new metric unit, which is capable of interacting with the irregular contours of the Sirius Red-stained collagen islets distinguished by means of the pattern recognition of the histological slices of bioptic samples (see fig. 1). In conclusion, the power of resolution that makes the measuring unit (metre) capable of detecting quantitative information about the state of each single collagen area (whose irregularity excludes the use of Euclidean geometry) is given by rectifying the standard metre of the international system by an elongation factor calculated from the fractal dimension of the object being measured. This fractal rectification is the crucial novelty of this method, and makes the one-dimensional Euclidean metre come fairly close to a unit capable of measuring the irregularities of every
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plane object that cannot be measured using the standard linear metre. This ‘‘fractalised metre’’ provides scalars that are the closest to the real magnitude of irregular objects, excluding any subjective apportionment.
4.3. Internal control estimate We have controlled for any effects due to the surgical or technical manipulation of the histological preparation. In order to obtain the correction by means of the internal control, we investigated the ratio: L=l pffiffiffiffiffiffiffi pffiffiffiffiffiffi where L equals AH and l equals aH . The former indicates the side length of the mean squared area of all the hepatocytes (the most representative and repetitive liver cells) in the tissue slide, and is indicated by the symbol AH; the latter corresponds to the side length of the mean squared area of 3000 apparently disease-free hepatocytes, and is indicated by the symbol aH. In this ratio, l corresponds to 15.85 mm. In our laboratories, we refer to this reference unit (approximated to 16 mm) as the jm, a symbol derived from the two words, jecur (in Latin ¼ liver) and metre (measurement). The ratio L/jm expresses the possible systematic bias of the measurements of the slide components due to surgical or technical handling; its inverse ratio jm/L indicates the corrective factor of the rectified measure.
4.4. Some results Tables 1 and 2 show the measurements of the perimeters and areas covered by fibrosis in the liver biopsy samples of three subjects (one without inflammatory lesions, one with chronic hepatitis, and one with HCVrelated cirrhosis) obtained using traditional morphometry and our new metre, and clearly shows the differences resulting from dimensional rectification. The numerical data of the perimeter and area were used to define a new parameter called wrinkledness which, regardless of the size and amount fibrosis, is being studied in order to verify the parameters influencing it (table 3).
4.5. New facts learned The method provides objective and rigorous measures by considering the irregular components of liver collagen as asymptotic fractals, thus making
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Table 1 Outline values of four prototypical cases Fibrosis estimation Quantitative measurements Qualitative evaluation
Pm
Pmf
No fibrosis Minimal inflammation Extended inflammation Cirrhosis
182.06 507.50 763.31 1177.93
483.37 1441.59 2315.78 4146.31
Dp index 1.37 1.41 1.45 4.56
Pm ¼ morphometrical perimeter (mm); Pmf ¼ fractal corrected perimeter (mm); Dp ¼ fractal dimension of the morphometrical perimeter. Table 2 Surface values of four prototypical cases Fibrosis estimation Quantitative measurements (mm2) Qualitative evaluation
% AM
% AMF
AB
DA index
No fibrosis Minimal inflammation Extended inflammation Cirrhosis
2.26 3.66 6.38 12.89
2.65 4.13 6.88 13.44
4.83 12.63 13.80 9.93
1.40 1.49 1.53 1.63
AM ¼ morphometrical area (%); AMF ¼ fractal corrected area (%); AB ¼ biopsy area (mm2); DA ¼ fractal dimension of the morphometrical area.
Table 3 Wrinkledness values of four prototypical cases Fibrosis estimation Quantitative measurements Qualitative evaluation
W index
No fibrosis Minimal inflammation Extended inflammation Cirrhosis
381.24 563.40 670.90 1012.77
it possible to evaluate the true area of a biopsy using an ad hoc metre. It identifies the nearest-to-reality length of the perimeter and extension of the area of collagen islets, thus making it possible to define and observe their wrinkledness (Dioguardi et al., 2003), a new parameter obtained from the
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ratio between the perimeter and the square root of the area. Wrinkledness affects the shape and size of collagen islets and, at high magnification, reveals details that are not perceptible at low magnification (the scaling effect). This makes it indispensable to define rigorously, and at an appropriate resolution, both the scale of observation and the length of the stick used as the unit of measurement. In our case, the measurements were made using at 200 microscopic enlargements. The geometrical structure of fibrosis can therefore be described using the following measurable parameters: (1) the perimeter and area indicating its magnitude; (2) the fractal dimension designing its position in Euclidean space; (3) the wrinkledness characterising all natural objects, which is dependent on the ratio between the perimeter and area of the collagen islets; (4) the self-similarity of its component parts (the collagen islets). The quantitative evaluation of fibrosis is expressed as the percentage of the true area of the histological preparation covered by collagen. The method is completely automatic and replaces the operator in the steps of biopsy image acquisition and calculus, including automatic movement and focusing. The time of analysis needed by the computer-aided system with our technological device is about 30 s/mm2 of the true area of the biopsy slice (Dioguardi et al., 2003). In order to obtain reliable data, tissue losses due to manipulation must be avoided and the area of the bioptic slice should not be less than 5 mm2, which means that the best results obtained using our system are available in not less than 450 s. The identification of quantitative methods suggests reconsidering the significance of the magnitudes that characterise them: it should not be seen as a more sophisticated means of revealing what is observed, but rather as a different way of perceiving it. In our experience, it is necessary to determine the most appropriate way of using the measurement of the physical status of fibrosis bearing in mind that, the rupture of physiological fractal complexity can occur as a result of the appearance of excessive order (pathological periodicity) or outright disorder. The common thread uniting the two pathways to the disease is the degradation of the correlated multi-scalar irregularity of natural living objects.
5. CONCLUSIONS The aspects of fibrosis made available by the use of metric measurements reopens the problem of how to use liver biopsies in clinically interpreting chronic liver diseases.
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This in turn reopens the vexata questio of the representativeness of the sample. The variability of the measurements of a preparation in relation to others belonging to different levels of the same sample leads to the realisation that even the introduction of a broader class of variables in order to extend the analytical possibilities of the system provides results that question how opportune the identifying sizes that represent those of the other areas of the organ are. In this case, it follows that there is a need to find other means of analysis that do not consider just their physical state but also the essence of their processes, and which also evaluate the influence they have on their behaviour and function, metabolism, and repair. Grading and staging of the liver chronic diseases are currently evaluated with semi-quantitative or morphometrical scores of the necroinflammation and fibrosis histological patterns. The reason for the wide survival of the highly criticised semi-quantitative scores can be ascribed both to the descriptive information of the best strengthened medical tradition, which makes them easily understood by clinicians, and the comforting belief that the level of observer error is relatively low. The more objective classic morphometrical methods are less frequently used because it takes too long to analyse the entire histological section. Moreover, they give metric data that may be a poor approximation of reality. This is due to the one-dimensional smooth standard metre that cannot interact with the high wrinkled collagen isles forming the fibrosis mass. The technological problems solved in constructing an ad hoc fractal dimension-rectified metre giving measures more close to real fibrosis magnitude involved microscope light standardisation, digitalisation of the entire histological section, automated focussing, and the construction of an easy to use software. The mathematical and geometrical problems lay in the image analysis. The rectification of the standard metre and the contrivance of an ‘‘internal’’ measure unit in this investigation allows to discriminate as a function of the thickness to discriminate possible stadia of fibrosis network mesh. The solutions to these problems provided a technology, able to furnish a set of data forming a sort of ‘‘hepatogram’’ in about 30 s/mm2 of specimen surface (Dioguardi et al., 2003). The basic novelty of the method is the metrics based on some of the principles of fractal geometry, which provides measures including the majority of the irregular unevenness escaping the standard linear metre of the international system (Dioguardi et al., 2003). All the measurements of the collagen isles are executed at a fixed microscope magnification in order to standardise the scaling effects on their shape and size. The collating of the ratios between the set of scalars labelling the liver section of patient reckoned onto different Knodell
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categories shows that semi-quantitative evaluations remain indispensable to construct diagnosis, which result in being insufficient for evaluations in the research field. This makes it possible to say that semi-quantitative and metric methodologies belong to two different kinds of medical rationales. Selective scalars also recognising small differences of magnitude allowed the discrimination of minimal and maximal values of collagen concentration in our case list. This allowed us to establish, with the straight line of real numbers, a geometrical model of a state-space that contains all the possible fibrosis states (collagen concentrations). This model represents all the possible stadia of the dynamics of collagen evolution. The projection of each bioptic sample measure onto this linear state-space allows us to discriminate the covered walk between 0 and 48.84%; i.e. the maximum collagen concentration acquired by our results (see fig. 4). The metric measure of the collagen area, covering the histological section of the biopsy liver sample as an index of the fibrosis state of the whole liver, had to be taken with extreme care. In fact, the results on successive sections of the same liver specimen gave results indicating that the measures reflect only the state of that section. This is an old question that is refuelled by the metric measures. The wrinkledness of fibrosis represents a new and concrete variable of the fibrosis state drawn by the metric area and perimeter measurements relationship. It correlates with perimeter length, but not with surface area. Wrinkledness is a typical property of the fibrosis. As is true of all natural objects, its state is certainly influenced by many factors. We expect to obtain interesting results from a planned study of the relationship between its magnitude and some observable inflammation. In conclusion, let us stress that metric data had to be considered as quantitative measurements rather than meticulous description of histological patterns. In other words, the metric method proposed in this chapter offers the basis for concrete knowledge of the state of the natural objects that we observe under a microscope. With the contrived metrics our knowledge of whole intercellular matrix had been differentiated with numbers, or other kind of invariants of fibrosis states in such a way that states, bearing the same label had been considered alike, and states, bearing different labels had been considered different. Reviewing what we have learned from having measured, recognised, and classified the fibrosis and its collagen components we arrive at several conclusions. The first concerns the fractal shapes of biological objects, which demonstrate that life is based not only on genetic processes, but on universal mathematical and geometrical principles that apply to all entities in the universe, and that undoubtedly predate the formation of our planet. Second, it is inappropriate to apply the standard
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metre of the international system in the morphological measurements of irregular objects, because differences in spatial dimension preclude interaction between the unit of measurements and the object being measured. Finally, this research highlights the canonical importance of fractal mathematics and geometry in the theory of measurement. Specific acquirements arise on the meaning of the metric analysis of the liver biopsy for the control of the therapeutical results on the tissue lesions. Technical questions arise from the opportunity to follow up the destiny of the antiviral responder patients after the elimination of aetiological agent and the ethical role of the liver biopsy as a function of the possible contraction of the fibrous tissue of the scars resulting from necro-inflammatory process which can determine a post-aetiological pathology dependent by intra-organ circulatory defects able to self-maintain intercellular matrix deposition.
ACKNOWLEDGEMENTS In addition to the author, a physician, this research has involved Fabio Grizzi, a biologist, Barbara Franceschini, a histologist, Carlo Russo, a computer scientist of Istituto Clinico Humanitas, and Giacomo Aletti, a mathematician of the Department of Mathematics and Statistics of the University of Milan. The work was sponsored by the Michele Rodriguez Foundation for the study of metric measures in medicine.
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De Groote, J., Desmet, V.J., Credigk, P., Korb, G., Popper, H., Poulsen, H., Schmid, M., Nehlinger, E., Wepler, W.A., 1968. A classification of chronic hepatitis. Lancet 1, 626–628. Desmet, V., Gerber, M., Hoofnagle, J.H., Manns, M., Scheuer, P.J., 1994. Classification of chronic hepatitis: diagnosis, grading and staging. Hepatology 19, 1513–1520. Desmet, V.J., 1996. What more can we ask from the pathologist? J. Hepatol. Suppl. 1, 25–29. Dioguardi, N., 1992. Fegato a piu` dimensioni. RCS, Etas Libri, Milan. Dioguardi, N., Grizzi, F., 2001. Mathematics and Biosciences in Interaction. Birkhauser Press, Basel, Boston, Berlin, pp. 113–120. Dioguardi, N., Grizzi, F., Bossi, P., Roncalli, M., 1999. Fractal and spectral dimension analysis of liver fibrosis in needle biopsy specimens. Anal. Quant. Cytol. Histol. 21, 262–266. Dioguardi, N., Franceschini, B., Aletti, G., Russo, C., Grizzi, F., 2003. Fractal dimension rectified meter for quantification of liver fibrosis and other irregular microscopic objects. Anal. Quant. Cytol. Histol. 25, 312–320. Feigl, H., 1956. Levels of scientific inquiry. University Minnesota Medical Bullettin 28, 90–97. Feldmann, G., 1995. Critical analysis of the methods used to morphologically quantify hepatic fibrosis. J. Hepatol. 22, 49–54. Forns, X., Ampurdanes, S., Llovet, J.M., Aponte, J., Quinto, L., Martinez-Bauer, E., Bruguera, M., Sanchez-Tapias, J.M., Rodes, J., 2002. Identification of chronic hepatitis C without hepatic fibrosis by a simple predictive model. Hepatology 36, 986–992. George, K.K., 2001. Chronic hepatitis C: grading, staging, and searching for reliable predictors of outcome. Hum. Pathol. 32, 899–903. Grizzi, F., Dioguardi, N., 1999. A fractal scoring system for quantifying active collagen synthesis during chronic liver diseases. Int. J. Chaos Theory Appl. 4, 39–44. Hastings, H.M., Sugihara, G., 1993. Fractals. A User’s Guide for the Natural Sciences. Oxford Science Publications, New York. Hausdorff, F., 1919. Dimension and measures. Mathematische Annalen 79, 157–179. Hubsher, S.G., 1998. Histological grading and staging in chronic hepatitis: clinical applications and problems. J. Hepatol. 29, 1015–1022. Imbert-Bismut, F., Ratziu, V., Pieroni, L., Charlotte, F., Benhamou, Y., Poynard, T., 2001. Biochemical markers of liver fibrosis in patients with hepatitis C virus infection: a prospective study. Lancet 357, 1069–1075. Ishak, K., Baptista, A., Bianchi, L., Callea, F., De Groote, J., Gudat, F., Denk, H., Desmet, V., Korb, G., MacSween, R.N., 1995. Histological grading and staging of chronic hepatitis. J. Hepatol. 22, 696–699. Junqueira, L.C., Bignolas, G., Brentani, R.R., 1979. Picrosirius staining plus polarization microscopy, a specific method for collagen detection in tissue sections. Histochem. J. 11, 447–455. Kage, M., Shimamatu, K., Nakashima, E., Kojiro, M., Inoue, O., Yano, M., 1997. Longterm evolution of fibrosis from chronic hepatitis to cirrhosis in patients with hepatitis C: morphometric analysis of repeated biopsies. Hepatology 25, 1028–1031. Knodell, R.G., Ishak, K.G., Black, W.C., Chen, T.S., Craig, R., Kaplowitz, N., Kiernan, T.W., Wollman, J., 1981. Formulation and application of a numerical scoring system for assessing histological activity in asymptomatic chronic active hepatitis. Hepatology 1, 431–435.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
23 A network approach to living tissues Frank T. Vertosick, Jr. The Neurosurgery Group, Pittsburgh, Pennsylvania, USA
1. INTRODUCTION Interest in biological networks has recently exploded. However, the application of network models to human therapeutics remains in its infancy, given our poor understanding of how such networks operate in vivo. Nevertheless, the network paradigm holds great promise, not only for human medicine but also for the biological sciences in general. Some understanding of this field will soon become mandatory for all those working in the life sciences. A network is an ensemble of identical nodes linked together into a single computational machine; a node is defined as a non-linear input/output device possessing a certain degree of intrinsic memory. The most rudimentary node is the simple light switch, which converts input (the motion of someone’s hand on the switch) into an output (either ‘‘on’’ or ‘‘off ’’). The switch is non-linear because it has only two discrete states. The switch also has a small amount of memory, in that when turned on it stays on, and when off, it stays off; the switch ‘‘recalls’’ its previous state indefinitely, or at least until another input causes it to flip states. The switch represents a simple binary node. A somewhat more interesting node is the variable light switch, or rheostat. In the rheostat, on and off states are separated by a finite region in which output is linearly dependent upon input. The operator turns the switch on, then adjusts the intensity of light over a continuous range from total darkness to maximum brightness. The rheostat represents a sigmoidal node, so named because a plot of its input versus output has an S-shape. Most computer-simulated network models use either binary or sigmoidal nodes (or some combination of both) (Special Section on Biological Networks, 2003). 431
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In living networks, the nodes may be quite complex. The brain’s nodes, i.e. the nerve cell, or neuron, are mammoth cells with enormous computational properties and hundreds of thousands of connections – hardly a rheostat. Network theory is now being applied to human networks (economies, the Internet); here, the nodes are individual people, endowed with the computational prowess of human brains. Although such complex nodes make for complex networks, certain organisational rules apply to all networks, regardless of their complexity or nodal composition.
2. THE NETWORK In formal network theory, each node receives numerical data from one or more outside nodes, which the node then adds linearly to obtain a single input. The node applies a predefined input/output function, also called the activation function, to convert the input into an output which is then redistributed to one or more companion nodes in the same network. Let us assume that a node receives data from three other nodes consisting of the values 0.2, 0.3, and 0.8. The node adds these to obtain a total input of 1.3. Suppose further that the activation function of that node is a simple step function – the node yields an output of zero if its total input is less than 2.0, and an output of 1.0 if the input is equal to, or greater than 2.0. In this case, the total input (1.3) is less than 2.0 and so an output of 0.0 is transmitted to other nodes in the network. If, at some point in the future, the same node’s incoming data set changes to 0.3, 0.9, and 0.9, the total changes to 2.1, which is now greater than 2.0; this causes the node to flip states and begin sending an output of 1.0 back into the network. In this way, the dynamic ebb and flow of inputs into each node causes that node to alter its output to other nodes, thereby altering their output, and so on, until the whole network is affected. Thus, changes in a few inputs can ripple throughout the network, potentially turning the network into an unstable cauldron of oscillating nodal states. Such oscillations do not make for a very promising computational device. However, we can solve this problem by adding an important modification: flexible connections. Consider two nodes, i and j, connected with a ‘‘weight’’ of w(i, j). When i sends an output signal to j, the weight, w(i, j) modulates that signal before it reaches j as input. For example, if w(i, j) ¼ 0.03 and i emits an output of 2.0 to j, j will actually receive a value of only 0.06 (2.0 0.03). A weight of zero means the nodes are, at least at that point in time, not connected at all, since zero times any value is zero.
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By scaling the connections, we can dampen network oscillations and allow a network to seek defined stable states. We can then go one (very important) step further by defining a learning rule, whereby the connection weights change as the network acquires experience over time. One of the simplest learning rules is the Hebbian rule, which states that connections between active nodes will strengthen over time (Hebb, 1949). The Hebbian rule allows recurring patterns of nodal activity to become imprinted into the network’s memory, allowing the network’s steady states to be mapped onto solutions of computational problems, particularly problems requiring pattern recognition. Which problems a network can solve will depend upon how the network is wired together (its topology), the nature of its nodes, the precise character of its learning rule, and so on. Networks can be categorised into two broad groups according to how they learn: 1. those that alter their connections internally, without any external guidance, and 2. those in which an external agency adjusts the connection weights during training. We can assume biological networks are generally of the first, or selforganising, variety, although externally trained networks may occur in the brain (see Arbib, 1998). Time and space do not permit any detailed explanation of how networks endowed with scalable connections learn and solve problems; interested readers are encouraged to read more in-depth reviews of network mechanics (see the classic text by Rummelhart et al., 1986, for example, or the review of Grossberg, 1988), but for now, we can summarise the key elements of a basic learning network: 1. nodes with a non-linear input/output behaviour (activation function); 2. a pattern of connectivity (topology) among the nodes; 3. a matrix of variable connection weights, w(i, j) among the connected nodes which modulates the flow of data inside the network; and finally, 4. a learning rule that defines how the connection weights are modified in response to self-directed learning (self-organising networks) or external training.
2.1. Computational properties of networks Networks are parallel processing devices. By distributing memory and computation over a large number of nodes, networks avoid the data bottlenecks which plague serial machines like the common personal
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computer (PC). The PC performs all the operations sequentially in a single processing unit and stores all memory in a separate location. The rate of computation in the PC is, therefore, limited by how rapidly the central processor can perform logical or arithmetical operations and by the rate at which data is exchanged between the processor and memory. Networks avoid these bottlenecks and achieve solutions to certain classes of problems very quickly, but at the expense of precision. Networks reach good solutions quickly; serial computers reach perfect solutions slowly. Networks differ from serial machines in four other important ways: 1. robustness; 2. problem sets; 3. programming requirements; and 4. the nature of problems that can optimally be addressed. Networks are robust in that they tolerate a certain degree of physical injury without failure and can obtain reasonable results even when presented with degraded data. In other words, networks can tolerate a low signal to noise ratio (SNR), while serial machines must have a very high, almost infinite SNR. Moreover, networks can be designed that programme themselves as they gain experience with different problem sets; serial machines, however, always must be programmed by an external agency. Finally, networks and serial machines excel at different problem sets. Those problems requiring pattern recognition or sorting/classification are best addressed by networks (Carpenter, 1989); those problems requiring numerical computation or logical analysis are better handled by serial machines. Networks make poor calculators, but are ideal for matching fingerprints. Living systems depend on pattern recognition for survival, not arithmetic, and network computation is ideally suited for biologically important problem sets. We see here the chief advantages of network computation for living systems: 1. no need for external programming; 2. robustness to injury; 3. ability to deal with imperfect data; 4. greater speed in achieving acceptable, if inexact, solutions to problems; and 5. excellent ability to recognise patterned data. There is also the issue of simplicity. Networks can be constructed from modular nodal structures ‘‘plugged together’’ using a few simple rules. The construction of serial machines, with massively complex central processors, is more difficult. Certain classes of networks solve problems by storing data in the form of minima on an energy landscape. Computation then becomes equivalent to traversing the energy landscape in search of a low energy state, known
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as an attractor, which corresponds to the solution to a given problem. In this paradigm, a network learns by modifying the geometry of its energy landscape (see Tank and Hopfield, 1987). By equating problem solving with relaxation into a minimal energy state, we can see how networks deal with incomplete or imperfect data sets. Let us assume that each attractor represents a perfect data set and further assume that each attractor lies at the bottom of an energy ‘‘basin’’. Picture the basin as a common kitchen bowl and picture the network’s current state as a marble. If we place the marble on the side of the bowl, we are ‘‘initialising’’ the network with an imperfect data set. However, the marble will roll to the bottom of the bowl on its own and reach the attractor, or perfect state. The closer we place the marble to the bottom, the more quickly it will reach a perfect solution. If we place the marble too far away from the edge of the bowl, however, the marble will never reach bottom. Thus, the basin defines the minimal amount of initial data needed by the network to achieve its solution. Consider the game ‘‘name that tune’’, wherein a contestant is given the first one or more notes of a popular song and is asked to recognise and name the song. The song’s name is the ‘‘solution’’ and the notes ‘‘initialise’’ the contestant’s brain at a certain point in an energy landscape of songs that experience has moulded into his or her brain. If the song has a broad basin, moulded by extensive exposure to the song in question, only one or two notes will be sufficient to start the brain rolling to the complete solution. If the basin is poorly formed and narrow, the listener may need many notes before the edge of the basin is reached and the solution achieved. If the contestant has no experience with the song at all, the brain has formed no basin and the marble will roll around forever and never reach a steady state attractor.
3. A BRIEF WORD ABOUT TOPOLOGIES Much of the recent excitement about biological networks centres around network topology. The topology of a network describes the degree of connectivity among its constituent nodes. The Hopfield network, for example, assumes that every node is connected to every other node (Hopfield, 1982). In a random, or Erdo¨s, network, the connectivity of the network follows a Gaussian distribution centred on the connectivity of the ‘‘average’’ node. In a scale-free network, on the other hand, the likelihood of any node being connected to k other nodes is equal to 1/kn. For biological networks, the value of n appears to be about 2. Thus, the
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probability that a node has one connection is 1.0, that it has two connections is 1/4, that it has three connections is 1/8, that it has four connections is 1/16, and so on. Stated another way, in a scale-free biological network model, there are 16 nodes with one connection for every one node with four connections (Baraba´si and Bonabeau, 2003). Clearly, given this inverse power law, a scale-free network necessarily possesses very few densely connected nodes and many sparsely connected nodes. The highly connected nodes act as hubs and function like glue, binding the network together. The scale-free network is not homogeneous, in that some nodes are more important to network behaviour than others. These networks are quite robust, in that most nodes, save for the hubs, can be jettisoned without significant degradation of overall network behaviour. Unfortunately, they are also vulnerable to an intelligent, targeted attack at the isolated ‘‘hub’’ nodes. Baraba´si and others, in the late 1990s, argued that all biological networks from the cytoplasm to the Internet seem to behave like scalefree networks with a common power law with n ¼ 2, implying that there is some deep-seated, unifying principle to biological network architecture (Baraba´si, 2002). Moreover, the hub-like topology of living networks has significant implications for disease states and for the possible therapeutic approach to those states. In the cytoplasmic network, as just one example, the scale-free model postulates that only a very few hub enzymes play key roles in any given metabolic pathway. Pathogens, due to evolutionary pressures, must learn the hub nodes in a host’s network critical to organismal integrity. We, in turn, can learn the hub nodes by studying the nodes most targeted by those pathogens. (In fact, the field of oncogenes arose in this fashion – critical growth genes in normal cells were identified by isolating the genes most targeted by oncogenic retroviruses – see Weinberg, 1989.) As Baraba´si and Bonabeau (2003) pointed out, the scale-free nature of ecological host–parasite networks has important epidemiological implications. If we can identify the ‘‘hubs’’ of a disease outbreak, for example, we might target vaccinations or quarantine efforts at those points and ignore the rest of the network. In fact, this approach may have helped contain the SARS epidemic. However, as important as the scale-free model of network topology is for biological networks, we must realise that it has some theoretical problems. First, this approach assumes that a connection weight between two nodes is either 1.0 (connected) or 0.0 (disconnected), when, in fact, the weight has infinite variability. Second, the model assumes that connections are fixed in time, when they are not – a connection weight of zero does not necessarily mean that two nodes are disconnected, it merely means
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that, at this point in time, they exchange no information. An example will clarify this situation: The US airport system is often cited as an example of a scale-free network, in that each airline uses only a few densely connected hubs to serve the remainder of the sparsely connected airports. US Airways, for example, has hubs in Pittsburgh and Charlotte. To go from Miami to Bangor on the USAirways system, a traveller must go through Pittsburgh. Bangor has only a few connections to other airports, while Pittsburgh has hundreds. However, while the system acts like a scale-free network, it is really a Hopfield network, in that every airport is potentially connected to every other airport. (In a Hopfield network, each node is connected to every other node, but that does not mean all connections must have a non-zero weight at every point in time.) There is nothing preventing USAirways physically from flying directly from Miami to Bangor; it simply chooses not to do so now for efficiency reasons. As I write this, USAirways is considering leaving Pittsburgh altogether, potentially deactivating that hub and shutting off its hundreds of connections to other airports. There is even talk of the entire airline system shifting from a hub-based system served with large jets to a Erdo¨s network served by smaller jets. The airline system is, in this sense, far more adaptable than the simple scale-free model allows, in that potential connections can be converted to real connections fairly easily and quickly. This fact should also be kept in mind by those wishing to exploit scalefree topology therapeutically. If we are able to shut down a ‘‘hub’’ enzyme in the scale-free metabolic networks of a cancer cell, there is no guarantee that the cell will not activate dormant connections and re-establish a new hub somewhere else in short order. We must remember that the essence of network behaviour is adaptability, and that the current topology of a network may not reflect all its true potential, but rather, reflects only a transient topology that best deals with the problems facing the network at that point in time.
4. PROTEOMICS AND CYTOPLASMIC NETWORKS Before discussing specific biological networks, we should stop and consider that network theory originated in the computer sciences as a means of simulating the circuits inside a brain. Originally, network nodes were either nerve cells or their electrical counterparts – vacuum tube or transistor amplifiers – and their connections were fixed axons or electrical wires, with the connection weights implemented by variable resistors (for wires) or variable synaptic efficiencies (for nerve cell axons). Applying network
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principles to living ensembles outside the brain required a paradigm shift in network application: nodes could now be mobile entities like enzymes or people. The ‘‘connections’’ were no longer wires, but the stochastic probability of interaction between fluid-phase entities. I, together with the late immunologist Robert Kelly, first suggested such a paradigm shift back in the 1980s, when we applied neural network architecture to a model of the immune system (Vertosick and Kelly, 1989). It has now become commonplace to think of ‘‘connections’’ as some form of interaction probability, as opposed to an electrical wire. For example, the new science of proteomics studies the mass behaviour of complex protein mixtures, like the cytoplasm, and it defines networks of proteins based upon their ability to bind to one another in a fluid phase. Recently, the experimental model of choice for exploring protein connectivity is the yeast two-hybrid system. To determine if two proteins are ‘‘connected’’ in a network, the investigator inserts their genes into a yeast cell genome along with transcription factor sequences that can activate a third, or reporter gene if the two proteins bind together. If, once transcribed, the two proteins bind sufficiently to allow the transcription sequence to activate the reporter gene product, the proteins are considered connected. If no reporter gene product is formed, the proteins are considered disconnected (see Liebler, 2002). Maps of cellular proteomes derived by the two-hybrid method have the typical second power scalefree topology described by Baraba`si and others. However, to assume that such two-hybrid maps represent the true nature of cytoplasmic networks is misleading and simplistic. By its very design, the two-hybrid method detects only those proteins which physically bind to each other to a degree necessary to activate a reporter gene. Lesser degrees of physical interaction, although potentially important, go undetected. More importantly, proteins may be coupled metabolically and yet have no direct physicochemical affinity for each other at all. Hjelmfelt and his colleagues (1991) proposed that enzymes could be considered coupled if the reactions they catalyse share common products, substrates, or intermediaries. For example, all kinases are coupled to a shared pool of cyclic nucleotides, using that pool as a source of phosphate groups; in this way, kinases are all connected to some degree, even if they share no physical affinity. Physical binding is indeed critical for certain proteins, like transcription factors, but physical binding alone cannot be the sole determinant for protein connectivity. Implicit in proteomic network models is the assumption that the nodes are the proteins themselves. As Bray (1995), Hjelmfelt et al. (1991), and others (Marijuan, 1991; Vertosick, 2002) have argued, the nodes may, in reality, be the reactions catalysed by protein enzymes, rather than
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the proteins themselves. Recall that nodes should have some form of binary or multi-stable behaviour with a certain intrinsic memory. Under ordinary conditions, most non-catalysed chemical reactions do not exhibit such behaviour, but catalysed reactions may manifest such non-linear behaviour, particularly if the catalysts are subject to feedback control and other regulatory influences (as enzymes are) (see Reich and Sel’kov, 1974; Jackson, 1993). I have suggested that the advent of enzymes, not the advent of genes, was the seminal event that injected computational prowess into organic networks by injecting non-linearities into common organic reactions, permitting such reactions to be linked into networks in the first place (Vertosick, 2003). If the ‘‘reaction as node’’ model supplants the ‘‘protein as node’’ model, the utility of protein–protein interaction maps becomes limited to those subsets of proteins that depend upon physicochemical affinity for their function. The nexus of proteomics and formal network theory may radically alter our view of the cell as an intelligent entity. Presently, we tend to view cells as tiny bags of limited, stereotyped chemical reflexes with little capacity to analyse or learn. Ironically, we forget that complex beings such as humans are derived from single cells (ova) and we often overlook the enormous computational machinery and data capacity a single cell must harbour in order to create such massively complex multicellular creations. Even the free-living amoeba in a freshwater pond must continuously sample its environment for temperature, ambient light, salinity, pH, food availability, and oxygenation, and make decisions regarding motility, cell division, and enzyme activation. The simplest cell in the most rudimentary environment faces problems requiring some degree of analysis, recall, and decision-making. Network theory, together with a deeper understanding of molecular computation (including quantum computation), may open our eyes to the intelligence of cellular life, and that may, in turn, lead to new avenues of therapy. The war on cancer is really a war on the miscreant eukaryotic cell, a creature more adaptable, cunning, and resilient than we might have imagined based on our preconceived notion of the cell as chemical simpleton. So far, exposing cells to massive doses of exogenous radiation or to metabolic poisons has been only partially effective in controlling malignancy, and so a new approach is in order. One of the chief attributes of network architecture is its robustness, but that is also one of the main obstacles to attacking network-based devices. The scale-free approach to cancer may hold some promise, i.e. by identifying and attacking the critical hubs binding cytoplasmic pathways together, we might disrupt cellular function with a minimal assault. Unfortunately, this approach seems to offer scant advantage over
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conventional ‘‘cidal’’ therapies intended to kill, rather than reprogramme, the transformed cell. Cancer is a refractory disease because the transformed cell differs only slightly from the normal cell; killing the tumor often means killing the host as well. Similarly, the scale-free tactic of targeting cellular hubs will work only if a cancer cell’s hubs differ from the normal cell’s hubs to an exploitable degree. A better approach lies in recognising that the transformed cell differs from the normal cell in a computational, not a metabolic sense. All cells, even normal ones, retain the pluripotential capacity to divide and to spread beyond their anatomic confines (metastasise) in response to the hormonal environment that envelops it. During embryogenesis, ‘‘transformed’’ behaviour is mandatory for organs to assemble, develop, and grow. Such behaviour is shut down in the completed foetus by extracellular signals which force mature cells into a stable phenotype. The resumption of transformed behaviour later – cancer – is a communication failure on the part of the malignant cell; for reasons yet unknown, the cancer cell fails to respond to its environment and shifts back into an embryonic state. This failure lies in the domain of information theory, not biochemistry per se; the communication breakdown that leads to the cancerous phenotype must be explored in terms of the language used by an intelligent being to communicate with its societal environment. I believe that the metabolic differences between malignant and normal cells are so small that any attempt to cure a wide spectrum of tumours using cytotoxic methods alone, whether based on conventional principles or on scale-free network principles, will be doomed. A ‘‘cure’’ will require acknowledging that the eukaryotic cell is intelligent, that it speaks a language, and that it can be redirected to a less aggressive state using that language. Rudimentary progress has been made along these lines using the so-called ‘‘differentiation’’ agents, but we are a long way from deciphering the complex molecular phrasing of the eukaryotic language. Understanding the intelligence of the cell will come from a continued exploration of enzymatic and genetic networks using a synthesis of molecular biology and computer science. One last note in this regard: the discontinuous phenotypic states found in multicellular organisms resemble the attractor basins of networks that use energy relaxation computational schemes. One feature of such relaxation schemes is the inability of the network to settle into states between attractors. Intermediate states are unstable. Thus, a cell can be an epithelial cell or a lymphocyte, but not something in between. During embryogenesis, a landscape is crafted with basins corresponding to each phenotypic state and the cells all settle into a certain basin (Mjolsness et al., 1991). It is possible for a cell to jump between basins, given enough
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‘‘energetic’’ assistance, but it would be difficult. The question for cancer biologists becomes: is cancer a unique phenotypic basin, or has the cancerous cell become uncoupled from the energy landscape of the body altogether, thereby rendered incapable of entering any steady state at all? I favour the latter, since the cancer cell most resembles embryonic cells that predate the formation of the phenotypic landscape entirely.
5. THE IMMUNE SYSTEM AS A NETWORK Ironically, the first non-neural system to be subjected to network modelling was the human immune system; I say ‘‘ironically’’ because immune network theory has fallen into disfavour recently, even as network modelling of other biological systems has become more popular. A recent large review of biological networks in Science did not mention the application of networks to immune function at all. In the early 1970s, Jerne (1974) first suggested that network forces regulate the immune response. Jerne based his network on internal idiotypic–antiidiotypic interactions that served to modulate or dampen the immune system after exposure to antigen. An idiotype is a unique antigenic determinant situated at or near the antigen-binding sites of immune receptors (antibodies and T-cell antigen receptors). As the number of binding sites is huge, up to a million or more in a vertebrate immune system, most idiotypes, being unique to only a few binding sites at most, are expressed at such low levels during early immunological development that they never induce tolerance. Thus, when an antibody’s titre increases in the bloodstream during an immune reaction, the idiotypic areas of the antibody induce an autoimmune reaction, known as an antiidiotypic reaction; the titres of the antiidiotype rise and the idiotype, now treated as a foreign antigen, is cleared from the bloodstream. However, the antiidiotypic antibodies also express their own idiotypes, and so anti-antiidiotypic antibodies are formed, and the cycle repeats itself until the whole immune system becomes active. Eventually, a steady state is reached. Jerne envisioned his network as a means of limiting the immune response, preventing the clonal expansion of lymphocytes during an immune response from deteriorating into lymphoid malignancy. In the context of modern network theory, the Jerne model is little more than a simple cybernetic feedback system with little or no resemblance to the parallel network models of the late 1980s and beyond (see Raff, 1977). Due to its limited sophistication, the Jerne model could make very few testable predictions of any value or interest, beyond explaining why every immune response did not turn into frank leukemia. We know
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that antiidiotypes exist and formed during the course of any immune response, but their role in regulating immunity in vivo remains undefined. In this historical context, it is easy to understand why interest in the model waned, even though the idea partially contributed to Jerne’s Nobel Prize. In the early 1990s, I pointed out how one aspect of the idiotype story might yet prove more interesting from a modern network perspective, namely, the Oudin–Cazenave phenomenon (OCP) (Oudin and Cazenave, 1971). In immunology parlance, an antigen is any large molecule that induces an antibody response (antibody generating molecule). An epitope is that tiny portion of an antigen that can be spanned by the variable binding site of a single antibody. A huge protein antigen, like bovine albumin, may express dozens of unique epitopes, given that the albumin molecule is far larger than the binding site of any single antibody. Curiously, when a large antigen enters the bloodstream and induces the production of different antibodies to different epitopes on its surface, those antibodies, although they have different binding sites, often share the same idiotype (for example, see Metzger et al., 1987). This is the OCP. In other words, it appears that the immune system uses the common idiotypic marker, via the OCP, to label antibodies directed against different sites on a single large antigen. The implications of this are enormous; it applies that the immune system is not designed solely to recognise single epitopes (as currently thought), but may instead be capable of integrating the response against multiple epitopes into a coherent ‘‘picture’’ of large antigens using the idiotypic system as a form of content-addressable memory. In this fashion, the immune system may use organ-level sensory integration to comprehend objects larger than those comprehended by single cells, just as the nervous system using inputs from retinal rods and cones to sense images much larger than could be detected by any single rod or cone (Vertosick and Kelly, 1991). Interestingly, the immune system is incapable of responding to a single epitope, but must be presented with multiple epitopes simultaneously before an immune response occurs (Rajewsky et al., 1969). This is further evidence that the immune system has some form of organ-level integration of sensory input which is yet to be detected (although no effort has been expended searching for it). This concept should be testable. If the immune system integrates complex patterns of multiple epitopes, it may show a ‘‘pattern completion’’ form of recall, just as the above mentioned ‘‘name that tune’’ contestant can recall the complete song pattern after being initialised with only a few notes. For example, in the United States, all infants are immunised with several vaccines simultaneously, including vaccines against pertussis, diphtheria, tetanus, measles, mumps, rubella, and polio. Later in life,
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booster vaccinations against measles and tetanus are also required. Thus, in a network model of immunity, the serum titres of diphtheria or pertussis antibodies may increase after re-vaccination with tetanus or measles by virtue of their mutual association during the training process, even when the immune system is not exposed to new diphtheria or pertussis antigen. This phenomenon, to my knowledge, has never been investigated. As in the case of cytoplasmic networks, the most important benefit of a network model of immunity may be a deeper appreciation for the intelligence of the living system we strive to manipulate therapeutically. Just as cancer therapy has been, to date, a wholly violent affair, immunosuppression in transplantation medicine wreaks havoc on the immune system. As we do not understand the immune system, we must beat it with a stick – and with some very undesirable consequences for patients. A network model of immunity allows hope that we may be able to modulate the immune response more judiciously by learning and using its own language.
6. THE BRAIN The only firm evidence of true network behaviour in living systems has been found, not surprisingly, in the central nervous system (for a comprehensive review, see Arbib, 1998). The brain is so monstrously complex that virtually every type of network architecture is likely to be found there. One interesting aspect of network theory that has been barely explored, however, is the link between network theory and psychiatric disease. Personality states also resemble discrete attractor basins in an energy landscape, akin to the phenotypic basins that control cellular differentiation. Schizophrenia, a thought disorder afflicting one percent of the adult population, is akin to the malignant cell phenotype, a brain state with no attractor. In schizophrenia, the failure of the mind to stabilise into a single personality attractor may be due to a pathologically high degree of noise (Servan-Schreiber et al., 1990). In networks that use energy relaxation computation, a certain level of noise is needed to shake the system out of inappropriate or outdated attractors. In the brain, the dopaminergic system appears to regulate the SNR in the brain. A normal brain varies its SNR according to the situation; during times of crisis the SNR increases to allow immediate, concrete solutions. During creative thought or daydreaming, the SNR falls as noise levels increase, permitting the brain to bounce like a shaken marble through its various energy landscapes. The schizophrenic brain has such a high degree of noise, due to some
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failure of dopaminergic regulation of the SNR, that it is in a perpetual state of fantasy.
7. CONCLUSIONS 1. Networks are ensembles of nodes connected into a single computational device; originally intended to model nerve cells and electrical amplifiers connected by fixed axons or wires, networks can now be used to model any ensemble of interacting elements. 2. Networks are fast, robust, handle patterned data well, and require no external programming. They can be built of simple repeated modules using a limited set of rules. All these features make them ideal for application in living systems. 3. It is likely that networks are the preferred architecture for all intelligent biosystems, from the cytoplasm to large ecosystems (perhaps natural selection is the ultimate ‘‘learning rule’’ in this regard, serving to train large ecosystems over geological time scales). The brain, the original inspiration for network theory, is just the latest version of a network paradigm that originated with the advent of life itself. 4. Network theory may allow a deeper insight into the intellect of biological machines, including the cancerous cell, the diseased brain, and the vertebrate immune system. If we recognise the depth of their intellect and learn to speak the language of these entities, we may be better able to manipulate them therapeutically. 5. The scale-free topology of living networks may afford an immediate insight into how to target living networks, although its utility may be limited by the inherent adaptability of living networks.
REFERENCES Arbib, M. (Ed.) 1998. The Handbook of Brain Theory and Neural Networks. Bantam, New York. Bara´basi, A.-L., 2002. Linked: The New Science of Networks. Perseus Publishing, New York. Bara´basi, A.-L., Bonabeau, E., 2003. Scale-free networks. Sci. Am. 288(5), 60–69. Bray, D., 1995. Protein molecules as computational elements in living cells. Nature 376, 307–312. Carpenter, G., 1989. Neural network models for pattern recognition and associative memory. Neural Networks 2, 243–257. Grossberg, S., 1988. Non-linear neural networks: Principles, mechanisms and architectures. Neural Networks 1, 17–61. Hebb, D.O., 1949. The Organization of Brain Behavior. John Wiley & Sons, New York.
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Hjelmfelt, A., Schneider, F., Ross, J., 1991. Chemical implementation of neural networks and Turing Machines. Proc. Natl. Acad. Sci. USA 88, 983–987. Hopfield, J., 1982. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558. Jackson, R.C., 1993. The kinetic properties of switch antimetabolites. J. Natl. Cancer Inst. 85, 538–545. Jerne, N.K., 1974. Toward a network theory of the immune system. Ann. Immunol. Inst. Pasteur 125C, 373–389. Liebler, D.C., 2002. Introduction to Proteomics. Humana, Totowa, NJ. Marijuan, P., 1991. Enzymes and theoretical biology: Sketch of an informational perspective of the cell. Biosystems 25, 259–273. Metzger, D., Miller, A., Sercarz, E., 1987. Sharing of idiotypic marker by monoclonal antibodies specific for distinct regions of hen lysozyme. Nature 287, 540–542. Mjolsness, E., Sharp, D., Reinitz, J., 1991. A connectionist model of development. J. Theor. Biol. 152, 429–453. Oudin, J., Cazenave, P., 1971. Similar idiotypic specificities in immunoglobulin fractions with different antibody functions or even without detectable antibody function. Proc. Natl. Acad. Sci. USA 68, 2616–2620. Raff, M., 1977. Immunologic networks. Nature 265, 205–207. Rajewsky, K., Schmirrmacher, V., Nasi, S., Jerne, N., 1969. The recognition of more than one antigenic determinant for immunogenicity. J. Exp. Med. 129, 1131–1138. Reich, J.G., Sel’kov, E.E., 1974. Mathematical analysis of metabolic networks. FEBS Letters 40, S119–S127. Rummelhart, D., McClelland, J., 1986. The PDP Research Group. Parallel Distributed Processing, Volume 1, MIT Press, Cambridge, MA. Servan-Schreiber, D., Printz, H., Cohen, J., 1990. A network model of catecholamine effects, gain, signal-to-noise ratio and behavior. Science 249, 892–895. Special Section of Biological Networks, 2003. Science 301, 1863–1877. Tank, D.W., Hopfield, J., 1987. Collective computation in neuronlike circuits. Sci. Am. 257, 104–114. Weinberg, R. (Ed.) 1989. Oncogenes and the Molecular Origin of Cancer, Cold Spring Harbor Press, New York. Vertosick, F.T., Kelly, R.H., 1989. Immune network theory: A role for parallel distributed processing? Immunology 66, 1–7. Vertosick, F.T., Kelly, R.H., 1991. The immune system as neural network: A multiepitope approach. J. Theor. Biol. 150, 225–237. Vertosick, F.T., 2002. The Genius Within: Exploring the Intelligence of Every Living Thing. Harcourt, New York.
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Studies in Multidisciplinarity, Volume 3 Editors: Ray Patony and Laura McNamara 2006 Elsevier B.V. All rights reserved.
24 Genetic algorithms in radiotherapy Olivier C. L. Haas and Colin R. Reeves Biomedical Engineering Systems Group, Control Theory and Applications Centre, Coventry University, Coventry, UK
1. INTRODUCTION: KEY FEATURES OF RADIOTHERAPY FROM AN OPTIMISATION VIEWPOINT Radiotherapy, used alone or in combination with surgery, chemotherapy, brachytherapy, or hyperthermia is one of the most successful cancer treatment techniques, with 30% of the patients cured by a combination of surgery and radiotherapy (Webb, 2001). Cancers are caused by uncontrolled growth of cells. Radiotherapy exploits the sensitivity of cells, and in particular cancerous cells, to ionising radiation by focusing ionising radiation beams onto cancerous sites. In contrast to chemotherapy, where drugs affect the whole body, radiotherapy is a more specific or focused technique, and as such it is best suited to spatially localised tumours. This chapter considers the optimisation of radiotherapy treatment using genetic algorithms (and derivatives thereof) to eradicate cancerous tissues enclosed within the so-called Planning Target Volume (PTV) specified by the clinical oncologist. If it were possible to irradiate all the cancerous tissues, with the appropriate amount of radiation, then 100% cure would be observed. However, radiation can potentially kill all cells. It is therefore necessary to ensure that healthy tissues, and, in particular, critical organs not affected by the cancer, do not receive a dose of radiation that would damage them. Limiting the dose received by healthy structures indirectly limits the maximum dose that can be delivered to the cancerous cells. It means that radiotherapy treatment planning attempts to find a trade-off between destroying cancerous cells and sparing critical structures and therefore minimising the amount of undesirable side effects.
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The factors that can be optimised to improve the selectivity and effectiveness of radiotherapy treatment include: Dose fractionation, i.e. number of fractions, time between fractions, and dose per fraction. The aim of dose fractionation is to reduce the side effects by exploiting the ability of tissues affected by radiation to regenerate themselves. It works by dividing the total dose prescription into a number of fractions delivered over a period of weeks. A remaining issue is the lack of accuracy of the models describing the effects of radiation on cells in vivo. It is therefore difficult to determine, for an individual patient, the best trade-off between regenerating healthy tissues and killing cancerous cells. Type of ionising radiation Several types of ionising radiation can be used to treat cancerous lesions; these include electrons, photons, and protons, or heavy ions. Each of these types of radiation interacts differently with human tissues, as depicted in fig. 1. Electrons are stopped fairly rapidly, resulting in a superficial dose. Electrons are usually used to treat skin lesions, as for example the new total skin electron treatment machine developed in collaboration between Coventry University and the University Hospitals Coventry and Warwickshire NHS Trust (Spriestersbach, 2002; Haas et al., 2003; Spriestersbach et al., 2003a). Protons can penetrate deeply into the body but ‘‘stop’’ abruptly, resulting in a dose that peaks sharply before decreasing almost to zero. Proton beams can, therefore, be tuned to deliver a high dose within the PTV and a relatively low dose elsewhere. Such particles are very
100.00
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30.00 20.00 10.00 0.00 0.00
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Fig. 1. Comparison between the relative penetration of photon, electron, and proton beams.
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effective for treating lesions close to critical structures such as the optic nerve. The main disadvantage of protons is that they require a large and expensive infrastructure to produce. Photons are comparatively cheap to produce, but they deliver a higher dose to healthy tissues than to the PTV. To increase the relative dose to the PTV, beams from various directions, overlapping on the PTV, are therefore combined. Photon beams in the range 4–25MV are by far the most widely used ionising radiation to treat cancer patients. When the photon beams are modulated they can produce a dose similar to protons where high dose is delivered to the PTV and a low dose elsewhere. Note that the larger the difference between the low dose and the high dose region, the bigger is the risk associated with a missed target. The aim of the oncologist should therefore be to select the best combination of ionising radiation to treat a specific patient. In most cases, the choice is limited and dictated by the resources available. Number and orientation of beams The aim of optimising the number and the orientation of the beams is to increase the dose differential between the PTV and the neighbouring critical structures by combining ionising beams from different angles of incidence. For example, it is possible to achieve a very high dose within a circular target by combining a large number of beams rotated about the centre of the targeted region and separated by equal angles, i.e. equispaced beams. Whilst some generic solutions can be found, the equipment used to deliver the treatment may add specific constraints with respect to the possible angle of incidence. For example, Meyer, 2001 and Meyer et al., 2001 illustrated the need to take into consideration the patient support system geometry when optimising the beam orientation, as shown in fig. 2. From an optimisation perspective, the search space is very large and comprises several equivalent solutions, i.e. local optima. In addition, the best beam orientation depends on the beam modulation device utilised. Shaping of X-ray beams – beam collimation The aim of beam shaping is to spare healthy tissues by shaping the beams to reproduce, as accurately as possible, the shape of the PTV as seen from the beam source. Beam shaping is currently implemented using multi-leaf collimators (MLCs) or lead blocks, see fig. 3. Beam shaping can produce so-called conformal treatment, but is unable to deliver a uniform dose over a concave volume. Beam modulation devices Beam modulation aims to focus the dose to a particular region of the body by inserting radiation attenuating devices into the path of the photons generated by a linear accelerator. The simplest form of
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Direction of rotation − +
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Fig. 2.
r3
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b1
The need to take into account constraints linked to the patient support system geometry. Beams b2 and b9 have to be shifted from their ideal positions.
Direction of high modulation Target
(a)
Direction of high modulation Target
(b)
Fig. 3. Target coverage depending on the arrangement of the MLC leaves: (a) MLC in longitudinal direction, (b) better target coverage when MLC leaves are rotated.
modulation device is lead blocks. Such blocks can be used to protect critical structure such as the spine by shielding them from radiation. As an improvement over simple blocks, lead blocks with a regular wedge shape (right-angled-triangle) were then developed. Wedges attenuate radiation progressively from one side of the field to the other. Wedges are differentiated according to their ‘‘wedge angle’’. The British Standard Institution (BSI5724, 1990) defines the wedge angles as the slope of the isodose contour at standard measurement depth (i.e. 10 cm depth) (ICRU50, 1993). Original wedges illustrated in fig. 4 could be inserted directly into the head of the treatment machine or positioned on a tray in the beam path. Modern wedges use a single motorised wedge and produce various wedge angles by combining an open field with a field including the largest possible wedge angle.
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45° wedge
30° wedge
Fig. 4. 308 and 458 wedges that can be inserted into the head of the linear accelerator to modulate the beam intensity across the field into a wedge shape (courtesy of Walsgrave Hospital, NHS Trust, Coventry, UK).
Compensator mulled into a solid block of MCP200
Compensator using tin granules filled into a mould
Compensator based on stereolithography model
Vacuum formed compensator that could be filled with liquid metal
Fig. 5. Illustration of various types of compensator that could be used to modulate radiotherapy X-ray beams. Note that these compensators were manufactured to be able to produce identical dose modulation.
At the next level in terms of complexity are patient-specific compensators, a good review of which is given in Meyer, 2001. Static beam modulation devices such as compensators, despite being accurate, robust, reliable, easy to use, and reproducible, are limited to a small number of fields owing to their manufacturing time. To overcome this problem, Xu et al. (2002) developed a system using a deformable attenuating material, shaped using hydraulic pistons to achieve a resolution of the order of 1 1 cm2. Yoda and Aoki (2003) developed a method involving a rapidly formed thermoplastic container filled with heavy alloy granules. Goodband et al. (2003, 2004) have developed liquid metal compensators where the liquid metal can be poured into a vacuum formed thermoplastic container, see fig. 5, or into a new specialised Perspex device, see fig. 6. This new device has been designed so that it can be optimised efficiently using an artificial neural network to deliver an intensity modulated dose (Goodband et al., 2004). This new multi-chamber compensator is aimed to be a cost-effective alternative to compensators or multi-leaf collimators. However, these ideas are new and are not yet implemented in any radiotherapy clinic.
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New experimental multichamber compensator that can be filled with liquid metal
Multileaf collimators (Courtesy of Elekta Ltd)
MiMic (courtesy of NOMOs Corporation)
Fig. 6. Other beam modulating devices.
Multi-leaf collimators have been designed as a practical ‘‘technological’’ alternative to patient-specific compensators. They modulate the intensity of the beam across the field by moving two banks of parallel-opposed tungsten leaves. As with compensators, the optimiser aims to conform the dose delivered to the PTV and spare healthy body structures. Interpreters are then used to translate the fluence matrix into a set of position and exposure time for each pair of MLC leaves. MLC can be used in a static manner where these leaves move to a small number of fixed positions with the dose being delivered once the leaves are in position. A faster technique moves the leaves continuously during exposure to radiation. Such a technique is however more difficult to assess qualitatively and assumes a perfectly predictable machine performance. Wedges are unable to produce a uniform dose distribution over a concave volume, whereas patient-specific compensators and MLCs can. For this reason, the authors believe that the selection and type of beam modulation device are the most important factors contributing to improve the physical selectivity of treatments. Target localisation – patient positioning The ability to shape and modulate the beams has increased the risks associated with missing the target. In particular, if the patient is not precisely positioned before and during the treatment, the modulated beams could result in severely overdosing critical structures close to the PTV and/or underdosing the PTV. To ensure that the highly conformal dose is delivered to the appropriate volume, use is made of an imaging device that provides real-time information regarding the position of the organs to be treated. A significant amount of work is currently being carried out by manufacturers to be able to position (and if necessary reposition) patients during the course of
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treatment using various imaging methods such as portal imaging, CT mounted on the linear accelerator, or X-ray devices mounted on the patient support system. The ultimate aim is to be able to adapt the movement of various machine components to organ movements and ensure that the treatment is delivered only to the PTV consistently and at every treatment fraction. This is often referred to as 4D IMRT where the fourth dimension is time. In Haas et al., 2005 and Spriestersbach et al., 2003b, a new control system is reported that should be able to reposition the patient support system automatically in a very accurate manner. All the above factors influencing radiotherapy treatment contribute to maximising the chances of success. However, in this chapter we shall consider only those factors that are optimised within so-called radiotherapy treatment planning systems, namely the beam number, weight, orientation, and modulation. The next section describes the radiotherapy treatment planning optimisation problem in terms of the formulation of objectives. The third section reviews the two main approaches adopted to solve general multi-objective optimisation problems with competing objectives. The fourth section describes the use of genetic algorithms and derivatives thereof for the optimisation of the beam weight, the beam number and orientation, the beam modulation, and the means to deliver intensity modulation with a multi-leaf collimator.
2. THE RADIOTHERAPY TREATMENT PLANNING OPTIMISATION PROBLEM The role of the clinician is to select the most appropriate means to ensure that the treatment benefits the patient. A number of tools have been developed to help clinicians reach such a decision. These tools are packaged within a treatment planning system (TPS). Every TPS includes dose calculation algorithms to predict the effect of ionising radiation and graphical tools to allow the planner to modify the beam orientation manually. A state-of-the-art TPS will also include software to determine the optimal beam collimation for MLC, to optimise the beam modulation, and to determine means to deliver the treatment using MLC in a static or in a dynamic mode. Some software even optimises the number and incidence of beams. The common problem facing these optimisation tools is the difficulty in expressing the multiple clinical requirements in the form of a suitable mathematical expression that can be solved numerically. In general, each objective is associated with a particular region of interest, namely the PTV, the organs at risk (OAR), each of which may
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react differently to radiation, and all the other structures – generally grouped into the so-called ‘‘other healthy tissues’’ (OHT). The objectives for OHT are in general relatively easy to achieve, whilst conflicts arise between PTV and OARs, especially when these two regions of interest are close to each other. There are two main ways to express objectives in radiotherapy treatment planning: dose-based (or physical objective functions) and probabilities (or radiological objective functions). A third approach occasionally used is based on objectives that describe the geometry of the treatment beams and devices. Originally, it was believed that the main advantage of biological models was their ability to account for dose volume effect. However, it was shown in Bortfeld (1999) that it is also possible to take into consideration dose volume constraints with physical objective functions by adopting a penalty based approach, where constraints (Bortfeld, 1999) or individual objective weightings (Haas et al., 1997) are calculated using dose and volume information. While biological objective functions may be functionally more useful, in oncological terms they are much less credible than dose-based objectives. Indeed Amols and Ling (2002) argue that biological scoring functions are based on incomplete and often questionable clinical or laboratory data. In an attempt to find a compromise between dose–volume-based and biological scoring functions Wu et al. (2002) introduced the concept of equivalent uniform dose (EUD). EUD has the advantage of being a single parameter, which can therefore facilitate the selection of a plan compared to dose–volume-based objectives, which may offer several dose distributions that all satisfy a set of constraints – and which then have to be further appraised. The disadvantage of EUD is that – as with some biological models – they are based on a parametric fit to biological and clinical data. Irrespective of the model, the key to an optimised plan is the mathematical formulation of the objectives and the setting of the parameters to describe these objectives (Ebert, 1997a,b,c). This section will review some of the objective functions proposed.
2.1. Dose-based objective functions Physical objective functions translate the objective of radiotherapy in terms of the amount of dose delivered to a specific volume. It is assumed that if the required dose can be delivered to the regions of interest identified, then a particular treatment outcome will be achieved. Physical objective functions only act as a surrogate for the outcomes that we would wish to model, which are based on the resulting quality of life – in particular
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the probability of achieving a cure, and the probability and severity of treatment side effects. The most widely used dose-based objective functions include general expressions of the form: nj m 1 X wij d^i di Cj ¼ nj i¼1
!k ðEq: 1Þ
where wij are weights or importance factors associated with the voxel receiving the dose d^i which is compared to the prescribed dose di expressed as an integer in the range [0, 100], m is a real number that is most often 0.5, 1, or 2, k is usually 1, but is set to 1/m in some cases (Xing et al., 1999; Yu et al., 2000; Starkschall et al., 2001; Kulik et al., 2002), nj is the number of voxels in the region of interest j. Numerous methods have been developed to select wij. The simplest is to keep wij constant for each region of interest. Other methods determine wij based on dose received or the dose received in combination with the location of the voxel. A traditional means of assessing radiotherapy treatment plan is to use a dose–volume histogram. This is a graphical representation indicating the percentage volume of tissue receiving a particular dose. Equation (1) can express the cost as a function of dose volume histogram by replacing the dose di and d^i by Vj (d ) and Vj (d^ ), respectively, where Vj (d ) indicates the fractional volume of the j th region of interest receiving a dose d or greater, while Vj (d^ ) indicates the ideal/desired dose volume histogram. Additional expressions used to help the search eliminate candidate solutions also include minimum (min) and maximum (max) criteria for the dose in the PTV, and max criteria for the dose in critical structures. These criteria have also been combined into expressions to assess the dose homogeneity in the PTV:
CPTV
maxðdPTV Þ minðdPTV Þ ¼ meanðdPTV Þ
ðEq: 2Þ
Criteria that describe the dose gradient between the PTV and neighbouring OARs have also been introduced: C¼
minðdPTV Þ maxðdOAR Þ
ðEq: 3Þ
Such criteria can help the optimisation algorithm find a solution where the ratio between the dose in the PTV and that in the OAR is large.
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A potential issue linked with taking a decision on a single point, i.e. the maximum and the minimum, is the sensitivity to ‘‘noise’’ and the accuracy of the dose calculation algorithm. Indeed, depending on the sampling adopted to describe the regions of interest, the minimum or maximum dose value may not be clinically representative. However, the authors believe that it could be possible to rank the dose in each region of interest and form an objective function based on a number of dose calculation points or voxels receiving a specific dose. Other constraints set dose thresholds. For example, to simplify calculation it is common to set the cost associated with a voxel to zero if the dose it receives is lower than that specified by a given prescription. This emphasise the importance of voxels that infringe the constraints.
2.2. Radiobiological objective functions Radiological objective functions are based on the biological effect of the treatment and use radiobiological models to express the tumour control probability (TCP), i.e. the ability to eradicate cancerous cells, and the normal tissue complication probability (NTCP), i.e. the likelihood for complications (Lyman, 1985; Niemierko, 1997; Wu et al., 2000; Brahme et al., 2001; Stavrev et al., 2001a,b). While the effects of radiation can be accurately modelled in vitro on cell cultures, it is significantly more difficult to predict the effects of radiation in vivo. Biological models are based on a hypothesised model of cellular response. For this reason, such criteria have not been used to determine an absolute prediction in terms of the number of fractions and the dose to deliver with respect to the outcome of the treatment, but to establish a relative ranking between alternative plans. The usefulness of either physical or radiobiological dose indices depends on the correlation of those indices with treatment outcome. Such validation requires evaluation of data from large-scale clinical trials. The problem is, however, that it is long and difficult to assess the outcome of radiotherapy treatment in terms of the ability to ‘‘control’’ the disease. Indeed, a patient is assumed to be cancer-free if there is no sign of recurrence of cancer within five years. Therefore, the assessment of measures such as TCP requires at least five years. In contrast, some complications linked with the irradiation of healthy tissues can be observed very rapidly in a matter of weeks, although for serious ‘‘late’’ effects this can take months or even years. Radiological models for tumour control are based on the relationship that describe cell kill. The most common model is the
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linear–quadratic-Poisson approach. A particular example of a model used to describe the TCP is TCP ¼
K X
eNs
ðEq: 4Þ
m¼1
with Ns ¼
N Y
2
vi eði di þi di Þ
ðEq: 5Þ
i¼1
where N represents the number of doses, di used to describe a dose volume histogram at discrete volume vi for a tumour with uniform cell density ; the parameters i and i describe the cellular radiosensitivity. More sophisticated TCP models also incorporate time factors to account for tumour repopulation. Biological effective dose (BED) is often used as an ‘‘isoeffect’’ measure to describe NTCP and TCP (i.e. any BED should correspond to one constant NTCP or TCP, unlike total dose, fraction size, etc). BED is usually calculated using a linear–quadratic model. Df BED ¼ n Df 1 þ =
ðEq: 6Þ
where the tissue receives n fractions of dose Df, and its cellular radiosensitivity is described by and . There are many and varied possible treatment side effects, and many of their exact mechanisms are at least partly unknown. Therefore, in the absence of a precise relationship between BED and NTCP (such as the Poisson relationship which links BED to TCP), NTCP is often estimated by simply extrapolating from experimental data, e.g. NTCP ¼ NTCPref þ
BED BEDref BEDref
ðEq: 7Þ
where NTCPref and BEDref are experimentally observed data points, and is the normalised gradient of the BED–NTCP relationship at this point. Many other NTCP models exist. It should also be noted that hybrid objective functions containing both physical and biological parameters have been used. Indeed approaches such as Pareto ranking, fully described in sections 3 and 4, could be advantageous to assess in parallel the relative costs in terms of physical and biological models.
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2.3. Geometrical objective function Despite the increase in computational speed, the optimisation of all the factors linked to radiotherapy treatment planning is still a very complex problem. Each intensity modulated beam can be composed of 100 or more variables characterising the intensity within the beam that would result in the required dose attenuation at a particular point in the patient. Intensity modulated treatment may involve from five to nine beam directions, leading to nearly 1000 variables to optimise. Each beam direction can also be optimized. Cho et al. (1999) showed that for a search space where the beam direction resolution is 58, a six beam treatment plan would lead to 3 1020 possible beam combinations. Taking inspiration from the work of Sherouse (1993), who proposed selecting the wedge angle using geometrical criteria, Haas et al. (1998) proposed and analysed the use of geometrical objectives to optimise coplanar beam orientation. The idea was refined by Wagner et al. (2001) to optimise the beam direction based on the ‘‘geometrical’’ beam’s eye view of the critical structures and the PTV. The original work (Haas et al., 1998) was recently extended by Schreibmann et al. (2003) to include three-dimensional beam volumes as well as beam shaping for use with multi-leaf collimators or beam shaping blocks. Both Haas et al. (1998) and Schreibmann et al. (2003) define objectives whose aim is to assess the conformity of all the beam intersections with respect to the PTV and the amount of critical structure in the beam path. In Haas et al. (1998) the objective was to minimise the difference between the area (coplanar beams) created by the intersection of all the beams and the area of the PTV, denoted PTVa:
CPTVa ¼
N\ beam
!k Bi PTVa
ðEq: 8Þ
i¼1
where Bi, i ¼ 1 . . . Nbeam are the polygons representing the individual beam paths and k is a positive integer, usually greater than 1 in order to emphasise small differences in areas. Note that k is only useful when the various objectives are combined in a weighted sum. When the objectives are solved in parallel, k can be kept to unity. The objective for the OARs was expressed as:
COARj ¼
N beam X i¼1
areaðBi \ OARj Þ Nbeam
ðEq: 9Þ
Genetic algorithms in radiotherapy
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where is set to 1 for IMRT treatment and to a number greater than one for standard conformal treatments to penalise beam entries that were close to the OAR: OAR 5PTA , ¼ ðPTA OAR Þ ðEq: 10Þ OAR PTA , ¼ 1 where OAR is the distance between the projection of the centre ‘‘J ’’ of the OAR onto the central axis and the beam entry point, PTA is the distance between the isocentre ‘‘I ’’ of the PTVa and the beam entry point and 2
