Modelling in Medicine and Biology VIII (Wit Transactions on Biomedicine and Health)

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Modelling in Medicine and Biology VIII

WIT Press publishes leading books in Science and Technology. Visit our website for new and current list of titles. www.witpress.com

WITeLibrary Home of the Transactions of the Wessex Institute. Papers presented at Modelling in Medicine and Biology VIII are archived in the WIT eLibrary in volume 13 of WIT Transactions on Biomedicine and Health (ISSN 1743-3525). The WIT eLibrary provides the international scientific community with immediate and permanent access to individual papers presented at WIT conferences. Visit the WIT eLibrary at www.witpress.com.

EIGHTH INTERNATIONAL CONFERENCE ON MODELLING IN MEDICINE AND BIOLOGY

BIOMEDICINE VIII

CONFERENCE CHAIRMAN C.A. Brebbia Wessex Institute of Technology, UK

INTERNATIONAL SCIENTIFIC ADVISORY COMMITTEE C. Bignardi A. Doi W.J. Federspiel M. Hyre W. Lakin A. Macpherson S. Mekaoui A. Peratta D. Poljak K. Shimano R.M. Shoucri M. Ursino

Sponsored by WIT Transactions on Biomedicine and Health. Organised by Wessex Institute of Technology, UK

WIT Transactions Transactions Editor Carlos Brebbia Wessex Institute of Technology Ashurst Lodge, Ashurst Southampton SO40 7AA, UK Email: [email protected]

Editorial Board B Abersek University of Maribor, Slovenia Y N Abousleiman University of Oklahoma, USA P L Aguilar University of Extremadura, Spain K S Al Jabri Sultan Qaboos University, Oman E Alarcon Universidad Politecnica de Madrid, Spain A Aldama IMTA, Mexico C Alessandri Universita di Ferrara, Italy D Almorza Gomar University of Cadiz, Spain B Alzahabi Kettering University, USA J A C Ambrosio IDMEC, Portugal A M Amer Cairo University, Egypt S A Anagnostopoulos University of Patras, Greece M Andretta Montecatini, Italy E Angelino A.R.P.A. Lombardia, Italy H Antes Technische Universitat Braunschweig, Germany M A Atherton South Bank University, UK A G Atkins University of Reading, UK D Aubry Ecole Centrale de Paris, France H Azegami Toyohashi University of Technology, Japan A F M Azevedo University of Porto, Portugal J Baish Bucknell University, USA J M Baldasano Universitat Politecnica de Catalunya, Spain J G Bartzis Institute of Nuclear Technology, Greece A Bejan Duke University, USA

M P Bekakos Democritus University of Thrace, Greece G Belingardi Politecnico di Torino, Italy R Belmans Katholieke Universiteit Leuven, Belgium C D Bertram The University of New South Wales, Australia D E Beskos University of Patras, Greece S K Bhattacharyya Indian Institute of Technology, India E Blums Latvian Academy of Sciences, Latvia J Boarder Cartref Consulting Systems, UK B Bobee Institut National de la Recherche Scientifique, Canada H Boileau ESIGEC, France J J Bommer Imperial College London, UK M Bonnet Ecole Polytechnique, France C A Borrego University of Aveiro, Portugal A R Bretones University of Granada, Spain J A Bryant University of Exeter, UK F-G Buchholz Universitat Gesanthochschule Paderborn, Germany M B Bush The University of Western Australia, Australia F Butera Politecnico di Milano, Italy J Byrne University of Portsmouth, UK W Cantwell Liverpool University, UK D J Cartwright Bucknell University, USA P G Carydis National Technical University of Athens, Greece J J Casares Long Universidad de Santiago de Compostela, Spain, M A Celia Princeton University, USA A Chakrabarti Indian Institute of Science, India

A H-D Cheng University of Mississippi, USA J Chilton University of Lincoln, UK C-L Chiu University of Pittsburgh, USA H Choi Kangnung National University, Korea A Cieslak Technical University of Lodz, Poland S Clement Transport System Centre, Australia M W Collins Brunel University, UK J J Connor Massachusetts Institute of Technology, USA M C Constantinou State University of New York at Buffalo, USA D E Cormack University of Toronto, Canada M Costantino Royal Bank of Scotland, UK D F Cutler Royal Botanic Gardens, UK W Czyczula Krakow University of Technology, Poland M da Conceicao Cunha University of Coimbra, Portugal A Davies University of Hertfordshire, UK M Davis Temple University, USA A B de Almeida Instituto Superior Tecnico, Portugal E R de Arantes e Oliveira Instituto Superior Tecnico, Portugal L De Biase University of Milan, Italy R de Borst Delft University of Technology, Netherlands G De Mey University of Ghent, Belgium A De Montis Universita di Cagliari, Italy A De Naeyer Universiteit Ghent, Belgium W P De Wilde Vrije Universiteit Brussel, Belgium L Debnath University of Texas-Pan American, USA N J Dedios Mimbela Universidad de Cordoba, Spain G Degrande Katholieke Universiteit Leuven, Belgium S del Giudice University of Udine, Italy G Deplano Universita di Cagliari, Italy I Doltsinis University of Stuttgart, Germany M Domaszewski Universite de Technologie de Belfort-Montbeliard, France J Dominguez University of Seville, Spain

K Dorow Pacific Northwest National Laboratory, USA W Dover University College London, UK C Dowlen South Bank University, UK J P du Plessis University of Stellenbosch, South Africa R Duffell University of Hertfordshire, UK A Ebel University of Cologne, Germany E E Edoutos Democritus University of Thrace, Greece G K Egan Monash University, Australia K M Elawadly Alexandria University, Egypt K-H Elmer Universitat Hannover, Germany D Elms University of Canterbury, New Zealand M E M El-Sayed Kettering University, USA D M Elsom Oxford Brookes University, UK A El-Zafrany Cranfield University, UK F Erdogan Lehigh University, USA F P Escrig University of Seville, Spain D J Evans Nottingham Trent University, UK J W Everett Rowan University, USA M Faghri University of Rhode Island, USA R A Falconer Cardiff University, UK M N Fardis University of Patras, Greece P Fedelinski Silesian Technical University, Poland H J S Fernando Arizona State University, USA S Finger Carnegie Mellon University, USA J I Frankel University of Tennessee, USA D M Fraser University of Cape Town, South Africa M J Fritzler University of Calgary, Canada U Gabbert Otto-von-Guericke Universitat Magdeburg, Germany G Gambolati Universita di Padova, Italy C J Gantes National Technical University of Athens, Greece L Gaul Universitat Stuttgart, Germany A Genco University of Palermo, Italy N Georgantzis Universitat Jaume I, Spain G S Gipson Oklahoma State University, USA P Giudici Universita di Pavia, Italy F Gomez Universidad Politecnica de Valencia, Spain R Gomez Martin University of Granada, Spain

D Goulias University of Maryland, USA K G Goulias Pennsylvania State University, USA F Grandori Politecnico di Milano, Italy W E Grant Texas A & M University, USA S Grilli University of Rhode Island, USA R H J Grimshaw, Loughborough University, UK D Gross Technische Hochschule Darmstadt, Germany R Grundmann Technische Universitat Dresden, Germany A Gualtierotti IDHEAP, Switzerland R C Gupta National University of Singapore, Singapore J M Hale University of Newcastle, UK K Hameyer Katholieke Universiteit Leuven, Belgium C Hanke Danish Technical University, Denmark K Hayami National Institute of Informatics, Japan Y Hayashi Nagoya University, Japan L Haydock Newage International Limited, UK A H Hendrickx Free University of Brussels, Belgium C Herman John Hopkins University, USA S Heslop University of Bristol, UK I Hideaki Nagoya University, Japan D A Hills University of Oxford, UK W F Huebner Southwest Research Institute, USA J A C Humphrey Bucknell University, USA M Y Hussaini Florida State University, USA W Hutchinson Edith Cowan University, Australia T H Hyde University of Nottingham, UK M Iguchi Science University of Tokyo, Japan D B Ingham University of Leeds, UK L Int Panis VITO Expertisecentrum IMS, Belgium N Ishikawa National Defence Academy, Japan J Jaafar UiTm, Malaysia W Jager Technical University of Dresden, Germany Y Jaluria Rutgers University, USA C M Jefferson University of the West of England, UK

P R Johnston Griffith University, Australia D R H Jones University of Cambridge, UK N Jones University of Liverpool, UK D Kaliampakos National Technical University of Athens, Greece N Kamiya Nagoya University, Japan D L Karabalis University of Patras, Greece M Karlsson Linkoping University, Sweden T Katayama Doshisha University, Japan K L Katsifarakis Aristotle University of Thessaloniki, Greece J T Katsikadelis National Technical University of Athens, Greece E Kausel Massachusetts Institute of Technology, USA H Kawashima The University of Tokyo, Japan B A Kazimee Washington State University, USA S Kim University of Wisconsin-Madison, USA D Kirkland Nicholas Grimshaw & Partners Ltd, UK E Kita Nagoya University, Japan A S Kobayashi University of Washington, USA T Kobayashi University of Tokyo, Japan D Koga Saga University, Japan A Konrad University of Toronto, Canada S Kotake University of Tokyo, Japan A N Kounadis National Technical University of Athens, Greece W B Kratzig Ruhr Universitat Bochum, Germany T Krauthammer Penn State University, USA C-H Lai University of Greenwich, UK M Langseth Norwegian University of Science and Technology, Norway B S Larsen Technical University of Denmark, Denmark F Lattarulo, Politecnico di Bari, Italy A Lebedev Moscow State University, Russia L J Leon University of Montreal, Canada D Lewis Mississippi State University, USA S lghobashi University of California Irvine, USA K-C Lin University of New Brunswick, Canada A A Liolios Democritus University of Thrace, Greece

S Lomov Katholieke Universiteit Leuven, Belgium J W S Longhurst University of the West of England, UK G Loo The University of Auckland, New Zealand J Lourenco Universidade do Minho, Portugal J E Luco University of California at San Diego, USA H Lui State Seismological Bureau Harbin, China C J Lumsden University of Toronto, Canada L Lundqvist Division of Transport and Location Analysis, Sweden T Lyons Murdoch University, Australia Y-W Mai University of Sydney, Australia M Majowiecki University of Bologna, Italy D Malerba Università degli Studi di Bari, Italy G Manara University of Pisa, Italy B N Mandal Indian Statistical Institute, India Ü Mander University of Tartu, Estonia H A Mang Technische Universitat Wien, Austria, G D, Manolis, Aristotle University of Thessaloniki, Greece W J Mansur COPPE/UFRJ, Brazil N Marchettini University of Siena, Italy J D M Marsh Griffith University, Australia J F Martin-Duque Universidad Complutense, Spain T Matsui Nagoya University, Japan G Mattrisch DaimlerChrysler AG, Germany F M Mazzolani University of Naples “Federico II”, Italy K McManis University of New Orleans, USA A C Mendes Universidade de Beira Interior, Portugal, R A Meric Research Institute for Basic Sciences, Turkey J Mikielewicz Polish Academy of Sciences, Poland N Milic-Frayling Microsoft Research Ltd, UK R A W Mines University of Liverpool, UK C A Mitchell University of Sydney, Australia

K Miura Kajima Corporation, Japan A Miyamoto Yamaguchi University, Japan T Miyoshi Kobe University, Japan G Molinari University of Genoa, Italy T B Moodie University of Alberta, Canada D B Murray Trinity College Dublin, Ireland G Nakhaeizadeh DaimlerChrysler AG, Germany M B Neace Mercer University, USA D Necsulescu University of Ottawa, Canada F Neumann University of Vienna, Austria S-I Nishida Saga University, Japan H Nisitani Kyushu Sangyo University, Japan B Notaros University of Massachusetts, USA P O’Donoghue University College Dublin, Ireland R O O’Neill Oak Ridge National Laboratory, USA M Ohkusu Kyushu University, Japan G Oliveto Universitá di Catania, Italy R Olsen Camp Dresser & McKee Inc., USA E Oñate Universitat Politecnica de Catalunya, Spain K Onishi Ibaraki University, Japan P H Oosthuizen Queens University, Canada E L Ortiz Imperial College London, UK E Outa Waseda University, Japan A S Papageorgiou Rensselaer Polytechnic Institute, USA J Park Seoul National University, Korea G Passerini Universita delle Marche, Italy B C Patten, University of Georgia, USA G Pelosi University of Florence, Italy G G Penelis, Aristotle University of Thessaloniki, Greece W Perrie Bedford Institute of Oceanography, Canada R Pietrabissa Politecnico di Milano, Italy H Pina Instituto Superior Tecnico, Portugal M F Platzer Naval Postgraduate School, USA D Poljak University of Split, Croatia V Popov Wessex Institute of Technology, UK H Power University of Nottingham, UK D Prandle Proudman Oceanographic Laboratory, UK

M Predeleanu University Paris VI, France M R I Purvis University of Portsmouth, UK I S Putra Institute of Technology Bandung, Indonesia Y A Pykh Russian Academy of Sciences, Russia F Rachidi EMC Group, Switzerland M Rahman Dalhousie University, Canada K R Rajagopal Texas A & M University, USA T Rang Tallinn Technical University, Estonia J Rao Case Western Reserve University, USA A M Reinhorn State University of New York at Buffalo, USA A D Rey McGill University, Canada D N Riahi University of Illinois at UrbanaChampaign, USA B Ribas Spanish National Centre for Environmental Health, Spain K Richter Graz University of Technology, Austria S Rinaldi Politecnico di Milano, Italy F Robuste Universitat Politecnica de Catalunya, Spain J Roddick Flinders University, Australia A C Rodrigues Universidade Nova de Lisboa, Portugal F Rodrigues Poly Institute of Porto, Portugal C W Roeder University of Washington, USA J M Roesset Texas A & M University, USA W Roetzel Universitaet der Bundeswehr Hamburg, Germany V Roje University of Split, Croatia R Rosset Laboratoire d’Aerologie, France J L Rubio Centro de Investigaciones sobre Desertificacion, Spain T J Rudolphi Iowa State University, USA S Russenchuck Magnet Group, Switzerland H Ryssel Fraunhofer Institut Integrierte Schaltungen, Germany S G Saad American University in Cairo, Egypt M Saiidi University of Nevada-Reno, USA R San Jose Technical University of Madrid, Spain F J Sanchez-Sesma Instituto Mexicano del Petroleo, Mexico

B Sarler Nova Gorica Polytechnic, Slovenia S A Savidis Technische Universitat Berlin, Germany A Savini Universita de Pavia, Italy G Schmid Ruhr-Universitat Bochum, Germany R Schmidt RWTH Aachen, Germany B Scholtes Universitaet of Kassel, Germany W Schreiber University of Alabama, USA A P S Selvadurai McGill University, Canada J J Sendra University of Seville, Spain J J Sharp Memorial University of Newfoundland, Canada Q Shen Massachusetts Institute of Technology, USA X Shixiong Fudan University, China G C Sih Lehigh University, USA L C Simoes University of Coimbra, Portugal A C Singhal Arizona State University, USA P Skerget University of Maribor, Slovenia J Sladek Slovak Academy of Sciences, Slovakia V Sladek Slovak Academy of Sciences, Slovakia A C M Sousa University of New Brunswick, Canada H Sozer Illinois Institute of Technology, USA D B Spalding CHAM, UK P D Spanos Rice University, USA T Speck Albert-Ludwigs-Universitaet Freiburg, Germany C C Spyrakos National Technical University of Athens, Greece I V Stangeeva St Petersburg University, Russia J Stasiek Technical University of Gdansk, Poland G E Swaters University of Alberta, Canada S Syngellakis University of Southampton, UK J Szmyd University of Mining and Metallurgy, Poland S T Tadano Hokkaido University, Japan H Takemiya Okayama University, Japan I Takewaki Kyoto University, Japan C-L Tan Carleton University, Canada M Tanaka Shinshu University, Japan E Taniguchi Kyoto University, Japan

S Tanimura Aichi University of Technology, Japan J L Tassoulas University of Texas at Austin, USA M A P Taylor University of South Australia, Australia A Terranova Politecnico di Milano, Italy E Tiezzi University of Siena, Italy A G Tijhuis Technische Universiteit Eindhoven, Netherlands T Tirabassi Institute FISBAT-CNR, Italy S Tkachenko Otto-von-GuerickeUniversity, Germany N Tosaka Nihon University, Japan T Tran-Cong University of Southern Queensland, Australia R Tremblay Ecole Polytechnique, Canada I Tsukrov University of New Hampshire, USA R Turra CINECA Interuniversity Computing Centre, Italy S G Tushinski Moscow State University, Russia J-L Uso Universitat Jaume I, Spain E Van den Bulck Katholieke Universiteit Leuven, Belgium D Van den Poel Ghent University, Belgium R van der Heijden Radboud University, Netherlands R van Duin Delft University of Technology, Netherlands P Vas University of Aberdeen, UK W S Venturini University of Sao Paulo, Brazil

R Verhoeven Ghent University, Belgium A Viguri Universitat Jaume I, Spain Y Villacampa Esteve Universidad de Alicante, Spain F F V Vincent University of Bath, UK S Walker Imperial College, UK G Walters University of Exeter, UK B Weiss University of Vienna, Austria H Westphal University of Magdeburg, Germany J R Whiteman Brunel University, UK Z-Y Yan Peking University, China S Yanniotis Agricultural University of Athens, Greece A Yeh University of Hong Kong, China J Yoon Old Dominion University, USA K Yoshizato Hiroshima University, Japan T X Yu Hong Kong University of Science & Technology, Hong Kong M Zador Technical University of Budapest, Hungary K Zakrzewski Politechnika Lodzka, Poland M Zamir University of Western Ontario, Canada R Zarnic University of Ljubljana, Slovenia G Zharkova Institute of Theoretical and Applied Mechanics, Russia N Zhong Maebashi Institute of Technology, Japan H G Zimmermann Siemens AG, Germany

Modelling in Medicine and Biology VIII EDITOR: C.A. Brebbia Wessex Institute of Technology, UK

Editor: C.A. Brebbia Wessex Institute of Technology, UK

Published by WIT Press Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK Tel: 44 (0) 238 029 3223; Fax: 44 (0) 238 029 2853 E-Mail: [email protected] http://www.witpress.com For USA, Canada and Mexico Computational Mechanics Inc 25 Bridge Street, Billerica, MA 01821, USA Tel: 978 667 5841; Fax: 978 667 7582 E-Mail: [email protected] http://www.witpress.com British Library Cataloguing-in-Publication Data A Catalogue record for this book is available from the British Library ISBN: 978-1-84564-183-2 ISSN: 1747-4485 (print) ISSN: 1743-3525 (on-line) The texts of the papers in this volume were set individually by the authors or under their supervision. Only minor corrections to the text may have been carried out by the publisher. No responsibility is assumed by the Publisher, the Editors and Authors for any injury and/ or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. The Publisher does not necessarily endorse the ideas held, or views expressed by the Editors or Authors of the material contained in its publications. © WIT Press 2009. Printed in Great Britain by MPG Book Group. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the Publisher.

Preface

Considerable advances have been made in computational modelling of complex problems in biomedicine, as demonstrated by the continuous success of this International Conference on Modelling in Medicine and Biology. The first meeting started in Southampton (1991), followed by one in Bath (1993), and others in Milano (1995), Acquasparta (1997), Ljubljana (2003), Bologna (2005), The New Forest (2007) and culminating in the 2009 meeting in Crete. This book contains most of the papers presented at that last meeting. Advances in medical and biological technology are due to the increasing interaction and collaboration between medical and engineering scientists. Computer models which have successfully been developed to represent a series of biomedical systems are now becoming increasingly used for a wide range of applications ranging from cardiovascular modelling to virtual reality and simulation in surgery. The books resulting from these Conferences, containing a series of outstanding papers, are produced by WIT Press, the academic publisher of Wessex Institute of Technology. Since 1993, all WIT conference papers have been archived in an electronic database where they are easily and rapidly available to the international scientific community (see http://library.witpress.com/). All the papers published in this book can also be found there. The contributions in this volume are divided into the following topics: • • • • • •

Cardiovascular system Computational fluid mechanics Biomechanics Physiological processes Data acquisition and analysis Virtual reality in medicine

The Editor is grateful to all authors for their excellent contributions and to members of the International Scientific Advisory Committee and other colleagues who helped to review the work published in this volume. The Editor Crete, 2009

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Contents Section 1: Cardiovascular system Equivalence of two approaches to study the stress-strain relation in the myocardium R. M. Shoucri ..........................................................................................................3 The variation of dobutamine induced heart stress with heart rate A. K. Macpherson, S. Neti, C. Chutakositkanon, M. Averbach & P. A. Macpherson .............................................................................................17 Prediction of stent endflare, arterial stresses and flow patterns in a stenotic artery M. R. Hyre, R. M. Pulliam & J. C. Squire ...........................................................27 Fractal behaviour of pathological heart rate variability dynamics G. D’Addio, A. Accardo, G. Corbi, F. Rengo & N. Ferrara ...............................39 Microvascular disorders induced by malaria infected red blood cells: a computational mechanical study using the biological particle method T. Yamaguchi, H. Kondo, Y. Imai & T. Ishikawa ................................................49 Mechanical characterization of deep vein thrombosis in a murine model using nanoindentation K. C. McGilvray, R. Sarkar & C. M. Puttlitz........................................................57 Section 2: Computational fluid dynamics Comparison of blood flow patterns in cerebral aneurysms K. Shimano, T. Kudo & Y. Enomoto.....................................................................71 Modelling of flow through the circle of Willis and cerebral vasculature I. D. Šutalo, A. Bui, S. Ahmed, K. Liffman & R. Manasseh.................................83

Computational hemodynamics analysis in realistic 3D geometries of the human coronary atherosclerosis S. I. Bernad, T. Bărbat, E. Bernad & R. Susan-Resiga .......................................93 Numerical investigation of the flow field in the upper human airways G. Eitel, W. Schröder & M. Meinke ...................................................................103 Numerical simulations of high frequency respiratory flows in a model bifurcating lung geometry N. Valleru, S. Smirnov, J. Tan, S. Parameswaran & R. Raj ..............................115 Numerical prediction of the focal sites of ozone-induced tissue injury in the respiratory tract B. Keshavarzi, J. Ultman & A. Borhan ..............................................................123 Computational hemodynamics coupled with mechanical behaviour of the surrounded materials, in the specific case of the brachial artery R. Paulus, S. Erpicum, B. J. Dewals, S. Cescotto & M. Pirotton......................133 Section 3: Biomechanics Biomechanical consideration for dorsal-lumbar and lumbar sagittal spine disorders C. Bignardi, A. Ramieri & G. Costanzo.............................................................149 A new brace for the treatment of scoliosis M. G. Antonelli, P. Beomonte Zobel, P. Raimondi, T. Raparelli & G. Costanzo.....................................................................................................159 Parameters of kinaesthesis during gaits derived from an ultrasound-based measuring system R. M. Kiss............................................................................................................171 Evaluating elbow joint kinematics with the Stewart Platform Mechanism M. Alrashidi, İ. Yıldız, K. Alrashdan & İ. Esat ..................................................181 Dynamics of the human stomach R. Miftahof & N. Akhmadeev..............................................................................191

Section 4: Physiological processes The human body exposed to a magnetotherapy device magnetic field D. Poljak, S. Sesnic, D. Cavka, M. Titlic & M. Mihalj......................................203 Electronic active model for saccadic eye movements O. Terán & E. Suaste..........................................................................................213 Vestibular apparatus: dynamic model of the semicircular canals L. Gastaldi, S. Pastorelli & M. Sorli..................................................................223 A mathematical model to predict the performance of advanced therapies in wound healing J. Ko, S. Dickman & V. W. Li.............................................................................235 Modeling of capacitance relaxation phenomena in a malignant membrane T. K. Basak, K. Bhattacharya, S. Halder, S. Murugappan, V. Cyril Raj, T. Ravi, G. Gunasekaran & P. Shaw ................................................247 Section 5: Data acquisition and analysis A novel 3D torso image reconstruction procedure using a pair of digital stereo back images A. Kumar & N. Durdle........................................................................................257 Computer simulations and modeling in oncology: methods and applications C. Guiot , P. Paolo Delsanto & A. S. Gliozzi.....................................................267 PKAIN: an artificial immune network for parameter optimization in pharmacokinetics L. Liu, C.-H. Lai, S.-d. Zhou, F. Xie & H.-w. Lu ...............................................277 Readability of reassigned scalograms and extraction of spectra features for signal analysis S. Mekaoui, A. Houacine & T. Gharbi...............................................................287

Section 6: Virtual reality in medicine An internal examination training system supporting abnormal labor conditions A. Doi, K. Noguchi, K. Katamachi, T. Ishii, H. Uno, S. Mega & K. Matsui.........................................................................................................303 Development of a training system for interventional radiology M. Ide, Y. Fujii, B. Fujioka, T. Komeda, H. Koyama, S. Yamamoto, M. Mohri & P. Beomonte Zobel .........................................................................313 Author Index .....................................................................................................323

Section 1 Cardiovascular system



3

Equivalence of two approaches to study the stress-strain relation in the myocardium R. M. Shoucri Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada

Abstract A method to study the mechanics of ventricular contraction was developed in previous publications by the author. In those studies, the active force of the myocardium is represented as force per unit volume of the myocardium. Other authors have developed studies in which the active force of the myocardium is included in the expression of the total stress derived from the constitutive relations. The purpose of the present study is to show how to make the connection between these two approaches. Derivation is done in a general way, expressions for the stress components are derived and application to experimental data is presented. The possibility of relating the pseudo strain energy function to the tension generated by the muscular fibre is also shown. Keywords: cardiac mechanics, mathematical modelling of ventricular contraction, pressure-volume relation, active force of the myocardium, pseudo strain energy function.

1

Introduction

In previous studies by the author a method to study the stress-strain relation in the myocardium was developed in which the active force generated by the myocardium was represented as force per unit volume of the myocardium [1-6]. This mathematical approach used a cylindrical model of the left ventricle and was successfully developed by using both large elastic deformation [1, 2] and linear elasticity [3, 4], the transition from large elastic deformation to linear elasticity was discussed in [6]. Most other studies that have been developed focus on the way the expression of the total stress can be derived from the constitutive relations [9-11]. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line) doi:10.2495/BIO090011

4 Modelling in Medicine and Biology VIII In this study the myocardium is represented as a thick-walled incompressible cylinder in which the myocardial fibres are imbedded in a helical way in a soft incompressible medium (see fig. 1). The contraction of the cylinder is modelled is a way to take into consideration torsion and shear, it turns out that their effect is small for the purpose of the numerical calculation of this study. In the quasistatic approximation used in this study, inertia forces and viscous forces are neglected. The total stress induced in the passive medium of the myocardium tij is written in the form t ij = σ ij + q ij , where qij is the stress induced by the muscular fibre tension T and reflects the directional character of the stress; σij is the stress resulting from the deformation of the passive medium of the myocardium (passive medium assumed isotropic). A similar approach can de found in Spencer [11]. Nevo and Lanir [8] have introduced a quantity similar to qij as the derivative of a hydrostatic pressure, and Arts et al. [12] have used an approach where σij is replaced by a hydrostatic pressure. The purpose of this study is to show the equivalence of the formalism developed in [1-6] by the author with the formalism developed by Humphrey and Yin [9] in which the total stress tij induced in the myocardium is derived from a pseudo strain energy function W. It is also shown how W can be directly related to the muscular fibre tension T, and that the splitting of W = Wiso + Waniso into an isotropic and an anisotropic component [9, 13, 14] is equivalent to the aforementioned splitting of the total stress tij.

2

Mathematical formalism: first approach

2.1 Equilibrium conditions This is the approach used in [9, 10], in which the calculation is carried out by using the total stress tij. By assuming symmetry around the z-axis (solution independent of θ), the conditions of local equilibrium the myocardium (div t = 0) can be written as follows in cylindrical coordinates

∂t rr t rr − tθθ ∂t zr + + =0 r ∂z ∂r

(1a)

2 1 ∂ (r t rθ ) ∂t zθ + =0 ∂r ∂z r2

(1b)

1 ∂ (rt rz ) ∂t zz + =0 r ∂r ∂z

(1c)

The stress can be dependent on the z variable, but we shall simplify the mathematical formalism by assuming that tzr, tzθ and tzz are independent of z as in [9]. In this case eqns (1b) and (1c) give WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


r 2 t rθ = const = H 1

rt rz = const = H 2

5

(2)

The radial stress boundary conditions on the surface of the cylinder are given by (see fig. 1).

t rr (ri ) = − Pi

t rr (ro ) = − Po

(3)

2.2 Deformation gradient The contraction of the myocardium is assumed to change the stress free configuration (R,Θ, Z) to the end-diastolic configuration (red, θed, zed) and finally to (r, θ, z) during the systolic phase according to the relations

red = red ( R),

θ ed = α 1 Θ,

z ed = k1 Z

(4)

r = r (red ), θ = α 2θ ed + ψ 2 z ed + χ (red ),

(5)

z = k 2 z z ed + k 2θ θ ed + ω (red ) which combined together give

r = r ( R), θ = αΘ + ψZ + χ ( R), z = k z Z + kθ Θ + ω ( R)

(6)

The deformation gradient F1 for the transformation from the stress free configuration (R,Θ, Z) to the end-diastolic configuration (red, θed, zed) in cylindrical coordinates is given by [10]

∂red 1 ∂red  ∂red  ∂R R ∂Θ ∂Z    ∂θ r ∂θ ed ∂θ F1 = red ed ed red ed ∂R R ∂Θ ∂Z     ∂z ed ∂z ed 1 ∂z ed  R ∂Θ ∂Z  ∂R

  dred   dR        = 0 α 1        0    

WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

0

red R 0

0

     0     k1   

(7)

6 Modelling in Medicine and Biology VIII The deformation gradient F2 for the transformation from the end-diastolic configuration (red, θed, zed) to the final configuration (r, θ, z) is given by

 ∂r  ∂r  re   ∂θ F2 = r  ∂red    ∂z   ∂red by

1 ∂r red ∂θ ed r ∂θ red ∂θ ed 1 ∂z red ∂θ ed

 ∂r   dr 0 0    dr ∂z ed    ed       r ∂θ   dχ rψ 2  (8) r α2 = r    dred red ∂z ed          k 2θ ∂z dω   k2z  ∂z ed   dred red 

The deformation gradient F = F2.F1 of the combined transformation is given

 ∂r  ∂R    ∂θ F = r  ∂R    ∂z  ∂Z

 ∂r   dr 0 0   ∂Z   dR        r r ∂θ ∂θ   dχ = r rψ  r α  R R ∂Θ ∂Z   dR         1 ∂z ∂z  kθ dω   k z R ∂Θ ∂Z   dR R 

1 ∂r R ∂Θ

(9)

where α = α2α1, ψ = ψ2k1, kθ = k2θα1, kz = k2zk1. By assuming that the transformations take place at constant volume, the incompressibility constraint can be written as follows

I 3 = (det F ) 2 = (det F2 ) 2 (det F1 ) 2 = 1

(10)

where I3 is the third strain invariant. By calculating the determinants in eqn (10) one obtains

dr R = , dR Kr

Kr 2 − R 2 = Kri 2 − Ri2


(11)


dred R = , dR K 1 red r dr = ed , dred K 2 r

2 K 1 red2 − R 2 = K 1 ried − Ri2

2 K 2 r 2 − red2 = K 2 ri 2 − ried

7

(12)

(13)

We have K1 = α1k1 = det(F1), K2 = α2k2z - ψ2k2θ = det(F2) and K = K1K2 = det(F) = α1k1α2k2z - α1k2θk1ψ2 = αkz - kθψ, with α = α1α2, kz = k1k2z, ψ = ψ2k1, kθ = α1k2θ. The inner radii are respectively Ri and ri in the stress free configuration and during the systolic phase. A muscular fibre in the myocardium is supposed to have a helical form on a cylindrical surface. In the undeformed configuration a unit vector N with fibre angle Γ(R) is transformed into a vector n in the deformed configuration with fibre angle γ(r) calculated with respect to the circumferential direction. With λN representing the stretch ratio in the direction of the muscular fibre, we have

n = [0, cos(γ (r ), sin(γ (r )]T ,

N = [0, cos(Γ( R), sin(Γ( R)]T (14)

with

n=

1

λN

F .N

(15)

By using eqns (9) and (15) we get

cos(γ ( r )) =

1 αr [ cos(Γ( R)) + ( rψ ) sin(Γ( R))] λN R

(16)

sin(γ (r )) =

1 kθ [ cos(Γ( R)) + k z sin(Γ( R))] λN R

(17)

2.3 Constitutive relations Relations between the components of the stress and deformation are known as constitutive relations. By assuming transverse isotropy with respect to the z-axis of the cylinder, Humphrey and Yin [9] have focused on a subclass of transverse isotropic material with pseudo strain energy function W given by the expression

W = W (I1 , λ N )

(18)

where I1 is the first strain invariant I1 = tr(B), and B = F.FT is the left CauchyGreen deformation tensor. Written explicitly we have WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

8 Modelling in Medicine and Biology VIII

Figure 1:

Cross-section of a cylinder representing the left ventricle. The dotted circle represents the projection of a helical fibre on the cross-section. Dr(r) is the radial active force/unit volume of the myocardium. Pi is the ventricular pressure, Po is the outer pressure, ri is the inner radius, ro is the outer radius, h = b – a is the thickness of the myocardium.

 dr 2 ( )  dR   dr dχ B = r  dR dR    dr dω   dR dR

r

dr dχ dR dR

(r

dχ 2 α 2 r 2 ) + 2 + ( rψ 2 ) dR R

r

dχ dω αrkθ + 2 + rψk z dR dR R

     dχ dω αrkθ r + 2 + rψk z  dR dR R   2  k dω ( ) 2 + θ2 + k z2  dR R  dr dω dR dR

(19) The Cauchy stress t (force/current area) can be expressed by using eqn (18) in the form [9]

t ij = − pδ ij + 2W1 Bij + WλN λ N n i n j where W1 =

(20)

∂W ∂W and W λN = , p is a Lagrange multiplier introduced to ∂I 1 ∂λ N

express the incompressibility condition for the myocardium. The first two terms in eqn (20) have an isotropic symmetry and the third term (the components of ni are shown in eqn (14), part one) has a directional character corresponding to the WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


9

direction of the muscular fibre in the myocardium. We are now in a position to make the junction with the second approach developed in [1-6].

3 Mathematical formalism: second approach 3.1 Equilibrium conditions We shall now see that it can be more instructive to work with the components σij and qij of tii = σij + qij. T(r,z) is the stress in the direction of the muscular fibre in the myocardium. By assuming that a muscular fibre in the myocardium has a helical cylindrical shape as in the previous section, one can derive for the components of the stress qij the following relations as in [2, 15]

q rr = 0,

qθθ = T (cos γ (r )) 2 ,

q zθ = T sin γ (r ) cos γ (r ),

q zz = T (sin γ (r )) 2 q rθ = q rz = 0

(21)

It is also possible to write the following relations

Dr =

T (cos γ (r )) 2 , r

q zθ = rDr tan γ ,

q zz = rDr tan 2 γ (22)

where Dr is obtained by substituting tij = σij + qij in eqns (1) and by writing the terms containing qij in the following way

Dr =

qθθ , r

Dθ = −

∂q zθ , ∂z

Dz = −

∂q zz ∂z

(23)

The quantities Dr, Dθ and Dz have the units of force/unit volume of the myocardium expressed in the three orthogonal directions of a cylindrical coordinate system. By using this notation, eqns (1) can be written in the form

∂σ rr σ rr − σ θθ ∂ ∂σ rr σ rr − σ θθ ∂σ zr + + − Dr = + + (σ zr −∫ D r dz ) ∂r r ∂z ∂r r ∂z z (24a)

1 ∂ (r σ rθ ) ∂σ zθ 1 ∂ (r σ rθ ) ∂ + − Dθ = 2 + (σ zθ − ∫ Dθ dz ) (24b) 2 ∂r ∂z ∂r ∂z r r z 2

2

1 ∂ (rσ rz ) ∂σ zz 1 ∂ (rσ rz ) ∂ + − Dz = + (σ zz − ∫ D z dz ) r ∂r ∂z r ∂r ∂z z WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

(24c)

10 Modelling in Medicine and Biology VIII Because trθ = σr θ (qrθ = 0) and trz = σrz (qrz = 0) we can write in a way similar to eqns (2)

r 2σ rθ = const = H 1

rσ rz = const = H 2

(25)

We assume that no external moment is applied to the myocardium, consequently the moment of forces M around the z-axis is zero ro

M = 2π ∫ (σ zθ +q zθ ) r 2 dr = 0

(26)

ri

which gives

σ zθ = −q zθ

(27)

Equilibrium of forces in the longitudinal direction gives

σ zz + q zz + τ av = 0

(28)

where τav is the average traction on the cross-section and is given by [8]

τ av =

Pi ri 2 − Po ro2 ro2 − ri 2

(29)

It is assumed that the average stress τav is independent of r and z. 3.2 Constitutive relations It is assumed that the muscular fibre tension T(r,z), and consequently qij, is uniformly distributed throughout the myocardium. By writing tij = σij + qij and by comparing eqns (21) with the last term of eqn (20) we can write

q ij = WλN λ N ni n j

(30)

with WλN appropriately chosen such that

T = WλN λ N

(31)

From eqn (20), the stress σij can be expressed as follows

σ ij = − pδ ij + 2W1 Bij WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

(32)


11

This last equation can be written with the help of eqn (19) in explicit form as follows

σ rθ = 2W1 r

dr dχ H 1 = dR dR r 2

(33)

σ rz = 2W1

dr dω H 2 = dR dR r

(34)

dχ dω αrkθ + 2 + rψk z ] dr dR R

σ zθ = 2W1 [r

σ zz

2 dω 2 k θ = − p + 2W1 [( ) + 2 + k z2 ] dr R

σ θθ = − p + 2W1 [(r σ rr = − p + 2W1 (

dχ 2 αr 2 ) + ( ) + ( rψ ) 2 ] R dr

dr 2 R ) = − p + 2W1 ( ) 2 dR Kr

(35)

(36)

(37)

(38)

These equations are used in the experimental application described in what follows. The term Dr appearing in eqn (24a) is similar, but not identical, to the introduction of a derivative of a hydrostatic pressure in eqn (26) of [8].

4 Application and results The fibre angle γ(r) (referred to the circumferential direction) is supposed to be constant with respect to the axial and circumferential directions. The radial variation of the fibre angle is supposed to be linear and given by

γ = γ end (

ro − r r − ri ) + γ epi ( ) ro − ri ro − ri

(39)

where γend = 45o is the fibre angle at the endocardium, and γepi = - 45o is the fibre angle at the epicardium. The dimensions of the left ventricle in the diastolic configuration are outer radius ro = 3.38 cm, inner radius ri = 1.02 cm and length l = 3.06 cm as taken from experiment on dog reported in Feit [7]. The corresponding radii in the reference stress free configuration were estimated from eqn (11), part two, as Ro = 3.4474 cm and Ri = 1.1 cm. The tension T developed by the muscular by the fibre near the end-diastolic phase is taken from fig. 7a of Feit [7] and is reproduced in fig. 2 (left) of this study, fig. 2 (right) WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


Figure 2:

Radial variation from endocardium to epicardium of the fibre tension T reproduced from [7] (left), and of the radial active force/unit volume of the myocardium Dr (right).

shows the variation of Dr calculated from eqn (22), part one and (39). Similarly the active stress components qzθ and qzz are calculated respectively from eqn (22), parts two and three, σzθ and σzz are calculated respectively from eqns (27) and (28) and shown in fig. 3. We took the ventricular pressure Pi = 10 mmHg and the epicardial pressure Po = 0 mmHg in the calculation of τav from eqn (29). The two quantities dχ/dr and dω/dR are small and have be neglected in the calculation that follows. Consequently from eqns (35) – (38) one can derive the following equation to calculate σrr

σ zθ (k αr ) / R 2 + k zψr = 2 θ2 σ zz − σ rr kθ / R + k z2 − R 2 /( Kr ) 2 and the following equation to calculate σ θθ σ zθ (kθ αr ) / R 2 + k zψr = σ θθ − σ rr (αr ) 2 / R 2 + (ψr ) 2 − R 2 /( Kr ) 2

(40)

(41)

The radial variation of σrr and σθθ is shown respectively in the left and right side of fig. 4. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


13

Figure 3:

Radial variation from endocardium to epicardium of the stress σzθ (left), and of the axial stress σzz (right).

Figure 4:

Radial variation from endocardium to epicardium of the radial stress σrr (left), and of the circumferential stress σθθ (right).



Figure 5:

Radial variation of the total circumferential stress tθθ from endocardium to epicardium.

In the calculation of σrr and σθθ we have made use of the two following conditions, first the incompressibility condition

αk z − ψ kθ = K

(42)

The second condition is that numerator of eqn (41) for σzθ is zero for rzero = 2.2 cm from fig. 3 (R2zero = 5.1160 from eqn (11), part two), which gives 2 αkθ + ψk z R zero =0

(43)

Eqns (42) and (43) are solved to express α and ψ in terms of kz and kθ as follows

ψ =−

kθ K 2 kθ + k z2 R zero

(44)

α=

2 k z KR zero 2 kθ2 + k z2 R zero

(45)

2

These values of ψ and α are substituted into eqn (40) evaluated at ri (σrr = Pi = 10 mmHg) and at ro (σrr = -Po = 0) with σzz calculated from eqn (28). The two equations obtained in this way are solved by using the Newton iteration WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


15

algorithm to calculate the two roots kθ and kz of a system of two coupled equations. For ri = 1.02 cm, ro = 3.38 cm, K = 1.028, Ri = 1.1 cm, Ro = 3.4474 cm, we have calculated kθ = -0.1472, kz = 1.0043, eqns (44) and (45) give α = 1.0228 and ψ = 0.0057. These are the values used to calculate the results of fig. 4. From the results shown in figs 3 to 6, the radial variation of each of the stress components appears to be similar to that reported in ref. [9] with a difference of sign probably due to the fact that we use the convention that a negative stress represents compression, a positive stress represents tension. It is also important to note the difference between the stress components σij and tij as is clear for instance by comparing fig. 4 (right) and fig. 5, and also how the three quantities W1, WλN and Dr can be expressed directly in terms of the muscular fibre T.

Figure 6:

5

Radial variation from endocardium to epicardium of WλN (eqn (31)) (left), and of W1 (eqn (38)) (right).

Conclusion

By introducing the concept of radial active force/unit volume of the myocardium, we have shown that it is possible to calculate the stress induced in the passive medium of the myocardium and the components of the active stress generated by the muscular fibre. One should note that all the calculations have been carried out without having to assume a model for the pseudo strain energy function; instead knowledge of the muscular fibre stress generated in the direction of the muscular fibre was necessary for our calculation. It is also WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

16 Modelling in Medicine and Biology VIII evident that the trend in the literature to split the pseudo strain energy function into an isotropic and a directional component is equivalent to the splitting of the total stress into two components as explained in this study.

References [1] Shoucri, R.M., The pressure-volume relation and the mechanics of left ventricular contraction, Japanese Heart Journal, 31, pp. 713-729, 1990. [2] Shoucri, R.M., Theoretical study of pressure-volume relation in left ventricle, American Journal of Physiology, 260, pp. H282-H291, 1991. [3] Shoucri, R.M., Active and passive stresses in the myocardium, American Journal of Physiology, 279, pp. H2519-H2528, 2000. [4] Shoucri, R.M., The calculation of the intramyocardial stress, Technology and health Care, 10, pp. 11-22, 2002. [5] Shoucri, R.M., Studying the mechanics of left ventricular contraction, IEEE engineering in Medicine and Biology Magazine, 17, pp. 95-101, May/June 1998. [6] Shoucri, R.M., Comparison between linear elasticity and large elastic deformation in the study of the contraction of the myocardium, Modelling in Medicine and Biology VII, ed. C.A. Brebbia, WIT Press: Southampton & Boston, pp. 3-13, 2007. [7] Feit, T.S., Diastolic pressure-volume relations and distribution of pressure and fiber extension across the wall of a model left ventricle, Biophysical Journal, 28, pp. 143-166, 1979. [8] Nevo, E. & Lanir, Y., Structural finite deformation model of the left ventricle during diastole and systole, Journal of Biomechanical Engineering, 111, pp. 342-349, 1989. [9] Humphrey, J.D. & Yin, F.C.P., Constitutive relations and finite deformations of passive cardiac tissue II: stress analysis in the left ventricle, Circulation Research, 65, pp. 805-817, 1989. [10] Guccione, J.M., McCulloch, A.D. & Waldman, L.K., Passive material properties of intact ventricular myocardium determined from a cylindrical model, Journal of Biomechanical Engineering, 113, pp. 42-45, 1991. [11] Spencer, A.J.M., Deformation of fiber-reinforced Materials, Clarendon Press: Oxford, U.K., p. 82, 1972. [12] Arts, T., Bovendeerd, P.H.M., Prinzen, F.W. & Reneman, R.S., Relation between left ventricular cavity pressure and volume and systolic fiber stress and strain in the wall, Biophysical Journal, 59, 93-102, 1991. [13] Driessen N.J.B., Bouten C.V.C. & Baaijens F.P.T., A structural constitutive model for collagenous cardiovascular tissues incorporating the angular fiber distribution, Journal of Biomechanical Engineering, 127, 494-503, 2005. [14] Zulliger M.A., Fridez P., Hayashi K. & Stergiopoulos N., A strain energy function for arteries accounting for wall composition and structure, Journal of Biomechanics, 37, 989-1000, 2004. [15] Chadwick, R.S., Mechanics of the left ventricle, Biophysical Journal, 39, 279-288, 1982. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


17

The variation of dobutamine induced heart stress with heart rate A. K. Macpherson1, S. Neti1, C. Chutakositkanon1, M. Averbach2 & P. A. Macpherson3 1

Institute of Biomedical Engineering and Mathematical Biology, Lehigh University, USA 2 Radiology Department, St Luke’s Hospital, USA 3 Department of Applied Technology, Rogers State University, USA

Abstract Dobutamine stress echocardiography is a common test to provoke myocardial ischemia in patients unable to undergo routine exercise stress testing. Heart rate elevation, achieved by staged increases in dobutamine doses, acts as a surrogate for exercise. The physicians monitor the ECG of the patient and echocardiographic images to evaluate for myocardial ischemia. However, the actual mechanical stress on the heart is not readily available to the physician. The motivation for the present preliminary study is to both investigate the feasibility of producing such information for clinicians as well as to investigate the variation between different patients as the heart rate varies. Echocardiograms were obtained from three patients undergoing dobutamine stress tests. Using standard equations of motion, the surface shear stress at the surface of the left ventricle was calculated. The average shear stress around the left ventricle is shown, as well as the peak stresses at selected locations as a function of time. It was found that generally the surface shear stress increased with heart rate around most of the left ventricle. While the time averaged shear stress may be important for diagnosis, the maximum shear stress is probably the limiting factor in terminating testing. Keywords: heart stress, dobutamine testing, heart rate, heart diagnosis.

WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line) doi:10.2495/BIO090021


1

Introduction

Dobutamine stress echocardiography is a common test to provoke myocardial ischemia in patients unable to undergo routine exercise stress testing. Heart rate elevation, achieved by staged increases in dobutamine doses, acts as a surrogate for exercise. A study is currently underway relating isolated myocardial stress to neurologic activity, without other confounding factors. The effects of shear stress on the heart are very extensive. Two surveys [1,2] showed that stress can cause changes in the genetic structure of the heart. In patient review it would be useful for a clinician to have details of the stress being applied to the heart. The dobutamine stress test is stopped if a patient develops concerning symptoms or demonstrates evidence of significant myocardial ischemia. In making a decision to terminate a test, information on the level of stress being experienced by the patient would be useful information for the clinician. As the present preliminary study was both a feasibility study as well as a preliminary investigation for a neural cardiovascular study, available echocardiogram results were used. Three-dimensional MRI results will be used in subsequent studies.

2

Method of calculation

The general method of calculation used here has been described previously [3,4]. In the solution the bloodflow into the left atrium is simulated by a source distributed throughout the atrium. In order to conserve mass sinks are distribute around the periphery of the integration domain. The change in shape is obtained from the echocardiograms and used as boundary conditions for the flow. The source strength has to match the change in volume of the ventricle. The valves have to be modelled as thicker than in reality as Lagranian integration must go around both sides of the valve. The Navier-Stokes equations are then solved with a predictor corrector scheme [4]. The Navier Stokes equations defined on an x-y Cartesian co-ordinate system for an incompressible fluid are  ∂uˆ  + uˆ • ∇uˆ  + ∇p = µ∇ 2 uˆ + Fˆ  ∂t 

ρ

∇uˆ = 0

(1) (2)

where uˆ is the velocity vector, ρ is the density, t is the time, p is the pressure and the viscosity is µ . The boundary force Fˆ arising from the heart muscles is L

(

)

Fˆ (xˆ , t ) = ∫ fˆ (s, t )δ xˆ − Xˆ (s, t ) ds 0


(3)


19

Here fˆ is the force on the boundary element at the point s defined on a Lagrangian system where xˆ is defined on the Cartesian system and Xˆ n is the nth point on the Lagrangian system The flow velocities and pressures can be used to calculate the stresses on the surface of the heart walls. These forces can then be used to examine the microscopic interaction with the cells in the heart wall (endocardium). The first step in the solution involves obtaining the shape of the ventricle at various times. This is often difficult as echocardiogram images are sometimes indistinct. Following a method often used by echocardiographers only five images in a cardiac cycle were selected. One image when the valves were closed, a second image when the valves were fully open, a third just before the atrium starts to contract, one at the end of the ventricle filling (diastole) stage and a final one as the aortic valve opens. A linear variation was assumed between each image, time frame. It was assumed that the motion of the wall would be normal to the surface. As described below the times required for valve opening and atrium contraction can be obtained from Doppler measurements of the velocity through the mitral valve and the shape was obtained from the echocardiogram contained many irregularities. The echocardiogram tracing was obtained as a digital image. If the source were allowed to start while the valves were closed then the program would fail due to excessive pressure. Similarly the wall could not be allowed to start moving until the source started. Thus an initial short period was required without source or wall motion to allow the valves to start opening (these events are independent of fluid motion are dependent on cardiac electrical signals). The second step required the simulation of the atrium. The atrium changes shape during the diastole stage and thus changes the pressure. However the use of a source in place of the correct inflow pattern to the atrium was an artifice that made the actual atrium shape unimportant. The atrium shape was fixed at near hemispherical shape with valves in the closed and early open positions. After some time the atrium contracts for a period before the mitral valve closed. The shape was expanded and contracted as required for the different sized mitral valves. The source strength was increased slowly as the valves opened in accordance with the increase in volume of the ventricle. Once the calculation of the flow velocities and pressures were completed the stresses at the walls were calculated. In accordance with the aim of the research, evaluation of wall stresses, the boundary layer had to be modelled properly. Two points were chosen as close to the wall as possible along a line normal to the surface. A finite difference method was used to obtain the derivative of the velocity along this line. Similarly the velocity normal to the wall was calculated along the same line. As only pressure gradients are used in the calculations, an arbitrary constant was added to the pressure to make it relative to atmospheric pressure. The method of the microscopic calculation of the blood, to obtain details on the affinity involved the effects of dobutamine contained in the blood, on the cells of the myocardium will not be discussed here. It is necessary to have a length scale in between the continuum calculation and the above microscopic WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

20 Modelling in Medicine and Biology VIII scale. This is undertaken using a Monte Carlo method. These details are presented elsewhere [4]. The basic process of describing the effects of dobutamine starts with the Landau equation which for the test particle takes the form below and has been described as a generalized diffusion equation in velocity space by Chandrasekhar [5]. Expressed in a non-dimensional form it becomes [6]

∂φτ = ∂ vr ( − Fr + 0.5∂ sTrs )φ

(4)

where φ is the velocity distribution, the v r differentiation is with respect to nondimensional velocity v/2kT, subscript τ is differentiation with respect to the nondimensional time defined below. The solution is obtained in terms of the drag force Fr and a random force Trs .

Fr = −8v −1G ( v )vr Trs = 2v −1H ( v )δ rs + 2v −3 E ( v )vr vs

(5) (6)

The movement of the blood components assumes they are sufficiently far apart so that collisions between the components will not occur. This is the usual assumption made for the application of the Landau equation. Under these circumstances the force on an ion will consist of a drag due to G(v) and a random force due to H(v). The docking mechanism for dobutamine with the receptor is unknown. It is useful in considering the present results to have an estimate of the fraction of dobutamine, which will dock with the receptor. Both dobutamine and Losartan dock with a G-protein so in order to make an estimate of the fraction of dobutamine absorbed, the docking of Losartan was calculated under the various conditions simulated in the present paper. The density of dobutamine receptors was used to estimate the affinity of the dobutamine to the receptor based on the affinity values calculated for Losartan. This is only presented in order to provide an indication of the possible outcome.

3

Results

The m-mode tracings were not available so that the opening and closing of the valves had to be obtained from the one EKG recording and the heart rate provided. The EKG recording is shown in the bottom left of figure 1. The heart rate is shown as 67 on the bottom right. The results of the stress calculations are presented for four regions of the ventricle. The regions are the apex (A), the mid endocardium (ME), across the mitral valves (MV) and in the middle of the septum (SE) as shown in figure 2. Typical variation of maximum and average shear stress over the whole ventricle is shown as a variation of time in figure 3. It can be seen that the peak maximum stress occurs when the aortic valve opens. The average of the shear stress over the whole ventricle is shown as a dashed line. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


Figure 1:

Figure 2:

21

Typical echo recording showing EKG recording and heart rate.

Areas over which the averaged stress was calculated.



Figure 3:

The variation of shear stress over the whole ventricle at a resting heart rate of 63 BPM for patient 1.

Figure 4:

The variation of shear stress over the whole ventricle at the maximum heart rate of 154 BPM for patient 1.



Figure 5:

23

The variation of shear stress over the septum at the heart rate of 150 BPM for patient 1.

It can be seen that the peak stress is more than 50% higher at 154 BP than at 63 BPM over the whole ventricle. Over the septum the peak stress is shifted to the opening of the aortic valve and is less than the peak stress over the endocardium. The variation of maximum shear stress around the whole ventricle is shown in figure 6 for the three patients. It can be seen that it increases very rapidly with heart rate. Patient 1 was a 55 year old woman, Patient 2 was a 75 year old woman and Patient 3 was a 75 year old woman. An unresolved problem is whether the maximum stress causes the onset of hypertrophy or the average stress applied over an extended time. In [4] it was shown that there is a finite length of time required for the angiotensin II to dock with the AT receptors on the G-protein. Thus it appears reasonable to assume it is the average sustained shear stress that is the more important stress for the onset of hypertrophy. The time averaged shear stress over one heart beat in the ME region, as a function of heat rate is shown for the three patients in figures 7. It can be seen in all patients that the effect of a moderate increased heart rate is to increase the stress very rapidly. However with further increase in heart rate there is comparatively small increase in the time-averaged heart rate. In the case of Patient 3 the time averaged shear stress decreases with high heart rate. This may be a valid result or it could be due to the interpretation of the echocardium. Further study using MRI output will resolve this result.



(a)

(b)

(c) Figure 6:

4

The variation of the maximum shear stress on left ventricle with heart rate. (a) Patient 1, (b) patient 2, (c) patient 3.

Conclusions and future work

As the time averaged stress only increases slowly with high heart rate then it appears that the time averaged stress is not the best criteria for terminating the testing. As seen in Figure 6 the maximum shear stress around the ventricle increases very rapidly with the heart rate. Therefore the best termination criterion probably is the maximum stress at any point around the ventricle. Values of the average shear stress would be useful for the physician in determining treatment. Only limited results have been presented for conditions along the septum. However hypertrophy of the septum can occur and will been addressed in future work. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


(a)

25

(b)

(c) Figure 7:

Variation of time averaged shear stress over on heartbeat as a function of heart rate. (a) Patient 1, (b) patient 2, (c) patient 3. The location is in the ME region as in figure 2.

This preliminary study has shown that data useful to a clinician monitoring dobutamine testing can be obtained. In addition diagnostic results can be extracted from the data. Future studies will use MRI data the output of which can be automated. This will be used in a study of a heart-brain study presently underway.

References [1] Sadoshima J. and Izumo S. The cellular and molecular response of cardiac myocytes to mechanical stress Ann. Revs of Physiology, 59, 551–571, 1997. [2] Ruwhof C, van der Laarse A. Mechanical stress-induced cardiac hypertrophy: mechanisms and signal transduction pathways Cardiovascular Research, 47, 23–37, 2000. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

26 Modelling in Medicine and Biology VIII [3] Macpherson AK and Neti S, “The effect of Angiotensin II on heart blood flow and hypertension”, Advances Fluid Mechanics IV, eds M. Rahman, R. Verhoeven, C.A. Brebbla, WIT press, Southampton, 1–12, 2002.1–12, 2002. [4] Macpherson AK, Neti S, Macpherson PA, Houser SR, Hari M and Marzillier J. Mechanical Stress and Hypertrophy, Modelling in Medicine and Biology VI, eds M. Ursino, C.A. Brebbia, G. Pontrelli, E. Magasso, WIT Press, Southampton, 171–179, 2005. [5] Chandrasekhar, S. Principles of Stellar Dynamics, Uni. Of Chicago Press, Chicago, 1942. [6] Balesu, R. Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York, 1975.co.



27

Prediction of stent endflare, arterial stresses and flow patterns in a stenotic artery M. R. Hyre1, R. M. Pulliam2 & J. C. Squire1 1

Department of Mechanical Engineering, Virginia Military Institute, USA Department of Mechanical Engineering, Villanova University, USA

2

Abstract Restenosis remains a significant problem in coronary intervention. While stent migrations, collapses, and positioning difficulties remain serious issues, it is the problem of restenosis that is the most common long term problem in treating atherosclerotic coronary arteries with stents. While much attention has focused on biocompatibility, thrombosis and neointimal pathology, less attention has been given to matching stents to the inflation balloon, artery and occlusion size. Results from this study indicate a 100% increase in balloon overhang results in a 4% increase in maximum endflare and a 39% change in peak arterial stress. At the end of expansion, which is of the most clinical importance, the increase in maximum endflare is 2% and the increase in maximum arterial stress is 93% at the balloon point of contact and 45% at the point of contact with the far proximal and distal ends of the stent. When comparing the results of calcified and cellular plaque, a maximum endflare of about 55% was observed for both the calcified and cellular plaque cases during expansion. At the end of expansion the increase in maximum endflare was 10% for the cellular plaque and 40% for the calcified plaque. The peak equivalent stress seen by the artery was about 100% larger in the cellular case than in the calcified plaque case. Keywords: stent, vascular injury, balloon, restenosis, finite element analysis.

1

Introduction

Atherosclerotic stenosis and its ischemic complications necessitate arterial reconstruction. Current strategies to restore normal blood flow in stenotic coronary arteries include angioplasty, intracoronary stents, and coronary artery WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line) doi:10.2495/BIO090031

28 Modelling in Medicine and Biology VIII bypass surgery. Depending on the method of treatment, the incidence of restenosis is high: up to 40% within six months after angioplasty [1], 25% after stenting [2], and 20% after bypass surgery [3]. Therefore, restenosis remains a significant problem in coronary intervention. Advances in prosthetic science and engineering have spurred the rapid development of many new permanent implants such as arterial reinforcement grafts, venous filters, myocardial perforation-sealing clamshells, and stents that strengthen and scaffold the biliary duct, urethra, veins, and arteries. These devices are typically attached to a delivery catheter and threaded to the site of interest where they are expanded. The very nature of the remote delivery systems make the mechanical details of implantation difficult to ascertain, yet this is important to quantify since there may be a link between how the devices are emplaced and the body’s acute and chronic response. Endovascular stents in particular are ideal devices to quantify these relationships because of the extreme levels of stress they impose and because of their ubiquity; more than one million are annually implanted in the U.S. alone [4]. These studies suggest an upper limit exists to the success of purely biomedical approaches for managing post-device implantation, and a return to examining the mechanical initiators of vascular injury that occur during implantation. A complete understanding of the manner that stents expand may thus lead to both a new understanding of the processes of vascular adaptation to implants and possibly to the design and development of less-injurious devices. Experimental data are indirect; stents are too thin to be fully radioopaque, and methods of bringing a camera to the stent, such as intravascular ultrasound, are blocked by the balloon that expands the stent during the critical moments of implantation. Post mortem examinations indicate that restenosis is paradoxically more severe in the parts of the artery immediately outside the stented region, and animal studies have shown an unusual pattern of endothelial cell denudation occurring at a regular pattern at the center of stent struts, a superficial injury that may be a marker for deep vascular injury [8]. These data are not explained by current finite element analyses of arterial stresses in a stent-expanded artery [912] because no finite element models included the expansion of a balloon catheter in the model of a plastically-deformed stent. The inclusion of the balloon catheter in the stent expansion model is not trivial. The problem is highly non-linear and includes complex contact problems between the stent, balloon, and arterial wall. Additionally, the balloon properties change dramatically depending on whether it is fully or partially inflated.

2

Geometry

The finite element stress analysis was performed on a three-dimensional stent/balloon/plaque/artery geometry. In addition to the usual difficulties in modeling the mechanical behavior of soft tissue, the overall system response is highly nonlinear due to the large plastic/multilinear-elastic/hyperelastic deformations of the individual components. The component geometries and constitutive material models are described below. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


29

2.1 Artery The coronary artery modeled was 30mm in length, with an inside diameter of 2.8mm and thickness of 0.3mm. Average element size was about 0.5mm long with a thickness of 0.15mm. This configuration yielded a total of 7,680 elements. The artery elements were defined by eight nodes capable of large deflections and hyperelasticity 2.2 Plaque The plaque has a semi-parabolic profile and corresponds to percent blockage data presented by Lally et al. [12]. The plaque was 16mm in length with a maximum thickness of 0.48 mm. This configuration corresponds to a maximum percent blockage of about 60%. The characteristic shape of plaque can be seen in Figure 1.

Figure 1:

Figure 2:

Characteristic plaque curve.

Balloon geometry, shown with mounted slotted tube stent.


30 Modelling in Medicine and Biology VIII 2.3 Balloon The balloon was modeled in its unfolded state, and already assumed to be in contact with the stent. The balloon dimensions are given at 0 Pa, before stent expansion occurs. Depending on the amount of balloon overhang, the overall length of the balloon can range from 22-23 mm. For 1mm balloon overhang, the total length of end balloon is 1mm, or 0.5 mm on each side of the inside balloon, yielding a total balloon length of 22 mm. For 2 mm balloon overhang, the total length of balloon overhang is 2 mm, or 1 mm on each side, yielding a total balloon length of 23 mm (see fig. 2). The balloon was meshed using triangular shell elements with an average base size of 0.05 mm and an average side length of 0.05 mm. This yielded 54,456 elements for the 2 mm overhang case and 51,616 elements for the 1 mm overhang case. For finite element analysis, elements capable of modeling shell structures, large deflections and plasticity were used. 2.4 Stent A three dimensional model of the slotted tube geometry intravascular stent was created. The stent is 16 mm in length (L), with an inside diameter (ID) of 1 mm, and a thickness (t) of 0.1 mm. The diamond-shaped stent consists of 5 slots in the longitudinal direction and 12 slots in the circumferential direction with a length of 2.88 mm. The slots were cut such that in a cross-section, the angle describing the slot was approximately 23 degrees, and the angle describing the metal between slots was 6.9 degrees (see figs. 3 and 4). These dimensions refer to the model in an unexpanded state [10, 12]. The stent was meshed using hexahedral elements. There are two elements through the thickness of the stent yielding a total of 12,036 elements. The stent was assigned an element type of solid45 for finite element analysis in ANSYS. These elements are defined by eight nodes and are capable of large deflections and plasticity.

Figure 3:

Medial slice of modeled slotted tube stent.



Figure 4:

Side view: stent geometry.

Figure 5:

31

Final model geometry.

A cross-section of the final model geometry with the stent/balloon/artery and plaque is shown in fig. 5.

3

Materials

3.1 Artery The material properties of the artery are based on a previous study by Lally et al. [12]. This model describes the behavior of the artery using a five parameter, third-order, Mooney-Rivlin hyperelastic constitutive equation. This model has been found to be suitable for modeling an incompressible isotropic material [13]. Prendergast et al. developed the constants for this model by fitting the fiveparameter Mooney-Rivlin expression to uniaxial and equibiaxial tension tests of human femoral arterial tissue data [14]. See Table 1. 3.2 Plaque The material properties of the plaque are based on a previous study by Loree et al. [15]. Two histological classifications of plaques were modeled: cellular and calcified. The cellular and calcified specimen results were chosen to provide models of stent expansion dynamics with plaques whose stress-strain slopes differed significantly. This model describes the behavior of the plaque using a five parameter, third-order Mooney-Rivlin hyperelastic constitutive equation. This model for plaque behavior neglects the artery laminate compositions, tissue anisotropy as well as the residual strain and active smooth muscle stresses [6]. The final form of the strain density function used to model the artery is given in eqn. (1). W = a10(I1 – 3) + a01(I2 – 3) + a20(I1 – 3)2 + a11(I1 – 3)(I2 – 3) + a30(I1 – 3)3 (1) The constants were developed for this model by fitting the five-parameter Mooney-Rivlin expression to uniaxial tension tests of human aortic atherosclerotic tissue data [15]. The hyperelastic constants for the plaques are given in Table 2. 3.3 Balloon To model the mechanical properties of the balloon without evaluating the balloon’s behavior during unfolding, empirical data was used. The stress-strain WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

32 Modelling in Medicine and Biology VIII Table 1:

Hyperelastic constants for the artery.

Hyperelastic Constants [Pa] a10 = 0.01890 a01 = 0.00275 a20 = 0.08572 a11 = 0.59043 a02 = 0

Table 2:

Hyperelastic constants for plaque.

Hyperelastic Constants [Pa] Cellular Plaque Calcified Plaque a10 = -0.088314 a10 = -3.0254 a01 = 0.10619 a01 = 3.1073 a20 = 0.11373 a20 = 107.39 a11 = 0.89382 a11 = -234.7 a02 = -0.96676

a02 = 137.22

curve for the full expansion of the balloon produced a linear piecewise function. The first segment of the piecewise function is representative of the unfolding balloon, while the second is of the balloon expansion after unfolding. 3.4 Stent The stent was modeled after the slotted tube geometry given by Migliavacca et al. [10]. This model assumes the stent to be made of 316LN stainless steel. The Poisson ratio is 0.3 and the Young Modulus is 200 GPa.

4

Boundary conditions

The artery, balloon, plaque, and stent were all constrained in the rotational directions allowing no rotation. The artery was constrained axially at the distal ends. The artery was at a minimum, 7mm longer than the stent on each side and 3.5mm longer than the end of the balloon on each side. This constraint on the artery did not affect the behavior of the artery at the point of contact with the stent or balloon because of the extra length of the artery on both sides. The same axial constraint was placed on the balloon. To model the expansion of the balloon the balloon was assigned a ramped internal pressure load.

5

Deformed geometry export and solution

In order to examine the blood flow patterns thorough the stented artery, a conversion module was written to export the final expanded stent/plaque/artery system for meshing and use within a finite volume computational fluid dynamics code (FLUENT/UNS). The deformed geometry was exported to STL format and the internal geometry (solid mirror of the stent/plaque/artery) was meshed using a hex dominant grid. Holes and seams between the various geometry parts were automatically filled within the meshing algorithms. The inlet boundary condition was specified as a velocity inlet using the time dependent flow rate equation of Womersley found in [16]. The flow was WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


33

assumed to enter the simulation with a constant cross-sectional velocity. A noslip condition where the stent/plaque/artery surfaces were in contact with the blood was assumed. The Casson model was used to evaluate the viscosity of the blood since the artery was relatively large and inhomogeneities associated with Fahraeus effects were negligible.

6

Results and discussion

Figure 6 shows the endflare during stent expansion for the 1mm and 2mm balloon overhang cases when there is no plaque included in the models. Endflare is defined as the ratio of the stent diameter at the distal ends to the diameter at the stent centerline. There is a significant difference in the endflare both at the point of peak endflare and at the end of expansion, indicating that the amount of balloon overhang can have a significant impact on vascular injury. Figure 7 shows the endflare during stent expansion for the 2mm balloon overhang case when calcified and cellular plaque are included in the models. The endflare with plaque present in the model is significantly higher than when it was not included. This is because the distal ends of the stent were located such that they did not contact the plaque. Therefore, the effective diameter against which the stent was expanding was significantly larger in this area leading to a lower expansion resistance. There is a significant difference in the endflare both at the point of peak endflare and at the end of expansion, indicating that the amount of balloon overhang can have a significant impact on vascular injury. Figure 8 shows the arterial stresses at the end of stent expansion when calcified and cellular plaque was included in the model. At the end of expansion, the increase in maximum endflare for the cellular plaque geometry over the calcified plaque geometry is about 200%. The increase in maximum arterial stress is 200% at the point of stent contact at the proximal and distal ends.

Figure 6:

Endflare without plaque for 2mm (upper line) and 1mm (lower line) overhang.

Figure 7:


Endflare with plaque for calcified (upper line) and cellular (lower line) plaque.


Figure 8:

Arterial/plaque stresses for calcified (top) and cellular (lower) plaque.

Figure 9:

Max arterial stresses for calcified (lower line) and cellular (upper line) plaque.

Figure 10:

Arterial stresses (radial, hoop, and axial) for calcified plaque.

Figure 11:

Arterial stresses (radial, hoop, and axial) for cellular plaque.

Figure 9 shows the max arterial stress during the expansion process for the cellular and calcified plaque cases. The cellular plaque case results in much higher stresses at a given balloon expansion pressure than the calcified plaque case. Figures 10 and 11 show the directional stresses when calcified and cellular plaque are included in the model. As expected, the arterial stresses were significantly lower for the calcified plaque cases when compared to the cellular case. This is the result of the much higher rigidity of the cacified plaque layer over the celluar plaque. This is further supported by the higher stresses seen by the plaque in the calcified case as compared to the cellular case. It should be mentioned that no plaque breakup model was included in the simulations. It would be expected that the calcified plaque would break up before the high stresses at the end of expansion predicted by the model.



35

As one would expect, the most significant compenent of stress is the hoop. The smallest compenent is the axial. The clinical significance of the directional stresses on vascular injury is unclear. Future experimental studies will be aimed at determining the most appropriate stress to analyze when evaluating vascular injury (von Misses, maximum principal, directional, etc.). The current model does not include the anisotropic behavior of the artery and plaque materials. Additionally, no distinction was made between the passive arterial medium and the active fibers, the orentations of which may vary from inner to the outer layers of the arterial wall. This is currently being included in a more sophisticated model which also includes arterial prestresses. Finally, Figure 12 shows the preliminary results of the flow pattern within the final stented geometry. The development of Poiseuille flow is apparent as the blood moves from the model entrance along the artery and plaque surface (not show) and through the stented portion of the artery. The strain rates are quite interesting and show a decrease after the initial entry into the arterial section. However, they rapidly increase as the blood travels through the stented portion of the artery. This CFD model is now being used to evaluate the diffusion process associated with drug eluting stents, as well as modeling neointima formation, thrombus formation mechanics, and blood flow patterns. It has been found that standing vortices and regions of stagnation are responsible for the rises in concentrations of platelet-activating agents within those regions. Platelets accumulate preferentially in the regions of large platelet-activating agent concentrations and low fluid velocities. Figure 13 shows a contour plot at 0.05 m/s. Regions of the domain near where the stent contacts the plaque exhibit

Figure 12:

Velocity magnitudes and strain rates in stented artery.



Figure 13:

Iso-contour at 0.05 m/s on region near plaque/stent interface.

zones of low velocity. These regions are potential locations for thrombus formation. Additionally, the wall shear rates and blood strain rates at the wall can be evaluated to determine if they exceed a critical embolizing limit.

7

Clinical significance of report

Concerns that drug-eluting stents interfere with the process of reendothelization and thus may encourage long-term thrombosis have spurred interest in understanding the mechanisms causing acute deendothelization during the stenting procedure. This model aids in the prediction of regions of endothelial cell (EC) denudation during stent implantation. This is an important phenomenon since regions of EC denudation profoundly impact drug absorption/loading profiles of anti-proliferative agents in drug-eluting stents (DES). Additionally, anti-proliferative drugs are hypothesized to inhibit EC regrowth causing increased rates of long-term thrombosis, so predictive capability of regions of EC denudation during implantation provides the tool to reduce thrombosis rates of DES. The model developed also helps in the prediction of regions of high arterial stresses, which may cause vascular injury. Acute superficial and deep vascular injury has been found to be a strong predictor of chronic restenosis. This method provides a predictive tool to evaluate the degree of acute vascular injury of new stent geometries prior to in-vivo studies. Finally, the ability to examine blood flow patterns in stented arteries allows for the prediction of standing vortices and high platelet-activating substances capable of trapping and stimulating platelets for aggregation. It also allows for the evaluation of embolizing stresses acting on a thrombus. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


37

References [1] Schillinger, M., Exner, M., Mlekusch, W., Haumer, M., Sabeti, S., Ahmadi, R., Schwarzinger, I., Wagner, O., Minar, E., Restenosis after femoropopliteal PTA and elective stent implantation: predictive value of monocyte counts. Journal of Endovascular Theory, 10, pp. 557-565, 2003. [2] Antoniucci, D., Valenti, R., Santoro, G., Bolognese, L., Trapani, M., Cerisano, G., Fazzini, P. Restenosis after coronary stenting in current clinical practice, American Heart Journal, 135(3), pp. 510-518, 1998. [3] Griffiths, H., Bakhai, A., West, D., Petrou, M., De Souza, T., Moat, N., Pepper, J., Di Mario, C., Feasibility and cost of treatment with drug eluting stents of surgical candidates with multi-vessel coronary disease. European Journal of Cardiothroacic Surgery, 26, pp. 528-534, 2004. [4] Feder, B.J., Panel Urges Caution on Coated Stents, New York Times Health p. 1, Dec. 9, 2006 [5] Kuchulakanti, P.K., Chu, W.W., Torguson, R., Ohlmann, P., et al. Correlates and long-term outcomes of angiographically proven stent thrombosis with sirolimus- and paclitaxel-eluting stents. Circulation. 113, pp. 1108 –1113, 2006. [6] McFadden, E.P., Stabile, E., Regar, E., Cheneau, E., et al. Late thrombosis in drug-eluting coronary stents after discontinuation of antiplatelet therapy. The Lancet, 364, pp. 1519-1521, 2004. [7] Ong, A.T., McFadden, E.P., Regar, E., de Jaegere, P.P., van Domburg, R.T., Serruys, P.W. Late angiographic stent thrombosis events with drug eluting stents. Journal of the American College of Cardiology, 45, pp. 2088-2092, 2005. [8] Rogers, C., Parikh, S., Seifert, P., Edelman, E.R. Endogenous cell seeding: Remnant endothelium after stenting enhances vascular repair. Circulation, 11, pp. 2909-2914, 1996. [9] Auricchio, F., Di Loreto, M., Sacco, E., Finite element analysis of a stenotic artery revascularization through stent insertion, Computer Methods in Biomechanics and Biomedical Engineering, 4, pp. 249-263, 2001. [10] Migliavacca, F., Petrini, L., Colombo, M. et al. Mechanical behavior of coronary stents investigated through the finite element method. Journal of Biomechanics, 35, pp. 803-811, 2002. [11] Petrini L, Migliavacca F, Dubini G, Auricchio F. Evaluation of intravascular stent flexibility by means of numerical analysis. Proc. Of the 2003 Summer Bioengineering Conference, June 25-29, Key Biscayne, FL, pp. 251-252, 2003. [12] Lally, C., Dolan, F, and Prendergast, P.J., “Cardiovascular stent design and vessel stresses: a finite element analysis, Journal of Biomechanics, 38, pp. 1574-1581, 2005. [13] Lally, C, Prendergast, P.J., An investigation into the applicability of a Mooney–Rivlin constitutive equation for modeling vascular tissue in cardiovascular stenting procedures. Proceedings of the International


38 Modelling in Medicine and Biology VIII Congress on Computational Biomechanics. Zaragoza, Spain, pp. 542-550, 2003. [14] Prendergast, P.J., Lally, C., Daly, S., Reid, A.J., Lee, T.C., Quinn, D., Dolan, F., Analysis of prolapse in cardiovascular stents: a constitutive equation for vascular tissue and finite element modeling. ASME Journal of Biomechanical Engineering, 125, pp. 692-699, 2003. [15] Loree, H.M., Grodzinsky, A.J., Park, S.Y., Gibson, L.J., Lee, R.T., Static circumferential tangential modulus of human artherosclerotic tissue. Journal of Biomechanics, 27, pp. 195-204, 1994. [16] Nichols, W.W., O'Rourke, M.F. McDonald's Blood Flow in Arteries Theoretical, Experimental and Clinical Principles. Oxford University Press: New York, 1998.



39

Fractal behaviour of pathological heart rate variability dynamics G. D’Addio1, A. Accardo2, G. Corbi3, F. Rengo1,4 & N. Ferrara1,3 1

S. Maugeri Foundation, Italy DEEI University of Trieste, Italy 3 University of Molise, Italy 4 University Federico II of Naples, Italy 2

Abstract Heart rate variability analysis (HRV) is a well recognized tool in the autonomic control assessment. It has been suggested that nonlinear analysis of HRV might provide more valuable information than traditional linear methods. Several non linear fractal techniques recently gained wide interest: that based on indirect fractal dimension (FD) estimation from the 1/f spectral power relationship, and that based on a direct FD estimation from HRV time sequences. Aim of the study was to assess whether FD discriminates pathological HRV dynamics, comparing results with normal subjects and traditional linear indexes. We studied 7 groups of 10 ECG 24h-Holter recordings in normal and different pathologies: obstructive pulmonary disease, stroke, hypertension, post myocardial infarction, heart failure, heart transplanted. HRV was assessed by spectral power in very low, low and high frequency bands and standard deviation between normal beats. FD was estimated directly from the HRV sequences by Higuchi method (HM) and from the 1/f slope of spectral power relationship (beta). Results showed differences in the autonomic control impairments better described by FD than by traditional linear methods. Although HM and beta tried to measure the same FD property, the latter seemed to be rather insensitive to changes in autonomic control. These preliminary results clearly suggest that FD, estimated by HM, contains relevant information related to different HRV pathological dynamics. Keywords: HRV, fractal analysis, nonlinear dynamics.

WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line) doi:10.2495/BIO090041


1

Introduction

Heart rate variability (HRV) is a well known noninvasive tool in the investigation of the heart autonomic control. Although most studies on HRV have been performed using time- and frequency-domain linear methods, it has been suggested that HRV nonlinear analysis might provide more valuable information for physiological interpretation of heart rate fluctuations and for cardiac risk assessment [1]. Fractal analysis is an emerging nonlinear technique and, among several methods proposed so far to measure the fractal behaviour of the HRV signal, that based on spectral power-law relationship [2–7], and that based on iterative algorithms directly from RR time series, [8,9] have gained wide interest in the last years. The first way has traditionally been approached following the chaostheory, with the aim of modelling the attractor extracted from HRV sequences [6], estimating the fractal dimension from the slope of the 1/f-like relationship [7]. Alternatively a fractal dimension value can be directly estimated from HRV sequences by means of Higuchi algorithm [9]. All two the approaches were followed in this study, estimating fractal features by beta exponent of the 1/f (beta) and by fractal dimension of the Higuchi algorithm (HM). The latter method, whose good reproducibility has been already studied in congestive heart failure [10], allows a better fractal estimation, eliminating the errors due to the indirect estimation of FD from the spectral power. HRV has been usually investigated in cardiac patients, where abnormalities of the autonomic control to the heart have a common diagnostic and prognostic use [11,12]. Evidences of clinically significant impairment of the autonomic nervous system are known in two others widely diffuse pathologies like stroke and chronic obstructive pulmonary disease, although only limited data are available on the use of HRV in the assessment in these not strictly cardiac patients. Impaired cardiovascular autonomic regulation has been described in stroke patients with abnormalities hypothesized to be mediated by the central nervous system as a result of the cerebrovascular event, whereas the mechanism of this phenomenon is not fully understood [13,14]. Respiratory arrhythmia in chronic obstructive pulmonary disease, represents the most recognizable evidence of a functional link between neural cardiac and respiratory controls. Changes in respiratory patterns and lung volumes in these patients influence the autonomic outflows by complex reflex adjustments, mediated by both vagal and sympathetic efferent activity [15,16]. Aim of the study was to assess whether FD discriminates pathological HRV dynamics, comparing results with normal subjects and traditional linear indexes.



2

41

Study population

All enrolled patients were admitted to S. Maugeri Foundation Rehabilitation Institute of Telese Terme, Italy. We studied 7 groups of ECG 24h-Holter recordings in normal (NR) and different pathologies: hypertension (HY), post myocardial infarction (MI), heart failure (HF), heart transplanted (TR), obstructive pulmonary disease (COPD), stroke (SP). Hypertension diagnosis was defined as systolic blood pressure 140 mm Hg and/or diastolic blood pressure 90 mm Hg. A prior diagnosis or ECG evidence of Q waves was used to define MY patients. The diagnosis of chronic systolic heart failure was based on a HF history of at least 6 months and previous echocardiographic and/or scintigraphic evidence of an ejection fraction of 0.05

N vs SP

P < 0.001

P > 0.05

P > 0.05

N vs HY

P < 0.001

P > 0.05

N vs MI

P < 0.001

LF

HF

SDNN

P > 0.05

P > 0.05

P < 0.001

P > 0.05

P < 0.001

P > 0.05

P > 0.05

P > 0.05

P > 0.05

P < 0.01

P > 0.05

P < 0.001

P > 0.05

P > 0.05

N vs HF

P < 0.001 P < 0.001

P < 0.05

P < 0.001

P > 0.05

P < 0.05

N vs TR

P < 0.001 P < 0.001 P < 0.001 P < 0.001

P < 0.01

P < 0.001

P < 0.001 P < 0.001

Discussion

These preliminary results allow to discuss the following three findings. First of all, only FD by Higuchi method and LF parameters showed very significant differences between Normal and pathological studied groups, while beta and other linear indexes were not so able to detect significant differences. The second novel finding is that the sensitivity of the HM and beta exponent parameters in regard to the severity of the central nervous system damage appears to be different. Indeed, the Higuchi's index strongly changes passing from normal to pathological subjects. The beta exponent, on the contrary, seems rather insensitive to changes in autonomic cardiovascular regulation. These considerations suggest that, although the two algorithms try to measure the same fractal property of HRV, they provide non superimposable results. This could be WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

46 Modelling in Medicine and Biology VIII due to the fact that the beta exponent is usually calculated considering only the low band of the signal ( Longitudinal p = 0.002 Radial > Longitudinal p Longitudinal p Longitudinal p 1 , instead of L + 1 points as in the classical simplex method. In this paper, a partition-based concurrent simplex mutation is examined. The new cells cnew generated by the clone and mutation steps of the clonal selection process for a given memory cell c are considered as a natural partition group. The number of simplex mutated cells is denoted as N c , N c > L + 1 . After executing the concurrent simplex method to obtain cnew , there are N c − L number of new cells that have been updated. The partition-based concurrent simplex mutation is described as the following steps. (1) Order Order the cells of cnew to satisfy η (c1 ) ≥ ... ≥ η (cL ) ≥ ... ≥ η (cL +i ) ≥ ... ≥ η (cN c ), i = 1, 2,..., N c − L . Calculate the centroid of L number of cells with higher fitness values, c = (c1 + c2 + ... + c L ) / L . (2) Reflection For each c L +i cell, compute the reflection point c r by using

c r = c + ρ (c − c L +i )

(6)

Calculate the fitness η r = η (c r ) . If η (cL ) < η r < η (c1 ) , accept

c L +i = c r and

terminate the operation. (3) Expansion e

r If η r ≥ η (c1 ) , expand the point c to c by using

c e = c + ρχ (c − cL+i )

(7)

Calculate the fitness η e = η (ce ) . If η e > η r , accept c L +i = c and terminate the e

r operation; otherwise, accept cL +i = c and terminate the operation.


282 Modelling in Medicine and Biology VIII (4) Outside Contraction o If η (cL +i ) < η r < η (cL ) , compute the outside contraction point c as

c o = c + ργ (c − cL +i )

(8)

Calculate the fitness η = η (c ) . If η > η , accept cL +i = c and terminate the operation. o

o

o

r

o

(5) Inside Contraction i If η r < η (cL ) and η (cL +i ) ≥ η r , compute an inside contraction point c as

c i = c − γ (c − c L + i )

(9)

i i Calculate the fitness η i = η (ci ) . If η > η (cL +i ) , accept c L+i = c and terminate the operation. There are coefficients of reflection ( ρ ), expansion ( χ ), and contraction ( γ ). The usual choices of these coefficients are ρ = 1, χ = 2, γ = 0.5 . The shrinking operator of the classical simplex method is replaced with the mutation step of the clonal selection process.

3 A distributed PKAIN method In order to obtain numerical solution of eq. (3) accurately by means of a temporal integration method, temporal intervals [t p , t p +1 ] should be small. Unfortunately, concurrent computation of all time steps in a temporal integration method is impossible. It seems that to achieve a distributed algorithm to yield a de-coupling of the original problem is almost impossible. However in the ICIL algorithm, the numerical solutions X p , p = 1, ..., N may be computed concurrently and, thus, the total computational time of becomes significantly reduced. In this paper, we examine a two-level temporal decomposition method which stems from our previous work of concurrency in time domain computation [10, 11]. Assuming the N temporal steps of serial calculation are equally divided into N coarse parts, each represents a coarse temporal interval ∆T . In the secondary temporal decomposition, each ∆T is divided into N fine parts of finer temporal intervals ∆t , ∆ T = N fine .∆ t . First, a number of numerical solutions of the nonlinear equation, using the concept of the Laplace transform and its iterative inverse, are obtained on a coarser temporal mesh, t ∈ [ T p − 1 , T p ] , p ∈{1,…, N coarse} . Second, each coarse temporal mesh t ∈ [T p −1 , T p ] can be into several finer temporal meshes t ∈ [T p −1 , T p −1 + t i ] ， i ∈ {1, … , N fine − 1} . The numerical solutions on the coarser temporal mesh obtained in the former step are used as initial conditions on the finer temporal mesh. Solutions defined on a finer temporal mesh for each of the coarse temporal mesh are now being obtained concurrently using a temporal integration method. This linearization leads to a distributed version of the fitness calculation process decomposed



283

for the PKAIN. Suppose the fitness calculation can be distributed into p processors, the pseudocode of the fitness calculation is described as below. FUNCTION Distributed fitness calculation Decode the network cell c into parameters. FOR p = 1 TO N coarse , do coarser temporal mesh on t ∈[T p−1 , T p ] Find X p from X p −1 ; END-FOR Distribute p = 0 TO N coarse − 1 ， X p to processors， For i = 1 To N fine − 1 , do finer temporal mesh on t ∈ [Tp , Tp + ti ] Find X p + i from X p + (i −1) ; END-Distribute and receive X p + i . n

n

i =1

i =1

η = 1 − ∑ wi ( xi − X i ) 2 / ∑ ( xi − x )

END-FUNCTION

4

Experiments and discussion

A typical nonlinear pharmacokinetic model for drug concentration is often described by Michaelis-Menten equation. In this section, the PKAIN algorithm is used to optimize Michaelis-Menten pharmacokinetic parameters of the bolus intravenous examples 1 and 2 as described in [12]. Optimal parameters are compared to the solutions given by the accurate linear regression (ALR), improved Hanes-Woolf method (HW), and combined Runge-Kutta method (RKPS) in the literature. The equation of drug concentration described by Michaelis-Menten equation consists of two parameters is given as follow. V X dX =− m (10) dt Km + X Table 1: Method PKAIN HW ALR RK-PS

Comparison of optimal parameters for example 1. Km

Vm

R

10.907 10.5135 9.3936 9.9804

4.016 3.9615 3.9573 3.9994

0.042690 2.260105 0.293910 0.111829

In other words, candidate solutions of c = {Vm , Km} are encoded into memory cells. Optimal parameters for example 1 obtained by PKAIN, ALR, HW, and RK-PS methods are shown in Table 1. Optimal parameters for example 2 are shown in Table 2. In order to compare these parameters, the relative residual WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

284 Modelling in Medicine and Biology VIII R = ∑ (( xi − X i ) 2 / xi ) is

calculated. The smaller the weighted residual is, the better the parameters are. The results demonstrated that the PKAIN method outperforms HW, ALR, and PK-PS algorithms in parameter optimization of nonlinear pharmacokinetic models.

5

Table 2:

Comparison of optimal parameters for example 2.

Method PKAIN HW ALR RK-PS

Km

Vm

R

33.2223 28.0806 27.5851 29.5126

13.4414 11.2978 11.2828 13.0842

1.5718282 9.292684 8.509200 1.817844

Conclusions

In this paper, the artificial immune network PKAIN is designed to optimize nonlinear pharmacokinetic parameters. The method to obtain numerical solutions of nonlinear system is integrated into its fitness calculation process. Experimental results obtained by the PKAIN algorithm are better than those obtained by HW, ALR, and PK-PS methods. Together with our previous work, the PKAIN algorithm is capable of obtaining optimal parameters for both linear and nonlinear pharmacokinetics. In addition, the two-level temporal decomposition method is used to parallelize the nonlinear pharmacokinetic model using an iterative inverse Laplace transformation. The efficiency of the PKAIN algorithm can be greatly improved when it is implemented in a distributed environment due to the fact that there is no data dependence of the fine temporal mesh computation.

Acknowledgement The authors acknowledge support from innovation team project JNIRT0702 of Jiangnan University.

References [1] de Castro, L.N., Timmis, J., Artificial immune systems as a novel soft computing paradigm. Soft Computing, 7(8), pp.526-544, 2003. [2] Xie, K.G., Zeng, X.H., Li, C.Y., et al., Comparative analysis between immune algorithm and other random searching algorithms. Journal of Chongqing University, 26(11), pp.43-47, 2003, (in Chinese). [3] de Castro, L.N, Timmis, J., An artificial immune network for multimodal function optimization. Proc. of IEEE Congress on Evolutionary Computation, IEEEE Service Center, Honolulu, USA, pp.674-699, 2004. [4] de Franca, F.O., Von Zuben, F.J., de Castro, L.N., An artificial immune network for multimodal function optimization on dynamic environments. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


[5] [6] [7] [8] [9]

[10] [11]

[12]

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Proc. of the GECCO conf, ACM Press, Washington DC, pp. 289-296, 2005. Liu, L., Zhou, S.D., Lu, H.W., et al., Parameter optimization of pharmacokinetics based on artificial immune network. Applied Mathematics And Mechanics-English Edition, 29(4), pp.549-559, 2008. Lai, C.H., Parrott, A.K., Rout, S., A Distributed Algorithm for European Options with Nonlinear Volatility. Computers and Mathematics with Applications, 49, pp.885-894, 2005. de Castro, L.N., Von Zuben, F.J., Learning and optimization using the clonal selection principle. IEEE Trans on Evol Comp, 6(3), pp.239-251, 2002. Jeffrey, C.L., James, A.R., Margaret, H.W., et al., Convergence properties of the Nelder-Mead simplex method in low dimensions. Society for Industrial and Applied Mathematics, 9(1), pp.112-147, 1998. Yen, J., Liao, J., Randolph, D., Lee, B., A Hybrid approach to modelling metabolic systems using a genetic algorithms and the simplex method. IEEE Transactions on Systems; Man; and Cybernetics; 28(2), pp.173-191, 1998. Lai, C.H., On transformation methods and concurrency in time domain computation. Proc. of the DCABES 2007, pp. 5-6, 2007. Lai, C.H., Numerical solutions of certain nonlinear models in European options on a distributed computing environment. Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing, ed. Matthias Ehrhardt, Nova Science Publisher, pp.283-298, 2008. Su, Y.F., Optimizing method of Michaelis-Menten pharmacokinetic parameters of bolus intravenous administration. Chin J Clin Pharmacol Ther 10(10), pp.1198-1200, 2005, (in Chinese).




287

Readability of reassigned scalograms and extraction of spectra features for signal analysis S. Mekaoui1, A. Houacine1 & T. Gharbi2 ¹Department of Telecommunications, L.C.P.T.S., USTHB, Algiers, Algeria ²Institut des Microtechniques, Laboratoire d’ Optique P.M. Duffieux, UFR Besançon, France

Abstract In this paper, a wavelet scalogram is used. The wavelet scalogram presents some disadvantages. This is particularly true for time-frequency analysis and representation, which present inconvenient cross-terms. Mechano-myogram (MMG) signals are acquired via a home probe highly sensitive optical sensor. The data obtained from two healthy subjects and two patients tested under drastic conditions are analyzed to characterize the dynamic properties of the MMG and also to determine their frequency contents. We developed the reassignment form of the scalogram, which improves its resolution and readability. A plot of the scalogram contours is also presented to test the direct readability of the scalogram representations. Spectra features are extracted and relevant parameters are assessed, such as the power spectral density, the mean frequency, the average frequency and the well known ratio HF% that characterizes the dynamic characteristics of the tested muscles. For that purpose, the number of subjects had been increased to 24 healthy subjects and up to 18 patients affected by different specific muscular diseases. Keywords: mechano-myogram (MMG) signals, reassigned wavelet scalogram, power spectral density, mean and average frequencies, MMG rms value, MMG average value, HF% ratio value.

1

Introduction

Muscular sounds actually known as mechano-myogram (MMG) signals are acquired with the help of a highly sensitive optical sensor. These signals are nonWIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line) doi:10.2495/BIO090271

288 Modelling in Medicine and Biology VIII stationary and of random form with a very low amplitude. The study is focused on the characterization of their frequency contents and the extraction of spectra features that represent their dynamic properties. For that purpose, we tested the forearm muscles (e.g. flexors) of many healthy subjects and patients. Timefrequency analysis was implemented to overcome the shortcomings of the FFT analysis. Among several TFA methods was the most popular, called the Hitherto method [1–3], which initiated the time-frequency plane. The Hitherto method is specifically devoted to the analysis of non-stationary signals [2, 3]. The TFA methods revealed their limitations on finding a good trade-off between time and frequency resolutions. The limitation imposed by the Heisenberg-Gabor inequality [1–6, 10], which made the trade-off unavoidable, compelled the authors to find a solution. Thus, a compromise was to be found between time and frequency resolutions for whatever non-stationary signal. To overcome these drawbacks, other authors [2–6, 10, 14] proposed other time varying signal analysis tools on a concept of scale rather than frequency, such as the Wavelet scalogram [2, 6]. Other tools, such as the affine smoothed version of the PseudoWigner-Ville distribution [2, 10], were also implemented. However, bilinear time-frequency distributions such as the Wigner-Ville distribution have good concentration in the time-frequency plane, but present the disadvantage of interference terms (cross-terms) that can blur the readability in the time frequency plane of auto-terms (this is significant). Many attempts had been tried by the authors to overcome these inconvenient drawbacks. Unfortunately, those attempts were all tending toward a loss in time-frequency concentration [9–12, 14–16]. The wavelet scalogram is limited by the Heisenberg-Gabor inequality and presents the same weaknesses in the time scale-plane. To remove these shortcomings, the authors implemented a modified form of the wavelet scalogram called the reassignment method of the wavelet scalogram [1–4, 6, 12]. This method preserved energy properties and made both time and scale resolutions rightly enhanced.

2

Wavelet scalogram background

2.1 Continuous wavelet scalogram The concept of the continuous wavelet scalogram is to subdivide a signal x(t) into a set or a family of zero mean functions called the “wavelets”, derived from an elementary function Ψ (the “mother wavelet”), by translation in time and dilation in scale of the later. Then the following relation is tenable, [1, 2, 5, 6, 12, 14–16]: +∞

CWTx (t , a,ψ ) = ∫ x(t )ψ t*,a (s )ds ,

with:

 s −t   . (1)  a 

ψ tx,a (x ) = (a −1/ 2 )ψ 

−∞

The parameter a corresponds to a scale factor. Time and frequency resolutions are limited by the Heisenberg-Gabor inequality [1–5].



289

2.2 Wavelet scalogram The wavelet scalogram is then defined by:

SC ( x, T , a ) = CWTx (t , a,ψ ) , 2

(2)

where ψ is the wavelet function. The scalogram is interpreted as the smoothed version of the Pseudo-WignerVille distribution. One should refer to [2, 6, 10, 12, 14–16] to learn more. 2.3 Reassignment method of the wavelet scalogram The concept of reassignment was based on the previous assumptions. As depicted, one has to find a compromise between time and frequency resolutions. It appears that it was necessary to enhance the readability of the scalogram and make the concentration of significant terms greatly localized in the scalogram and get more improved readability reducing the maximum cross-terms. So, we chose the reassignment form to attain these goals [2, 6].

3

Methods

3.1 Subjects Four adults, two healthy subjects and two patients, were tested in this study. The MMG signals were acquired via a home probe. Many other patients affected with muscle diseases, such as current dystrophies and atrophies, were tested. Some of them were affected by Steinert and one by Marie-Charcot-Tooth disease. 3.2 Data analysis 3.2.1 Power spectral density Power spectral density is to be extracted from the MMG’s spectra. This parameter is estimated using the Welsh method and then noted as:

S( f ) =

1 L ∑ Sl ( f ) , L l

(3)

where l represents the index of the interval in respect to the frequency limits of the MMG’s range (e.g. 0–45 Hz). 3.2.2 The average frequency The average frequency in a determined range of frequencies is defined by: f1

Fav = where S ( f

∑ f .S ( f )

f = f0 f1

∑ S( f )

,

f = f0

) is the power spectral density.


(4)

290 Modelling in Medicine and Biology VIII 3.2.3 Mean frequency The mean frequency is given by: Fmean

∑ S( f ) =

f = f0

f1

∑ S( f ) ,

(5)

f = Fmean

where Fmean is the mean frequency and S ( f ) is the power spectral density. 3.2.4 Mean value of the MMG signal The mean value of the MMG corresponds to the mean time average value of the rectified MMG signal (in micrometers) and is given by: rectified Vmean = YMMG ,

(6)

where YMMG is the amplitude of the MMG signal. 3.2.5 Root-mean-square value of the MMG The root-mean-square value of the MMG signal is calculated from the previous equation of the power spectral density in the limits of the MMG’s determined frequency range 0–45 Hz and is determined by:

Vrms =

f1 =45

∑ S ( f ) ; where: f 0 =0

f 0 = 0 Hz and f1 = 45 Hz.

(7)

3.2.6 The ratio HF% This ratio was defined as the ratio of the power spectral density in the range of 0–45 Hz to the power spectral density in the range of 6–45 Hz for whatever type of muscle, thus: 45

∑S( f )

HF%= f45=15 . ( ) S f ∑

(8)

f =6

This ratio reflects the contribution of the fast fibers. 3.2.7 Statistics Twenty-four healthy subjects and up to 18 patients were tested in a clinical environment. Then, for each extracted feature, a statistical analysis is produced with the help of the well-known Origin 6.1 software.

4

Results and discussion

4.1 Reassigned wavelet scalogram results The results presented in this section concern two healthy subjects and two patients respectively. The first sub-section of results is organized so that for each MMG signal there exists four sub-windows. The first sub-window gives the WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


291

display of the acquired MMG signal, whereas the second shows the power spectral density of the analyzed signal. The third sub-window displays the reassigned wavelet scalogram and finally the fourth illustrates the contour plot of the scalogram. The healthy subjects are named Heal.1 and Heal.2 whereas the patients are named Pat.1 and Pat.2. Considering Figure 1, which gives the results for the healthy subjects, it can be noticed that there are good concentrations of energy peaks around 10 Hz and 20 Hz and a poor concentrations around 12 Hz and 15 Hz (Heal.1). The reassigned wavelet contour plot clearly shows this assertion and reveals several frequencies at the same instant. The power spectral density displayed shows a concentration of frequencies in the lower range of the power spectrum whose frequency axis is normalized to the highest value. These observed differences in frequencies at different instants are mainly due to the fact that force increases along with the increasing number of fibers that are recruited since contraction. This process seems to evolve steadily until the subject is in a state of total exhaustion. The readability of reassigned wavelet scalograms for Heal.2 indicates that energy peaks are distributed around 5 Hz and 12 Hz with a high level of brightness, and are relatively poor around 10 Hz, 15Hz and 20 Hz (Heal.2). Nevertheless, we should notice the appearance of the blurring 7 Hz (Heal.2), well known by the clinicians to correspond to only muscle tremors. The examination of the power spectral density yields the same observation as in the case of Heal.1. In the case of the patients, Figure 2 gives the patients results, which are organized as in the case of the healthy subjects. It can be seen from the displayed reassigned scalograms that Pat.1 had developed a very poor effort probably due to the nature of the muscular disease and hence an awful grasping of the strain gauge as the scalogram shows few energy peaks at around 5 Hz and 10 Hz and a very small number with very poor energy at around 15 Hz and 20 Hz. Only tremors and clearly noticeable large transients are observed in the acquired MMG signal. The contours plot neatly reveals this fact. Real exhaustion at the beginning of the measurement protocol is obvious. Similar observations are noticed in the second case (Pat.2) who did his best to firmly grasp the strain gauge, but was unsuccessful and was unable to fulfill the fixed force consigns of the experimental protocol. The generated frequencies revealed by both the scalogram and the contours plot are confusedly dispersed around 5 Hz and 20 Hz with lower intensities. Obviously, only fast fibers responded to the excitation as the frequencies are localized in the high frequency range of the most significant of the MMG’s frequency range. Patients were not able to stand more than 15 seconds of experimentation. 4.2 Statistical results and analysis Figures 3–6 provide graphic representations of the extracted spectra features of the MMG signals namely: average frequency versus average force, mean frequency versus average force, MMG amplitude rms value versus maximum force, and HF% ratio versus maximum force, for either healthy subjects or patients. The subject group consists of 24 healthy subjects and 18 patients. The group of patients was organized in accordance with the nature of the WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


Figure 1:

Results of two healthy subjects. For each of them, the first subwindow gives the acquired MMG signal, the second sub-window the power spectral density of the MMG signal. The third and fourth illustrate respectively the reassigned wavelet scalogram of the MMG signal and its contours plot.



Figure 2:

293

Results of two unhealthy subjects. For each of them the first subwindow gives the acquired MMG signal, the second sub-window the power spectral density of the MMG signal. The third and fourth illustrate respectively the reassigned wavelet scalogram of the MMG signal and its contours plot.



Average

Frequency

in

Hz

(a) 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Y = 9.48743 + (0.00451)*X (linear regression) (standard deviation) with : σ = 1.43973 R = 0.14666 (regression coefficient)

0 20 40 60 80 100 120 140 160 180 200 220 240 Average force in Newton

Average

Frequency in Hz

(b)

Figure 3:

10,0 9,5 9,0 8,5 8,0 7,5 7,0 6,5 6,0 5,5 5,0 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0

Y = 5.45159 + (0.04152)*X (linear regression) (standard deviation) with: σ = 1.60381 R= 0.49068 (regression coefficient)

0

10

20 30 Average

40 50 60 70 80 force in Newton

90

Average frequency in Hz versus average force in Newton, (a) in the case of healthy subjects, (b) in the case of patients.


Mean frequency in

Hz


13 12 11 10 9 8 7 6 5 4 3 2 1 0

(a)

Y = 8.73749 + (0.00457)*X (linear regression) with : σ = 1.91959 (standard deviation) R = 0.11204 (regression coefficient)

0 20 40 60 80 100 120 140 160 180 200 220 240

Mean

frequency

in

Hz

Average

10,0 9,5 9,0 8,5 8,0 7,5 7,0 6,5 6,0 5,5 5,0 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0

force

in

Newton

(b)

Y= 3.82434 + (0.05038)*X (linear regression) with : σ = 1.79811 (standard deviation) R = 0.52035 ( regression coefficient )

0

10

20

30

Average

Figure 4:

295

40

50

force in

60

70

80

90

Newton

Mean frequency versus average force in (a) healthy subjects, (b) patients.



MMG rms value ( in µm )

(a)

1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0

-5

-7

2

Y = 0.82228+(-7.65784*10 )*X + (4.62216*10 )*X (quadratic) with: σ = 0.13662 ( standard deviation ) 2 R = 0.05233 (quad. reg. coefficient )

0 50 100 150 200 250 300 350 400 450 500 550 600

MMG rms value ( in µm )

Maximum force in Newton

(b)

1,8 1,7 1,6 1,5 1,4 1,3 1,2 1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0

-6

2

Y = 1.01514+(-0.00162)*X+(5.78208*10 )*X (quadratic) with : σ = 0.44966 ( standard deviation ) 2 R = 0.06897 ( quad. reg. coefficient )

0

50 100 150 200 250 300 350 400 450 500


Figure 5:

MMG rms value versus maximum force in (a) healthy subjects, (b) patients.


HF% ratio ( in percentages )


297

(a)

32,5 30,0 27,5 25,0 22,5 20,0 17,5 15,0 12,5 10,0 7,5 5,0 2,5 0,0 0

50 100 150 200 250 300 350 400 450 500 550 600


(b)

HF% ratio ( in percentages )

30 25 20 15 10 5 0

0

50

100 150 200 250 300 350 400 450 500

Maximum

Figure 6:

force in Newton

HF% ratio versus maximum force in (a) healthy subjects, (b) patients.


298 Modelling in Medicine and Biology VIII muscular diseases and named Pat.1 through to Pat.18 and distributed as follows: Steinert (Pat.1, 2, 13, 14, 15 and 16); Belt dystrophies (Pat.3, 4, 6, 7, 8, 10, 11, 12, 17 and 18); Charcot-Marie-Tooth (Pat.5 only). Figure 3 gives the statistical variation of the average frequency versus average force in both groups, which made the comparison easier. This feature characterizes the evolution of the MMG signal amplitude in the period of stability of the muscular contraction. The linear regression estimated yields a positive slope. It can be observed that in the case of the healthy subjects few values are dispersed whereas in the case of the patients, we observed dispersed values with a greater standard deviation. In both cases, the average frequency varies linearly with the force. In order to check on this tendency we have chosen to study the mean frequency of the MMG signal versus average force. Figure 4 gives the results of this second spectrum feature and its assessment. So, we noticed in the case of the healthy subjects that the mean frequency takes smaller values and a greater standard deviation when the regression is still linear with a positive slope inferring to a linear function of the average force. In the case of the patients, the mean frequency seems to behave similarly. Globally the values of the mean frequency are well correlated with a higher regression coefficient. Figure 5 illustrates the MMG rms value in terms of maximum force for either the healthy subjects or the patients. The only relevancy is the poor and dispersed values in the case of the patients and the quadratic form of this feature. This compelled us to test and estimate another interesting feature that the MMG acquired and which in fact best characterizes the activity of fast muscle fibers. This parameter is called the HF% ratio. Figure 6 gives the variations of this important feature in terms of maximum force. Examining figure 6, we observed that this ratio varies from 5% to 35%. In the case of patients affected with different muscular diseases it appears that the maximum of this ratio is 30% and the minimum is around 5%. In this case we did not notice significant differences with the healthy subjects except that for special diseases like Steinert and Charcot-Marie-Tooth the values of HF% are smaller than in the case of healthy subjects.

5

Conclusion

The first aim of this work was to show the readability of the reassigned wavelet scalogram of the MMG signals acquired from the flexors forearm muscles of many healthy subjects and patients affected with some well-known muscular diseases. The most relevant fact is the improvement of the readability of the reassigned wavelet scalograms and hence, a better concentration of the most significant frequencies is obtained in both cases. The contours plot emphasizes these observations and the estimated power spectral densities confirmed the frequency range of the MMG signals. Moreover, tremors were read on the reassigned wavelet scalograms, particularly in the case of the patients. We found that these tremors were revealed by concentration of frequencies in the vicinity of 7 Hz and were due to awful adaptation with the grasping of the gauge. Also, as had been observed for the patients, the power spectra were shifted to the lower WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


299

frequencies during fatigue. Moreover, reassigned scalograms showed a better localization in time of the frequency contents. The second part of this work dealt with the statistical assessment of some spectra features that can best characterize the muscle dynamic properties such as average frequency, mean frequency, average value and the rms value of the MMG signal, and finally the important HF% ratio. The average and rms value of the MMG amplitude are known as features that represent the evolution of the MMG amplitude for whatever healthy or patient subject. The analysis of these parameters clearly illustrated that the frequency and amplitude of MMG signals are in linear relationship with force for both cases of subjects. We also found that the disparity of values of the rms MMG and its average are in the same order whereas for the average frequency it is smaller than the mean frequency for both groups. In addition, these two parameters are in linear relationship with force whereas those previously cited are in quadratic relationship with force. Then, we implemented the HF% ratio, which can serve as a good tool to assess the contribution of fast fibers as a peculiar indicator for affected muscles.

References [1] Z. Peng, F. Chu and Y. He, Vibration Signal Analysis and Feature Extraction based on Reassigned Wavelet Scalograms. Journal of Sound and Vibration, 253 (5), pp. 1087–1100, 2002. [2] F. Auger and P. Flandrin, Improving the Readability of Time-Frequency and Time-Scale Representations by the Reassignment Method. IEEE Transactions on Signal Processing, Vol. 43, N°5, pp. 1068–1089, 1995. [3] B. Gramatikov, J. Brinker, S. Y. Chun, N. V. Thakor, Wavelet analysis and time-frequency distributions of the body surface ECG before and after angioplasty. Elsevier Method and Programs in Biomedicine, 62, pp. 87–98, 2000. [4] I. Djurovic and L. Stankovic, Time-frequency representation based on the reassigned S-Method. J. of Signal Processing, Vol. 77, Issue 1, pp. 115– 120, 1999. [5] O. Rioul and P. Flandrin, Time-Scale Energy Distributions: a general class extending Wavelet Transforms. IEEE Trans. On Signal Processing, SP40(7), pp. 1746–1757, 1992. [6] P. Flandrin, E. Chassande-Mottin, P. Abry, Reassigned Scalograms and their fast Algorithms. Proceedings of the SPIE-95, 2569, pp.152-158, San Diego, USA, 1995. [7] J. Lin, Feature Extraction of Machine Sound using Wavelet and its Application in Fault Diagnosis. Elsevier NDT & E International 34, pp. 25– 30. [8] D. Barchiesi and T. Gharbi, Local spectral information in the near field with wavelet analysis and entropy. J. of Applied Optics, Vol. 38, N° 31, pp. 6587- 6596, 1999. [9] C. Li, C. Zheng and C. Tai, Detection of ECG characteristic points using Wavelet Transforms. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

300 Modelling in Medicine and Biology VIII [10] Leon Cohen, Time-frequency Distributions – A Review, Proceedings of the IEEE, Vol. 77, N°7, [11] T. Gharbi et al, Optical near field data analysis through time-frequency distributions application to characterization and separation of the image content by reassignment. J. of Optical Society of America, Vol.17, N 12, 2000. [12] C. Torrence and G.P. Compo, A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society, 61-78, Vol.79, 5, 1998. [13] J.C. Wood and D.T. Barry, Time-Frequency Analysis of Skeletal Muscle and Cardiac Vibrations. Proceedings of the IEEE Vol. 84, N 9, 1986. [14] Marie Farge, Wavelet Transforms and their Applications to Turbulence. Annual Review Fluid Mechanics, 24, pp.395–457, 1992. [15] G. Kaïser, A Friendly Guide to Wavelets (Book, Sixth printing), (1999) Library of Congress and Cataloguing, Printed by Quin Woodbine, Woodbine N.J. USA. [16] R. Polikar, Fundamental Concepts and an Overview of the Wavelet Theory, Wavelet tutorial (2002), Second edition, Engineering, Rowan, 2002, USA. [17] S.R. Perry et al, Mean Power Frequency and amplitude of the Mechanomyographic and Electromyographic Signals during incremental cycle Ergometry. J. of Electromyography and Kinesiology, 11 pp. 299–305, 2001. [18] P. Madeleine, P. Bajaj, K. Sognard and L.A. Nielsen, Mechanomyography and Electromyography force Relationships during Concentric and Eccentric Contractions. J. of Electromyography and Kinesiology 11, pp. 113–121, 2001. [19] W.A. Mackay, D.J. Gramond, H.C. Kwan and J.J. Murphay, Measurements of Human Forearm Viscoelasticity. Journal of Biomechanics, Vol 19, N°3, pp. 231–238, 1986, UK. [20] M. Ouamer, M. Boiteux, M. Petitjean, L. Travens, A. Salès, Acoustic myography during voluntary isometric contraction reveals non-propagative lateral vibration. Journal of Biomechanics 32, 1279–1285, 1999.


Section 6 Virtual reality in medicine



303

An internal examination training system supporting abnormal labor conditions A. Doi1, K. Noguchi1, K. Katamachi1, T. Ishii2, H. Uno3, S. Mega4 & K. Matsui4 1

Iwate Prefectural University, Japan The Japanese Red Cross Hokkaido College of Nursing, Japan 3 KOKEN Co., Ltd, Japan 4 JFP, Inc., Japan 2

Abstract For obstetricians and midwives, “internal examination” refers to an important diagnostic technique in which the progress of labor is examined using the index and middle fingers inserted into the vagina or rectum. Training of this internal examination technique has been commonly performed using a model of the human body (manikin). However, with this method, it was impossible to determine visually where and how the examining fingers are touching, making it difficult for trainers to teach advanced examination skills efficiently and evaluate training achievements. Against this background, we have developed a training system for internal examination that enables simulation of normal and abnormal conditions of labor by detecting the position and direction of the examining fingers in real-time via tactile and visual perceptions using anatomical and virtual models. This system allows trainees to experience both normal and abnormal fetal descent into the pelvis. Keywords: virtual models, manikin, magnetic sensor, internal examination, a training system.

1

Introduction

Previously developed training systems for internal examination include our own system [1–3], ePelvis [4–6] developed by a group from Stanford University, and the peripartum diagnosis/delivery assistance training system [7]. The ePelvis attaches several sensors inside the mother’s body and is not suitable for close WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line) doi:10.2495/BIO090281

304 Modelling in Medicine and Biology VIII monitoring of fingers and the evaluation of examination techniques. The peripartum diagnosis/delivery assistance training system is basically a visual learning system using video images, and is suitable for teaching and explanation but not for training of the internal examination itself. Our approach in our training systems described in references [1–3] is different in comparison with the two systems, ePelvis and the peripartum diagnosis/delivery assistance training system. We utilize magnetic sensors that are attached with two fingers, and monitor the motions of the two fingers during an internal examination. Model Sensor

Location

MFC Wearing of the location sensors

Figure 1:

System configuration.

Our previous system was used to simulate the normal labor condition and thus was not suitable for simulating various abnormalities that can occur during labor. We thus developed a system based on fetal models that could reproduce various abnormal labor conditions (frank breech presentation, complete breech presentation, placenta previa, and face presentation). Our newly developed internal examination training system consists of models of maternal body parts, including the vagina and the uterine ostium, and fetal body parts (anatomical models), a personal computer (PC), and a magnetic sensor (Fig. 1). The magnetic sensor consists of a transmitter (XMTR), a location sensor, and a controller (miniBIRD, Ascension Technology Corp.). Magnetic information transmitted from the transmitter is detected by the location sensor, and the location information is received by the PC. The location sensor is attached and WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


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fixed to a fingerstall made of silicon rubber, which is worn on the index and middle fingers, with which the internal examination is performed.

2

System overview

Figure 2 shows the external appearance of the training system. The system supports normal labor conditions of one-finger dilatation, two-finger dilatation, full dilatation and type C (another type of full dilatation) and abnormal labor conditions of frank breech presentation, complete breech presentation, placenta previa and face presentation. Other conditions can be added if necessary. The monitor displays geometric models (i.e. virtual models of the human body, examining fingers, etc.) of the same size as the anatomical models. An advantage of the system is that it can display on the monitor the position and the direction of the examining fingers during an internal examination via the magnetic sensors worn on the examining fingers. The system thus allows trainers to evaluate visually the skill level and accuracy of examination techniques on the monitor. Inside the human body model shown in Figure 2 is a guiding structure to install models of the pelvis and the fetus. An appropriate anatomical model of the fetus should be placed in the human body model before starting training. The skin in the virtual model was created by measuring the skin with a non-contact 3D digitizer, and converting this to a polygonal shape.

Figure 2:

Our internal examination training system.

The entire fetal models are created by a computer aided design (CAD) software. All generated polygonal models are combined, and both color and optical information are added. The anatomical models of the pelvis and the body were created as follows: a 3D image of the pelvis was taken with a 3D-computed tomography (CT) system, the 3D image was appropriately smoothed and isosurfaced, and the surface shape of the pelvis and the body was created. The anatomical model of the pelvis and the fetus was made by a rapid proto-typing device (3D printer). The skin of the mother’s body enclosing the pelvis was created by plastic material and vinyl cloth.



3

Our training method

Eight anatomical models of the fetus, including four normal and four abnormal models, were prepared. Figure 3 shows four normal cases (left top: type C (near full dilation), right top: full dilation, left bottom: two-finger dilation, right bottom: one-finger dilation). Figure 4 shows four abnormal cases (left top: incomplete foot presentation, right top: complete breech presentation, left bottom: placenta previa, right bottom: face presentation). These models create only the parts that are touched by the examining fingers, and are displayed together with the whole image of the fetus. After a fetal model was placed in the system, the virtual model of the selected fetal model was selected on the dialogue on the display, and the anatomical model and the virtual model were adjusted. The position of both anatomical and virtual models is adjusted by using the location sensor. Figure 5 shows how a fetal model is displayed when it has been changed (before and after change). Figure 6 shows the dialogue for the selection of an anatomical model of a fetus (normal one-finger dilatation has been selected) and the control displays of each model (i.e. models of the mother’s skin, pelvis, vagina, and fingers). The display control allows the selection of the constitutive models to display, the mode of display (i.e. wireframe (display with lines) or shading), transparency, and the display color. The system can also display internal views with four cross-sectional images (left, right, front, and back views) (Fig. 7). Normal and abnormal conditions of different fetuses can be incorporated into the system by performing the following actions: 1) creating an anatomical model of the fetus; 2) measuring or modeling the anatomical model to create a virtual model; and 3) registering the new anatomical and virtual models into the system. The positions of the anatomical and virtual models can be adjusted automatically simply by indicating the zero point of a scale called “station” with an index finger pointer on the screen at the first application start-up.

Figure 3:

Anatomical models of fetus for normal cases.



Figure 4:

Anatomical models of fetus for abnormal cases.

Fetal

Figure 5: Transparency ratio

model

Change of a fetal model. Display color Display type (Display mode)

Model type (Skin, Bone, Baby, Fingers)

Baby status

Display on/off

Figure 6:

Fetal model selection dialogue and display function.


307


Skin of the mother displayed in wireframe model

(a) Figure 7:

4

(b)

(c)

(d)

Display function of the internal examination training system. (a) Cross-section: left view. (b) Cross-section: right view. (c) Crosssection: anterior view. (d) Cross-section: posterior view.

Fetal presentation

Fetal presentation refers to the orientation of the fetus in the uterus and is classified as “longitudinal presentation”, “transverse presentation,” or “oblique presentation”. Longitudinal presentation is further divided based on the position of the fetal head into the “head presentation” (i.e. the fetal head is facing down) and “pelvic presentation” (i.e. the fetal pelvis is facing down; also known as the breech position). All fetal presentations other than head position are considered abnormal. It is known that less than 5% of fetuses are delivered in breech position. Delivery of fetuses in breech position carries a higher risk of experiencing difficulty in pushing out the head and causing compression of the umbilical cord than does delivery of fetuses with their head facing down (i.e. head presentation). Breech position is roughly divided into frank breech presentation, full breech presentation, knee presentation, and foot presentation. The fetal presentation in which fetal feet are facing up and the hips facing down is referred to as the frank breech presentation, that in which both feet are facing down is referred to as complete breech presentation, and that in which only one foot is facing up is referred to as incomplete breech presentation. “Knee presentation” is the condition in which the fetal knee is flexed and facing down during delivery (i.e. the fetus descends with its knee presenting first), and is further divided into “complete knee presentation” (i.e. both knees facing down) and “incomplete knee presentation” (i.e. only one knee facing down). “Foot presentation” is the condition in which the fetus descends with its extended legs presenting first during delivery. Some breech babies can be delivered naturally through the vaginal canal if they are in frank breech presentation or full breech presentation. Breech babies in knee or foot



309

presentation have less chance to be delivered naturally and are usually delivered by Caesarian section (cutting) [8].

5

System evaluation

We conduct a survey of eight students at our university, and make inquiries for our system, and evaluate it for understanding where the position of ischiadic thorn, baby head, and uterine ostium. We also check that it is easy to understand the rotation of baby head and the open of the uterine ostium. In the lecture of an internal examination, first we teach an internal examination in the classical method using a manikin only. Next, we teach them by using our system and make inquiries for our system with unregistered style. We check understanding of the students for several questions before and after looking images in our system. The result of several questions shows that the understanding of all students is improved by using our system [9].

Figure 8:

Fetal models of normal conditions (left: one-finger dilatation; right: two-finger dilatation).

Figures 8 and 9 show fetal models of normal conditions supported by the internal examination training system (i.e. one-finger dilatation, two-finger dilatation, type C (almost full dilatation), and full dilatation). Figures 10 and 11 show fetal models of abnormal conditions (incomplete foot presentation (frank breech presentation), complete breech presentation, placenta previa, and face presentation). We have been evaluating the usefulness of the present technique by disseminating its use as a learning tool and presenting it at international meetings and exhibitions. At the exhibition of the 21st Japan Academy of Midwifery Scientific Meeting (Oita prefecture in Japan, March 10 and 11, 2007), we presented and demonstrated our internal examination training system and a number of people experienced the training procedure and answered a questionnaire about the usefulness of the system. Over 100 people attended our presentation, approximately 60 of whom experienced the training procedure and provided feedback. Most of those who experienced the training system at the exhibition of the 21st Japan Academy of Midwifery Scientific Meeting provided positive WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

310 Modelling in Medicine and Biology VIII comments, although some requested improvements or the addition of functions. These requests included the addition of various abnormal labor conditions, more measurement functions (e.g. distance between two fingers and distance to the head of fetus), an automatic calibration function, and an examination rating function.

Figure 9:

Fetal models of normal conditions (left: type C; right: full dilatation).

Figure 10:

Fetal models of abnormal conditions (left: incomplete foot presentation; right: complete breech presentation).

We have satisfied one of the requests by developing 4 abnormal labor conditions (frank breech presentation, complete breech presentation, placenta previa and face presentation) and have included them in the latest training system. We have also added measurement functions using one or two fingers; the location sensors mounted on the index and middle fingers enable the acquisition of position information in space (i.e. spatial position and rotation). Using this measurement function, we can precisely measure spatial distances estimated on the basis of the distance between the two fingers or the measurer’s experience. In future studies, we aim to perform more detailed examinations of abnormal labor conditions. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


Figure 11:

6

311

Fetal models of abnormal conditions (left: placenta previa; right: face presentation).

Conclusion

We have developed an internal examination training system that supports the learning of abnormal labor conditions. The system provides a unique learning experience that cannot be gained in daily practice. The use of the system in teaching practice will help to nurture competent obstetricians and midwives in a short period. On the basis of specialist feedback, we included 4 abnormal fetal models in the training system. The availability of additional abnormal fetal models will make the system more relevant to actual clinical situations. Although the present system was developed specifically for internal examination of the fetus, it can also be applied for such purposes as medical training and preoperative planning for other parts of the body (e.g. thorax and abdomen) by using different anatomical and virtual models.

References [1] Ishii, T., Doi, A., Katamachi, K., Noguchi, K., and Uno, H., Medical Training Device, Japan Patent Application No. 2005-032614, Reference No. 4-1130, Receipt No. 50500225450, Patent Applicant: KOKEN Co., Ltd. (August 2004) [2] Ishii, T., Doi, A., Katamachi, K., Noguchi, K., and Uno, H., Medical Training Device, International patent application (European Patent Office), Reference No. GP05-1033PCT, Receipt No. 50600235406, Application No. Notification: PCT/JP2006/30219, Patent Applicant: KOKEN Co., Ltd. [3] Doi, A., Matsui, K., Katamachi, K., Noguchi, K., Ishii, T., Uno, H., A computer assisted medical training system for checking status of delivery by using virtual reality technique and physical models, CARS2007, p. 156, 2007. [4] Carla M. Pugh, et al., The E-Pelvis: A Pelvic Examination Simulator, SUMMIT (Stanford University Medical Media & Information



[5] [6] [7] [8] [9]

Technologies) Project Overview, http://summit.stanford.edu/publications/ tear_index.html SUMMIT (Stanford University Medical Media & Information Technologies, e-Pelvis, http://summit.stanford.edu/research/epelvis.html Shreve, J., ePelvis for simulation of gynecologic internal examination, http://hotwired.goo.ne.jp/news/technology/story/20020320307.html MC Medica Shuppan, 3D CG Peripartum Diagnosis/Delivery Assistance Training System, http://www.medica.co.jp/3d-bunben/#top Yajima, S., Nakano, H., and Taketani, Y., NEW Gynecologic Sciences, Nankodo; 2nd Edition (July 2004). Noguchi, K., and Ishii, T., Computer-assisted Educational Evaluation, Presentation at Japan Academy of Nursing Education, August 2, 2006.



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Development of a training system for interventional radiology M. Ide1 , Y. Fujii2 , B. Fujioka2, T. Komeda2 , H. Koyama2 , S. Yamamoto2 , M. Mohri3 & P. Beomonte Zobel4 1 Shibaura

Institute of Technology, Functional Control Systems, Japan Shibaura Institute of Technology, Systems Engineering, Japan 3 Mohri Hospital, Japan 4 University of L’Aquila,facolta di ingegneria, Laboratorio di Automazione a Fluido, Italy 2

Abstract The objective of the study reported here was to develop a master slave system for catheter-guided vascular surgery conducted by interventional radiology. By using a master slave system, the surgeon is not exposed to x-rays during the operation because the master tool managed by an operator is located away from the slave tool, which is near the patient. The system must provide vivid realism to the surgeon, particularly with regard to force information, because this surgery is performed in three dimensions while the surgeon watches a two-dimensional monitor. In this study, we developed a training system for a catheter guide in order to upgrade the surgeon’s skills because it is difficult to upgrade a master slave system without training. The system consists of a human interface device as the master tool, a control box, and a simulator. This training simulator is for the master slave system, which we developed. The master tool has a force display function using an electrorheological fluid. Two advantages of the fluid actuator are that it can be used without force feedback control and there is mechanical safety, as the surgeon does not experience any accidental force. An open loop control is used to achieve a simple mechanism and algorithm. Our results of preliminary experiments indicated that the output force achieved correlated with that sent from the PC. Three surgeons evaluated this training system under a variety of conditions. The operation of the master tool is simple. The thrust and rotation movements of the catheter can be handled instinctively and without complicated instructions. In addition, accurate force display, response, and stability were achieved with the electrorheological fluid. In the future, the training will need for a realistic depiction of interventional radiology, and the system provides accurate readings for aspiration and blood flow. Keywords: interventional radiology, training system, force feedback. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line) doi:10.2495/BIO090291


1 Introduction Interventional Radiology (IR) is a minimally invasive surgery. Its use has increased in the last 20 years. IR requires a catheter approach through a blood vessel to the diseased area where the surgery is to be performed with the use of small tools. With this procedure, Digital Subtraction Angiography (DSA) is used to determine the position of the catheter within the body with a vascular contrast medium. DSA transmits a continuous x-ray that is used to determine the position of the catheter, and, as a result, medical personnel are exposed to x-rays even when protection is worn. The motivation to conduct this study was the need to develop a Master Slave System (MSS) for catheter-guided IR surgery through the blood vasculature. The MSS is required to prevent the exposure of medical personnel to x-rays. The operator manages a master tool at a remote location from the slave tool, which is placed near the patient and under the DSA device. The force display between the master and slave is important to warn the surgeons when a surgery error occurs. However, the force display is not only for patient safety. A surgeon can view the vasculature from within with the use of a monitor during the IR procedure; however, the picture is two-dimensional information, making it important to display the force in order to accurately estimate the image depth. In addition, the force display is used for error recovery as well as an assessment of the heartbeat, aspiration, and affected area. These innovations are used to achieve a higher degree of realism. We have developed an MSS for interventional radiology [1]. However, generally, an MSS is difficult to adopt unless training is provided. Specialized training is necessary before this system can be adopted. Training to use the system is a problem due to its cost. A training system has been developed with virtual reality for cost reduction [2]. Research for the training system has indicated that training for catheterization effectively enhances the skill of the surgeon [3]. Therefore, for the purposes of this study, we developed a catheter simulator to use for teaching an advanced technique for catheterization. The operation of catheter is possible to conduct the catheter movement in the twist and insertion direction [4]. During an IR procedure, the operator estimates the depth of the blood vessel while watching a monitor with two degrees of freedom. In this case, the force reflection is important to confirm the contact between the catheter and a blood vessel [5]. The force reflection is an advantage to the surgeon [6]. Therefore, the display of force assists the individual who places the catheter in the field of the blood vessel in three dimensions while viewing the monitor in two dimensions. As a result, patient safety is improved. There are some previous studies involving catheter training systems [7,8]. Most of these studies focus on catheter function and movement. However, none of the existing devices displays the force reflection or heartbeat [9], and there are no specific interfaces to be used with force feedback [10] or to demonstrate differences in the actual IR image [11].



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Recently, Mentice, Inc. (www.mentice.com) developed a Procedicus Vascular Intervention System Trainer (VISTTM ). This system, as a treatment tool, displays force in three dimensions and accurately depicts a patient’s ailment. The simulator, however, does not provide an accurate display of the heartbeat, blood flow, and aspiration. For this study, the training system was developed for an existing MSS [1]. Furthermore, although the device requires specific instruments, such as a computer board, it is generally assumed that it can be used in conjunction with a common PC connected with a universal serial bus (USB). In addition, with the use of an IR, it should be possible to assess the heartbeat, blood flow, and aspiration.

2 Training simulator A system overview is shown in Fig. 1. The configuration diagram of the haptic device, console box, and simulator is shown in Fig. 2. The haptic device is used to accurately recreate an IR procedure with two degrees of freedom for insertion and rotation. The catheter with a two-dimensional image is guided toward the target by the operator. The operators were able to sense heartbeat during the training sessions.

Figure 1: Overview of the training simulator. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


Figure 2: Diagram of the configuration of the haptic device, console box, and simulator image.

2.1 Haptic device [1] This haptic device, shown in Fig. 3, has a ball screw; it rotates in synchronicity with all components and identifies the position of the thrust movement with the use of an encoder. The electrorheological (ER) fluid is placed in a case with a disk that is connected to a ball screw. The disk rotates with the ball screw, and the operator senses the force because of the resistance from the rotation caused by the voltage given to the ER fluid. The ER fluid is functional. It changes the shear viscosity or dynamic viscous elasticity according to the supplied electric field. This is the principle generating the force feedback. The ball screw is supported by bearings, and there are two seals used to retain the ER fluid within the case. When using it, the operator grasps the outer frame and moves the nut of the ball screw forward and backward as the thrust movement. At this moment, a disk rotates within the case. If the ER fluid changes viscosity, the disk reacts to the friction created. The fluid prevents smooth movement, and the operator senses force and torque from the ball screw. In comparison to an electric motor, the manner of force display is simpler in this system. The operator receives force feedback when the thrust shafts rotate with the disk. However, the contact points on the ball screw are the ball bearings and the seals so that the friction is at a minimum for the performance of the force feedback. The sensor for position is equipped with two encoders to detect the thrust (360[ppr]) and rotation (360[ppr]) direction. The operator holds the nut of the ball screw with one hand and the outer frame with the other. The operator may conduct two movements. The axis of ball screw is directly connected to the encoder axis and to the disk for the force display. The WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


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Figure 3: The haptic device has a ball screw that can rotate in synchronicity with all components and detect the position of the thrust movement using an encoder. The ER fluid is in a case with a disk that is connected to a ball screw. The disk rotates with the ball screw, and the operator can feel the force because of the resistance from the rotation caused by the voltage given to the ER fluid.

Figure 4: Volt-force curve of the haptic device.

weight of this device is about 200 [g], the length is 250 [mm], and the diameter is 48 [mm]. The volt-force curve is shown in Fig. 4. 2.2 Console box The console box distributes the commands from the haptic device and the simulator. The catheter on the simulator moves on the basis of the information received from the console box. Moreover, the force on the catheter in the simulator is defined in the program and is then sent to the console box so that the collision WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)

318 Modelling in Medicine and Biology VIII force between catheter and the wall of the vessel and interference can be displayed to the operator. Generally, controls or measurements from a PC, such as those obtained from ER fluid, an encoder, or haptic devices, require specific instruments, such as a pulse counter or DA boards. However, the simulator considered here was intended for a general case because it is difficult to use a common PC due to its lack of the required instruments. This system can be connected to a PC with a USB port.

3 Modeling of IR 3.1 Modeling of catheter and wall of vessel A dynamic model for simulation is shown in Fig. 5. The blood vessel assumes a rigid body. When the catheter collides, the wall becomes deformed in the direction of insertion. The tip of the catheter is bent in order to determine the direction for the branch connection of the vessel. Furthermore, the catheter can also be deformed when it collides with a vessel. For realizing this condition, the catheter constructed discrete model that is connected contact point of rigid stick. 3.2 Collision force and simulator image The collision force generally consists of elasticity and viscosity. However, this haptic device uses ER fluid for force reflection so that only viscosity was expressed. Only if viscosity reflection causes, the operator can sense the collision so that the patient’s security can preserve because it is a passive force reflection. The image used is an angiographic picture [12]. The image was displayed on the simulation monitor with a texture mapping method of OpenGL.

Figure 5: Dynamic simulation model. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


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Figure 6: Principle of collision detection. 3.3 Collision detection The coordinates of the parts of the wall of the vessel face on the image were extracted for collision detection. One of the links of catheter was assumed to be a segment of a line. The wall of the vessel was assumed to be a flat surface. The image of collision detection is shown in Fig. 6. The collision is detected when one joint point put front side and when other joint point put behind side as condition of collision. The joint is indicated by a point, P0 , on the vessel wall; the normal vector of the vessel wall is n; and the points at both ends are P1 , P2 . The collision detection is circulated from the inner product of P0 P1 , P0 P2 , and vector n. The condition equation is shown as Eq. (1). When a collision occurs, the angle of P0 P1 and vector n will be blunt. The value of the inner product is negative. On the other hand, the angle of P0 P2 and vector n will be sharp so that the value of the inner product is positive. When this value is negative, a collision is detected; when it is positive, no collision is detected. −−−→ → −−−→ − → n · P0 P1 × − n · P0 P2 ≤ 0

(1)

3.4 Catheter inflection Although a catheter is generally made of a flexible material, such as nylon or polyurethane, in this study, the catheter model is a polyarticular link mechanism capable of inflection for simplification. As shown in Fig. 7, the operator inserts the catheter in the direction of insertion, and the simulator detects the collision. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


Figure 7: Catheter inflection.

Figure 8: View of the calculation of the catheter inflection. The program then calculates the inflection angle of the catheter using collision force. Moreover, the reaction force is calculated by acceleration of the catheter. The acceleration is calculated by a second-order differential of displacement of the catheter. The catheter mass is mc ; the displacement when there is a collision of the catheter is Xc; the reaction force Fcw is shown in Eq. (2). The mass of the catheter is defined as 10 [g]. As shown in Fig. 8, the inflection angle of the catheter is K[deg]; the reaction force by collision is Fcw; the catheter length is lc; the longitudinal elastic modulus of the catheter is Ec; and the geometrical moment of inertia is Ic. The angle of the inclination slope of the cantilever equation is shown in Eq. (3). WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


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Figure 9: Vascular bifurcation.

Fcw

d2 X c = mc 2 dt

(2)

FcW l2 cos ∅ 2Ec Ic

(3)

K=

Link ab of the tip of the catheter revolves A [deg] around joint b. Link bc revolves B [deg] around joint c. Link cd revolves C [deg] around joint d. After revolution, the detection repeats to the next collision. The guide on the vascular bifurcation is possible, as shown in Fig. 9.

4 Surgeon’s evaluation Three surgeons evaluated the training simulator under a variety of conditions. The haptic device was easy to use. The thrust and the rotation of the catheter could be handled instinctively by the surgeon without complicated instructions. The surgeons could use a suitable thrust velocity of the catheter because it could be controlled with the gain. When the catheter came in contact with the vascular wall, the surgeons could evaluate the pressure with the haptic device.

5 Conclusions For this study, a training system was developed for an existing MSS. Moreover, a console box and a simulation program with a connected haptic device were developed. This system can be connected to a PC with a USB port. Its usefulness was assessed by surgeons. In the future, a simulator capable of more detail would enhance the practicality of the system.

Acknowledgements The author would like to thank ERtec and the Brain Science and Life Technology Research Foundation. WIT Transactions on Biomedicine and Health, Vol 13, © 2009 WIT Press www.witpress.com, ISSN 1743-3525 (on-line)


References [1] Masaru Ide et al.: “Development of a master slave system for interventional radiology”, International Journal of Computer Assisted Radiology and Surgery, Volume 3, Supplement 1, pp. 343, 2008 [2] Kostas Vlachos, Evangelos Papadopoulos, Senior Member,Design and Implementation of a Haptic Device for Training in Urological Operations, IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 19, NO. 5, pp. 801–809 [3] Scott A. Engum, et al.:Intravenous catheter training system: Computerbased education versus traditional learning method The American Journal of surgery 186, pp. 67–74, 2003 [4] F. Arai, R. Fujimura, T. Fukuda, and M. Negoro: “New Catheter Driving Method Using Linear Stepping Mechanism for Intravascular Neurosurgery,” Proc. of the IEEE Int. Conf. on Robotics and Automation, pp. 2944–2949, 2002 [5] M.Tanimoto, F.Arai, T. Fukuda: “Force Display Method for Intravascular Neurosurgery,” Proc. of the IEEE SMC ’99 Conf., Vol. 4, pp. 1032–1037, 1999 [6] Christopher R. Wagner, Robert D.Howe: “Force Feedback Benefit Depends on Experience in Multiple Dgree of Freedom Robotic Surgery Task,” IEEE Trans on Robotics, Vol. 23, No. 6, pp. 1235–1240, 2007 [7] Julien Lenoir, Stephane Cotin, at al., Interactive physically-based simulation of catheter and guidewire, Computers & Graphics 30, pp. 416–422, 2006 [8] Jan Egger, et al., A Fast Vessel Centerline Extraction Algorithm for Catheter Simulation, Twentieth IEEE Int. Symp. on Computer- Based Medical Systems, pp. 177–182 [9] W. Lawton, et al. Tubes in Tubes: Catheter Navigation in Blood Vessels and its Applications, International Journal of Solids and Structures, Vol.37, Issue 22, pp. 3031–3054, 2000 [10] Suraj Bhat, et al., A physically-based model for guidewire simulation on patient-specfic data, International Congress Series, Vol. 1281, pp. 479–484, 2005 [11] Y.Y.Cai, et al., Tactile VR for hand-eye coordination in simulated PTCA, Computers in Biology and Medicine, Vol. 36, pp. 167–180, 2006 [12] DEAGOSTINI FInside Human BodyCUNIT75



323

Author Index Accardo A.................................. 39 Ahmed S. ................................... 83 Akhmadeev N. ......................... 191 Alrashdan K............................. 181 Alrashidi M.............................. 181 Antonelli M. G......................... 159 Averbach M. .............................. 17 Bărbat T. .................................... 93 Basak T. K. .............................. 247 Beomonte Zobel P. .......... 159, 313 Bernad E. ................................... 93 Bernad S. I. ................................ 93 Bhattacharya K. ....................... 247 Bignardi C................................ 149 Borhan A.................................. 123 Bui A.......................................... 83 Cavka D. .................................. 203 Cescotto S. ............................... 133 Chutakositkanon C..................... 17 Corbi G. ..................................... 39 Costanzo G. ..................... 149, 159 Cyril Raj V. ................................247 D’Addio G. ................................ 39 Dewals B. J. ............................. 133 Dickman S. .............................. 235 Doi A. ...................................... 303 Durdle N. ................................. 257 Eitel G...................................... 103 Enomoto Y................................. 71 Erpicum S. ............................... 133 Esat İ. ....................................... 181 Ferrara N.................................... 39 Fujii Y...................................... 313 Fujioka B. ................................ 313 Gastaldi L. ............................... 223 Gharbi T................................... 287 Gliozzi A. S. ............................ 267

Guiot C. ................................... 267 Gunasekaran G. ......................... 247 Halder S. .................................. 247 Houacine A.............................. 287 Hyre M. R.................................. 27 Ide M. ...................................... 313 Imai Y........................................ 49 Ishii T....................................... 303 Ishikawa T. ................................ 49 Katamachi K. ........................... 303 Keshavarzi B. .......................... 123 Kiss R. M................................. 171 Ko J.......................................... 235 Komeda T. ............................... 313 Kondo H. ................................... 49 Koyama H................................ 313 Kudo T....................................... 71 Kumar A. ................................. 257 Lai C.-H................................... 277 Li V. W.................................... 235 Liffman K. ................................. 83 Liu L. ....................................... 277 Lu H.-w.................................... 277 Macpherson A. K....................... 17 Macpherson P. A. ...................... 17 Manasseh R. .............................. 83 Matsui K. ................................. 303 McGilvray K. C.......................... 57 Mega S..................................... 303 Meinke M. ............................... 103 Mekaoui S................................ 287 Miftahof R. .............................. 191 Mihalj M.................................. 203 Mohri M................................... 313 Murugappan S. ........................ 247 Neti S. ........................................ 17 Noguchi K. .............................. 303

324 Modelling in Medicine and Biology VIII Paolo Delsanto P...................... 267 Parameswaran S....................... 115 Pastorelli S............................... 223 Paulus R................................... 133 Pirotton M................................ 133 Poljak D. .................................. 203 Pulliam R. M.............................. 27 Puttlitz C. M. ............................. 57 Raimondi P. ............................. 159 Raj R. ....................................... 115 Ramieri A. ............................... 149 Raparelli T. .............................. 159 Ravi T. ........................................247 Rengo F...................................... 39 Sarkar R. .................................... 57 Schröder W. ............................. 103 Sesnic S.................................... 203 Shaw P. .......................................247 Shimano K. ................................ 71 Shoucri R. M................................ 3

Smirnov S. ............................... 115 Sorli M..................................... 223 Squire J. C. ................................ 27 Suaste E. .................................. 213 Susan-Resiga R.......................... 93 Šutalo I. D.................................. 83 Tan J. ....................................... 115 Terán O.................................... 213 Titlic M.................................... 203 Ultman J................................... 123 Uno H. ..................................... 303 Valleru N. ................................ 115 Xie F. ....................................... 277 Yamaguchi T. ............................ 49 Yamamoto S. ........................... 313 Yıldız İ..................................... 181 Zhou S.-d. ................................ 277

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