Medical Image Computing and Computer-Assisted Intervention - MICCAI 2007, 10 conf., part 2

Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris ...

Author: Nicholas Ayache | Sebastien Ourselin | Anthony Maeder

11 downloads 1602 Views 21MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

4792

Nicholas Ayache Sébastien Ourselin Anthony Maeder (Eds.)

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007 10th International Conference Brisbane, Australia, October 29 – November 2, 2007 Proceedings, Part II

13

Volume Editors Nicholas Ayache INRIA, Asclepios Project-Team 2004 Route des Lucioles, 06902 Sophia-Antipolis, France E-mail: [email protected] Sébastien Ourselin Anthony Maeder CSIRO ICT Centre, e-Health Research Centre 20/300 Adelaide St., Brisbane, Queensland 4000, Australia E-mail: {sebastien.ourselin, anthony.maeder}@csiro.au

Library of Congress Control Number: 2007937392 CR Subject Classification (1998): I.5, I.4, I.3.5-8, I.2.9-10, J.3, J.6 LNCS Sublibrary: SL 6 – Image Processing, Computer Vision, Pattern Recognition, and Graphics ISSN ISBN-10 ISBN-13

0302-9743 3-540-75758-9 Springer Berlin Heidelberg New York 978-3-540-75758-0 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 12175437 06/3180 543210

Preface

The 10th International Conference on Medical Imaging and Computer Assisted Intervention, MICCAI 2007, was held at the Brisbane Convention and Exhibition Centre, South Bank, Brisbane, Australia from 29th October to 2nd November 2007. MICCAI has become a premier international conference in this domain, with in-depth papers on the multidisciplinary fields of biomedical image computing, computer assisted intervention and medical robotics. The conference brings together biological scientists, clinicians, computer scientists, engineers, mathematicians, physicists and other interested researchers and offers them a forum to exchange ideas in these exciting and rapidly growing fields. The conference is both very selective and very attractive: this year we received a record number of 637 submissions from 35 countries and 6 continents, from which 237 papers were selected for publication. Some interesting facts about the distribution of submitted and accepted papers are shown graphically at the end of this preface. A number of modifications were introduced into the selection process this year. 1. An enlarged Program Committee of 71 members was recruited by the Program Chair and Co-chair, to get a larger body of expertise and geographical coverage. 2. New key words regrouped within 7 new categories were introduced to describe the content of the submissions and the expertise of the reviewers. 3. Each submitted paper was assigned to 3 Program Committee members whose responsibility it was to assign each paper to 3 external experts (outside of the Program Committee membership) who provided scores and detailed reports in a double blind procedure. 4. Program Committee members provided a set of normalized scores for the whole set of papers for which they were responsible (typically 27 papers). They did this using the external reviews and their own reading of the papers and had to complete missing reviews themselves. Program Committee members eventually had to provide a recommendation for acceptance of the top 35% of their assigned papers. 5. During a 2 day meeting of about 20 members of the Program Committee in Sophia-Antipolis, France, borderline papers were examined carefully and the final set of papers was accepted to appear in the LNCS proceedings. A top list of about 100 papers was scrutinized to provide the Program Chair and Co-chair with a list of 54 potential podium presentations. 6. From this list, the Program Chair and Co-chair selected 38 podium presentations to create a program with a reasonable number of oral sessions and spread of content.

VI

Preface

7. Because 199 excellent contributions would be presented as posters, it was decided in consultation with the MICCAI Society Board to augment the time allocated to the poster sessions, and replace the oral poster teasers by continuous video teasers run on large screens during the conference. The selection procedure was very selective, and many good papers remained among the 400 rejected. We received 9 factual complaints from the authors of rejected papers. A subcommittee of the Program Committee treated all of them equally, checking carefully that no mistake had been made during the selection procedure. In a few cases, an additional review was requested from an independent Program Committee member. In the end, all the original decisions were maintained, but some additional information was provided to the authors to better explain the final decision. Seven MICCAI Young Scientist Awards were presented by the MICCAI Society on the last day of the conference. The selection was made before the conference by nominating automatically the 21 eligible papers with the highest normalized scores (provided by the Program Committee during the reviewing procedure), and regrouping them into the 7 main categories of the conference. A subgroup of the Program Committee had to vote to elect one paper out of 3 in each category. The 2007 MedIA-MICCAI Prize was offered by Elsevier to the first author of an outstanding article in the special issue of the Medical Image Analysis Journal dedicated to the previous conference MICCAI 2006. The selection was organized by the guest-editors of this special issue. We want to thank wholeheartedly all Program Committee members for their exceptional work, as well as the numerous external expert reviewers (who are listed on the next pages). We should also acknowledge the substantial contribution made towards the successful execution of MICCAI 2007 by the BioMedical Image Analysis Laboratory team at the CSIRO ICT Centre / e-Health Research Centre. It was our pleasure to welcome MICCAI 2007 attendees in Brisbane. This was the first time the conference had been held in Australia, indeed only the second time outside of Europe/North America, the other being MICCAI 2002 in Japan. This trend will continue with MICCAI 2010, which is planned for Beijing. The vibrant sub-tropical river city of Brisbane with its modern style and world-class conference venue was a popular choice and a convenient point of departure for delegates who took the opportunity while there to see more of the Australian outback. We thank our two invited keynote speakers, Prof. Peter Hunter from the Bioengineering Institute at the University of Auckland, New Zealand, and Prof. Stuart Crozier from Biomedical Engineering at the University of Queensland, Brisbane, whose excellent presentations were a highlight of the conference. We also acknowledge with much gratitude the contributions of Terry Peters, MICCAI 2007 General Co-Chair, whose strong connection with the MICCAI Society and past MICCAI conferences proved invaluable to us. We also note our thanks

Preface

VII

to our sponsors, without whose financial assistance the event would have been a far lesser one. We look forward to welcoming you to MICCAI 2008, to be held 4-8 September in New York City, USA, and MICCAI 2009, scheduled to be held in London, UK. October 2007

Nicholas Ayache Sébastien Ourselin Anthony Maeder

VIII

Preface

MICCAI 2007 Papers by Topic Computer Assisted Interventional Systems and Robotics 14%

Computational Physiology 6%

Computational Anatomy Visualization and 8% Interaction 3%

General Biological Image Computing 3%

None Specified 1% Neuroscience Image Computing 8% Innovative Clinical and Biological Applications 11%

General Medical Image Computing 46%

General Medical Image Computing

Computer Assisted Interventional Systems and Robotics

Statistical image analysis Other (Computer Assisted Interventional Systems and Robotics)

9

Processing X-ray, CT, MR (anatomical, functional, diffusion, spectroscopic), SPECT,

9

39

PDEs and Level Sets methods

4

Other (General Medical Image Computing)

Instrument & Patient Localization and Tracking

3

17

21

Non linear registration and fusion 9

Morphometric and functional segmentation Image-guided robotized intervention

4

3

Methodological tools for validation 1

Grid-enabled image processing algorithms 4

Advanced Medical Robotics

Extraction of visual features : texture, shape, connectivity, motion, etc

19

Fig. 1. View at a glance of MICCAI 2007 accepted submissions based on the declared primary keyword. A total of 237 full papers were presented.

206

Africa 0% 1%

Asia

North America

Full paper submissions: 637

24 22

15% 5%

19

Asia Australia and Oceania 58

7

Europe

2

Europe

an Ta iw

el

Ja pa n Ko re a, So ut h Si ng ap or e

hi na H

on g

C

South America

Ira n

USA

Ko ng

Canada

In di a

North America 38%

Others 31

67 48

7

6

5 1

Is ra

41%

52

19

bi a ol om C

an d

ia st ra l

Ze al ew

2

N

Eg yp t

2

Br az il

1

Au

y

1

UK

rk e Tu

er la

nd

en

1

i tz

ain

ed

Sp

Sw

Sl ov

en

ia

l

y

ga

wa

rtu

or N

5

2

1

Po

ly

2

Sw

ec h

10

7

5

4

ds

1

It a

2

er lan

1

Re pu bl D e ic nm ar k Fi nl an d Fr an ce Ge rm an y Gr ee ce H un ga ry

um lg i Cz

Au

Be

str

ia

2

Ne th

8

6

Fig. 2. Distribution of MICCAI 2007 submissions (637 in total) by continent

MICCAI Young Scientist Awards

The MICCAI Young Scientist Award is a prize of US$500 awarded to the first author (in person) for the best paper in a particular topic area, as judged by reviewing and presentation (oral or poster). At MICCAI 2007, up to 7 prizes were available, in the topic areas publicised in the conference CFP: 1. 2. 3. 4. 5. 6. 7.

General Medical Image Computing Computer Assisted Intervention Systems and Robotics Visualization and Interaction General Biological and Neuroscience Image Computing Computational Anatomy Computational Physiology Innovative Clinical and Biological Applications

All current first author students and early career scientists attending MICCAI 2007 were eligible. The awards were announced and presented at the closing session of the conference on Thursday, 1st November 2007.

MICCAI 2005 Student Awards Image Segmentation and Analysis: Pingkun Yan, “MRA Image Segmentation with Capillary Active Contour” Image Registration: Ashraf Mohamed, “Deformable Registration of Brain Tumor Images via a Statistical Model of Tumor Induced Deformation” Computer-Assisted Interventions and Robotics: Henry C. Lin, “Automatic Detection and Segmentation of Robot Assisted Surgical Motions” Simulation and Visualization: Peter Savadjiev, “3D Curve Inference for Diffusion MRI Regularization” Clinical Application: Srinivasan Rajagopalan, “Schwarz Meets Schwann: Design and Fabrication of Biomorphic Tissue Engineering Scaffolds”

MICCAI 2006 Student Awards Image Segmentation and Registration: Delphine Nain, “Shape-Driven 3D Segmentation Using Spherical Wavelets” Image Analysis: Karl Sj¨ ostrand, “The Entire Regularization Path for the Support Vector Domain Description”

X

MICCAI Young Scientist Awards

Simulation and Visualization: Andrew W. Dowsey, “Motion-Compensated MR Valve Imaging with COMB Tag Tracking and Super-Resolution Enhancement” Computer-Assisted Interventions and Robotics: Paul M. Novotny, “GPU Based Real-Time Instrument Tracking with Three Dimensional Ultrasound” Clincial Applications: Jian Zhang, “A Pilot Study of Robot-Assisted Cochlear Implant Surgery Using Steerable Electrode Arrays”

The 2007 MedIA-MICCAI Prize This prize is awarded each year by Elsevier to the first author of an outstanding article of the previous MICCAI conference, which is published in the MICCAI special issue of the Medical Image Analysis Journal. In 2006, the prize was awarded to T. Vercauteren, first author of the article: Vercauteren, T., Perchant, A., Pennec, X., Malandain, G., Ayache, N.: Robust mosaicing with correction of motion distortions and tissue deformations for in vivo fibered microscopy. Med. Image Anal. 10(5), 673–692 (2006) In 2005, the prize was awarded to D. Burschka and M. Jackowski who are the first authors of the articles: Burschka, D., Li, M., Ishii, M., Taylor, R.H., Hager, G.D.: Scale invariant registration of monucular endoscopic images to CT-Scans for sinus surgery. Med. Image Anal. 9(5), 413–426 (2005) Jackowski, M., Kao, C.Y., Qiu, M., Constable, R.T., Staib, L.H.: White matter tractography by anisotropic wave front evolution and diffusion tensor imaging. Med. Image Anal. 9(5), 427–440 (2005)

Organization

Executive Committee General Chair General Co-chair Program Chair Program Co-chair

Anthony Maeder (CSIRO, Australia) Terry Peters (Robarts Research Institute, Canada) Nicholas Ayache (INRIA, France) Sébastien Ourselin (CSIRO, Australia)

Program Committee Elsa Angelini (ENST, Paris, France) Simon R. Arridge (University College London, UK) Leon Axel (University Medical Centre, USA) Christian Barillot (IRISA, Rennes, France) Margrit Betke (Boston University, USA) Elizabeth Bullitt (University of North Carolina, Chapel Hill , USA) Albert Chung (Hong Kong University of Science and Technology, China) Ela Claridge (The University of Birmingham, UK) Stuart Crozier (University of Queensland, Australia) Christos Davatzikos (University of Pennsylvania, USA) Marleen de Bruijne (University of Copenhagen, Denmark) Rachid Deriche (INRIA, Sophia Antipolis, France) Etienne Dombre (CNRS, Montpellier, France) James S. Duncan (Yale University, USA) Gary Egan (Howard Florey Institute, Australia) Randy Ellis (Queens University, Canada) Gabor Fichtinger (Johns Hopkins University, USA) Alejandro Frangi (Pompeu Fabra University, Barcelona, Spain) Guido Gerig (University of North Carolina, Chapel Hill, USA) Polina Golland (Massachusetts Institute of Technology, USA) Miguel Angel Gonzalez Ballester (University of Bern, Switzerland) Richard Hartley (Australian National University, Australia) David Hawkes (University College London, UK) Pheng Ann Heng (The Chinese University of Hong Kong, China) Robert Howe (Harvard University, USA) Peter Hunter (The University of Auckland, New Zealand) Tianzi Jiang (The Chinese Academy of Sciences, China) Sarang Joshi (University of Utah, USA)

XII

Organization

Leo Joskowicz (The Hebrew University of Jerusalem, Israel) Hans Knustsson (Linkoping University, Sweden) Rasmus Larsen (Technical University of Denmark, Denmark) Boudewijn Lelieveldt (Leiden University Medical Centre, Netherlands) Cristian Lorenz (Philips, Hamburg, Germany) Frederik Maes (Katholieke Universiteit Leuven, Belgium) Gregoire Malandain (INRIA, Sophia Antipolis, France) Jean-Francois Mangin (CEA, SHFJ, Orsay, France) Dimitris Metaxas (Rutgers University, New Jersey, USA) Kensaku Mori (Mori Nagoya University, Japan) Nassir Navab (TUM, Munich, Germany) Poul Nielsen (The University of Auckland, New Zealand) Wiro Niessen (Erasmus Medical School, Rotterdam, Netherlands) Alison Noble (Oxford University, UK) Jean-Christophe Olivo-Marin (Institut Pasteur, Paris, France) Nikos Paragios (Ecole Centrale de Paris, France) Xavier Pennec (INRIA, Sophia Antipolis, France) Franjo Pernus (University of Ljubljana, Slovenia) Josien Pluim (University Medical Center, Utrecht, Netherlands) Jean-Baptiste Poline (CEA, SHFJ, Orsay, France) Jerry L. Prince (Johns Hopkins University, USA) Richard A. Robb (Mayo Clinic, College of Medicine, Rochester, Minnesota, USA) Daniel Rueckert (Imperial College, London, UK) Tim Salcudean (The University of British Columbia, Canada) Yoshinobu Sato (Osaka University, Japan) Achim Schweikard (Institute for Robotics and Cognitive Systems, Germany) Pengcheng Shi (Hong Kong University of Science and Technology, China) Stephen Smith (Oxford University, UK) Lawrence Staib (Yale University, USA) Colin Studholme (University of California, San Francisco, USA) Gabor Székely (ETH, Zurich, Switzerland) Russell Taylor (Johns Hopkins University, USA) Jean-Philippe Thiran (EPFL, Lausanne, Switzerland) Jocelyne Troccaz (CNRS, Grenoble, France) Bram van Ginneken (University Medical Center, Utrecht, Netherlands) Koen Van Leemput (HUS, Helsinki, Finland) Baba Vemuri (University of Florida, USA) Simon Warfield (Harvard University, USA) Sandy Wells (Massachusetts Institute of Technology, USA) Carl-Fredrik Westin (Westin Harvard University, USA) Ross Whitaker (University of Utah, USA) Chenyang Xu (Siemens Corporate Research, USA) Guang Zhong Yang (Imperial College, London, UK)

Organization

XIII

MICCAI Board Nicholas Ayache, INRIA, Sophia Antipolis, France Alan Colchester, University of Kent, Canterbury, UK James Duncan, Yale University, New Haven, Connecticut, USA Gabor Fichtinger, Johns Hopkins University, Baltimore, Maryland, USA Guido Gerig, University of North Carolina, Chapel Hill, North Carolina, USA Anthony Maeder, University of Queensland, Brisbane, Australia Dimitris Metaxas, Rutgers University, Piscataway Campus, New Jersey, USA Nassir Navab, Technische Universität, Munich, Germany Mads Nielsen, IT University of Copenhagen, Copenhagen, Denmark Alison Noble, University of Oxford, Oxford, UK Terry Peters, Robarts Research Institute, London, Ontario, Canada Richard Robb, Mayo Clinic College of Medicine, Rochester, Minnesota, USA

MICCAI Society Society Officers President and Board Chair Executive Director Executive Secretary Treasurer Elections Officer

Alan Colchester Richard Robb Nicholas Ayache Terry Peters Karl Heinz Hoehne

Society Staff Membership Coordinator Publication Coordinator

Gabor Székely, ETH, Zurich, Switzerland Nobuhiko Hata, Brigham and Women’s Hospital, Boston, USA Communications Coordinator Kirby Vosburgh, CIMIT, Boston, USA Industry Relations Coordinator Tina Kapur, Brigham and Women’s Hospital, Boston, USA

Local Planning Committee Sponsors and Exhibitors Registration and VIP Liaison Tutorials and Workshops Posters Social Events Technical Proceedings Support Professional Society Liaison Webmaster Student & Travel Awards

Oscar Acosta-Tamayo Tony Adriaansen Pierrick Bourgeat Hans Frimmel, Olivier Salvado Justin Boyle Jason Dowling Brian Lovell Jason Pickersgill & Josh Passenger Olivier Salvado

XIV

Organization

Sponsors CSIRO ICT Centre e-Health Research Centre Northern Digital, Inc. Medtronic, Inc. The Australian Pattern Recognition Society CSIRO Preventative Health Flagship Siemens Corporate Research GE Global Research

Reviewers Abend, Alan Abolmaesumi, Purang Acar, Burak Acosta Tamayo, Oscar Acton, Scott T. Adali, Tulay Aja-Fern´ andez, Santiago Alexander, Daniel Allen, Peter Alterovitz, Ron Amini, Amir An, Jungha Andersson, Mats Antiga, Luca Ardekani, Babak Ashburner, John Atkins, Stella Atkinson, David Avants, Brian Awate, Suyash Aylward, Stephen Azar, Fred S. Azzabou, Noura Babalola, Kolawole Bach Cuadra, Meritxell Baillet, Sylvain Bajcsy, Ruzena Bansal, Ravi Bardinet, Eric Barmpoutis, Angelos Barratt, Dean Bartoli, Adrien

Bartz, Dirk Basser, Peter Batchelor, Philip Baumann, Michael Bazin, Pierre-Louis Beckmann, Christian Beichel, Reinhard Bello, Fernando Benali, Habib Berger, Marie-Odile Bhalerao, Abhir Bharkhada, Deepak Bhatia, Kanwal Bilston, Lynne Birkfellner, Wolfgang Bischof, Horst Blanquer, Ignacio Blezek, Daniel Bloch, Isabelle Bockenbach, Olivier Boctor, Emad Bodensteiner, Christoph Bogunovic, Hrvoje Bosch, Johan Botha, Charl Bouix, Sylvain Boukerroui, Djamal Bourgeat, Pierrick Bresson, Xavier Brummer, Marijn Bucki, Marek Buehler, Katja

Organization

Buelow, Thomas Bueno Garcia, Gloria Buie, Damien Buzug, Thorsten Caan, Matthan Cai, Wenli Calhoun, Vince Camara, Oscar Cameron, Bruce Cammoun, Leila Camp, Jon Cardenas, Valerie Carneiro, Gustavo Carson, Paul Cates, Joshua Cathier, Pascal Cattin, Philippe Cavusoglu, Cenk Celler, Anna Chakravarty, Mallar Chaney, Edward Chang, Sukmoon Chappelow, Jonathan Chefd’hotel, Christophe Chen, Jian Chen, Ting Chi, Ying Chinzei, Kiyoyuki Chiu, Bernard Christensen, Gary Chua, Joselito Chui, Chee Kong Chui, Yim Pan Chung, Adrian Chung, Moo Chung, Pau-Choo Cinquin, Philippe Ciuciu, Philippe Clarysse, Patrick Clatz, Olivier Cleary, Kevin Cois, Constantine Collins, Louis Collins, David Colliot, Olivier

Commowick, Olivier Cootes, Tim Corso, Jason Cotin, Stephane Coulon, Olivier Coupe, Pierrick Crouch, Jessica Crum, William D’Agostino, Emiliano Dam, Erik Dan, Ippeita Darkner, Sune Dauguet, Julien Davis, Brad Dawant, Benoit De Craene, Mathieu Deguchi, Daisuke Dehghan, Ehsan Delingette, Hervé DeLorenzo, Christine Deng, Xiang Desai, Jaydev Descoteaux, Maxime Dey, Joyoni Diamond, Solomon Gilbert Dieterich, Sonja Dijkstra, Jouke Dillenseger, Jean-Louis DiMaio, Simon Dirk, Loeckx Dodel, Silke Dornheim, Jana Dorval, Thierry Douiri, Abdel Duan, Qi Duay, Valérie Dubois, Marie-Dominique Duchesne, Simon Dupont, Pierre Durrleman, Stanley Ecabert, Olivier Edwards, Philip Eggers, Holger Ehrhardt, Jan El-Baz, Ayman

XV

XVI

Organization

Ellingsen, Lotta Elson, Daniel Ersbøll, Bjarne Fahmi, Rachid Fan, Yong Farag, Aly Farman, Allan Fenster, Aaron Fetita, Catalin Feuerstein, Marco Fieten, Lorenz Fillard, Pierre Fiorini, Paolo Fischer, Bernd Fischer, Gregory Fitzpatrick, J. Michael Fleig, Oliver Fletcher, P. Thomas Florack, Luc Florin, Charles Forsyth, David Fouard, Celine Freiman, Moti Freysinger, Wolfgang Fripp, Jurgen Frouin, Frédérique Funka-Lea, Gareth Gangloff, Jacques Garnero, Line Gaser, Christian Gassert, Roger Gavrilescu, Maria Gee, James Gee, Andrew Genovesio, Auguste Gerard, Olivier Ghebreab, Sennay Gibaud, Bernard Giger, Maryellen Gilhuijs, Kenneth Gilmore, John Glory, Estelle Gobbi, David Goh, Alvina Goksel, Orcun

Gong, Qiyong Goodlett, Casey Goris, Michael Grady, Leo Grau, Vicente Greenspan, Hayit Gregoire, Marie Grimson, Eric Groher, Martin Grunert, Ronny Gu, Lixu Guerrero, Julian Guimond, Alexandre Hager, Gregory D Hahn, Horst Hall, Matt Hamarneh, Ghassan Han, Xiao Hansen, Klaus Hanson, Dennis Harders, Matthias Hata, Nobuhiko He, Huiguang He, Yong Heckemann, Rolf Heintzmann, Rainer Hellier, Pierre Ho, HonPong Hodgson, Antony Hoffmann, Kenneth Holden, Mark Holdsworth, David Holmes, David Hornegger, Joachim Horton, Ashley Hu, Mingxing Hu, Qingmao Hua, Jing Huang, Junzhou Huang, Xiaolei Huang, Heng Hutton, Brian Iglesias, Juan Eugenio J¨ ager, Florian Jain, Ameet

Organization

James, Adam Janke, Andrew Jannin, Pierre Jaramaz, Branislav Jenkinson, Mark Jin, Ge John, Nigel Johnston, Leigh Jolly, Marie-Pierre Jomier, Julien Jordan, Petr Ju, Tao Kabus, Sven Kakadiaris, Ioannis Karjalainen, Pasi Karssemeijer, Nico Karwoski, Ron Kazanzides, Peter Keil, Andreas Kerdok, Amy Keriven, Renaud Kettenbach, Joachim Khamene, Ali Kier, Christian Kikinis, Ron Kindlmann, Gordon Kiraly, Atilla Kiss, Gabriel Kitasaka, Takayuki Knoerlein, Benjamin Kodipaka, Santhosh Konietschke, Rainer Konukoglu, Ender Korb, Werner Koseki, Yoshihiko Kozerke, Sebastian Kozic, Nina Krieger, Axel Kriegeskorte, Nikolaus Krissian, Karl Krol, Andrzej Kronreif, Gernot Krupa, Alexandre Krupinski, Elizabeth Krut, Sébastien

Kukuk, Markus Kuroda, Kagayaki Kurtcuoglu, Vartan Kwon, Dong-Soo Kybic, Jan Lai, Shang-Hong Lambrou, Tryphon Lamperth, Michael Lasser, Tobias Law, W.K. Lazar, Mariana Lee, Su-Lin Lee, Bryan Leemans, Alexander Lekadir, Karim Lenglet, Christophe Lepore, Natasha Leung, K. Y. Esther Levman, Jacob Li, Kang Li, Shuo Li, Ming Liao, Shu Liao, Rui Lieby, Paulette Likar, Bostjan Lin, Fuchun Linguraru, Marius George Linte, Cristian Liu, Yanxi Liu, Huafeng Liu, Jimin Lohmann, Gabriele Loog, Marco Lorenzen, Peter Lueders, Eileen Lum, Mitchell Ma, Burton Macq, Benoit Madabhushi, Anant Manduca, Armando Manniesing, Rashindra Marchal, Maud Marchesini, Renato Marsland, Stephen

XVII

XVIII

Organization

Martel, Sylvain Martens, Volker Mart´ı, Robert Martin-Fernandez, Marcos Masood, Khalid Masutani, Yoshitaka McGraw, Tim Meas-Yedid, Vannary Meier, Dominik Meikle, Steve Melonakos, John Mendoza, Cesar Merlet, Jean-Pierre Merloz, Philippe Mewes, Andrea Meyer, Chuck Miller, James Milles, Julien Modersitzki, Jan Mohamed, Ashraf Monahan, Emily Montagnat, Johan Montillo, Albert Morandi, Xavier Moratal, David Morel, Guillaume Mueller, Klaus Mulkern, Robert Murgasova, Maria Murphy, Philip Nakamoto, Masahiko Nash, Martyn Navas, K.A. Nelson, Bradley Nichols, Thomas Nicolau, Stephane Niemeijer, Meindert Nikou, Christophoros Nimsky, Christopher Novotny, Paul Nowinski, Wieslaw Nuyts, Johan O’Donnell, Lauren Ogier, Arnaud Okamura, Allison

O’Keefe, Graeme Olabarriaga, Silvia ´ Olafsd´ ottir, Hildur Oliver, Arnau Olsen, Ole Fogh Oost, Elco Otake, Yoshito Ozarslan, Evren Padfield, Dirk Padoy, Nicolas Palaniappan, Kannappan Pang, Wai-Man Papademetris, Xenios Papadopoulo, Théo Patriciu, Alexandru Patronik, Nicholas Pavlidis, Ioannis Pechaud, Mickael Peine, William Peitgen, Heinz-Otto Pekar, Vladimir Penney, Graeme Perperidis, Dimitrios Peters, Terry Petit, Yvan Pham, Dzung Phillips, Roger Pichon, Eric Pitiot, Alain Pizer, Stephen Plaskos, Christopher Pock, Thomas Pohl, Kilian Maria Poignet, Philippe Poupon, Cyril Prager, Richard Prastawa, Marcel Prause, Guido Preim, Bernhard Prima, Sylvain Qian, Zhen Qian, Xiaoning Raaymakers, Bas Radaelli, Alessandro Rajagopal, Vijayaraghavan

Organization

Rajagopalan, Srinivasan Rasche, Volker Ratnanather, Tilak Raucent, Benoit Reinhardt, Joseph Renaud, Pierre Restif, Christophe Rettmann, Maryam Rexilius, Jan Reyes, Mauricio Rhode, Kawal Rittscher, Jens Robles-Kelly, Antonio Rodriguez y Baena, Ferdinando Rohlfing, Torsten Rohling, Robert Rohr, Karl Rose, Chris Rosen, Jacob Rousseau, Fran¸cois Rousson, Mikael Ruiz-Alzola, Juan Russakoff, Daniel Rydell, Joakim Sabuncu, Mert Rory Sabuncu, Mert Sadowsky, Ofri Salvado, Olivier San Jose Estepar, Raul Sanchez Castro, Francisco Javier Santamaria-Pang, Alberto Schaap, Michiel Schilham, Arnold Schlaefer, Alexander Schmid, Volker Schnabel, Julia Schwarz, Tobias Seemann, Gunnar Segonne, Florent Sermesant, Maxime Shah, Shishir Sharma, Aayush Sharp, Peter Sharp, Greg Shekhar, Raj

Shen, Hong Shen, Dinggang Shimizu, Akinobu Siddiqi, Kaleem Sielhorst, Tobias Sijbers, Jan Sinha, Shantanu Sj¨ ostrand, Karl Sled, John Smith, Keith Soler, Luc Sonka, Milan Stewart, Charles Stewart, James Stindel, Eric Stoel, Berend Stoianovici, Dan Stoll, Jeff Stoyanov, Danail Styner, Martin Suetens, Paul Sugita, Naohiko Suinesiaputra, Avan Sun, Yiyong Sundar, Hari Szczerba, Dominik Szilagyi, Laszlo Tagare, Hemant Talbot, Hugues Talib, Haydar Talos, Ion-Florin Tanner, Christine Tao, Xiaodong Tarte, Segolene Tasdizen, Tolga Taylor, Zeike Taylor, Jonathan Tek, Huseyin Tendick, Frank Terzopoulos, Demetri Thévenaz, Philippe Thirion, Bertrand Tieu, Kinh Todd-Pokropek, Andrew Todman, Alison

XIX

XX

Organization

Toews, Matthew Tohka, Jussi Tomazevic, Dejan Tonet, Oliver Tong, Shan Tosun, Duygu Traub, Joerg Trejos, Ana Luisa Tsao, Jeffrey Tschumperlé, David Tsechpenakis, Gavriil Tsekos, Nikolaos Twining, Carole Urschler, Martin van Assen, Hans van de Ville, Dimitri van der Bom, Martijn van der Geest, Rob van Rikxoort, Eva van Walsum, Theo Vandermeulen, Dirk Ventikos, Yiannis Vercauteren, Tom Verma, Ragini Vermandel, Maximilien Vidal, Rene Vidholm, Erik Vilanova, Anna Villa, Mari Cruz Villain, Nicolas Villard, Caroline von Berg, Jens von Lavante, Etienne von Siebenthal, Martin Vosburgh, Kirby Vossepoel, Albert Vrooman, Henri Vrtovec, Tomaz Wang, Defeng Wang, Fei Wang, Guodong Wang, Yongmei Michelle Wang, Yongtian Wang, Zhizhou Wassermann, Demian

Weese, J¨ urgen Wegner, Ingmar Wein, Wolfgang Weisenfeld, Neil Wengert, Christian West, Jay Westenberg, Michel Westermann, Ruediger Whitcher, Brandon Wiemker, Rafael Wiest-Daessle, Nicolas Wigstrom, Lars Wiles, Andrew Wink, Onno Wong, Ken Wong, Kenneth Wong, Stephen Wong, Tien-Tsin Wong, Wilbur Wood, Bradford Wood, Fiona Worsley, Keith W¨ orz, Stefan Wˇsrn, Heinz Wu, Jue Xia, Yan Xie, Jun Xu, Sheng Xu, Ye Xue, Hui Xue, Zhong Yan, Pingkun Yang, King Yang, Lin Yang, Yihong Yaniv, Ziv Yeo, Boon Thye Yeung, Sai-Kit Yogesan, Kanagasingam Yoshida, Hiro Young, Alistair Young, Stewart Yu, Yang Yue, Ning Yuen, Shelten

Organization

Yushkevich, Paul Zacharaki, Evangelia Zemiti, Nabil Zerubia, Josiane Zhan, Wang Zhang, Fan Zhang, Heye Zhang, Hui Zhang, Xiangwei

Zhang, Yong Zheng, Guoyan Zheng, Yefeng Zhou, Jinghao Zhou, Kevin Zhou, Xiang Ziyan, Ulas Zollei, Lilla Zwiggelaar, Reyer

XXI

Table of Contents – Part II

Computer Assisted Intervention and Robotics - II Real-Time Tissue Tracking with B-Mode Ultrasound Using Speckle and Visual Servoing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexandre Krupa, Gabor Fichtinger, and Gregory D. Hager Intra-operative 3D Guidance in Prostate Brachytherapy Using a Non-isocentric C-arm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ameet K. Jain, A. Deguet, Iulian I. Iordachita, Gouthami Chintalapani, J. Blevins, Y. Le, E. Armour, C. Burdette, Danny Y. Song, and Gabor Fichtinger A Multi-view Opto-Xray Imaging System: Development and First Application in Trauma Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joerg Traub, Tim Hauke Heibel, Philipp Dressel, Sandro Michael Heining, Rainer Graumann, and Nassir Navab Towards 3D Ultrasound Image Based Soft Tissue Tracking: A Transrectal Ultrasound Prostate Image Alignment System . . . . . . . . . . . . . Michael Baumann, Pierre Mozer, Vincent Daanen, and Jocelyne Troccaz A Probabilistic Framework for Tracking Deformable Soft Tissue in Minimally Invasive Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peter Mountney, Benny Lo, Surapa Thiemjarus, Danail Stoyanov, and Guang Zhong-Yang Precision Targeting of Liver Lesions with a Needle-Based Soft Tissue Navigation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L. Maier-Hein, F. Pianka, A. Seitel, S.A. M¨ uller, A. Tekbas, M. Seitel, I. Wolf, B.M. Schmied, and H.-P. Meinzer Dynamic MRI Scan Plane Control for Passive Tracking of Instruments and Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simon P. DiMaio, E. Samset, Gregory S. Fischer, Iulian I. Iordachita, Gabor Fichtinger, Ferenc A. Jolesz, and Clare MC Tempany Design and Preliminary Accuracy Studies of an MRI-Guided Transrectal Prostate Intervention System . . . . . . . . . . . . . . . . . . . . . . . . . . . Axel Krieger, Csaba Csoma, Iulian I. Iordachita, Peter Guion, Anurag K. Singh, Gabor Fichtinger, and Louis L. Whitcomb

1

9

18

26

34

42

50

59

XXIV


Thoracoscopic Surgical Navigation System for Cancer Localization in Collapsed Lung Based on Estimation of Lung Deformation . . . . . . . . . . . . Masahiko Nakamoto, Naoki Aburaya, Yoshinobu Sato, Kozo Konishi, Ichiro Yoshino, Makoto Hashizume, and Shinichi Tamura

68

Visualization and Interaction Clinical Evaluation of a Respiratory Gated Guidance System for Liver Punctures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.A. Nicolau, Xavier Pennec, Luc Soler, and Nicholas Ayache

77

Rapid Voxel Classification Methodology for Interactive 3D Medical Image Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qi Zhang, Roy Eagleson, and Terry M. Peters

86

Towards Subject-Specific Models of the Dynamic Heart for Image-Guided Mitral Valve Surgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cristian A. Linte, Marcin Wierzbicki, John Moore, Stephen H. Little, Gérard M. Guiraudon, and Terry M. Peters

94

pq-space Based Non-Photorealistic Rendering for Augmented Reality . . . Mirna Lerotic, Adrian J. Chung, George P. Mylonas, and Guang-Zhong Yang

102

Eye-Gaze Driven Surgical Workflow Segmentation . . . . . . . . . . . . . . . . . . . . A. James, D. Vieira, Benny Lo, Ara Darzi, and Guang-Zhong Yang

110

Neuroscience Image Computing - I Prior Knowledge Driven Multiscale Segmentation of Brain MRI . . . . . . . . Ayelet Akselrod-Ballin, Meirav Galun, John Moshe Gomori, Achi Brandt, and Ronen Basri

118

Longitudinal Cortical Registration for Developing Neonates . . . . . . . . . . . Hui Xue, Latha Srinivasan, Shuzhou Jiang, Mary A. Rutherford, A. David Edwards, Daniel Rueckert, and Joseph V. Hajnal

127

Regional Homogeneity and Anatomical Parcellation for fMRI Image Classification: Application to Schizophrenia and Normal Controls . . . . . . Feng Shi, Yong Liu, Tianzi Jiang, Yuan Zhou, Wanlin Zhu, Jiefeng Jiang, Haihong Liu, and Zhening Liu

136

Probabilistic Fiber Tracking Using Particle Filtering . . . . . . . . . . . . . . . . . . Fan Zhang, Casey Goodlett, Edwin Hancock, and Guido Gerig

144

SMT: Split and Merge Tractography for DT-MRI . . . . . . . . . . . . . . . . . . . . U˘gur Bozkaya and Burak Acar

153


XXV

Tract-Based Morphometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lauren J. O’Donnell, Carl-Fredrik Westin, and Alexandra J. Golby

161

Towards Whole Brain Segmentation by a Hybrid Model . . . . . . . . . . . . . . . Zhuowen Tu and Arthur W. Toga

169

Computational Anatomy - II A Family of Principal Component Analyses for Dealing with Outliers . . . J. Eugenio Iglesias, Marleen de Bruijne, Marco Loog, Fran¸cois Lauze, and Mads Nielsen Automatic Segmentation of Articular Cartilage in Magnetic Resonance Images of the Knee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jurgen Fripp, Stuart Crozier, Simon K. Warfield, and Sébastien Ourselin Automated Model-Based Rib Cage Segmentation and Labeling in CT Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tobias Klinder, Cristian Lorenz, Jens von Berg, Sebastian P.M. Dries, Thomas B¨ ulow, and J¨ orn Ostermann

178

186

195

Efficient Selection of the Most Similar Image in a Database for Critical Structures Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Olivier Commowick and Grégoire Malandain

203

Unbiased White Matter Atlas Construction Using Diffusion Tensor Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hui Zhang, Paul A. Yushkevich, Daniel Rueckert, and James C. Gee

211

Innovative Clinical and Biological Applications - II Real-Time SPECT and 2D Ultrasound Image Registration . . . . . . . . . . . . Marek Bucki, Fabrice Chassat, Francisco Galdames, Takeshi Asahi, Daniel Pizarro, and Gabriel Lobo

219

A Multiphysics Simulation of a Healthy and a Diseased Abdominal Aorta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert H.P. McGregor, Dominik Szczerba, and G´ abor Székely

227

New Motion Correction Models for Automatic Identification of Renal Transplant Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ayman S. El-Baz, Georgy Gimel’farb, and Mohamed A. El-Ghar

235

Detecting Mechanical Abnormalities in Prostate Tissue Using FE-Based Image Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Patrick Courtis and Abbas Samani

244

XXVI


Real-Time Fusion of Ultrasound and Gamma Probe for Navigated Localization of Liver Metastases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thomas Wendler, Marco Feuerstein, Joerg Traub, Tobias Lasser, Jakob Vogel, Farhad Daghighian, Sibylle I. Ziegler, and Nassir Navab Fast and Robust Analysis of Dynamic Contrast Enhanced MRI Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Olga Kubassova, Mikael Boesen, Roger D. Boyle, Marco A. Cimmino, Karl E. Jensen, Henning Bliddal, and Alexandra Radjenovic

252

261

Spectroscopic and Cellular Imaging Functional Near Infrared Spectroscopy in Novice and Expert Surgeons – A Manifold Embedding Approach . . . . . . . . . . . . . . . . . . . . . . . . Daniel Richard Leff, Felipe Orihuela-Espina, Louis Atallah, Ara Darzi, and Guang-Zhong Yang

270

A Hierarchical Unsupervised Spectral Clustering Scheme for Detection of Prostate Cancer from Magnetic Resonance Spectroscopy (MRS) . . . . . Pallavi Tiwari, Anant Madabhushi, and Mark Rosen

278

A Clinically Motivated 2-Fold Framework for Quantifying and Classifying Immunohistochemically Stained Specimens . . . . . . . . . . . . . . . . Bonnie Hall, Wenjin Chen, Michael Reiss, and David J. Foran

287

Cell Population Tracking and Lineage Construction with Spatiotemporal Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kang Li, Mei Chen, and Takeo Kanade

295

Spatio-Temporal Registration Spatiotemporal Normalization for Longitudinal Analysis of Gray Matter Atrophy in Frontotemporal Dementia . . . . . . . . . . . . . . . . . . . . . . . . Brian Avants, Chivon Anderson, Murray Grossman, and James C. Gee Population Based Analysis of Directional Information in Serial Deformation Tensor Morphometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Colin Studholme and Valerie Cardenas Non-parametric Diffeomorphic Image Registration with the Demons Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tom Vercauteren, Xavier Pennec, Aymeric Perchant, and Nicholas Ayache Three-Dimensional Ultrasound Mosaicing . . . . . . . . . . . . . . . . . . . . . . . . . . . Christian Wachinger, Wolfgang Wein, and Nassir Navab

303

311

319

327


XXVII

General Medical Image Computing - III Automated Extraction of Lymph Nodes from 3-D Abdominal CT Images Using 3-D Minimum Directional Difference Filter . . . . . . . . . . . . . . Takayuki Kitasaka, Yukihiro Tsujimura, Yoshihiko Nakamura, Kensaku Mori, Yasuhito Suenaga, Masaaki Ito, and Shigeru Nawano Non-Local Means Variants for Denoising of Diffusion-Weighted and Diffusion Tensor MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nicolas Wiest-Daesslé, Sylvain Prima, Pierrick Coupé, Sean Patrick Morrissey, and Christian Barillot Quantifying Calcification in the Lumbar Aorta on X-Ray Images . . . . . . . Lars A. Conrad-Hansen, Marleen de Bruijne, Fran¸cois Lauze, L´ aszl´ o B. Tank´ o, Paola C. Pettersen, Qing He, Jianghong Chen, Claus Christiansen, and Mads Nielsen Physically Motivated Enhancement of Color Images for Fiber Endoscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christian Winter, Thorsten Zerfaß, Matthias Elter, Stephan Rupp, and Thomas Wittenberg Signal LMMSE Estimation from Multiple Samples in MRI and DT-MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Santiago Aja-Fern´ andez, Carlos Alberola-L´ opez, and Carl-Fredrik Westin Quantifying Heterogeneity in Dynamic Contrast-Enhanced MRI Parameter Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.J. Rose, S. Mills, J.P.B. O’Connor, G.A. Buonaccorsi, C. Roberts, Y. Watson, B. Whitcher, G. Jayson, A. Jackson, and G.J.M. Parker Improving Temporal Fidelity in k-t BLAST MRI Reconstruction . . . . . . . Andreas Sigfridsson, Mats Andersson, Lars Wigstr¨ om, John-Peder Escobar Kvitting, and Hans Knutsson Segmentation and Classification of Breast Tumor Using Dynamic Contrast-Enhanced MR Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuanjie Zheng, Sajjad Baloch, Sarah Englander, Mitchell D. Schnall, and Dinggang Shen Automatic Whole Heart Segmentation in Static Magnetic Resonance Image Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jochen Peters, Olivier Ecabert, Carsten Meyer, Hauke Schramm, Reinhard Kneser, Alexandra Groth, and J¨ urgen Weese

336

344

352

360

368

376

385

393

402

XXVIII


PCA-Based Magnetic Field Modeling: Application for On-Line MR Temperature Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Maclair, B. Denis de Senneville, M. Ries, B. Quesson, P. Desbarats, J. Benois-Pineau, and C.T.W. Moonen

411

A Probabilistic Model for Haustral Curvatures with Applications to Colon CAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . John Melonakos, Paulo Mendon¸ca, Rahul Bhotka, and Saad Sirohey

420

LV Motion Tracking from 3D Echocardiography Using Textural and Structural Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andriy Myronenko, Xubo Song, and David J. Sahn

428

A Novel 3D Multi-scale Lineness Filter for Vessel Detection . . . . . . . . . . . H.E. Bennink, H.C. van Assen, G.J. Streekstra, R. ter Wee, J.A.E. Spaan, and Bart M. ter Haar Romeny Live-Vessel: Extending Livewire for Simultaneous Extraction of Optimal Medial and Boundary Paths in Vascular Images . . . . . . . . . . . . . . Kelvin Poon, Ghassan Hamarneh, and Rafeef Abugharbieh A Point-Wise Quantification of Asymmetry Using Deformation Fields: Application to the Study of the Crouzon Mouse Model . . . . . . . . . . . . . . . ´ Hildur Olafsd´ ottir, Stephanie Lanche, Tron A. Darvann, Nuno V. Hermann, Rasmus Larsen, Bjarne K. Ersbøll, Estanislao Oubel, Alejandro F. Frangi, Per Larsen, Chad A. Perlyn, Gillian M. Morriss-Kay, and Sven Kreiborg Object Localization Based on Markov Random Fields and Symmetry Interest Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . René Donner, Branislav Micusik, Georg Langs, Lech Szumilas, Philipp Peloschek, Klaus Friedrich, and Horst Bischof

436

444

452

460

2D Motion Analysis of Long Axis Cardiac Tagged MRI . . . . . . . . . . . . . . . Ting Chen, Sohae Chung, and Leon Axel

469

MCMC Curve Sampling for Image Segmentation . . . . . . . . . . . . . . . . . . . . . Ayres C. Fan, John W. Fisher III, William M. Wells III, James J. Levitt, and Alan S. Willsky

477

Automatic Centerline Extraction of Irregular Tubular Structures Using Probability Volumes from Multiphoton Imaging . . . . . . . . . . . . . . . . . . . . . . A. Santamar´ıa-Pang, C.M. Colbert, P. Saggau, and Ioannis A. Kakadiaris Γ -Convergence Approximation to Piecewise Smooth Medical Image Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jungha An, Mikael Rousson, and Chenyang Xu

486

495


Is a Single Energy Functional Sufficient? Adaptive Energy Functionals and Automatic Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chris McIntosh and Ghassan Hamarneh A Duality Based Algorithm for TV-L1 -Optical-Flow Image Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thomas Pock, Martin Urschler, Christopher Zach, Reinhard Beichel, and Horst Bischof Deformable 2D-3D Registration of the Pelvis with a Limited Field of View, Using Shape Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ofri Sadowsky, Gouthami Chintalapani, and Russell H. Taylor Segmentation-driven 2D-3D Registration for Abdominal Catheter Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Martin Groher, Frederik Bender, Ralf-Thorsten Hoffmann, and Nassir Navab Primal/Dual Linear Programming and Statistical Atlases for Cartilage Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ben Glocker, Nikos Komodakis, Nikos Paragios, Christian Glaser, Georgios Tziritas, and Nassir Navab Similarity Metrics for Groupwise Non-rigid Registration . . . . . . . . . . . . . . . Kanwal K. Bhatia, Joseph V. Hajnal, Alexander Hammers, and Daniel Rueckert A Comprehensive System for Intraoperative 3D Brain Deformation Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christine DeLorenzo, Xenophon Papademetris, Kenneth P. Vives, Dennis D. Spencer, and James S. Duncan Bayesian Tracking of Tubular Structures and Its Application to Carotid Arteries in CTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Michiel Schaap, Rashindra Manniesing, Ihor Smal, Theo van Walsum, Aad van der Lugt, and Wiro Niessen Automatic Fetal Measurements in Ultrasound Using Constrained Probabilistic Boosting Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gustavo Carneiro, Bogdan Georgescu, Sara Good, and Dorin Comaniciu

XXIX

503

511

519

527

536

544

553

562

571

Quantifying Effect-Specific Mammographic Density . . . . . . . . . . . . . . . . . . Jakob Raundahl, Marco Loog, Paola C. Pettersen, and Mads Nielsen

580

Revisiting the Evaluation of Segmentation Results: Introducing Confidence Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christophe Restif

588

XXX


Error Analysis of Calibration Materials on Dual-Energy Mammography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xuanqin Mou and Xi Chen

596

Computer Assisted Intervention and Robotics - III A MR Compatible Mechatronic System to Facilitate Magic Angle Experiments in Vivo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haytham Elhawary, Aleksandar Zivanovic, Marc Rea, Zion Tsz Ho Tse, Donald McRobbie, Ian Young, Martyn Paley, Brian Davies, and Michael Lampérth

604

Variational Guidewire Tracking Using Phase Congruency . . . . . . . . . . . . . Greg Slabaugh, Koon Kong, Gozde Unal, and Tong Fang

612

Endoscopic Navigation for Minimally Invasive Suturing . . . . . . . . . . . . . . . Christian Wengert, Lukas Bossard, Armin H¨ aberling, Charles Baur, G´ abor Székely, and Philippe C. Cattin

620

On Fiducial Target Registration Error in the Presence of Anisotropic Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Burton Ma, Mehdi Hedjazi Moghari, Randy E. Ellis, and Purang Abolmaesumi Rotational Roadmapping: A New Image-Based Navigation Technique for the Interventional Room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Markus Kukuk and Sandy Napel Bronchoscope Tracking Without Fiducial Markers Using Ultra-tiny Electromagnetic Tracking System and Its Evaluation in Different Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kensaku Mori, Daisuke Deguchi, Kazuyoshi Ishitani, Takayuki Kitasaka, Yasuhito Suenaga, Yosihnori Hasegawa, Kazuyoshi Imaizumi, and Hirotsugu Takabatake Online Estimation of the Target Registration Error for n-Ocular Optical Tracking Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tobias Sielhorst, Martin Bauer, Oliver Wenisch, Gudrun Klinker, and Nassir Navab Assessment of Perceptual Quality for Gaze-Contingent Motion Stabilization in Robotic Assisted Minimally Invasive Surgery . . . . . . . . . . George P. Mylonas, Danail Stoyanov, Ara Darzi, and Guang-Zhong Yang Prediction of Respiratory Motion with Wavelet-Based Multiscale Autoregression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Floris Ernst, Alexander Schlaefer, and Achim Schweikard

628

636

644

652

660

668


Multi-criteria Trajectory Planning for Hepatic Radiofrequency Ablation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Claire Baegert, Caroline Villard, Pascal Schreck, and Luc Soler

XXXI

676

General Biological Imaging Computing A Bayesian 3D Volume Reconstruction for Confocal Micro-rotation Cell Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yong Yu, Alain Trouvé, and Bernard Chalemond

685

Bias Image Correction Via Stationarity Maximization . . . . . . . . . . . . . . . . T. Dorval, A. Ogier, and A. Genovesio

693

Toward Optimal Matching for 3D Reconstruction of Brachytherapy Seeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christian Labat, Ameet K. Jain, Gabor Fichtinger, and Jerry L. Prince Alignment of Large Image Series Using Cubic B-Splines Tessellation: Application to Transmission Electron Microscopy Data . . . . . . . . . . . . . . . Julien Dauguet, Davi Bock, R. Clay Reid, and Simon K. Warfield Quality-Based Registration and Reconstruction of Optical Tomography Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wolfgang Wein, Moritz Blume, Ulrich Leischner, Hans-Ulrich Dodt, and Nassir Navab Simultaneous Segmentation, Kinetic Parameter Estimation, and Uncertainty Visualization of Dynamic PET Images . . . . . . . . . . . . . . . . . . . Ahmed Saad, Ben Smith, Ghassan Hamarneh, and Torsten M¨ oller

701

710

718

726

Neuroscience Image Computing - II Nonlinear Analysis of BOLD Signal: Biophysical Modeling, Physiological States, and Functional Activation . . . . . . . . . . . . . . . . . . . . . Zhenghui Hu and Pengcheng Shi

734

Effectiveness of the Finite Impulse Response Model in Content-Based fMRI Image Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bing Bai, Paul Kantor, and Ali Shokoufandeh

742

Sources of Variability in MEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wanmei Ou, Polina Golland, and Matti H¨ am¨ al¨ ainen

751

Customised Cytoarchitectonic Probability Maps Using Deformable Registration: Primary Auditory Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lara Bailey, Purang Abolmaesumi, Julian Tam, Patricia Morosan, Rhodri Cusack, Katrin Amunts, and Ingrid Johnsrude

760

XXXII


Segmentation of Q-Ball Images Using Statistical Surface Evolution . . . . . Maxime Descoteaux and Rachid Deriche Evaluation of Shape-Based Normalization in the Corpus Callosum for White Matter Connectivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hui Sun, Paul A. Yushkevich, Hui Zhang, Philip A. Cook, Jeffrey T. Duda, Tony J. Simon, and James C. Gee Accuracy Assessment of Global and Local Atrophy Measurement Techniques with Realistic Simulated Longitudinal Data . . . . . . . . . . . . . . Oscar Camara, Rachael I. Scahill, Julia A. Schnabel, William R. Crum, Gerard R. Ridgway, Derek L.G. Hill, and Nick C. Fox Combinatorial Optimization for Electrode Labeling of EEG Caps . . . . . . Mickaël Péchaud, Renaud Keriven, Théo Papadopoulo, and Jean-Michel Badier

769

777

785

793

Computational Anatomy - III Analysis of Deformation of the Human Ear and Canal Caused by Mandibular Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sune Darkner, Rasmus Larsen, and Rasmus R. Paulsen

801

Shape Registration by Simultaneously Optimizing Representation and Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yifeng Jiang, Jun Xie, Deqing Sun, and Hungtat Tsui

809

Landmark Correspondence Optimization for Coupled Surfaces . . . . . . . . . Lin Shi, Defeng Wang, Pheng Ann Heng, Tien-Tsin Wong, Winnie C.W. Chu, Benson H.Y. Yeung, and Jack C.Y. Cheng Mean Template for Tensor-Based Morphometry Using Deformation Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Natasha Leporé, Caroline Brun, Xavier Pennec, Yi-Yu Chou, Oscar L. Lopez, Howard J. Aizenstein, James T. Becker, Arthur W. Toga, and Paul M. Thompson Shape-Based Myocardial Contractility Analysis Using Multivariate Outlier Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Karim Lekadir, Niall Keenan, Dudley Pennell, and Guang-Zhong Yang

818

826

834

Computational Physiology - II Orthopedics Surgery Trainer with PPU-Accelerated Blood and Tissue Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wai-Man Pang, Jing Qin, Yim-Pan Chui, Tien-Tsin Wong, Kwok-Sui Leung, and Pheng Ann Heng

842


XXXIII

Interactive Contacts Resolution Using Smooth Surface Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jérémie Dequidt, Julien Lenoir, and Stéphane Cotin

850

Using Statistical Shape Analysis for the Determination of Uterine Deformation States During Hydrometra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Harders and G´ abor Székely

858

Predictive K-PLSR Myocardial Contractility Modeling with Phase Contrast MR Velocity Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Su-Lin Lee, Qian Wu, Andrew Huntbatch, and Guang-Zhong Yang

866

A Coupled Finite Element Model of Tumor Growth and Vascularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bryn A. Lloyd, Dominik Szczerba, and G´ abor Székely

874

Innovative Clinical and Biological Applications - III Autism Diagnostics by 3D Texture Analysis of Cerebral White Matter Gyrifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ayman S. El-Baz, Manuel F. Casanova, Georgy Gimel’farb, Meghan Mott, and Andrew E. Switala

882

3-D Analysis of Cortical Morphometry in Differential Diagnosis of Parkinson’s Plus Syndromes: Mapping Frontal Lobe Cortical Atrophy in Progressive Supranuclear Palsy Patients . . . . . . . . . . . . . . . . . . . . . . . . . . Duygu Tosun, Simon Duchesne, Yan Rolland, Arthur W. Toga, Marc Vérin, and Christian Barillot

891

Tissue Characterization Using Fractal Dimension of High Frequency Ultrasound RF Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mehdi Moradi, Parvin Mousavi, and Purang Abolmaesumi

900

Towards Intra-operative 3D Nuclear Imaging: Reconstruction of 3D Radioactive Distributions Using Tracked Gamma Probes . . . . . . . . . . . . . . Thomas Wendler, Alexander Hartl, Tobias Lasser, Joerg Traub, Farhad Daghighian, Sibylle I. Ziegler, and Nassir Navab Instrumentation for Epidural Anesthesia . . . . . . . . . . . . . . . . . . . . . . . . . . . . King-wei Hor, Denis Tran, Allaudin Kamani, Vickie Lessoway, and Robert Rohling Small Animal Radiation Research Platform: Imaging, Mechanics, Control and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mohammad Matinfar, Owen Gray, Iulian I. Iordachita, Chris Kennedy, Eric Ford, John Wong, Russell H. Taylor, and Peter Kazanzides

909

918

926

XXXIV


Proof of Concept of a Simple Computer–Assisted Technique for Correcting Bone Deformities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Burton Ma, Amber L. Simpson, and Randy E. Ellis

935

Global Registration of Multiple Point Sets: Feasibility and Applications in Multi-fragment Fracture Fixation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mehdi Hedjazi Moghari and Purang Abolmaesumi

943

Precise Estimation of Postoperative Cup Alignment from Single Standard X-Ray Radiograph with Gonadal Shielding . . . . . . . . . . . . . . . . . Guoyan Zheng, Simon Steppacher, Xuan Zhang, and Moritz Tannast

951

Fully Automated and Adaptive Detection of Amyloid Plaques in Stained Brain Sections of Alzheimer Transgenic Mice . . . . . . . . . . . . . . . . . Abdelmonem Feki, Olivier Teboul, Albertine Dubois, Bruno Bozon, Alexis Faure, Philippe Hantraye, Marc Dhenain, Benoit Delatour, and Thierry Delzescaux

960

Non-rigid Registration of Pre-procedural MR Images with Intra-procedural Unenhanced CT Images for Improved Targeting of Tumors During Liver Radiofrequency Ablations . . . . . . . . . . . . . . . . . . . . . . N. Archip, S. Tatli, P. Morrison, Ferenc A. Jolesz, Simon K. Warfield, and S. Silverman

969

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

979

Real-Time Tissue Tracking with B-Mode Ultrasound Using Speckle and Visual Servoing Alexandre Krupa1 , Gabor Fichtinger2 , and Gregory D. Hager2 1

2

IRISA - INRIA Rennes, France [email protected] Engineering Research Center, Johns Hopkins University, USA {gabor,hager}@cs.jhu.edu

Abstract. We present a method for real-time tracking of moving soft tissue with B-mode ultrasound (US). The method makes use of the speckle information contained in the US images to estimate the in-plane and out-of-plane motion of a fixed target relative to the ultrasound scan plane. The motion information is then used as closed-loop feedback to a robot which corrects for the target motion. The concept is demonstrated for translation motions in an experimental setup consisting of an ultrasound speckle phantom, a robot for simulating tissue motion, and a robot that performs motion stabilization from US images. This concept shows promise for US-guided procedures that require real-time motion tracking and compensation.

1

Introduction

Quantitative ultrasound guidance (US) has great potential for aiding a wide range of diagnostic and minimally invasive surgical applications. However, one of the barriers to wider application is the challenge of locating and maintaining targets of interest within the US scan-plane, particularly when the underlying tissue is in motion. This problem can be alleviated, to some degree, through the use of recently developed 3D ultrasound systems. However, a more practical solution is to create a means of stabilizing a traditional B-mode ultrasound imager relative to a target. This capability can be exploited in many applications, for example to automatically move the US probe to maintain an appropriate view of moving soft tissues during US scanning or to synchronize the insertion of a needle into a moving target during biopsy or local therapy. In this paper, we present a system that is capable of fully automatic, realtime tracking and motion compensation of a moving soft tissue target using a sequence of B-mode ultrasound images. Contrary to prior work in this area, which has relied on segmenting structures of interest [1,2], we make direct use of the speckle information contained in the US images. While US speckle is usually considered to be noise from an imaging point of view, it in fact results from the

The authors acknowledge the support of the National Science Foundation under Engineering Research Center grant EEC-9731748.

N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 1–8, 2007. c Springer-Verlag Berlin Heidelberg 2007

2

A. Krupa, G. Fichtinger, and G.D. Hager

Fig. 1. (left) Experimental decorrelation curves obtained by measuring the correlation value between 25 patches of B-scan I1 and their corresponding patches in B-scan I2 along the elevation distance d (right)

coherent reflection of microscopic structures contained in soft tissue. As such, it is spatially coherent. Furthermore, an US beam is several mm wide. As a result, there is substantial overlap between US scan planes with small lateral displacements and, therefore, substantial correlation of the speckle information between successive images. Speckle correlation occurs for both in-plane and outof-plane motion, thereby making it possible to track both out-of plane and inplane motion, and raising the possibility of calculating full 6-DOF relative pose of speckle patches. Initially, speckle information has been used to estimate multi-dimensional flow in 2D ultrasound image ([3]). Recently several authors ([4,5]) have published speckle decorrelation techniques to allow freehand 3D US scanning without a position sensor on the US probe. Their techniques depend on experimentally calibrating speckle decorrelation curves from real soft tissues and/or speckle simulating phantoms. These curves (Fig. 1) are obtained by capturing B-mode images at known distances d along the elevation direction (i.e. orthogonal to the image plane) and measuring the normalized correlation coefficients for a finite number of rectangular patches fixed in the images. The imaging procedure then entails capturing an US stream by moving the probe in a given direction. The relative in-plane and out-of-plane position between each image is then estimated, off-line, from the estimated elevation distances from at least 3 non-collinear patches in the image plane. These distances are computed from the calibrated decorrelation curves using the measured inter-patch correlation value for each image patch. In our experimental scenario, we also perform an offline calibration procedure to relate speckle decorrelation to elevation motion. However, we subsequently servo the US probe to track a user-selected B-scan target in a fully automatic, online manner. The 6-DOF motion of the target B-scan is extracted by an estimation method using the speckle information and an image region tracking algorithm based on grey level intensity. A visual servoing scheme is then used

Real-Time Tissue Tracking with B-Mode Ultrasound

3

to control the probe displacement. Section 2 presents the methods used to extract 6-DOF rigid motion of the target B-scan image. The visual servoing control laws are developed in section 3 and section 4 presents first results obtained from ex-vivo experiments where only translation motions are considered.

2

Motion Extraction

The overall tracking problem is to minimize the relative position between the current B-scan (denoted by a Cartesian frame {c}) and a target B-scan (denoted by a Cartesian frame {i}). The full 6 DOF target plane position can be decomposed by two successive homogeneous transformations: c Hi = c Hp p Hi where c Hp and p Hi describing the in-plane and out-of-plane displacement of the target, respectively. Note that {p} corresponds to an intermediate “virtual” plane. The in-plane displacement corresponds to the translations x and y along the X and Y axes of the current image plane and the angular rotation γ around the Z axis (orthogonal to the image), such that: ⎛ ⎞ cos(γ) − sin(γ) 0 x ⎜ sin(γ) cos(γ) 0 y ⎟ c ⎟ Hp = ⎜ (1) ⎝ 0 0 1 0⎠ 0 0 01 We use a classical template tracking technique [6] to extract the in-plane motion parameters x, y, γ. This information is then used to relate the image coordinates of patches in the two images for the purposes of estimating out-of-plane motion using speckle decorrelation. To extract the out-of-plane motion, we use the Gaussian model introduced in [4]. From experimental observations (Fig. 1), we found that the elevation distance between a patch in the target plane and the corresponding patch in the σ 2 ln(ρ), where σ ˆ = 0.72 mm is the current image can be estimated by dˆ = −2ˆ mean resolution cell width (identified from experimental decorrelation curves). To compute the full out-of-plane motion, we compute the elevation distance of a grid of patches (25 in our current system), and fit a plane to this data. However, the Gaussian model does not detect the sign of the elevation distance for a given patch. Thus, we employ the following algorithm to estimate the out-ofplane position of the target plane with respect to the virtual plane {p}. We first set a random sign on each inter-patch distance and estimate (with a least-square algorithm) an initial position of the target plane using these signs. We then use the iterative algorithm we presented in [7] to determine the correct signed distances and the associated plane. This algorithm, which minimizes the leastsquare error of the estimated target plane, converges to two stable solutions that are symmetrical around plane {p}. The two solutions correspond to the positive and negative elevation distances z, respectively. Note that from one solution we can easily determine the second. By formulating the out-of-plane relative position as a combination of a translation z along the Z axis of plane {p} and

4


two successive rotations α, β around the Y and X axes of {p}, we obtain the following homogeneous transformation matrix for out-of-plane motion: ⎛ ⎞ cos(α) cos(α) sin(θ) sin(α) cos(θ) 0 ⎜ 0 cos(θ) − sin(θ) 0 ⎟ p ⎟ Hi = ⎜ (2) ⎝ − sin(α) cos(α) sin(θ) cos(α) cos(θ) z ⎠ 0 0 0 1 The two symmetrical solutions for the 6 DOF motion are then given by the estimates: c

i (+) = H

c

p pH i (+) H

and

c

i (−) = H

c

p pH i (−) H

(3)

where (+) indicates the solution obtained for zˆ > 0, with α ˆ = atan(ˆ a/ˆ c), θˆ = −asin(ˆb) and (-) indicates the solution corresponding to zˆ < 0 with α ˆ = atan(−ˆ a/ˆ c), θˆ = −asin(−ˆb). Here (ˆ a, ˆb, cˆ) is the normal vector of the estimated target plane that is obtained for the solution zˆ > 0. The subscript ˆ denotes values provided by the template tracking and plane estimation methods. It will be purposely dropped in the next of the paper for clarity of presentation. This method works only locally about the target region due to the rapid rate of speckle decorrelation with out-of-plane motion. Therefore, in order to increase the range of convergence, we augment the basic algorithm with a FIFO buffer of intermediate planes {i} between the target {t} and current plane {c}. These planes, which are acquired online as the probe moves, are chosen to be close enough to be well “speckle correlated” and thus provide a “path” of ultrasound images that can be traced back to the target. The complete algorithm summarizing our method for extracting target plane position is described in Fig. 2 (for positive elevation distances) and Fig. 3 (for negative elevation distances.) At initialization, the target plane is captured in the initial B-scan image and stored in a FIFO buffer (plane) starting with index i = 0. The current image is also stored as the target image (imageref erence = currentplane). A small negative elevation displacement is then applied to the probe in order to obtain an initial positive elevation distance z[0] ≥ s > 0 of plane[0] with respect to the current B-scan plane. Here s is a small threshold distance fixed to guarantee speckle correlation between US images. The algorithm goes to the case of positive elevation distance. The array index is then incremented and an intermediate plane is stored (plane[i] = currentplane) with the homogeneous matrix i Hi−1 = c Hi−1 (+) describing the position of plane[i − 1] with respect to plane[i] and given by (3). Each time an intermediate plane is added, the target image used by the in-plane motion tracker is also updated (imageref erence = currentplane). After initialization, the configuration of planes corresponds to case 1 in Fig. 2, where the target plane position

1 is c Ht = c Hi (+) i k Hk−1 . Now, we suppose that the target plane moves for some reason. By computing (3) for c Hi and c Hi−1 , we can: 1) determine the consistent pair of solutions that express the current plane relative to plane[i] and plane[i − 1], 2) determine which of cases 1, 2 or 3 is valid and 3) compute the target elevation position c Ht accordingly. As shown, the three cases are:


5

Fig. 2. (top) possible planes configurations and (bottom) process used to manage the intermediates planes when the target elevation distance is positive

1) if the current plane moves a distance s beyond the top of the FIFO array, then a new intermediate plane is added or 2) if the current plane is between the top two planes of the FIFO array, then no change occurs, or 3) if the elevation distance decreases, then the last intermediate plane is removed from the FIFO array. In the latter case, a special situation arises when there are only two planes (i = 1) in the array. In this case, if the absolute value of the target elevation distance reaches the threshold s, then the algorithm switches to the second mode described in Fig. 3 which is the symmetric logic for negative elevations. For this mode, the possible configurations of planes are illustrated by cases 4 to 6 in Fig. 3. The algorithm switches back to the first mode when the target plane elevation position becomes positive again.

3

Visual Servoing

Now, as the position of the B-scan target with respect to the current plane has been estimated, we move the robot (holding the probe) in order to follow the target plane. In our approach, a 3D visual servoing control scheme is used to minimize the relative position between the current and target planes. The T T describing the error vector is the 6 dimensional pose vector x = (t PT c , θu )

6


Fig. 3. (top) possible planes configurations and (bottom) process used to manage the intermediates planes when the target elevation distance is negative

position of the current plane frame {c} with respect to the target plane frame {t}. Here t Pc is the translation vector obtained directly from the 4th column of t t Hc = c H−1 t , and θu is the angle-axis representation of the rotation Rc [8]. The variation of x is related to the velocity screw v = (vx , vy , vz , ωx , ωy , ωz )T of the ultrasound probe by x˙ = Ls v. In visual servoing, Ls is called the interaction matrix and is given in this case by (cf. [9]): t Rc 03 (4) Ls = 0 I − θ [u] + (1 − sincθ )[u] 3 3 × × 2 sinc2 θ2 where I3 is the 3 × 3 identity matrix and [u]× is the skew matrix of the vector preproduct linked with u. The visual servoing task (cf. [9]) can then be expressed as a regulation to zero of the pose x and is performed by applying the following control law: v = −λL−1 s x where λ is the proportional coefficient involved for a exponential convergence.

4

Experiments and Results

We have tested the motion stabilization method on 2-DOF motions combining a translation along the image X axis (in-plane translation) and elevation Z axis


phantom

7

robot 2

US probe image

X

Z X

Z

robot 1 Tracking error (mm)

position of the two robotsX(mm) axis 30 20 10

x robot 1 z robot 1 x robot 2 z robot 2

4

x (in−plane)

3

z (out−plane)

2 1

0

0

−10

−1 −2

−20

−3 −30 0

50

100 time (s)

150

200

−4 0

50

100 time (s)

150

200

Fig. 4. (top) experimental setup - (bottom-left) evolution of the robots positions (bottom-right) tracking error

(out-of-plane translation). The experimental, setup, shown in Fig. 4, consists of two X-Z Cartesian robots fixed and aligned on an optical table. The first robot provides a ground truth displacement for an US speckle phantom. The second robot holds a transrectal 6.5 Mhz US transducter and is controlled as described above to track a target plane. The US image is 440 × 320 pixels with resolution of 0.125 mm/pixel. A laptop computer (Pentium IV 2 Ghz) captures the US stream at 10 fps, extracts the target plane position by using a grid of 25 patches and computes the velocity control vector applied to the probe holding robot. The plots in Fig. 4 show the evolution of the robots positions and the tracking error when sinusoidal motions (magnitude of 30 mm on each axis) were applied to the phantom. The dynamic tracking error was below 3 mm for in-plane translation and 3.5 mm for the elevation translation. This error is attributed the dynamics of the target motion, time delays in the control scheme, and the dynamics of the probe holding robot. These errors could be reduced if a prediction of its variation was introduced into the control law by some method such as Kalman filter or generalized predictive controller [10]. Adopting recent

8


methods [11] for more accurate and efficient identification of fully developed speckle patches should also improve on tracking performance and may allow estimation of relative motion between different soft tissue elements. In order to determine the static accuracy of the tracking robotic task, we applied a set of 140 random positions to the phantom by using ramp trajectories while tracking the target plane by the robotized probe. When the probe stabilized at a position, the phantom was held motionless for 2 seconds and the locations of the two robots were recorded. We recorded a static error of 0.0219±0.05 mm (mean ± standard deviation) for the in-plane tracking and 0.0233±0.05 mm for the out-of-plane tracking, which is close to the positioning accuracy of the robots (± 0.05 mm). In conclusion, results obtained from 2-DOF in-plane and out-of-plane motions demonstrated the potential of our approach. We are presently adding rotational stages to the robots to experimentally validate full 6-DOF motion tracking and visual servoing capabilities of the current algorithm described in this paper.

References 1. Abolmaesumi, P., Salcudean, S.E., Zhu, W.H., Sirouspour, M., DiMaio, S.: Imageguided control of a robot for medical ultrasound. IEEE Trans. Robotics and Automation 18, 11–23 (2002) 2. Hong, J., Dohi, T., Hashizume, M., Konishi, K., Hata, N.: An ultrasound-driven needle insertion robot for percutaneous cholecystostomy. Physics in Medicine and Biology 49(3), 441–455 (2004) 3. Bohs, L.N., Geiman, B.J., Anderson, M.E., Gebhart, S.C., Trahey, G.E.: Speckle tracking for multi-dimensional flow estimation. Ultrasonics 28(1-8), 369–375 (2000) 4. Gee, A.H., Housden, R.J., Hassenpflug, P., Treece, G.M., Prager, R.W.: Sensorless freehand 3D ultrasound in real tissues: Speckle decorrelation without fully developed speckle. Medical Image Analysis 10(2), 137–149 (2006) 5. Chang, R.-F., Wu, W.-J., Chen, D.-R., Chen, W.-M., Shu, W., Lee, J.-H., Jeng, L.-B.: 3-D US frame positioning using speckle decorrelation and image registration. Ultrasound in Med. & Bio. 29(6), 801–812 (2003) 6. Hager, G.D., Belhumeur, P.N.: Efficient region tracking with parametric models of geometry and illumination. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(10), 1025–1039 (1998) 7. Krupa, A., Fichtinger, G., Hager, G.D.: Full Motion Tracking in Ultrasound Using Image Speckle Information and Visual Servoing. In: ICRA 2007. IEEE Int. Conf. on Robotics and Automation, Roma, Italy, IEEE Computer Society Press, Los Alamitos (2007) 8. Craig, J.J.: Introduction to Robotics: Mechanics and Control, 2nd edn. AddisonWesley, London, UK (1989) 9. Chaumette, F., Hutchinson, S.: Visual Servo Control, Part I: Basic Approaches. IEEE Robotics and Automation Magazine 13(4), 82–90 (2006) 10. Ginhoux, R., Gangloff, J., de Mathelin, M., Soler, L., Sanchez, M.M.A., Marescaux, J.: Active Filtering of Physiological Motion in Robotized Surgery Using Predictive Control. IEEE Transactions on Robotics 21(1), 67–79 (2005) 11. Rivaz, H., Boctor, E., Fichtinger, G.: Ultrasound Speckle Detection Using Low Order Moments. In: IEEE International Ultrasonics Symposium, Vancouver, Canada, IEEE Computer Society Press, Los Alamitos (2006)

Intra-operative 3D Guidance in Prostate Brachytherapy Using a Non-isocentric C-arm A. Jain1,3 , A. Deguet1 , I. Iordachita1 , G. Chintalapani1 , J. Blevins2 , Y. Le1 , E. Armour1 , C. Burdette2 , D. Song1 , and G. Fichtinger1 1

Johns Hopkins University Acoustic MedSystems Inc. Philips Research North America 2

3

Abstract. Intra-operative guidance in Transrectal Ultrasound (TRUS) guided prostate brachytherapy requires localization of inserted radioactive seeds relative to the prostate. Seeds were reconstructed using a typical C-arm, and exported to a commercial brachytherapy system for dosimetry analysis. Technical obstacles for 3D reconstruction on a nonisocentric C-arm included pose-dependent C-arm calibration; distortion correction; pose estimation of C-arm images; seed reconstruction; and C-arm to TRUS registration. In precision-machined hard phantoms with 40-100 seeds, we correctly reconstructed 99.8% seeds with a mean 3D accuracy of 0.68 mm. In soft tissue phantoms with 45-87 seeds and clinically realistic 15o C-arm motion, we correctly reconstructed 100% seeds with an accuracy of 1.3 mm. The reconstructed 3D seed positions were then registered to the prostate segmented from TRUS. In a Phase-1 clinical trial, so far on 4 patients with 66-84 seeds, we achieved intra-operative monitoring of seed distribution and dosimetry. We optimized the 100% prescribed iso-dose contour by inserting an average of 3.75 additional seeds, making intra-operative dosimetry possible on a typical C-arm, at negligible additional cost to the existing clinical installation.

1

Introduction

With an approximate annual incidence of 220,000 new cases and 33,000 deaths (United States) prostate cancer continues to be the most common cancer in men. Transrectal Ultrasound (TRUS) guided permanent low-dose-rate brachytherapy (insertion of radioactive seeds into the prostate) has emerged as a common & effective treatment modality for early stage low risk prostate cancer, with an expected 50,000 surgeries every year. The success of brachytherapy (i.e. maximizing its efficacy while minimizing its co-morbidity) chiefly depends on our ability to tailor the therapeutic dose to the patient’s individual anatomy. The main limitation in contemporary brachytherapy is intra-operative tissue expansion (edema), causing incorrect seed placement, which may potentially lead to insufficient dose to the cancer and/or excessive radiation to the rectum, urethra, or bladder. The former might permit the cancer to relapse, while the latter

Supported by DoD PC050170, DoD PC050042 and NIH 2R44CA099374.


10

A. Jain et al.

causes adverse side effects like rectal ulceration. According to a comprehensive review by the American Brachytherapy Society [1], the pre-planned technique used for permanent prostate brachytherapy has limitations that may be overcome by intra-operative planning. Prostate brachytherapy is almost exclusively performed under TRUS guidance. Various researchers have tried to segment the seeds from TRUS images by linking seeds with spacers, using X-rays to initialize segmentation, using vibro-acoustography or transurethral ultrasound as a new imaging modality, or segmenting them directly in TRUS images by using corrugated seeds that are better visible than conventional ones [2]. But even when meticulously handsegmented, up to 25% of the seeds may remain hidden in ultrasound. C-arms are also ubiquitous, though used only for gross visual assessment of the implanted seed positions (approximately 60% of the practitioners using it in the operating room [3]). In spite of significant efforts that have been made towards computational fluoroscopic guidance in general surgery [4], C-arms cannot yet be used for intra-operative brachytherapy guidance due to a plethora of technical limitations. While several groups have published protocols and clinical outcomes favorably supporting C-arm fluoroscopy for intra-operative dosimetric analysis [5,6,7], this technique is yet to become a standard of care across hospitals. In this paper we report a system to reconstruct 3D seed positions (visible in X-ray) and spatially register them to the prostate (visible in TRUS). Our primary contribution is our ability to use any typical non-isocentric uncalibrated Carm present in most hospitals, in comparison to the use of calibrated isocentric machines [5,6] or an approximate reconstruction [7], as reported in the literature.

2

Methods and Materials

The system is designed to easily integrate with commercial brachytherapy installations. We employ a regular clinical brachytherapy setup, without alteration, including a treatment planning workstation & stabilizer/stepper (Interplant , CMS, St Louis), TRUS (B&K Medical Pro Focus) and a C-arm (GE OEC

Seed Matching (MARSHAL)

3D Seed Locations

Prostate info from TRUS

Intra-operative Dose Guidance

C-arm Pose (FTRAC)

Fig. 1. Overview of the proposed solution. The FTRAC fiducial tracks C-arms, and also registers TRUS to C-arm images, making quantitative brachytherapy possible.

Intra-operative 3D Guidance in Prostate Brachytherapy

11

98/9900). The C-arm is interfaced with a laptop through an NTSC video line and frame grabber, making the image capture independent of the C-arm model. Workflow: The clinical workflow (Fig. 1) is identical to the standard procedure until the clinician decides to run a reconstruction and optimization. A set of Carm images are collected with a separation as wide as clinically possible (10−15o around AP-axis) and synchronously transferred to the laptop. After processing the images, the seeds are reconstructed and exported to the Interplant system. The physician uses standard Interplant tools to analyze, optimize and modify the remainder of the plan. The procedure concludes when the exit dosimetry shows no cold spots (under-radiated locations). Numerous technical obstacles have to be overcome to realize C-arm based intraoperative dosimetry: (a) C-arm calibration; (b) image distortion correction; (c) pose estimation of C-arm images; (d) seed reconstruction; (e) registration of Carm to TRUS; (f) dosimetry analysis; and finally (g) implant optimization. We have developed a system that overcomes these limitations in providing quantitative intra-operative dosimetry. In what follows, we will describe briefly each component of the system, skipping the mathematical framework for lack of space. C-arm Source Calibration and Image Distortion: Since both C-arm calibration and distortion are pose-dependent, contemporary fluoroscopy calibrates/ distortion-corrects at each imaging pose using a cumbersome calibration-fixture, which is a significant liability. Our approach is Wrong X-ray source ¯f a complete departure. Using a mathematical & True X-ray D ¯ source experimental framework, we demonstrated that f¯ P calibration is not critical for prostate seed reconP F struction. Just an approximate pre-operative calF F ibration suffices [8]. The central intuition is that F object reconstruction using a mis-calibrated C-arm ¯L changes only the absolute positions of the objects, L ¯ but not their relative ones (Fig. 2). Additionally, p F statistical analysis of the distortion in a 15o limited workspace around the AP-axis revealed that Fig. 2. Mis-calibration conjust a pre-operative correction can reduce the aver- serves relative reconstruction age distortion from 3.31 mm to 0.51 mm, sufficient between objects A and B (eg. for accurate 3D reconstruction. The numbers are seeds) expected to be similar for other C-arms too. 2

1

2

1

A

B

A

B

2

1

I

Pose Estimation: The most critical component for 3D reconstruction is C-arm pose estimation. C-arms available in most hospitals do not have encoded rotational joints, making the amount of C-arm motion unavailable. C-arm tracking using auxiliary trackers is expensive, inaccurate in the presence of metal (EM tracking) or intrudes in the operating room (optical tracking). There has been some work on fiducial based tracking, wherein a fiducial (usually large for accuracy) is introduced in the X-ray FOV and its projection in the image encodes the

12

A. Jain et al.

6 DOF pose of the C-arm. We proposed a new fluoroscope tracking (FTRAC) [9] fiducial design that uses an ellipse (key contribution), allowing for a small (3x3x5cm) yet accurate fiducial. In particular, the small size makes it easier to be always in the FOV & to be robust to image distortion. Extensive phantom experiments indicated a mean tracking accuracy on distorted C-arms of 0.56 mm in translation and 0.25o in rotation, an accuracy comparable to expensive external trackers. Seed Segmentation: We developed an automated seed segmentation algorithm that employs the morphological top-hat transform to perform the basic seed segmentation, followed by thresholding, region labeling, and finally a two-phase classification to segment both single seeds & clusters. The result of the segmentation is verified on the screen to allow for a manual bypass by the surgeon.

Fig. 3. The FTRAC fiducial mounted over the seedinsertion needle template using a mechanical connector. An X-ray image of the same.

Seed Correspondence & Reconstruction: The 3D coordinates of the implanted seeds can now be triangulated by resolving the correspondence of seeds in the multiple X-ray images. We formalized seed correspondence to a networkflow-based combinatorial optimization, wherein the desired solution is the flow with minimum cost. Using this abstraction, we proposed an algorithm (MARSHAL [10]) that runs in cubic-time using any number of images. In comparison, previous solutions have predominantly been heuristic explorations of the large search space (10300 ). In addition, the framework also robustly resolves all the seeds that are hidden in the images (typically 4-7% due to the high density). MARSHAL typically reconstructs 99.8% of the seeds and runs in under 5s in MATLAB (a 95% minimum-detection-rate is usually deemed sufficient [11]). Registration of C-arm to TRUS: The FTRAC is attached to the needle-insertion template by a precisely machined mechanical connector (Fig. 4) in a known relative way (pre-calibration). The template has already been calibrated to TRUS as per the usual clinical protocol. Thus a simple application of the various known frame transformations, registers the 3D seeds (FTRAC) to the prostate (TRUS).

Fig. 4. FTRAC & template pre-calibration using a rigid mount

System Implementation, Dosimetry Analysis and Implant Optimization: We have integrated all the above functions into a MATLAB program with a GUI. The package runs on a laptop that sends reconstructed seed positions (in template coordinates) to the Interplant system. In order to not require a new FDA approval, we maintain the integrity of the FDA-approved Interplant by not modifying the commercial software, and instead use a text file to export the 3D seed locations.


13

The physician uses standard Interplant tools (isodose coverage, etc.) for dose analysis, and if needed, modifies the residual plan to avoid hot spots or fill in cold spots. This process can be repeated multiple times during the surgery.

3

Phantom Experiments and Results

We have extensively tested the system and its components in various phantoms and in an ongoing Phase-1 clinical trial. To do so, we introduce the terms absolute and relative reconstruction errors. Using X-ray images, the seeds are reconstructed with respect to (w.r.t.) the FTRAC frame. In experiments where the ground truth location of the seeds w.r.t. the FTRAC is known, the comparative analysis is called absolute accuracy. Sometimes (eg. in patients), the true seed locations w.r.t. the FTRAC are not available and the reconstruction can only be compared to the seeds extracted from post-op data (using a rigid point-cloud transform), in which case the evaluation is called relative accuracy. Solid Seed Phantom: An acetol (Delrin) phantom consisting of ten slabs (5mm each) was fabricated (Fig. 5 (a)). This phantom provides a multitude of implants with sub-mm ground truth accuracy. The fiducial was rigidly attached to the phantom in a known way, establishing the accurate ground truth 3D location of each seed. Realistic prostate implants (1.56 seeds/cc, 40-100 seeds) were imaged within a 30o cone around the AP-axis. The true correspondence was manually established by using the 3D locations, known from the precise fabrication. Averaged results indicate that we correctly match 98.5% & 99.8% of the seeds using 3 & 4 images (100 & 75 total trials) respectively. The mean 3D absolute reconstruction accuracy was 0.65 mm (STD 0.27 mm), while the relative accuracy was 0.35 mm. Furthermore, using 4 images yielded only one poorly mis-matched seed from the 75 datasets, suggesting the use of 4 images for better clinical guidance. Soft Training Phantoms: We fully seeded three standard prostate brachytherapy phantoms (Fig. 5 (b)) with realistic implant plans (45, 49, 87 seeds). Seed

FTRAC X-ray

TRUS Display

Interplant

Spacers

Template FTRAC Patient Needle Insertion Template Prostate Phantom

TRUS Probe

TRUS Probe TRUS Stepper

TRUS Stepper

(a)

(b)

(c)

Fig. 5. (a) An image of the solid seed phantom attached to the fiducial with a typical X-ray image of the combination. (b) An annotated image of the experimental setup for the training phantom experiment. (c) The clinical setup from the Phase-I clinical trial.

14

A. Jain et al.

locations reconstructed from fluoro using realistic (maximum available clinically) image separation (about 15o ) were compared to their corresponding ground truth locations segmented manually in CT (1mm slice thickness). Additionally, the 45 & 87-seed phantoms were rigidly attached to the FTRAC, providing the absolute ground truth (from CT). The 49-seed phantom was used to conduct a full scale practice-surgery, in which case the 3D reconstruction could be compared only to the seed cloud from post-op CT (without FTRAC), providing just relative accuracy. Note that our reconstruction accuracy (as evident from the previous experiments) is better than the CT resolution. The absolute reconstruction errors for the 45, 87-seed phantoms were 1.64 mm & 0.95 mm (STD 0.17 mm), while the relative reconstruction errors for the 45, 49, 87-seed phantoms were 0.22 mm, 0.29 mm, 0.20 mm (STD 0.13 mm). A mean translation shift of 1.32 mm was observed in the 3D reconstructions, predominantly due to the limited C-arm workspace (solid-phantom experiments with 30o motion have 0.65 mm accuracy). It was observed that the shift was mostly random & not in any particular direction. Nevertheless, the accuracy is sufficient for brachytherapy, especially since a small shift still detects the cold spots. Patients: A total of 11 batches of reconstructions were carried out on 4 patients with 2 − 3 batches/patient & 22 − 84 seeds/batch. Since the seeds migrate by the time a post-operative CT is taken, there is no easy ground truth for real patients. Hence, for each reconstruction, 5 − 6 additional X-ray images were taken. The reconstructed 3D seed locations were projected on these additional images and compared to their segmented corresponding 2D locations. The results from 55 projections gave a 2D mean error of 1.59 mm (STD 0.33 mm, max 2.44 mm), indicating a sub-mm 3D accuracy (errors get magnified when projected). Registration Accuracy: To measure the accuracy of the fiducial to template registration, three batches of five needles each were inserted randomly at random depths into the template. Their reconstructed tip locations were then compared to their true measured locations (both in template coordinates). The limitedangle image-capture protocol was kept similar to that used in the clinic. The average absolute error (reconstruction together with registration) was 1.03 mm (STD 0.20 mm), while the average relative error was 0.36 mm (STD 0.31 mm), with an average translation shift of 0.97 mm. System Accuracy: To measure the full system error, 5 needles (tips) were inserted into a prostate brachytherapy training phantom, reconstructed in 3D and exported to the Interplant software. Manual segmentation of the needles in TRUS images (sagittal for depth and transverse for X-Y) provided ground truth. The mean absolute error for the 5 needle tips was 4 mm (STD 0.53 mm), with a translation shift of 3.94 mm. In comparison, the relative error for the complete system was only 0.83 mm (STD 0.18 mm). The shift can mainly be attributed to a bias in the Template-TRUS pre-calibration (∼ 3 mm) done as part of current clinical practice, & in the 3D reconstruction (∼ 1 mm). Nevertheless, we


15

removed this shift in the clinical cases by applying a translation-offset to the reconstructed X-ray seed coordinates. This offset was intra-operatively estimated by comparing the centroid of the reconstructed seeds with that of the planned seed locations, and by aligning the two together. Note that the centroid is a first-order statistic and robust to any spatially symmetric noise/displacement model. Though a heuristic, it provided excellent qualitative results according to the surgeon, who read the visual cues at the reconstructed seed locations in TRUS images. Based on the experiments so far and the surgeon’s feedback, the overall accuracy of the system is expected to be 1 − 2 mm during clinical use.

(a)

(b)

Fig. 6. (a) The system is able to detect cold spots. The 100% iso-dose contours (pink) as assumed by the planning system (top) and as computed by the proposed system (bottom), discovering 2 cold spots. Red marks the prostate boundary. The green squares delineate the seed coordinates, detecting 4 seeds that had drifted out of slice. (b) The system can visualize intra-operative edema (mean 4.6 mm, STD 2.4 mm, max 12.3 mm). The ’planned’ (red) versus the ’reconstructed’ (blue) seed positions as seen in the template view. A trend of outward radiation from their initial locations is observed.

Phase-I Clinical Trial: We have treated 4 patients so far (Fig. 5 (c)), out of a total of 6 that will be enrolled. Intra-operative dosimetry was performed halfway during the surgery, at the end, and after additional seed insertions. The current protocol adds 15 minutes to the OR time for each reconstruction, including the capture of extra images (validation), reconstruction, and dosimetry optimization. In regular clinical practice, we anticipate the need for only a single exit-dosimetry reconstruction, increasing the OR time by about 10 minutes. In all the patients the final dosimetry detected cold spots (Fig. 6 (a)). The clinician grew quickly to trust the system in detecting cold spots, and instead minimized potential hot spots during the surgery. All patients were released from the operating room with satisfactory outcomes. Intra-operative visualization of edema (prostate swelling) was also possible (Fig. 6 (b)), which was found to be 0.73, 4.64, 4.59, 4.05 mm (STD 1.1, 2.2, 2.34, 2.37 mm). The seeds (and hence the prostate) showed a clear tendency for outward migration from their drop positions (with maximums up to 15 mm). Edema is the single largest factor that makes the perfect delivery

16

A. Jain et al.

of the pre-planned dose nearly impossible. In almost all the patients, towards the end of the surgery, it was found that the apex of the prostate (surgeon-end) was under-dosed. The medical team found the intra-operative visualization of under-dosed regions valuable, inserting an additional 1, 2, 3, 9 seeds to make the 100% prescribed iso-dose contour cover the prostate. A further comparison of the exit implant to Day-0 CTs (2 mm slices) showed mean errors of 5.43, 6.16, 3.13, 5.15 mm (STD 2.46, 2.96, 2.02, 2.71 mm), indicating a further post-operative seed migration. Though, post-operative seed migration is an inherent limitation in brachytherapy, surgeons usually accommodate for it by slightly over-dosing the patient (note that sub-mm seed placement is non-critical). A study with 40 patients is currently being planned, to make a statistically relevant evaluation of the medical benefit of the system using clinical indicators.

4

Conclusion, Shortcomings and Future Work

A system for brachytherapy seed reconstruction has been presented, with extensive phantom and clinical trials. The absolute seed reconstruction accuracy from phantom trials is 1.3 mm using 15o C-arm motion, sufficient for detection of any cold spots. It shows usefulness and great potential from the limited Phase-1 patient trials. The system (a) requires no significant hardware; (b) does not alter the current clinical workflow; (c) can be used with any C-arm; & (d) integrates easily with any pre-existing brachytherapy installation, making it economically sustainable and scalable. There is some added radiation to the patient, though insignificant when compared to that from the seeds. Though not critical, primary shortcomings include (a) 15 minute additional OR time; (b) supervision during segmentation; & (c) a small translation bias. Furthermore, a TRUS based quantitative methodology is necessary to evaluate both the final system performance and clinical outcomes. Research is currently underway to remove these limitations, and to conduct a more detailed study using clinical indicators.

References 1. Nag, et al.: Intraoperative planning and evaluation of permanent prostate brachytherapy: report of the american brachytherapy society. IJROBP 51 (2001) 2. Tornes, A., Eriksen, M.: A new brachytherapy seed design for improved ultrasound visualization. In: IEEE Symposium on Ultrasonics, pp. 1278–1283. IEEE Computer Society Press, Los Alamitos (2003) 3. Prestidge, et al.: A survey of current clinical practice of permanent prostate brachytherapy in the united states. IJROBP 15, 40(2), 461–465 (1998) 4. Hofstetter, et al.: Fluoroscopy as an imaging means for computer-assisted surgical navigation. CAS 4(2), 65–76 (1999) 5. Reed, et al.: Intraoperative fluoroscopic dose assessment in prostate brachytherapy patients. Int. J. Radiat. Oncol. Biol. Phys. 63, 301–307 (2005) 6. Todor, et al.: Intraoperative dynamic dosimetry for prostate implants. Phys. Med. Biol. 48(9), 1153–1171 (2003)


17

7. French, et al.: Computing intraoperative dosimetry for prostate brachytherapy using trus and fluoroscopy. Acad. Rad. 12, 1262–1272 (2005) 8. Jain, et al.: C-arm calibration - is it really necessary? In: SPIE Medical Imaging; Visualization, Image-Guided Procedures, and Display (2007) 9. Jain, et al.: A robust fluoroscope tracking fiducial. Med. Phys. 32, 3185–3198 (2005) 10. Kon, R., Jain, A., Fichtinger, G.: Hidden seed reconstruction from c-arm images in brachytherapy. In: IEEE ISBI, pp. 526–529. IEEE Computer Society Press, Los Alamitos (2006) 11. Su, et al.: Examination of dosimetry accuracy as a function of seed detection rate in permanent prostate brachytherapy. Med. Phy. 32, 3049–3056 (2005)

A Multi-view Opto-Xray Imaging System Development and First Application in Trauma Surgery Joerg Traub1 , Tim Hauke Heibel1 , Philipp Dressel1 , Sandro Michael Heining2 , Rainer Graumann3 , and Nassir Navab1 1

2

Computer Aided Medical Procedures (CAMP), TUM, Munich, Germany Trauma Surgery Department, Klinikum Innenstadt, LMU Munich, Germany 3 Siemens SP, Siemens Medical, Erlangen, Germany

Abstract. The success of minimally invasive trauma and orthopedic surgery procedures has resulted in an increase of the use of fluoroscopic imaging. A system aiming to reduce the amount of radiation has been introduced by Navab et al. [1]. It uses an optical imaging system rigidly attached to the gantry such that the optical and X-ray imaging geometry is identical. As an extension to their solution, we developed a multi-view system which offers 3D navigation during trauma surgery and orthopedic procedures. We use an additional video camera in an orthogonal arrangement to the first video camera and a minimum of two X-ray images. Furthermore, tools such as a surgical drill are extended by optical markers and tracked with the same optical cameras. Exploiting that the cross ratio is invariant in projective geometry, we can estimate the tip of the instrument in the X-ray image without external tracking systems. This paper thus introduces the first multi-view Opto- Xray system for computer aided surgery. First tests have proven the accuracy of the calibration and the instrument tracking. Phantom and cadaver experiments were conducted for pedicle screw placement in spinal surgery. Using a postoperative CT, we evaluate the quality of the placement of the pedicle screws in 3D.

1

Introduction

Mobile C-arm systems are established in everyday routines in orthopedic and trauma surgery. The trend toward minimally invasive applications increases the use of fluoroscopic images within surgery and thus the radiation dose [2,3]. Nowadays the combined use of mobile C-arms, that are capable of 3D reconstruction, and a tracking system provide navigation information during surgery, e.g. [4]. Systems using this technique use so called registration free navigation methods based on a mobile C-arm with 3D reconstruction capabilities tracked by an external optical tracking system. The imaging device is tracked and the volume is reconstructed in the same reference frame in which the instruments and the patient are tracked. Hayashibe et al. [5] combined the registration free navigation approach using an intra-operative tracked C-arm with reconstruction capabilities and in-situ visualization by volume rendered views from any arbitrary position of a swivel arm mounted monitor. N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 18–25, 2007. c Springer-Verlag Berlin Heidelberg 2007

A Multi-view Opto-Xray Imaging System

19

Augmenting interventional imaging data using mirror constructions were proposed by Stetten et al. [6] for tomographic reflection on Ultrasound and Fichtinger et al. for navigated needle insertion based on CT [7] and MR [8]. Another approach for augmentation of intraoperative image data is the physical attachment of an optical camera to an X-ray source as proposed by Navab et al. [1]. It uses a single optical camera rigidly attached to the gantry such that the optical and X-ray imaging geometry is aligned. This enabled a real time video image and X-ray overlay that was registered by construction. No registration of the patient was required in their approach. This provided an accurate positioning and guidance of instruments in 2D. However, no depth control was possible. Thus their system was limited to applications where depth did not matter, like in intramedullary-nail locking as proposed by their group [9]. As an extension to their proposed system, we developed a system that is also capable of depth control during trauma surgery and orthopedic procedures using only one additional X-ray image and a second video camera that is rigidly attached to the C-arm. Furthermore, we implemented a system to track an instrument in 2D. Using cross ratio we estimate the position of the tip in the image. After one time calibration of the newly attached second video camera we are able to show the instrument tip in the orthogonal X-ray view. The feasibility of the system has been validated trough cadaver studies where we successfully identified all six pedicle screws placed using the procedure. The accuracy of the placement was validated using a postoperative CT.

2 2.1

System Setup System Components

The system consists of an Iso3D C-arm (Siemens Medical, Erlangen, Germany) with two attached Flea video color cameras (Point Grey Research Inc., Vancouver, BC, Canada) (see figure 1). The first camera is attached as proposed earlier by Navab et al. using a double mirror construction with X-ray transparent mirrors [1]. The second camera is attached orthogonal to the gantry such that its view is aligned with the X-ray image after a 90 degrees orbital rotation of the C-arm (see figure 1). Furthermore, the system includes a standard PC with a framegrabber card to access the analog images of the C-arm. A custom developed visualization and navigation software is used (see section 2.3). 2.2

System Calibration

For both cameras the calibration process can be devided in two consecutive steps. In the first step the cameras are physically attached such that the optical center and axis virtually coincide with the X-ray imaging system at all time for the gantry mounted camera and at particular C-arm positions for the orthogonal mounted camera. The second step is to compute the homographies to align the video images with the X-ray images. For both video cameras the distortion is computed using the Matlab camera calibration toolbox and the images

20

J. Traub et al.

Fig. 1. The C-arm with two attached optical cameras. The first camera is attached to the gantry with a double mirror construction. The second camera is attached in an orthogonal direction with a single mirror construction.

are undistorted using Intel OpenCV library. The use of flat panel displays or standard distortion correction methods is recommended 1 . Notation. Since we have images at different positions of the C-arm superscript 0 denote cameras and images at a 0 degree orbital rotation and superscript 90 denote cameras and images acquired by the C-arm after an orbital rotation around 90 degree. Furthermore subscript x is used for X-ray, g for gantry mounted, and o for the orthogonal mounted cameras. X-ray to Gantry Mounted Camera Calibration. Initially the gantry mounted camera is physically placed such, that its optical center and axis are aligned respectively with the X-ray source. This alignment is achieved by a bi-planar calibration phantom and mounting the camera using a double mirror construction. To superimpose the X-ray image onto the video image a homography HIg0 ←Ix0 is computed. Thanks to this homography the effects of X-ray distortions close to the image center are diminished. The procedure of the gantry mounted camera calibration is described in detail by Navab et al. [1]. X-ray to Orthogonal Mounted Camera Calibration. We constrained the attachment of the second camera to be orthogonal with respect to the gantry. This attachment provides best results for the depth navigation, assuming the instruments are always used down the beam as in the single camera navigation system [1]. The physical attachment and calibration of the second camera at alternative positions is also possible with the procedure described in this section. 1

See http://campar.in.tum.de/Events/VideoCamCSquare for a video demonstration of the calibration and navigation procedure.


21

To acquire an X-ray image Ix90 corresponding to the view Io0 of the orthogonal mounted camera, we have to ensure that after an orbital rotation the optical center and axis of the X-ray gantry and the orthogonal camera are aligned. Since the gantry mounted camera is already physically aligned with the X-ray device, the problem can be reduced to physically aligning the gantry mounted and orthogonal mounted camera after rotation. This alignment is achieved with a bi-planar calibration pattern. A set of markers is placed on each plane such that subsets of two markers, one on each plane, are aligned in the image of the gantry mounted camera Ig0 at the initial position of the C-arm (see figure 2(e)). In the next step, the C-arm is rotated by −90 degrees in orbital(see figure 2(c)). Now the orthogonal mounted camera is physically moved in six degrees of freedom, until all marker tuples from the calibration pattern are lined up in image Io−90 in exactly the same way as they were for the gantry mounted camera (see figure 2(f)). Note that the calibration only has to be performed once the system is constructed. Once the system is built, the alignment is preserved by construction. For a proper alignment of the X-ray image Ix90 at 90 degree rotation in orbital direction and the image Io0 of the orthogonal camera with no rotation, two homographies remain to be computed. A first homography HIg90 ←Ix90 that maps the X-ray image Ix90 to the gantry mounted image Ig90 and a second homography HIo0 ←Ig90 mapping the image of the gantry mounted camera to the image of the orthogonal mounted camera. The final homography used to map the X-ray image Ix90 onto the orthogonal mounted camera image Io0 uses the hompgraphy HIo0 ←Ix90 = HIo0 ←Ig90 · HIg90 ←Ix90 , a combination of the two homograpies computed earlier. Both homographies are computed using corresponding points in the images. Even though the gantry camera is rigidly mounted a second estimation of the homography HIg90 ←Ix90 is determined to approximately compensate distortion effects of the X-ray image after rotation. 2.3

Navigation System

The navigation does not require any further calibration or registration procedure. The previously described calibration routine has to be performed only once while the system is built and it is valid as long as the cameras do not move with respect to the gantry. For the navigation the acquisition of two X-ray images Ix0 and Ix90 with a precise orbital rotation, such that the acquired images correspond to the images of the gantry attached camera Ig0 and the orthogonal camera Io0 , has to be ensured. Therefore an image Io0 of the second camera is captured before the rotation. Using image overlay techniques of this captured image Io0 and a live video image Ig0→90 during the orbital rotation with the homography HIo0 ←Ig90 applied, we ensure that the first camera has the same position and orientation as the second camera before the rotation. Thus the X-ray image Ix90 we take from this position corresponds to the captured image Io0 . Furthermore, after precise rotation of the C-arm back to its original position, the orthogonal taken X-ray image Ix90 can be overlaid on the live image Io0 of the orthogonal mounted camera

22

J. Traub et al.

by applying the computed homography HIo0 ←Ix90 . The rotation back is ensured using combined X-ray and optical markers attached to the side of our surgical object that are visible in the X-ray image Ix90 and the image Io0 of the orthogonal camera. The acquisition of a second X-ray image Ix0 at position zero and the use of the homography HIg0 ←Ix0 enables the lateral control using the gantry mounted camera (see figure 3(a). The image Io0 of the orthogonal camera is used by an instrument tracking module (see figure 2.4). The estimated distal end of the instrument in the orthogonal image Ig0 is superimposed on the X-ray image Ix90 taken at 90 degree rotation (see figure 3(c)). 2.4

Instrument Tracking

The surgical tool is extended by three markers collinear arranged on the instrument axis. We use retro-reflective circular markers that are illuminated by an additional light source attached to the orthogonal camera. This setup results in the markers being seen by the orthogonal camera as bright ellipses, which can be easily detected by image thresholding. From the binary image all contours are extracted using the Intel OpenCV library. In a post-processing step we filter those contours having a low compactness value and those having a smaller area than a threshold (default values are 0.6 for the compactness and 50 pixels for the area). For all contours being retained by the filtering routine, the sub-pixel centroids are computed based on grayscale image moments. Finally those three contours yielding an optimal least squares line fitting are assumed to be the ones corresponding to our circular markers. Having three collinear markers detected in the 2D image plane, we are able to compute the position of the instrument tip. Given the 3D geometry of our instrument, i.e. the position of the distal end of the instrument with respect to the other three markers, we compute the tip of the instrument in the image based on the cross-ratio. cross =

Δx12 Δx23 Δy12 Δy23 d12 d23 = = d13 d24 Δx13 Δx24 Δy13 Δy24

(1)

Here dij are the distances between the markers i and j, respectively between a marker and the tool tip. Investigating the distances in x- and y-direction separately gives us Δxij and Δyij where Δx24 = |x2 − x4 | and Δy24 = |y2 − y4 | contain the unknown coordinates x4 and y4 of the instrument tip. Since the Xray image Ix90 is registered with the live video image Io0 of the second camera by HIo0 ←Ig90 , we know exactly the position of the tip in the X-ray image Ix90 taken at 90 degree rotation (see figure 3(c)).

3

Experiments and Results

First the feasibility of the system was tested on a spine phantom. We used a tracked awl, a pedicle probe and a T-handle to place pedicle screws. Using an


23

(a) X-ray with misaligned (b) Camera 1 with mis- (c) Camera 2 with mismarkers. aligned markers. aligned markers.

(d) X-ray markers.

with

aligned (e) Camera 1 with aligned (f) Camera 2 with aligned markers. markers.

Fig. 2. The calibration phantom in the different imaging systems

(a) First camera for lateral po- (b) Second camera (c) Superimposition of depth sitioning. for depth tracking. tracking onto the X-ray image. Fig. 3. The navigation interface including the lateral positioning of the instrument and the depth control using cross ratio

orthogonal control X-ray image we could visually verify the accuracy of the depth navigation. In a cadaver experiment we placed eight pedicle screws (Universal Spine System USS, Synthes, Umkirch) with a diameter of 6.2 mm in four vertebrae of the thoracic and lumbar spine (Th12-L3). The surgical procedure was carried out

24

J. Traub et al.

in three steps using a pedicle awl to open the cortical bone, a pedicle probe to penetrate the pedicle, and a T-handle for screw implantation. For the guided procedure both augmented views, the one for 2D positioning (see figure 4(a)) and the one for depth control (see figure 4(b)), were used simultaneously. After aligning the optical axis of the C-arm imaging system with the desired direction of the pedicle screws, the acquisition of only two X-ray images was required for each pedicle screw. This is a considerable reduction of radiation compared to standard fluoro based procedure. The accuracy of the pedicle screw placement was verified by a postinterventional CT-scan ((see figure 4(c) and 4(d))) using a clinical scale proposed by Arand et al. [10]. Five pedicle screws were classified by an medical expert to be in group A, i.e. central screw position without perforation. The other three screws were classified to be in group B, i.e. lateral screw perforation within thread diameter. For none of the eight pedicle screws a medial perforation in direction of the spinal canal occurred.

(a) Tracking.

(b) Control X-ray.

(c) Sagittal CT.

(d) Transversal CT.

Fig. 4. Evaluation of the developed system using a control X-ray Ix90 and postinterventional CT data

4

Discussion

We have extended a real-time video augmented X-ray to a multi-view Opto-Xray imaging system. The previously proposed single camera augmentation system has proven to be efficient for trauma surgery and orthopedic applications where 3D did not matter, e.g. intramedullary-nail locking. The original system was extended by a second camera mounted in an orthogonal arrangement to the first camera. The second camera, thanks to a calibration and navigation protocol, enables applications for trauma surgery that are only possible at the moment using permanent fluoroscopic imaging or C-arm with 3D reconstruction capabilities and external tracking systems, both resulting in considerable increase of the radiation dose. Our newly developed system proved that it is possible to perform these procedures with the use of only two X-ray images and the assumption that the object does not move after the X-ray acquisition. If the object moves, simply another pair of X-rays has to be acquired. Using our proposed system and calibration procedure we are neither limited to exactly two cameras nor to a specific physical arrangement. First cadaver experiments demonstrated that the new system can be easily integrated into the clinical workflow while reducing the


25

radiation dose compared to other methods. The observed accuracy during the experiments is clinically acceptable. Further work will compare quantified results with CT based and C-arm based standard navigation techniques. The invention and implementation of a system for real-time augmentation of orthogonal X-ray views of a surgery, opens the way for development of new C-arms with integrated 3D navigation capabilities with no further need for online calibration. Acknowlegments. Special thanks to Siemens Medical SP and Benjamin Ockert.

References 1. Navab, N., Mitschke, M., Bani-Hashemi, A.: Merging visible and invisible: Two camera-augmented mobile C-arm (CAMC) applications. In: IWAR, pp. 134–141 (1999) 2. Boszczyk, B.M, Bierschneider, M., Panzer, S., Panzer, W., Harstall, R., Schmid, K., Jaksche, H.: Fluoroscopic radiation exposure of the kyphoplasty patient. European Spine Journal 15, 347–355 (2006) 3. Synowitz, M., Kiwit, J.: Surgeon’s radiation exposure during percutaneous vertebroplasty. J. Neurosurg. Spine. 4, 106–109 (2006) 4. Siewerdsen, J.H., Moseley, D.J., Burch, S., Bisland, S.K., Bogaards, A., Wilson, B.C., Jaffray, D.A.: Volume ct with a flat-panel detector on a mobile, isocentric c-arm: Pre-clinical investigation in guidance of minimally invasive surgery. Medical Physics 32(1), 241–254 (2005) 5. Hayashibe, M., Suzuki, N., Hattori, A., Otake, Y., Suzuki, S., Nakata, N.: Surgical navigation display system using volume rendering of intraoperatively scanned ct images. Computer Aided Surgery 11(5), 240–246 (2006) 6. Stetten, G.D., Chib, V.: Magnified real-time tomographic reflection. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, Springer, Heidelberg (2001) 7. Fichtinger, G., Deguet, A., Masamune, K., Balogh, E., Fischer, G.S., Mathieu, H., Taylor, R.H., Zinreich, S.J., Fayad, L.M.: Image overlay guidance for needle insertion in ct scanner. IEEE Transactions on Biomedical Engineering 52(8), 1415– 1424 (2005) 8. Fischer, G.S., Deguet, A., Schlattman, D., Taylor, R., Fayad, L., Zinreich, S.J., Fichtinger, G.: Mri image overlay: Applications to arthrography needle insertion. In: Medicine Meets Virtual Reality (MMVR), vol. 14 (2006) 9. Heining, S.M., Wiesner, S., Euler, E., Mutschler, W., Navab, N.: Locking of intramedullary nails under video-augmented flouroscopic control: first clinical application in a cadaver study. In: Proceedings of CAOS, Montreal, Canada (2006) 10. Arand, M., Schempf, M., Fleiter, T., Kinzl, L., Gebhard, F.: Qualitative and quantitative accuracy of caos in a standardized in vitro spine model. Clin. Orthop. Relat. Res. 450, 118–128 (2006)

Towards 3D Ultrasound Image Based Soft Tissue Tracking: A Transrectal Ultrasound Prostate Image Alignment System Michael Baumann1,2 , Pierre Mozer1,3 , Vincent Daanen2 , and Jocelyne Troccaz1 1

Université J. Fourier, Laboratoire TIMC, Grenoble, France; CNRS, UMR 5525; Institut National Polytechnique de Grenoble 2 Koelis SAS, 5 av. du Grand Sablon, 38700 La Tronche, France 3 La Pitié-Salpêtrière Hospital, Urology Department, 75651 Paris Cedex 13, France [email protected]

Abstract. The emergence of real-time 3D ultrasound (US) makes it possible to consider image-based tracking of subcutaneous soft tissue targets for computer guided diagnosis and therapy. We propose a 3D transrectal US based tracking system for precise prostate biopsy sample localisation. The aim is to improve sample distribution, to enable targeting of unsampled regions for repeated biopsies, and to make post-interventional quality controls possible. Since the patient is not immobilized, since the prostate is mobile and due to the fact that probe movements are only constrained by the rectum during biopsy acquisition, the tracking system must be able to estimate rigid transformations that are beyond the capture range of common image similarity measures. We propose a fast and robust multiresolution attribute-vector registration approach that combines global and local optimization methods to solve this problem. Global optimization is performed on a probe movement model that reduces the dimensionality of the search space and thus renders optimization efficient. The method was tested on 237 prostate volumes acquired from 14 different patients for 3D to 3D and 3D to orthogonal 2D slices registration. The 3D-3D version of the algorithm converged correctly in 96.7% of all cases in 6.5s with an accuracy of 1.41mm (r.m.s.) and 3.84mm (max). The 3D to slices method yielded a success rate of 88.9% in 2.3s with an accuracy of 1.37mm (r.m.s.) and 4.3mm (max).

1 Introduction Computer-guidance for medical interventions on subcutaneous soft tissue targets is a challenging subject, since the target tracking problem is still not satisfactorily solved. The main difficulties are caused by the elasticity, mobility and inaccessibility of soft tissues. With 3D US a real-time volume imaging technology became available that provides enough spatial tissue information to make image-based tracking possible. Imagebased tracking is essentially a mono-modal image registration problem with a real-time constraint. The primary task is to find the physical transformation T in a transformation space T between two images of the same object. The choice of T depends on the underlying physical transformation (e.g. rigid, affine or elastic) and the requirements of the target application. An extensive review on registration methods is given in [1]. N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 26–33, 2007. c Springer-Verlag Berlin Heidelberg 2007

Towards 3D Ultrasound Image Based Soft Tissue Tracking

27

Nowadays, research on mono-modal 3D US registration of soft tissue images focusses on rapid deformation estimation. Most studies in this domain, however make the implicit assumption that the rigid part of the transformation to estimate is either small or known. Confronted with combinations of large rigid transformations and elastic deformations, the proposed solutions fail without rigid pre-registration. For many clinical applications large rigid transformations can be avoided by immobilizing both the patient and the US probe. In the case of interventions without total anesthesia this however causes considerable patient discomfort. Moreover, it is sometimes impossible to fix the US probe, e.g. when the probe serves as a guide for surgical instruments. The respiratory and the cardiac cycle can be additional sources of tissue displacements. In all these cases it is necessary to identify the rigid part of the transformation before carrying out image-based deformation estimation. Estimation of large rigid transformations is basically a global optimization problem since common similarity measures exhibit search-friendly characteristics (e.g. convexity) only in a small region near the global solution. The computational burden of global optimization in a 6-D rigid transformation space is prohibitive for tracking tasks. [2, 3] propose to reduce the intra-interventional computation time of global searches by precomputing a feature-based index hash table. During intervention, similarity evaluation is replaced by computation of the geometric index followed by a fast data-base lookup. In the context of US image tracking, this approach has the disadvantage of relying on feature extraction, which often lacks robustness when confronted with partial target images, speckle and US shadows. Also, it cannot reduce the complexity of the optimization problem and pre-computation time is not negligible. Relatively few investigations involving 3D US image based tracking of soft tissues have been reported. In the context of respiratory gated radiation treatment, [4] acquire a localized 3D US reference image of the liver or the pancreas in breath-hold state and register it rigidly with the treatment planning CT volume. During therapy, localized US slices of the organ are continuously compared with the reference volume using image correlation to retrieve the planning position of the organ. In [5] real-time 3D US images of the beating heart are registered multimodally with a set of 4-D MR images covering the entire cardiac cycle. A localizer is used to initialize the spatial registration process while the ECG signal serves for temporal alignment. The authors achieve precise rigid registration in an overall computation time of 1 second with a mutual information based rigid registration algorithm. In both studies relative rigid movements between probe and target organ are limited to movements caused by the respiratory or cardiac cycles, which are predictable and repeatable to a certain extent. The target application of this work is 3D transrectal ultrasound (TRUS) prostate biopsy trajectory tracking. Today, prostate biopsies are carried out using 2D TRUS probes equipped with a guide for spring needle guns. With the current standard biopsy protocol, consisting typically of 12 regularly distributed samples, it is impossible to know the exact biopsy locations after acquisition, which makes precise biopsy-based tumor localization, quality control and targeted repeated biopsies impossible. A TRUSbased prostate tracking system would make it possible to project all sample locations into a reference image of the prostate and thus to identify the exact sampling locations.

28

M. Baumann et al.

Image-based prostate biopsy tracking is, however, challenging: (i) the gland moves and gets deformed under the pressure of the TRUS probe. (ii) The patient is neither immobilized nor under total anesthesia. Most patients move significantly during the biopsy procedure. (iii) Since the probe serves also to guide the rigidly attached needle, probe movements are important. Rotations around the principal probe axis of more than 180◦ and tilting of up to 40◦ are frequent. Also, the probe head wanders over the gland surface during needle placement, which leads to relative displacements of up to 3cm. The global search problem thus fully applies to prostate alignment: tracking a reference on a calibrated TRUS probe cannot solve the problem due to (i) and (ii), and it is not very success promising to minimize similarity measures on biopsy images using only fast down-hill optimizers because of (iii). In this study we propose a solution to the global search problem for TRUS prostate image tracking, which consists in a search space reduction using a probe movement model. We further identify an efficient intensitybased similarity measure for TRUS prostate images and describe a fast multi-resolution optimization framework. Finally, the robustness, accuracy, precision and performance of the method are evaluated on 237 prostate volumes from 14 patients.

2 Methods 2.1 A Framework for US Image-Based Tracking The purpose of a tracking system is to provide the transformation between an object in reference space and the same object in tracking space at a given moment. In the case of image-based tracking, the reference space is determined by the choice of a reference image to which all subsequently acquired images will be registered. In the case of 3D TRUS prostate biospies, it is convenient to acquire a 3D US volume as reference just some minutes before the intervention. Unfortunately, most currently available 3D US systems do not provide real-time access to volume data. They can, however, visualize two or three orthogonal 2D (o2D) slices inside the field of view of the probe in real-time. These slices can be captured using a frame-grabber and used for registration with a previously acquired reference volume [4, 5]. Note that compared to 2D US images, o2D planes deliver considerably more spatial information, which potentially makes 3D to o2D registration more robust than 3D to 2D registration. In this work we will evaluate both 3D to 3D and 3D to o2D registration for image-based tracking. Registration algorithms can be separated into two main classes: intensity-based and feature-based algorithms. As it is challenging to define robust and fast feature extraction algorithms for US images of the prostate, due to the low SNR of US images and the absence of clearly identifiable geometric features in the prostate, this study focuses on intensity-based approaches. Intensity-based measures are known for their robustness in presence of noise and partial image overlaps [1]. Image registration can be modeled as a minimization process of an image similarity measure that depends on a transformation T . There exist robust and fast algorithms for local minimization of image similarity measures. The condition for convergency to the target transformation Tˆ is that the optimizer starts from a point inside the capture range


29

of Tˆ [6]. However, the capture range of common intensity measures (e.g. the Pearson correlation coefficient (CC) or normalized mutual information (NMI)) is relatively small compared to the transformation space that can be observed for TRUS prostate biopsies. This problem can be attacked from two sides: the first approach is to extend the capture range by improving the similarity measure, while the second method consists in finding a point inside the capture range using a priori knowledge on the probe position. Several parts of the registration approach require information about the prostate location in the reference image. For our purpose it is sufficient to set an axis-aligned bounding box on the prostate boundaries in the reference image. The bounding box has to be defined by the clinician. No bounding box is needed for the tracking images. 2.2 Extending the Capture Range Similarity Measure: We chose CC as similarity measure since it yields a larger capture range than NMI for mono-modal US registration. Compared to sums of squared distances (SSD), it is insensitive to linear intensity transformations and is capable of detecting inverse correlations. Intensity shifts can occur due to probe pressure variation, while inverse correlations can be observed when evaluating transformations far from the physical solution, in particular for gradient magnitude images. Multi-resolution pyramid: Optimizing on coarse resolution levels of a gaussian pyramid yields some important advantages: coarse levels are statistical aggregates of the original image which are free of high-frequency noise, in particular speckle noise. Once the optimization on the coarsest level is terminated, the solution will be refined on denser levels, but from a considerably better starting point. This approach not only improves the characteristics of the similarity measure by reducing noise, but also considerably speeds up registration time, as most of the optimization can be performed on low-resolution images. Attribute-vector approach: The capture range can be extended by combining measures of different aspects of the images to be compared [7, 8]. Since there is a strong probability that the similarity measure produces for every aspect a significant minimum near the correct solution, it is possible to amplify and widen the capture range of the solution by combining the measures. Also, it is less likely that noise-related local minima are produced at identical locations, which makes it possible to flatten them out in a combined measure. For this study we chose to evaluate the image intensity and its gradient magnitude (I and J are the images to be compared): EnIJ (T ) := (1 − CC(I, J ◦ T )) · (1 − CC(||∇I||, ||∇J ◦ T ||))

(1)

To improve performance and since gradient intensities are highly random on noisy highresolution images, attribute vectors are only used on low resolution levels of the image pyramid. Panorama images: The pyramid-like form of the US beam and the fact that the probe also serves to guide the biopsy needle makes it unavoidable that the gland is often only partially imaged. Hence at least the reference image should contain the entire prostate;

30

M. Baumann et al.

otherwise the similarity measure may yield random results when the image overlap gets too small during registration. We therefore acquire three partial prostate volumes using the following protocol: the operator first acquires one image where the prostate is centered in the US beam, and then takes two additional images with rotations of 60◦ around the principal axis of the probe. Care is taken to avoid deformation and US shadows. The panorama image resulting from compounding these acquisitions finally serves as reference. 2.3 Finding a Point in the Capture Range Mechanical probe movement model. To estimate large transformations between images, it is necessary to find a point inside the capture range of the similarity measure. Regular sampling of a 6-D rigid transformation space using a very sparse grid size of 10 already requires 106 function evaluations, which results in an unacceptable computational burden. The physical constraints exerted by the rectum on probe movements, and the fact that the probe head always remains in contact with the thin rectal wall at the prostate location lead to the following assumptions: 1) the probe head is always in contact with the prostate membrane, 2) the most important rotations occur around the principal axis of the probe, and 3) all other rotations have a rotation point that can be approximated by a unique fixed point F Prect in the rectum. With these assumptions it is possible to define a probe movement model based on a prostate surface approximation, the probe position in the US image (which is known) and a rotational fixed point in the rectum. As shown in Fig. 1(a), the prostate surface is approximated by a bounding-box aligned ellipsoid. The ellipsoid is modeled using a 2D polar parameterization P RSurf (α,β) . The origin P RSurf (0,0) of the parameterization corresponds to the intersection of the line from the prostate center CP ro to F PRect . As illustrated in Fig. 1(b), P RSurf (α,β) implements assumption 1) by determining plausible US transducer positions on the prostate surface. Assumption 3) is satisfied by requiring that the principal probe axis must always pass through F PRect . Finally, a rotation about the principal probe axis implements assumption 2) and thus adds a third DOF (See Fig. 1(c)).

(a)

(b)

(c)

Fig. 1. Mechanical probe movement model in 2D: (a) shows the computation of the search model surface origin P RSurf (0, 0) from the prostate center CP ro and the (hypothetical) rectal probe fixed point F PRect . In (b), a 2D polar parameterization is used to determine a surface point P RSurf (α, β). The probe is then rotated and translated such that its US origin OU S coincides with P RSurf (α, β). In (c), the probe is rotated around its principal axis by an angle λ.


31

Systematic Exploration. The 3D subspace defined by the probe movement model is systematically explored using equidistant steps. To minimize the computational burden, systematic exploration is performed on the coarsest resolution level. Since the exploration grid points do not change during an intervention, it is possible to precompute and to store all resclices of the panoramic image necessary for the evaluation of the intensity measure. The rotational space around the principal axis of the probe is unconstrained (360◦), while tilting ranges are limited to the maximum value determined on test data, plus a security margin. The number of steps per dimension are also experimentally determined. The five best results of the systematic exploration are stored with the constraint that all transformations respect a minimum distance between each other. If two results are too close, only the best one is stored. Next, a local search using the Powell-Brent algorithm is performed only on the coarsest pyramid level for each of the five results. The best result of the five local searches is finally used as the start point for a multi-level local optimization. The last level of the final search can be chosen in function of the desired precision and computation time. Note that compared to a single multi-level local search, five local optimizations on the coarsest level are negligible in terms of computation time.

3 Experiments and Results The presented method was validated on 237 3D images of the prostate acquired during biopsy of 14 different patients. The imaging device was a GE 3D US Voluson 730 equipped with a volume-swept transrectal probe (GE RIC5-9). All images, except the images used for panorama image creation, were acquired immediately after a biopsy shot. Both 3D to 3D and 3D to o2D registration were evaluated. All registrations were carried out in a post-processing step. The o2D images used in the tests were not framegrabbed but reconstructed from 3D images. The image resolution was 2003 . The voxel side lengths varied from 0.33mm to 0.47mm. A five-level resolution pyramid was used for 3D to 3D registration; for 3D to o2D only four levels were used. The final multilevel search was carried out from the coarsest to the third-finest level for 3D to 3D, and to the second-finest level for 3D to o2D registration. A total of 12960 grid points on the movement model were explored during a search run. Registration was carried out on a Pentium 4 with 3GHz. To measure reproducibility and registration success, 10 registrations were carried out for each volume pair from slightly perturbated start points by adding noise of 2mm and 2◦ . This yielded 10 transformations Ti that approximate the unknown rigid transformation between the prostate in both volumes. The average transformation T of the Ti was computed with the method presented in [9]. The euclidean distance error iE = ||Ti · C − T · C||, with C being the image center, and the angular error iA , which corresponds to the rotation angle of Ti−1 ·T , were used to compute the root mean square (r.m.s.) errors E and A . A registration was considered successful if E < 2.0mm and A < 5 degrees, and if the result T was visually satisfactory when superimposing both volumes in a composite image (See Fig. 2(c)). Reconstruction accuracy evaluation was more difficult to implement since there is no straight-forward gold standard. In some images, the needle trajectories from previous biopsies were still visible. In these cases, the trajectories were manually segmented, and

32

M. Baumann et al.

the angular error between corresponding needle trajectories were used to evaluate rotational accuracy. Also, some patients had significant and clearly visible calcifications inside the prostate. The distances between segmented calcifications were used to determine the translational accuracy. Tab. 1 and Fig. 2 show the results of the evaluations. Table 1. Test results: Numbers in brackets indicate the number of evaluated registrations

Registration success Average computation time Angular precision A (reproducibility, r.m.s.) Euclidean precision E (reproducibility, r.m.s.) Needle trajectory reconstruction (r.m.s.) Needle trajectory reconstruction (max) Calcification reconstruction (r.m.s.) Calcification reconstruction (max)

3D-3D

3D-o2D

96.7% (237) 6.5s (237) 1.75◦ (229) 0.62mm (229) 4.72◦ (10) 10.04◦ (10) 1.41mm (189) 3.84mm (189)

87.7% (237) 2.3s (237) 1.71◦ (208) 0.47mm (208) 4.74◦ (9) 10.5◦ (9) 1.37mm (181) 4.30mm (181)

The overhead introduced by the systematic model-based exploration accounts for about 25% of 3D-3D , and for 35% of 3D-o2D registration time. The five optimizations on the coarsest level account for about 10% in 3D-3D, and for 20% in 3D-o2D. Panorama image pre-processing and pre-computation of the images for systematic exploration are performed before the intervention and require about one minute of computation time.

(a)

(b)

(c)

(d)

Fig. 2. Registration accuracy: (a) shows the target image, and (b) the aligned panorama image. In (c) both volumes are superimposed to illustrate registration accuracy for the urethra (arrow), and (d) illustrates the registration accuracy in the upper gland.

4 Discussion This study presents a fast and robust rigid registration framework for TRUS prostate images in the context of unconstrained patient movements, of only anatomy-constrained probe movements and of probe-induced prostate displacements. The algorithm yields reproducible results and acceptable accuracy for both 3D-3D and 3D-o2D registration. The success-rate of 3D-3D registration is very satisfactory, since all failures were either due to significant US shadows caused by only partial contact of the probe head with the rectal wall or by air bubbles in the US contact gel, or to an insufficient US depth


33

with the result that parts of the gland membrane are not visible in the images. In these cases the similarity measure fails because of missing information in the image, and an algorithmic remedy probably does not exist. Additional failures can be observed for 3Do2D registration, in particular for very small prostates, for which the coronal plane does not contain any prostatic tissue. 3D-o2D registration is also more sensible to poor image quality (e.g. low contrast), to large deformations and to partial prostate images (for which often only one plane contains prostatic tissue). Note that the presented algorithm is not very sensible to bounding box placement precision. Computation time of local searches could be accelerated using the GPU for image reslicing (which corresponds to approximatively 95% of the computational burden of a similarity measure evaluation), while further optimization of the systematic exploration would require parallelization of the evaluations. The presented algorithm in particular accurately registers the prostate membranes that are distant to the probe head, and the urethra. The relatively high angular r.m.s. error observed in the needle reconstruction study can be explained with probe-related local deformations that are particularly strong at the needle entry point. We are currently working on a biomechanical gland deformation model that allows for estimation of deformations to improve the accuracy of tissue registration near the probe head. Acknowledgements. This work was supported by grants from the Agence Nationale de la Recherche (TecSan program, SMI project), from the French Ministry of Industry (ANRT agency), from the French Ministry of Health (PHRC program, Prostate-echo project) and from Koelis S.A.S., France. The clinical data were acquired at the urology department of the Pitié la Salpétrière hospital, Paris.

References 1. Zitova, B., Flusser, J.: Image registration methods: a survey. Image and Vision Computing 21, 977–1000 (2003) 2. Gu’eziec, A.P., Pennec, X., Ayache, N.: Medical image registration using geometric hashing. IEEE Comput. Sci. Eng. 4(4), 29–41 (1997) 3. Eadie, L.H., de Cunha, D., Davidson, R.B., Seifalian, A.M.: A real time pointer to a preoperative surgical planning index block of ultrasound images for image guided surgery. In: SPIE 2004, San Jose, California, USA, vol. 5295, pp. 14–23 (2004) 4. Sawada, A., Yoda, K., Kokubo, M., Kunieda, T., Nagata, Y., Hiraoka, M.: A technique for noninvasive respiratory gated radiation treatment based on a real time 3D ultrasound image correlation: A phantom study. Medical Physics 31(2), 245–250 (2004) 5. Huang, X., Hill, N.A., Ren, J., Guiraudon, G., Boughner, D.R., Peters, T.M.: Dynamic 3D ultrasound and MR image registration of the beating heart. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 171–178. Springer, Heidelberg (2005) 6. Shekhar, R., Zagrodsky, V.: Mutual information-based rigid and nonrigid registration of ultrasound volumes. IEEE Trans. Med. Imag. 21(1), 9–22 (2002) 7. Shen, D., Davatzikos, C.: Hammer: hierarchical attribute matching mechanism for elastic registration. IEEE Trans. Med. Imag. 21(11), 1421–1439 (2002) 8. Foroughi, P., Abolmaesumi, P.: Elastic registration of 3D ultrasound images. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 83–90. Springer, Heidelberg (2005) 9. Gramkow, C.: On averaging rotations. Journal of Mathematical Imaging and Vision 15, 7–16 (2001)

A Probabilistic Framework for Tracking Deformable Soft Tissue in Minimally Invasive Surgery Peter Mountney1,2, Benny Lo1,2, Surapa Thiemjarus1, Danail Stoyanov2, and Guang Zhong-Yang1,2 1

Department of Computing, Institute of Biomedical Engineering Imperial College, London SW7 2BZ, UK 2

Abstract. The use of vision based algorithms in minimally invasive surgery has attracted significant attention in recent years due to its potential in providing in situ 3D tissue deformation recovery for intra-operative surgical guidance and robotic navigation. Thus far, a large number of feature descriptors have been proposed in computer vision but direct application of these techniques to minimally invasive surgery has shown significant problems due to free-form tissue deformation and varying visual appearances of surgical scenes. This paper evaluates the current state-of-the-art feature descriptors in computer vision and outlines their respective performance issues when used for deformation tracking. A novel probabilistic framework for selecting the most discriminative descriptors is presented and a Bayesian fusion method is used to boost the accuracy and temporal persistency of soft-tissue deformation tracking. The performance of the proposed method is evaluated with both simulated data with known ground truth, as well as in vivo video sequences recorded from robotic assisted MIS procedures. Keywords: feature selection, descriptors, features, Minimally Invasive Surgery.

1 Introduction Minimally Invasive Surgery (MIS) represents one of the major advances in modern healthcare. This approach has a number of well known advantages for the patients including shorter hospitalization, reduced post-surgical trauma and morbidity. However, MIS procedures also have a number of limitations such as reduced instrument control, difficult hand-eye coordination and poor operating field localization. These impose significant demand on the surgeon and require extensive skills in manual dexterity and 3D visuomotor control. With the recent introduction of MIS surgical robots, dexterity is enhanced by microprocessor controlled mechanical wrists, allowing motion scaling for reducing gross hand movements and the performance of micro-scale tasks that are otherwise not possible. In order to perform MIS with improved precision and repeatability, intra-operative surgical guidance is essential for complex surgical tasks. In prostatectomy, for example, 3D visualization of the surrounding anatomy can result in improved neurovascular bundle preservation N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 34–41, 2007. © Springer-Verlag Berlin Heidelberg 2007

A Probabilistic Framework for Tracking Deformable Soft Tissue in MIS

35

and enhanced continence and potency rates. The effectiveness and clinical benefit of intra-operative guidance have been well recognized in neuro and orthopedic surgeries. Its application to cardiothoracic or gastrointestinal surgery, however, remains problematic as the complexity of tissue deformation imposes a significant challenge. The major difficulty involved is in the accurate reconstruction of dynamic deformation of the soft-tissue in vivo so that patient-specific preoperative/intraoperative data can be registered to the changing surgical field-of-views. This is also the prerequisite of providing augmented reality or advanced robotic control with dynamic active constraints and motion stabilization. Existing imaging modalities, such as intra-operative ultrasound, potentially offer detailed morphological information of the soft-tissue. However, there are recognised difficulties in integrating these imaging techniques for complex MIS procedures. Recent research has shown that it is more practical to rely on optical based techniques by using the existing laparoscopic camera to avoid further complication of the current MIS setup. It has been demonstrated that by introducing fiducial markers onto the exposed tissue surface, it is possible to obtain dynamic characteristics of the tissue in real-time [1]. Less invasive methods using optical flow and image derived features have also been attempted to infer tissue deformation [2]. These methods, however, impose strong geometrical constraints on the underlying tissue surface. They are generally not able to cater for large tissue deformation as experienced in cardiothoracic and gastrointestinal procedures. Existing research has shown that the major difficulty of using vision based techniques for inferring tissue deformation is in the accurate identification and tracking of surface features. They need to be robust to tissue deformation, specular highlights, and inter-reflecting lighting conditions. In computer vision, the issue of reliable feature tracking is a well researched topic for disparity analysis and depth reconstruction. Existing techniques, however, are mainly tailored for rigid man-made environments. Thus far, a large number of feature descriptors have been proposed and many of them are only invariant to perspective transformation due to camera motion [3]. Direct application of these techniques to MIS has shown significant problems due to free-form tissue deformation and contrastingly different visual appearances of changing surgical scenes. The purpose of this paper is to evaluate existing feature descriptors in computer vision and outline their respective performance issues when applied to MIS deformation tracking. A novel probabilistic framework for selecting the most discriminative descriptors is presented and a Bayesian fusion method is used to boost the accuracy and temporal persistency of soft-tissue deformation tracking. The performance of the proposed method is evaluated with both simulated data with known ground truth, as well as in vivo video sequences recorded from robotic assisted MIS procedures.

2 Methods 2.1 Feature Descriptors and Matching In computer vision, feature descriptors are successfully used in many applications in rigid man-made environments for robotic navigation, object recognition, video data mining and tracking. For tissue deformation tracking, however, the effectiveness of

36

P. Mountney et al.

existing techniques has not been studied in detail. To determine their respective quality for MIS, we evaluated a total of 21 descriptors, including seven different descriptors extended to work with color invariant space using techniques outlined in [4]. Color invariant descriptors are identified by a ‘C’ prefix. Subsequently, a machine learning method for inferring the most informative descriptors is proposed for Bayesian fusion. Table 1 provides a summary of all the descriptors used in this study. For clarity of terminology, we define a feature as a visual cue in an image. A detector is a low level feature extractor applied to all image pixels (such as edges and corners), whereas a descriptor provides a high level signature that describes the visual characteristics around a detected feature. Table 1. A summary of the feature descriptors evaluated in this study ID

Descriptor

SIFT, CSIFT[4]

Scale Invariant Feature Transform, robust to scale and rotation changes.

GLOH, CGLOH

Gradient Location Orientation Histogram, SIFT with log polar location grid.

SURF[5], CSURF

Speeded Up Robust Features, robust to scale and rotation changes.

Spin, CSpin

Spin images, a 2D histogram of pixel intensity measured by the distance from the centre of the feature.

MOM, CMOM

Moment invariants computed up to the 2nd order and 2nd degree.

CC, CCC

Cross correlation, a 9×9 uniform sample template of the smoothed feature.

SF, CSF

Steerable Filters, Gaussian derivatives are computed up to the 4th order.

DI, CDI

Differential Invariants, Gaussian derivatives are computed up to the 4th order.

GIH[6]

Geodesic-Intensity Histogram, A 2D surface embedded in 3D space is used to create a descriptor which is robust to deformation.

CCCI [7]

Color Constant Color Indexing, A color based descriptor invariant to illumination which uses histogram of color angle.

BR-CCCI

Sensitivity of CCCI to blur is reduced using the approach in[8].

CBOR [9]

Color Based Object Recognition, a similar approach to CCCI using alternative color angle

BR-CBOR

Sensitivity of CBOR to blur is reduced using the approach in[8].

For tissue deformation tracking and surface reconstruction, it is important to identify which features detected in an image sequence represent material correspondence. This process is known as matching and depending on the feature descriptor used, matching can be performed in different ways, e.g., using normalized cross-correlation over image regions or by measuring the Euclidean or Mahalanobis distance between descriptors. 2.2 Descriptor Selection and Descriptor Fusion With the availability of a set of possible descriptors, it is important to establish their respective discriminative power in representing salient visual features that are suitable for subsequent feature tracking. To this end, a BFFS algorithm is used. It is a machine


37

learning approach formulated as a filter algorithm for reducing the complexity of multiple descriptors while maintaining the overall inferencing accuracy. The advantage of this method is that the selection of descriptors is purely based on the data distribution, and thus is unbiased towards a specific model. The criteria for descriptor selection are based on the expected Area Under the Receiver Operating Characteristic (ROC) Curve (AUC), and therefore the selected descriptor yield the best classification performance in terms of the ROC curve or sensitivity and specificity for an ideal classifier. Under this framework, the expected AUC is interpreted as a metric which describes the intrinsic discriminability of the descriptors in classification. The basic principle of the algorithm is described in [13]. There are three major challenges related to the selection of the optimal set of descriptors: 1) the presence of irrelevant descriptors, 2) the presence of correlated or redundant descriptors and 3) the presence of descriptor interaction. Thus far, BFFS has been implemented using both forward and backward search strategies and it has been observed that the backward elimination suffers less from interaction [10,11,13]. In each step of the backward selection approach, a descriptor di which minimizes the objective function D (di ) will be eliminated from the descriptor set G (k ), resulting in a new set G − {d i }. To maximize the performance of the model, the standard BFFS prefers the descriptor set that maximizes the expected AUC. This is equivalent to discarding, at each step, the descriptor that contributes to the smallest change in the expected AUC. (k )

D (d i ) = E AUC (G (k ) ) − E AUC (G (k ) − {d i })

(1)

where G = {d j , 1 ≤ j ≤ n − k + 1} denotes the descriptor set at the beginning of the iteration k, and E AUC () () is a function which returns the expected AUC given by its parameter. Since the discriminability of the descriptor set before elimination E AUC (G (k ) ) is constant regardless of d i , omitting the term in general does not affect the ranking of the features. While irrelevant descriptors are uninformative, redundant descriptors are often useful despite the fact that their presence may not necessarily increase the expected AUC. With the evaluation function described in Eq. (1), irrelevant and redundant descriptors are treated in the same manner since both contribute little to the overall model performance. In order to discard irrelevant descriptors before removing redundant descriptors, the following objective function has been proposed: (k )

Dr (di ) = − (1 − ω1 ) × E AUC (G (k ) − {di }) + ω1 × E AUC (di )

(2)

where ω1 is the weighting factor ranging between 0 and 1. This function attempts to to maximise the discriminability of the selected descriptor set while minimizing the discriminability of the eliminated descriptors. Once the relevant descriptors are derived by using BFFS, a Naïve Bayesian Network (NBN) is used in this study to provide a probabilistic fusing of the selected descriptors. The result can subsequently be used for feature matching, where two features are classified as either matching or not matching by fusing the similarity measurements between descriptors to estimate the posterior probabilities. The NBN was trained on a subset of data with ground truth.

38

P. Mountney et al.

3 Experiments and Results To evaluate the proposed framework for feature descriptor selection, two MIS image sequences with large tissue deformation were used. The first shown in Fig. 1a-e is a simulated dataset with known ground truth, where tissue deformation is modeled by sequentially warping a textured 3D mesh using a Gaussian mixture model. The second sequence shown in Fig. 2a-d is an in vivo sequence from a laparoscopic cholecystectomy procedure, where the ground truth data is defined manually. Both sequences involve significant tissue deformation due to instrument-tissue interaction near the cystic duct. Low level features for these images were detected using the Difference of Gaussian (DoG) and the Maximally Stable Extremal Regions (MSER) detectors. Descriptor performance is quantitatively evaluated with respect to deformation using two metrics, sensitivity - the ratio of correctly matched features to the total number of corresponding features between two images and 1-specificity - the ratio of incorrectly matched features to the total number of non corresponding features. Results are presented in the form of ROC curves in Fig. 1 and Fig. 2. A good descriptor should be able to correctly identify matching features whilst having a minimum number of mismatches. Individual descriptors use a manually defined threshold on the Euclidean distance between descriptors to determine matching features. This threshold is varied to obtain the curves on the graphs. Our fusion approach has no manually defined threshold and is shown as a point on the graph. Ground truth data is acquired for quantitative analysis. On the simulated data, feature detection was performed on the first frame to provide an initial set of feature positions. These positions were identified on the 3D mesh enabling ground truth to be generated for subsequent images by projecting the deformed mesh positions back into the image plane. To acquire ground truth for in vivo data, feature detection was performed on each frame and corresponding features were matched manually. The AUC graph shown in Fig. 1 illustrates that by effective fusion of descriptor responses, the overall descriminability of the system is improved, which allows better matching of feature landmarks under large tissue deformation. The derived AUC curve (bottom left) indicates the ID of the top performing descriptors in a descending order. It is evident that after CGLOH, the addition of further feature descriptors does not provide additional performance enhancement to the combined feature descriptors. The ROC graph (bottom right) shows the performance of the fused descriptor when the top n descriptors are used (represented as Fn ). Ideal descriptors will have high sensitivity and low 1-specificity. It is evident from these graphs that descriptor fusion can obtain a higher level of sensitivity than that of individual descriptors for an acceptable specificity. This enables the fusion technique to match more features and remain robust. The best performing descriptor is Spin and its sensitivity is 11.96% less than the fusion method for the specificity achieved with fusion. To obtain the same level of sensitivity using only the Spin descriptor specificity has to be compromised resulting in a 19.16% increase and a drop in robustness of feature matching.


39

Fig. 1. (a-e) Example images showing the simulated data for evaluating the performance of different feature descriptors. The two graphs represent the AUC and the ROC (sensitivity vs. 1specificity) curves of the descriptors used. For clarity, only the six best performing descriptors are shown for the ROC graph.

Fig. 2. (a-d) Images form an in vivo laparoscopic cholecystectomy procedure showing instrument tissue interaction. The two graphs illustrate the AUC and the ROC (sensitivity vs. 1specificity) curves of the descriptors used. As in Fig. 1, only the six best performing descriptors are shown for the ROC graph for clarity.

For in vivo validation, a total of 40 matched ground truth features were used. Detailed analysis results are shown in Fig. 2. It is evident that by descriptor fusion, the discriminative power of feature description is enhanced. The fused method obtains a specificity of 0.235 which gives a 30.63% improvement in sensitivity over the best performing descriptor GIH at the given specificity. This demonstrates the fused descriptor is capable of matching considerably more features than any individual descriptor for deforming tissue. Detailed performance analysis has shown that for

40

P. Mountney et al.

MIS images, the best performing individual descriptors are Spin, SIFT, SURF, DIH and GLOH. Computing the descriptors in color invariant space has no apparent effect on discriminability but the process is more computationally intensive. By using the proposed Bayesian fusion method, however, we are able to reliably match significantly more features than by using individual descriptors. Fusion

Tissue deformation

SIFT

Tissue deformation

Fig. 3. 3D deformation tracking and depth reconstruction based on computational stereo by using the proposed descriptor fusion and SIFT methods for a robotic assisted lung lobectomy procedure. SIFT was identified by the BFFS as the most discriminative descriptor for this image sequence. Improved feature persistence is achieved by using the proposed fusion method, leading to improved 3D deformation recovery.

To further illustrate the practical value of the proposed framework, the fused descriptor was applied to 3D stereo deformation recovery for an in vivo stereoscopic sequence from a lung lobectomy procedure performed by using a daVinci® robot. The representative 3D reconstruction results by using the proposed matching scheme are shown in Fig. 3. Visual features as detected in the first video frame were matched across the entire image sequence for temporal deformation recovery. Features that were successfully tracked both in time and space were used for 3D depth reconstruction. The overlay of dense and sparse reconstructions with the proposed method indicates the persistence of features by using the descriptor fusion scheme. The robustness of the derived features in persistently matching through time is an important prerequisite of all vision-based 3D tissue deformation techniques. The results obtained in this study indicate the practical value of the proposed method in underpinning the development of accurate in vivo 3D deformation reconstruction techniques.


41

4 Discussion and Conclusions In conclusion, we have presented a method for systematic descriptor selection for MIS feature tracking and deformation recovery. Experimental results have shown that the proposed framework performed favorably as compared to the existing techniques and the method is capable of matching a greater number of features in the presence of large tissue deformation. To our knowledge, this paper represents the first comprehensive study of feature descriptors in MIS images. It represents an important step towards more effective use of visual cues in developing vision based deformation recovery techniques. This work has also highlighted the importance of adaptively selecting viable image characteristics that can cater for surgical scene variations.

Acknowledgments The authors would like to thank Adam James for acquiring in vivo data and Andrew Davison for constructive discussions.

References 1. Ginhoux, R., Gangloff, J.A., Mathelin, M.F.: Beating heart tracking in robotic surgery using 500 Hz visual servoing, model predictive control and an adaptive observer. In: Proc. ICRA, pp. 274–279 (2004) 2. Stoyanov, D., Mylonas, G.P., Deligianni, F., Darzi, A., Yang, G.Z.: Soft-tissue motion tracking and structure estimation for robotic assisted MIS procedures. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 139–146. Springer, Heidelberg (2005) 3. Mikolajczyk, K., Schmid, C.: A performance evaluation of local descriptors. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(10), 1615–1630 (2005) 4. Abdel-Hakim, A.E., Farag, A.A.: CSIFT: A SIFT Descriptor with Color Invariant Characteristics. In: Proc CVPR, pp. 1978–1983 (2006) 5. Bay, H., Tuytelaars, H., Van Gool, H.: SURF: Speeded Up Robust Features. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, Springer, Heidelberg (2006) 6. Ling, H., Jacobs, D.W.: Deformation invariant image matching. In: Proc. ICCV, pp. 1466– 1473 (2005) 7. Funt, B.V., Finlayson, G.D.: Color constant color indexing. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(5), 522–529 (1995) 8. van de Weijer, J., Schmid, C.: Blur Robust and Color Constant Image Description. In: Proc. ICIP, pp. 993–996 (2006) 9. Gevers, T., Smeulders, A.W.M.: Color Based Object Recognition. Pattern Recognition 32, 453–464 (1999) 10. Koller, D., Sahami, M.: Towards optimal feature selection. In: Proc. ICML, pp. 284–292 (1996) 11. Kohavi, R., John, G.H.: Wrappers for feature subset selection. Artificial Intelligence 97, 273–324 (1997) 12. Hu, X.P.: Feature selection and extraction of visual search strategies with eye tracking (2005) 13. Yang, G.Z., Hu, X.P.: Multi-Sensor Fusion. Body Sensor Networks, 239–286 (2006) 14. Thiemjarus, S., Lo, B.P.L., Laerhoven, K.V., Yang, G.Z.: Feature Selection for Wireless Sensor Networks. In: Proceedings of the 1st International Workshop on Wearable and Implantable Body Sensor Networks (2004)

Precision Targeting of Liver Lesions with a Needle-Based Soft Tissue Navigation System L. Maier-Hein1 , F. Pianka2 , A. Seitel1 , S.A. M¨ uller2 , A. Tekbas2 , M. Seitel1 , 1 2 I. Wolf , B.M. Schmied , and H.-P. Meinzer1 1

2

German Cancer Research Center, Div. Medical and Biological Informatics, Im Neuenheimer Feld 280, 69120 Heidelberg [email protected] University of Heidelberg, Dept. of General, Abdominal and Transplant Surgery Im Neuenheimer Feld 110, 69120 Heidelberg, Germany

Abstract. In this study, we assessed the targeting precision of a previously reported needle-based soft tissue navigation system. For this purpose, we implanted 10 2-ml agar nodules into three pig livers as tumor models, and two of the authors used the navigation system to target the center of gravity of each nodule. In order to obtain a realistic setting, we mounted the livers onto a respiratory liver motion simulator that models the human body. For each targeting procedure, we simulated the liver biopsy workflow, consisting of four steps: preparation, trajectory planning, registration, and navigation. The lesions were successfully hit in all 20 trials. The final distance between the applicator tip and the center of gravity of the lesion was determined from control computed tomography (CT) scans and was 3.5 ± 1.1 mm on average. Robust targeting precision of this order of magnitude would significantly improve the clinical treatment standard for various CT-guided minimally invasive interventions in the liver.

1

Introduction

Computer tomography (CT) guided minimally invasive procedures in the liver such as tumor biopsy and thermal ablation therapy frequently require the targeting of hepatic structures that are subject to breathing motion. Unfortunately, commercially available navigation systems are still restricted to applications for rigid structures, such as the skull and the spine. To allow application of existing navigation techniques to the liver, several research groups (e.g. [1,2,3,4,5,6,7]) are investigating methods for compensating organ motion during soft tissue interventions; however, a common approach for assessing the accuracy of the navigation systems developed in this context has not yet been established. Zhang et al. [5] implanted tumor models containing radio-opaque CT contrast medium into a silicon liver model mounted on

The present study was conducted within the setting of “Research training group 1126: Intelligent Surgery” funded by the German Research Foundation (DFG).


Precision Targeting of Liver Lesions

43

Fig. 1. Our soft tissue navigation concept. i) The navigation aids are inserted in the vicinity of the target. ii) A planning computed tomography (CT) scan is acquired. iii) The navigation aids are registered with the planning CT image, and the tracking coordinate system is registered with the CT coordinate system. iv) The navigation target point is chosen, and a trajectory is planned. v) A real-time deformation model is used to continuously estimate the position of the target point from the current positions of the optically tracked navigation aids, and a navigation display supports the targeting process accordingly.

a motion simulator and also conducted experiments in swine with agar injections as nodular targets. Kahn et al. [6] evaluated their navigation system in human cadavers, with three different targets: a predefined position within the ascending aorta, a calcified plaque in an artery, and the tip of a port catheter. Fichtinger et al. [8] conducted experiments in ventilated swine cadavers and used stainless-steel staples as targets. Several other studies were performed with rigid phantoms and did not incorporate organ shift or deformation (e.g. [3,4]). In a previous report [7], we introduced a needle-based navigation system for minimally invasive interventions in the liver, in which a real-time deformation model is used to estimate the position of a navigation target point continuously from a set of optically tracked navigation aids (Fig. 1). The accuracy of tracking, CT registration, and target position estimation throughout the breathing cycle have already been evaluated [7,9]. We have also investigated suitable visualization schemes to support soft tissue targeting procedures in cooperation with clinicians [10]. In this study, we assessed the overall targeting accuracy of the system and present a general workflow for evaluating the performance of a liver navigation system in a realistic setting.

2

Material and Methods

Our approach for assessing the targeting precision of our liver navigation system is based on simulation of the clinical liver biopsy workflow for porcine livers mounted onto a respiratory motion simulator. We used injected agar nodules as tumor models and determined the targeting error from control CT scans. The following sections describe the workflow in detail and present the experimental conditions used in this study.

44

L. Maier-Hein et al.

a)

b)

Fig. 2. Agar nodule in a porcine liver (a) and in a control CT image (b)

2.1

Workflow

Each targeting procedure comprises four steps: preparation, trajectory planning, registration, and navigation, as well as a post-processing procedure. While the preparation step is conducted only once for each liver, the trajectory must be planned separately for each lesion, and the remaining steps have to be repeated for each trial. The evaluation procedure was designed specifically for our navigation system but could readily be adapted for other navigation methods. The detailed workflow used for this study was as follows: 1. Preparation: We prepared each porcine liver according to the following procedure: (a) Based on the method proposed by Zhang et al. [5], a 5% agar dilution was prepared and mixed with contrast agent (1:15 v/v dilution). (b) Three to four agar nodules of volume 2 ml were then injected into the liver (Fig. 2a). In case of a spherical lesion, a volume of 2 ml corresponds to a diameter of approximately 1.5 cm. R plate) (c) The liver was sewn to the diaphragm model (i.e., the Plexiglas of the motion simulator introduced in [9] (Fig. 3). (d) Two 5 Degrees-of-Freedom (5DoF) navigation aids [7] were inserted into the liver (“diagonal arrangement”, Fig. 4b). (e) A planning CT scan of the motion simulator with the integrated porcine liver was acquired (Somatom Sensation 16 multidetector row scanner; Siemens, Erlangen, Germany). A fine resolution (0.75 mm slices) was necessary because our evaluation relies on accurate computation of the center of gravity of the agar nodule in both the planning CT and the control CT. (f) The motion simulator was used to simulate several breathing cycles (cranio-caudal displacement of the liver ≈ 15 mm [9]) reflecting the fact that the patients cannot hold their breaths between acquisition of the planning CT and registration.


45

Fig. 3. Schematic view of the respiratory liver motion simulator

2. Trajectory planning: For each lesion, we planned a trajectory in the CT image as follows: (a) The tumor was segmented semi-automatically on the basis of the graphcut algorithm [11]. (b) The navigation target point was set to the center of gravity of the segmented tumor. (c) An insertion point was chosen on the skin. 3. Registration: On the basis of the planned trajectory, we performed the initial registration: (a) The navigation aid models were registered with the planning CT image by the semi-automatic algorithm described in [9]. (b) The tracking coordinate system was registered with the CT coordinate system. For this purpose, we used the optical markers on the navigation aids as fiducials to compute a landmark-based rigid transformation as described in [7]. 4. Navigation: We used an optically tracked applicator to target a given agar nodule with the navigation system. The targeting procedure was conducted at end-expiration because it represents the natural state of the motion simulator (with the artificial lungs relaxed). As we performed gated experiments and only two navigation aids were utilized for motion compensation we chose a rigid deformation model [9]. A navigation monitor provided the visualization for the targeting process: (a) A two-dimensional projection view and a tool tip camera guided the user through the three steps tip positioning, needle alignment, and needle insertion as described in [10]. (b) Once the target was reached, the current position of the applicator was recorded. Then, the tool was released and its position was recorded again. The resulting tip “offset” was stored in image coordinates. This step was necessary because of the lack of tissue between the skin of the motion simulator (the foam) and the liver (Fig. 4b); once the applicator was released, the elastic skin relaxed and potentially pulled the tool several millimeters out of the liver.

46


a)

b)

Fig. 4. Navigation scenario: (a) Experimental setup for the targeting procedure, and (b) reconstructed three-dimensional view showing the liver (brown) with four injected agar nodules (yellow), the inserted applicator (green), the two navigation aids (blue R plate as diaphragm model (light blue), the artificial and turquoise), the Plexiglas skin (beige), the insertion point on the skin (white), and the target point (red)

5. Post-processing: The targeting accuracy was determined with a control CT: (a) A CT scan was acquired with the same settings as for the planning CT. (b) The tumor in the control CT image was segmented semi-automatically with the graph-cut algorithm [11]. (c) The navigation target point was set to the center of gravity of the segmented tumor as reference. (d) The applicator model was registered with the control CT image by the semi-automatic algorithm described in [7]. (e) The position of the applicator was corrected by the offset computed in the navigation step. (f) The distance between the computed target point and the (corrected) position of the applicator tip was recorded as the CT targeting error CT . 2.2

Experimental Conditions

In order to determine the overall targeting error of our navigation system, one technician (S1) and one fourth-year medical student (S2) conducted 20 targeting procedures in 10 tumor lesions following the workflow described above. Each participant simulated one biopsy from each lesion (Fig. 4a), and we recorded the following errors: – the fiducial registration error (FRE) which is the mean distance between the optical markers in image coordinates and the transformed optical markers originally located in tracking coordinates as described in [9]. – the virtual targeting error virtual , which is defined as the final distance between the applicator tip (given by the tracking system) and the estimated target point position (according to the deformation model). This error results


47

primarily from an inaccurate instrument insertion and depends crucially on the experience of the user. – the CT targeting error CT defined in section 2.1 (post-processing). It includes the registration error, the target position estimation error of the system, the tracking error, and the instrument insertion error. In addition, it is sensitive to changes in the applicator position between the instrument insertion step and the CT acquisition as discussed below.

3

Results

Our navigation system was successfully applied for simulating 20 liver biopsies according to the workflow described above. The applicator trajectory was generally non-parallel to the CT scanning plane, and the mean distance between the insertion point and the target point (±SD) was 11.6 ± 1.0 cm. Table 1. Virtual targeting error, virtual , and CT targeting error, CT , for participant S1, participant S2, and both participants (S1,S2) in mm. The mean error (μ), the standard deviation (σ), the root-mean-square (RMS ) error, the median error (median), and the maximum error (max ) for the entire set of lesions are listed. virtual (S1) virtual (S2) virtual (S1,S2) CT (S1) CT (S2) CT (S1,S2) μ±σ 0.5 ± 0.3 1.1 ± 1.1 0.8 ± 0.8 2.8 ± 0.6 4.1 ± 1.1 3.5 ± 1.1 0.6 1.5 1.1 2.9 4.3 3.6 RMS 0.4 0.7 0.6 3.0 4.2 3.3 median 1.3 4.0 4.0 3.8 5.4 5.4 max

The lesions were successfully hit in all trials with a mean fiducial registration error (±SD) of 0.6 ± 0.2 mm for computation of the coordinate transformation. The mean final distance CT μ (S1, S2) between the applicator tip and the center of gravity of the segmented agar nodule was 3.5 ± 1.1 mm averaged over all trials (Table 1). If we regard the first trial of subject S2 an outlier (virtual : 4.0 mm) and exclude it from consideration, the mean virtual targeting error was of the same order of magnitude for both participants (< 1 mm). The mean CT targeting error was, however, significantly larger for S2 (4.1±1.1 mm) than for S1 (2.8±0.6 mm). In addition, the virtual targeting error virtual estimated with our navigation system was generally significantly smaller than CT , averaging only 0.8±0.8 mm.

4

Discussion

We assessed the targeting precision of a novel soft tissue navigation system and obtained a mean error of 3.5 ± 1.1 mm. The proposed evaluation approach has three key features. First, we use agar nodules mixed with contrast agent as targets, as they are clearly distinguishable

48


from the surrounding liver tissue and can thus be segmented easily. In addition, they can be prepared such that they resemble real tumors in terms of shape and size. A second key feature is the utilization of the motion simulator as body model allowing us to model organ movement due to respiration, the most challenging problem in soft tissue interventions. Finally, the evaluation is performed in-vitro allowing us to perform experiments in moving organs, without recourse to animal experiments, which are time-consuming and expensive. To our knowledge, we are the first to combine in-vitro experiments with simulation of respiratory motion. The main drawback of our evaluation approach is the suboptimal fixation of the applicator in the body model. In our experience, small movements of the tool can occur relatively easily once it has been released, because it is held in position only by a layer of foam, several millimeters of (elastic) liver tissue and the relatively soft agar nodule itself (Fig. 4b). In other words, there is no assurance that the applicator will not shift further after the offset correction which potentially leads to inaccurate determination of the final applicator position and hence to an inaccurate error calculation. We consider that the large deviation between the and the CT targeting error CT can be attributed virtual targeting error virtual μ μ to this phenomenon. Similarly, we consider that the relatively large difference was due to inaccurate determinabetween the two observers with regard to CT μ tion of the applicator tip offset. The technician (S1), who was more experienced in use of the system, released the applicator very carefully after each targeting and calculated the offset correction only after ensuring that the applicator had assumed its final position and showed no more movement. We assume that the other participant (S2) conducted the process less carefully, causing a less accurate offset computation. In order to overcome these limitations, we propose use of a real biopsy needle as the applicator and marking of the final tip position with injected material. It is worth noting, that the navigation aids were better affixed within the tissue than the instrument because they were generally inserted considerably deeper into the liver (Fig. 4) and were less effected by the resilience of the foam. Since the same planning CT scan was used for all trials in one liver and the axes of the needles were nonparallel to each other, a shift of the navigation aids during one targeting procedure would have increased the registration error of the next trial. We obtained a very low FRE of only 0.6 mm on average, which suggests that the fixation of the navigations aids was sufficient. Moreover, the CT targeting error did not increase over time. To avoid problems related to this issue, however, we propose attaching the navigation aids to the skin. Despite the technical problems discussed above, our accuracy is higher than that published in related work. Zhang et al. [5] reported a success rate of 87.5% (n = 16) in a silicon liver mounted on a motion simulator and a median targeting error of 8.3 ± 3.7 mm (n = 32) in swine. Other groups obtained mean errors of 8.4 ± 1.8 mm (n = 42) in human cadavers [6] and 6.4 ± 1.8 (n = 22) in ventilated swine [8]. We evaluated the targeting precision of our needle-based soft tissue navigation system in-vitro and obtained a mean error of 3.5 ± 1.1 mm. Our clinical


49

colleagues have commented that a robust targeting precision of this order of magnitude would improve the treatment standard for CT-guided minimally invasive interventions in the liver dramatically. In order to advance clinical application of our navigation method, we are currently planning experiments in swine.

References 1. Schweikard, A., Glosser, G., Bodduluri, M., Murphy, M.J., Adler, J.R.: Robotic motion compensation for respiratory movement during radiosurgery. Comp. Aid. Surg. 5, 263–277 (2000) 2. Khamene, A., Warzelhan, J.K., Vogt, S., Elgort, D., Chefd’Hotel, C., Duerk, J.L., Lewin, J.S., Wacker, F.K., Sauer, F.: Characterization of internal organ motion using skin marker positions. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3217, pp. 526–533. Springer, Heidelberg (2004) 3. Nagel, M., Schmidt, G., Petzold, R., Kalender, W.A.: A navigation system for minimally invasive CT-guided interventions. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 33–40. Springer, Heidelberg (2005) 4. Nicolau, S., Garcia, A., Pennec, X., Soler, L., Ayache, N.: An augmented reality system to guide radio-frequency tumour ablation. Comput. Animat. Virt. W 16, 1–10 (2005) 5. Zhang, H., Banovac, F., Lin, R., Glossop, N., Wood, B.J., Lindisch, D., Levy, E., Cleary, K.: Electromagnetic tracking for abdominal interventions in computer aided surgery. Comp. Aid. Surg. 11(3), 127–136 (2006) 6. Khan, M.F., Dogan, S., Maataoui, A., Wesarg, S., Gurung, J., Ackermann, H., Schiemann, M., Wimmer-Greinecker, G., Vogl, T.J.: Navigation-based needle puncture of a cadaver using a hybrid tracking navigational system. Invest. Radiol. 41(10), 713–720 (2006) 7. Maier-Hein, L., Maleike, D., Neuhaus, J., Franz, A., Wolf, I., Meinzer, H.P.: Soft tissue navigation using needle-shaped markers: Evaluation of navigation aid tracking accuracy and CT registration. In: SPIE Medical Imaging 2007: Visualization, Image-Guided Procedures, and Display, vol. 6509, p. 650926 (2007) 8. Fichtinger, G., Deguet, A., Fischer, G., Iordachita, I., Balogh, E., Masamune, K., Taylor, R.H., Fayad, L.M., de Oliveira, M., Zinreich, S.J.: Image overlay for CTguided needle insertions. Comp. Aid. Surg. 10(4), 241–255 (2005) 9. Maier-Hein, L., M¨ uller, S.A., Pianka, F., M¨ uller-Stich, B.P., Gutt, C.N., Seitel, A., Rietdorf, U., Meinzer, H.P., Richter, G., Schmied, B.M., Wolf, I.: In-vitro evaluation of a novel needle-based soft tissue navigation system with a respiratory liver motion simulator. In: SPIE Medical Imaging 2007: Visualization, Image-Guided Procedures, and Display, vol. 6509, p. 650916 (2007) 10. Seitel, A., Maier-Hein, L., Schawo, S., Radeleff, B.A., Mueller, S.A., Pianka, F., Schmied, B.M., Wolf, I., Meinzer, H.P.: In-vitro evaluation of different visualization approaches for computer assisted targeting in soft tissue. In: CARS. Computer Assisted Radiology and Surgery (to appear, 2007) 11. Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE T Pattern Anal 26(9), 1124– 1137 (2004)

Dynamic MRI Scan Plane Control for Passive Tracking of Instruments and Devices S.P. DiMaio1 , E. Samset1,2 , G. Fischer3 , I. Iordachita3, G. Fichtinger3 , F. Jolesz1 , and C.M. Tempany1 1

Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA 2 Oslo University, Norway 3 Johns Hopkins University, Baltimore, MA, USA Abstract. This paper describes a novel image-based method for tracking robotic mechanisms and interventional devices during Magnetic Resonance Image (MRI)-guided procedures. It takes advantage of the multi-planar imaging capabilities of MRI to optimally image a set of localizing fiducials for passive motion tracking in the image coordinate frame. The imaging system is servoed to adaptively position the scan plane based on automatic detection and localization of fiducial artifacts directly from the acquired image stream. This closed-loop control system has been implemented using an open-source software framework and currently operates with GE MRI scanners. Accuracy and performance were evaluated in experiments, the results of which are presented here.

1

Introduction

Magnetic Resonance Imaging (MRI) is finding increased application for guiding clinical interventions, particularly percutaneous needle- and catheter-based procedures, due to its high soft-tissue contrast and multi-parametric imaging capabilities. In particular, applications of targeted ablation, biopsy and brachytherapy have been demonstrated for the management of breast and prostate cancer [1]. A variety of positioning devices and stereotactic templates have been developed for image-guided needle placement and efforts are currently underway to develop robotic assistants and focused ultrasound delivery systems for precise in-bore targeted therapy. Accurate calibration, tracking and navigation of such devices—as well as needles and catheters—are essential. This paper describes a novel image-based method for instrument tracking that makes use of the multi-planar imaging capabilities of MRI to dynamically servo the scan plane for optimal device localization and visualization1 . In prior work, device tracking in the MRI environment has been achieved using either active or passive markers. A variety of active tracking approaches have been presented in the past [2,3,4,5]. While typically fast and accurate, such methods can have drawbacks such as line-of-sight limitations, heating, sensitive 1

This publication was made possible by NIH grants R01-CA111288 and U41RR019703. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH.


Dynamic MRI Scan Plane Control

51

tuning, complex calibration and expense. A well known active approach tracks small receiver coils using the MRI scanner’s readout gradients aligned along the coordinate axes [3,4]. Krieger et al. discuss their use of such active tracking coils for navigating a robotic device in [6]. Passive tracking approaches, in which devices (e.g., needles, catheters, and robotic guidance mechanisms) are detected and tracked directly from the images, provide an alternative solution [7, 8, 6]. The advantages of an image-based passive tracking approach are that needles and devices do not require expensive instrumentation, and that both the interventional device and the patient’s anatomy are observed together in the same image space, thus eliminating a critical calibration step. There is, however, a compromise between imaging speed and quality that can degrade localization accuracy and reliability. In addition, MRI systems have been designed primarily for diagnostic imaging and are typically not equipped for closed-loop adaptive imaging that is often required for interventional navigation and guidance. Contemporary MRI hardware and software designs are optimised for sequential batch imaging prescriptions, which create awkward interventional workflows. As a result, most clinical MRI-guided procedures follow an iterative imaging approach in which the patient is moved in and out of the scanner for imaging and intervention (e.g., see [6] and references). In this work we demonstrate a general-purpose image-based approach for localizing devices in the bore of the magnet in order to enable simultaneous imaging and navigation for true image-guided intervention. This technology has been implemented using an open-source software framework and is currently available for use in GE MRI scanners. It is currently being used to develop a system for robot-assisted navigation of MRI-guided prostate biopsy and brachytherapy [9], as described in greater detail in our companion paper [10].

2

Methods

The concept of closed-loop scan-plane control for device localization is demonstrated here using a fiducial frame constructed from acrylic plastic, with seven embedded glass cylinders filled with MR-visible fluid (Beekley, Bristol, CT). Each of the seven cylinders forms a 3mm diameter, 60mm long MR-visible line fiducial, with the entire Z-frame arranged as shown in Figure 1. The position and orientation of the Z-frame can be computed from a single intersecting 2D image—based on the coordinates of the seven fiducial points observed in the image—as described in [11], where a similar fiducial frame was used in CT. The Z-frame was placed in an MRI scanner (GE Signa EXCITE 3T), on a rotating platform with marked angle gradations, initially aligned at the isocentre. A continuous real-time pulse sequence was used to image a crosssection of the frame (Fast Gradient Recalled Echo, TR=14.1ms, TE=5.7ms, flip angle=45◦, bandwidth=31.25kHz, matrix=256×256, NEX=1, FOV=16cm, slice thickness=2mm). The intersection points of the seven line fiducials—visible as seven bright disks (see Figure 1)—were automatically detected by a fast k-space template matching algorithm and used to compute the position and orientation

52

S.P. DiMaio et al.

of the Z-frame relative to the scan plane. The frame was then manually rotated on the platform, while a closed-loop control system continuously and automatically adjusted the position and orientation of the imaging plane to align with the centre of the fiducial frame. This is illustrated in the series of images shown in Figure 2.

Fig. 1. (a) The Z-frame with 7 MR-visible line fiducials. (b) A sample MR image of a cross section of the Z-frame.

Fig. 2. The imaging plane is adapted to automatically follow the motion of the fiducial frame in the scanner

System Architecture The software architecture for this system is shown in Figure 3. The MR scanner acquires 2D images continuously and transfers k-space data to a Raw Data Server that allows us to access image data in real-time. The raw data is passed through an Image Reconstruction algorithm (at present, the image reconstruction algorithm does not account for gradient warping) before being processed by


53

the Image Controller, which consists of algorithms for automatic fiducial detection, frame localization and scan plane control, as described below. The Image Controller passes images to a user interface for visualization and also closes the loop with the MRI scanner via the RSP Server, which provides the means to dynamically update pulse sequence parameters (RSPs), including those that determine scan plane position and orientation. Data interfaces between the tracking

Fig. 3. System architecture

application and the imaging system were developed using an extension of the OpenTracker framework [12] (these interfaces are indicated by “OT” annotations in Figure 3). This framework provides mechanisms for dynamic event passing between distributed computing systems over the MRI host’s TCP/IP network. The image visualization and graphical user interface was implemented using the Slicer Image Guided Navigator (SIGN), developed by Samset et al. [13]. Both OpenTracker and The SIGN are open-source software packages. Fiducial Detection and Localization The closed-loop fiducial detection and localization algorithm is detailed in the block diagram shown in Figure 4. Fiducials are detected by fast template matching (similar to that used in [7]), where the template mask m(u, v) is convolved with the latest MR image ii (u, v). In the spatial frequency domain (i.e., k-space) this corresponds to multiplication of M (ku , kv ) and Ii (ku , kv ), computed by Fast Fourier Transform of m and ii respectively. Fiducial matches are detected as local maxima in f (ku , kv ), with subpixel interpolation of peak coordinates (quadratic interpolation). The resulting fiducial pattern is validated against known geometric contraints of the Z-frame and the seven fiducial point matches are ordered as shown in Figure 1. The ordered set of fiducial point coordinates P are then used to compute the 6-DOF pose of the Z-frame with respect to the plane of image ii (for details of a closedform solution, see [11, 14]). Finally, the computed frame position/orientation is used to compute the new scan plane (i.e., for image ii+1 ) that passes through the centre of the Z-frame. Tracking accuracy and performance were measured in two sets of experiments: (a) tracking of freehand motion and (b) a calibrated accuracy study. Tracking of Freehand Motion The Z-frame was placed off-center on the rotating platform inside the scanner bore. With the closed loop tracking algorithm running, as shown in Figures 3

54

S.P. DiMaio et al.

and 4, the platform was manually rotated by approximately 10◦ increments from 0 − 70◦ . Accuracy Study In order to measure tracking accuracy, the Z-frame was fixed stationery within the scanner while varying the imaging position and orientation over three axes, namely x, z, and θ, as defined in Figure 1. For x- and z-axis displacements the images were aligned axially (i.e., with the x-axis in-plane and the zaxis normal to the imaging plane). In-plane motion (along the x-axis) was measured at approximately 1mm increments; out-of-plane motion (along the z-axis) was measured at approximately 2mm increments; rotational motion θ was measured at roughly 2◦ increments. For each axis, ten distinct positions/orientations were imaged, each ten times for a Fig. 4. Algorithm for detecting and localizing total of one hundred samthe fiducial frame ples per axis. For each sample, the known image position/orientation was compared against the estimated Z-frame position/orientation, computed with respect to the image. The position of the Zframe was initialized from an axial baseline image, such that all subsequent displacements were expressed with respect to this baseline.

3

Results

The closed-loop scan plane control system was able to follow continuous motion of the Z-frame, provided that it did not move out of the imaging plane or cause significant motion artifact during each 2-3s image acquisition period. Figure 5 shows the rotational motion component (θ) measured during the freehand motion experiment. Tracking performance was noticeably degraded for angles greater than 40 − 50◦ .


55

Fig. 5. Dynamically controlled image plane orientation θ during freehand manipulation of the Z-frame. Closed-loop imaging does not currently include GradWarp correction.

Results of the accuracy study are shown in Figure 6. The detection of inplane motion (along the x-axis) and rotational motion (θ) are shown in plots (a) and (b). In each case the scan plane postion/orientation and estimated displacement/rotation are superimposed. Error statistics are summarized in Table 1.

Fig. 6. Accuracy study results: (a) detection of out-of-plane motion along the z-axis, (b) detection of rotational motion about θ. GradWarp correction included, results summarized in Table 1. Table 1. Z-frame Localization Accuracy Axis In-plane (x) Out-of-plane (z) Rotation (θ)

Average Error Standard Deviation RMS Error Samples 0.017mm 0.026mm 0.031mm2 N = 100 0.089mm 0.11mm 0.14mm2 N = 100 ◦ ◦ 0.28 0.23 0.37◦ 2 N = 90

56

4

S.P. DiMaio et al.

Discussion and Conclusions

Experimental results demonstrate surprisingly good sub-millimeter and subdegree accuracy when tracking the Z-frame from a single 2D image. While it is not quantified in this study, localization accuracy depends upon the pixel size, field of view which in our experiments is image dimension = 0.625mm. Real-time tracking was noticeably degraded for large scan plane angles with respect to the axial plane, presumably due to the absence of gradient warp (GradWarp) correction. This limitation will be addressed in future work. The results of the accuracy study— listed in Table 1—were measured using a non-real-time pulse sequence in order to include GradWarp correction. This highlights one of the major challenges experienced in such research work, namely the absence of MRI pulse sequences and data flow mechanisms optimized for closed-loop interventional navigation. GE product pulse sequences were used without modification; however, custom interfaces were designed to interact with the raw data server and RSP modification mechanism, neither of which are supported GE products. The interfaces implemented in this work make use of open-source software architectures and are now publically available (http://www.ncigt.org/sign/download). At the time of publication, this interface is available only for GE MRI scanners; however, due to the modular architecture of its design, interface drivers for other imaging systems can be integrated without significantly affecting the overall control architecture. The OpenTracker interfaces shown in Figure 3 constitute a complete abstraction of hardware; therefore, this software framework can easily be adapted to MRI systems from other vendors. Plans are already underway for this extension. A localization approach that does not rely upon additional instrumentation, and that is intrinsically registered to the imaging coordinate frame is highly desirable for navigating instruments in MRI-guided interventions. This work demonstrates that it is possible to use passive fiducial detection in 3T MRI images for dynamically locating and navigating targeted interventional devices with sufficient accuracy. The approach is primarily feasible for tracking relatively slow motion, as is the case with most clinical robotic assistants. In such applications [10], we are able to control motion in order to synchronize with image-based localization and tracking. However, the approach is not yet suitable for tracking rapid motions, such as may be found in free-hand applications. We are working to accelerate the image update rate—thereby reducing the effect of motion artifact—by means of parallel imaging techniques. In future work, we will develop custom pulse sequences that are further optimized for real-time tracking of fiducials and needles, by taking advantage of parallel imaging methods. This will help to reduce the effect of motion artifact and to increase the field of view. In this work, we did not explore whether localization accuracy is consistent throughout the imaging field of view. This may be an issue when imaging fiducials relatively far from the iso-center of the magnet, and needs to be studied further. The fiducial frame will be reduced in size and integrated with a robotic needle driver for targeted MRI-guided needle biopsy and brachytherapy applications


57

[10]. The minimum size of the fiducial frame is governed by image resolution, signal-to-noise requirements, the maximum tolerable motion between imaging frames, and the number of degrees of freedom to be measured. For the application described in [10] the current fiducial frame design is conservative and will be made more compact. In addition, we are extending the approach for the tracking and visualization of needle artifacts [8]. Finally, new standards and open-interfaces for scanner control and adaptive real-time imaging are required to move MRI beyond its standing as a largely diagnostic imaging modality, in order to enable promising new interventional applications.

References 1. D’Amico, A.V., Tempany, C.M., Cormack, R., Hata, N., Jinzaki, M., Tuncali, K., Weinstein, M., Richie, J.P.: Transperineal magnetic resonance image guided prostate biopsy. Journal of Urology 164(2), 385–387 (2000) 2. Silverman, S.G., Collick, B.D., Figueira, M.R., Khorasani, R., Adams, D.F., Newman, R.W., Topulos, G.P., Jolesz, F.A.: Interactive MR-guided biopsy in an openconfiguration MR imaging system. Radiology 197(1), 175–181 (1995) 3. Dumoulin, C.L., Souza, S.P., Darrow, R.D.: Real-time position monitoring of invasive devices using magnetic resonance. Magnetic Resonance in Medicine 29, 411– 415 (1993) 4. Derbyshire, J.A., Wright, G.A., Henkelman, R.M., Hinks, R.S.: Dynamic scanplane tracking using MRI position monitoring. J. Mag. Res. Imag. 8(4), 924–932 (1998) 5. Hushek, S.G., Fetics, B., Moser, R.M., Hoerter, N.F., Russell, L.J., Roth, A., Polenur, D., Nevo, E.: Initial Clinical Experience with a Passive Electromagnetic 3D Locator System. In: 5t h Interventional MRI Symp., Boston MA, pp. 73–74 (2004) 6. Krieger, A., Fichtinger, G., Metzger, G., Atalar, E., Whitcomb, L.L.: A hybrid method for 6-dof tracking of mri-compatible robotic interventional devices. In: Proceedings of the IEEE Int. Conf. on Rob. and Auto., Florida, IEEE Computer Society Press, Los Alamitos (2006) 7. de Oliveira, A., Rauschenberg, J., Beyersdorff, D., Bock, W.S.M.: Automatic detection of passive marker systems using phase-only cross correlation. In: The 6th Interventional MRI Symposium, Leipzig, Germany (2006) 8. DiMaio, S., Kacher, D., Ellis, R., Fichtinger, G., Hata, N., Zientara, G., Panych, L., Kikinis, R., Jolesz, F.: Needle artifact localization in 3t mr images. In: Studies in Health Technologies and Informatics (MMVR), vol. 119, pp. 120–125 (2005) 9. DiMaio, S., Fischer, G., Haker, S., Hata, N., Iordachita, I., Tempany, C., Kikinis, R., Fichtinger, G.: A system for mri-guided prostate interventions. In: Int. Conf. on Biomed. Rob. and Biomechatronics, Pisa, Italy, IEEE/RAS-EMBS (2006) 10. Fischer, G., et al.: Development of a robotic assistant for needle-based transperineal prostate interventions in mri. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. LNCS, Springer, Heidelberg (2007) 11. Susil, R., Anderson, J., Taylor, R.: A single image registration method for ct-guided interventions. In: Taylor, C., Colchester, A. (eds.) MICCAI 1999. LNCS, vol. 1679, pp. 798–808. Springer, Heidelberg (1999)

58

S.P. DiMaio et al.

12. Reitmayr, G., Schmalstieg, D.: Opentracker-an open software architecture for reconfigurable tracking based on xml. In: IEEE Virtual Reality Conference, IEEE Computer Society Press, Los Alamitos (2001) 13. Samset, E., Hans, A., von Spiczak, J., DiMaio, S., Ellis, R., Hata, N., Jolesz, F.: The SIGN: A dynamic and extensible software framework for Image-Guided Therapy. In: Workshop on Open Source and Data for MICCAI, Insight-Journal (2006), http://hdl.handle.net/1926/207 14. Lee, S., Fichtinger, G., Chirikjian, G.S.: Numerical algorithms for spatial registration of line fiducials from cross-sectional images. Medical Physics 29(8), 1881–1891 (2002)

Design and Preliminary Accuracy Studies of an MRI-Guided Transrectal Prostate Intervention System Axel Krieger1 , Csaba Csoma1 , Iulian I. Iordachita1, Peter Guion2 , Anurag K. Singh2 , Gabor Fichtinger1 , and Louis L. Whitcomb1 1

Department of Mechanical Engineering, Johns Hopkins University, Baltimore 2 Radiation Oncology Branch, NCI - NIH-DHHS, Bethesda

Abstract. This paper reports a novel system for magnetic resonance imaging (MRI) guided transrectal prostate interventions, such as needle biopsy, fiducial marker placement, and therapy delivery. The system utilizes a hybrid tracking method, comprised of passive fiducial tracking for initial registration and subsequent incremental motion measurement along the degrees of freedom using fiber-optical encoders and mechanical scales. Targeting accuracy of the system is evaluated in prostate phantom experiments. Achieved targeting accuracy and procedure times were found to compare favorably with existing systems using passive and active tracking methods. Moreover, the portable design of the system using only standard MRI image sequences and minimal custom scanner interfacing allows the system to be easily used on different MRI scanners.

1

Introduction

Background and Motivation: Prostate cancer is the most common noncutaneous cancer in American men. For 2007, Jemal et al. [1] estimate 218,890 new cases of prostate cancer and 27,050 deaths caused by prostate cancer in the United States. The current standard of care for verifying the existence of prostate cancer is transrectal ultrasound (TRUS) guided biopsy. TRUS provides limited diagnostic accuracy and image resolution. In [2] the authors conclude that TRUS is not accurate for tumor localization and therefore the precise identification and sampling of individual cancerous tumor sites is limited. As a result, the sensitivity of TRUS biopsy is only between 60% and 85% [3,4]. Magnetic Resonance Imaging (MRI) with an endorectal coil affords images with higher anatomical resolution and contrast than can be obtained using TRUS [2]. Targeted biopsies of suspicious areas identified and guided by MRI could potentially increase the sensitivity of prostate biopsies. Moreover, once a lesion is confirmed as cancerous, MR-guided targeted treatment of the lesion with injections of therapeutic agents, cryoablation, or radio frequency (RF) ablation could be used.

The authors gratefully acknowledge support under grants NIH 1R01EB002963 and NSF EEC-9731748.


60

A. Krieger et al.

Previous Work in MRI Guided Prostate Interventions: MRI guided transperineal prostate biopsy has been demonstrated inside an open MRI scanner [5] and conventional closed configuration MRI scanner [6]. The transrectal approach is generally well tolerated by patients and is considered the standard approach for biopsies. The alternative, transperineal access, requires a longer needle path which may increase patient discomfort. It also generally requires the patient to be sedated for procedures. Beyersdorff et al. report a MRI guided transrectal needle biopsy system, which employs a passive fiducial marker sleeve coaxial with the biopsy needle [7]. In this system, the needle position is manually adjusted while the passive marker is imaged. This approach requires repeated volume imaging of high resolution that takes considerable time to acquire. An endorectal imaging coil can not be used with this system, which compromises the quality of the MR images. Krieger et. al. report a MRI compatible manipulator for transrectal needle biopsy, using an active tracking method comprised of three micro-tracking coils, rigidly attached to the end-effector of the manipulator providing real-time tracking [8]. The manipulator contains an endorectal imaging coil and uses two fixed angle needle channels for biopsies of distal and proximal parts of the prostate. However, Krieger et al. identified three disadvantages of this tracking method [9]: (a) The method requires custom scanner programming and interfacing which limits the portability to different scanners. (b) Each tracking coil occupies one receiving scanner channel, limiting the number of imaging coils that can be used simultaneously. (c) Frequent failures in the micro-coils and electrical circuit significantly degrade the reliability of the tracking method. In contrast to these approaches, we have developed a MR guided transrectal prostate interventional system, which employs (a) novel manipulator mechanics with a steerable needle channel in combination with an endorectal imaging coil, (b) a hybrid tracking method, with the goals of shortened procedure time and significantly simplified deployment of the system on different scanners, while achieving millimeter needle placement accuracy.

2

System Design

Manipulator Design: The needle manipulator assists the physician in inserting a needle to a predetermined target. A manual actuated design for the manipulator was chosen over an automated design, since the manual actuation reduces development time and approval time for clinical trials. There is a strong current need for an MRI-guided prostate intervention system as a research validation tool. In particular, MR spectroscopy (MRS) and dynamic contrast enhanced (DCE) MRI are two promising developing MR imaging modalities, whose capabilities in finding cancerous lesions in the prostate can be tested using this intervention system. Moreover, manual actuation for insertion of the needle is preferable to many physicians to obtain visual confirmation of the needle alignment before insertion and haptic feedback during the insertion of the needle. Automated insertion of the needle inside the MRI scanner could potentially allow for real-time visualization of the needle insertion and enable detection of

Design and Preliminary Accuracy Studies

61

Fig. 1. Left: Photograph of the MRI guided transrectal manipulator with the endorectal imaging coil placed in a prostate phantom. Biopsy gun, surface imaging coil and mounting arm are also visible. Right: Closeup photograph of the manipulator. Turning the knobs on the left rotate the endorectal sheath with hinge and needle channel and change the angle of the steerable needle channel respectively. An endorectal, single loop imaging coil is integrated into the sheath.

prostate deformation, misalignment, and deflection of the needle. However, the design for a fully automated manipulator for prostate biopsy would be further complicated by the fact that the tissue specimen has to be removed after each biopsy, which is hard to achieve automatically. In our design, the patient is pulled out of the MRI scanner on the scanner table for the physician to manually actuate the manipulator and insert the biopsy needle. Figure 1 on the left shows the manipulator with its endorectal imaging coil placed in a prostate phantom (CIRS Inc, Norfolk, VA). The position of the manipulator is secured using a mounting arm. The manipulator guides the needle tip of a standard MR compatible biopsy gun (Invivo Germany GmbH, Schwerin, Germany) to a predetermined target in the prostate. A surface imaging coil is placed under the phantom to enhance the MRI signal. Figure 1 on the right shows a close up photograph of the manipulator. The endorectal sheath is inserted in the rectum, such that the hinge is placed close to the anus of the patient. The endorectal sheath contains a single loop imaging coil, which is glued into a machined groove on the sheath. A steerable needle channel is integrated into the sheath. The three degrees of freedom (DOF) to reach a target in the prostate are rotation of the sheath, angulation change of the steerable needle channel, and insertion of the needle. Rotation of the sheath is achieved by turning the larger diameter knob on the left of the manipulator, which directly rotates the sheath with hinge and needle channel. An internal spring washer applies sufficient axial pre-load to avoid unintentional rotation of the sheath. The sheath can be rotated 360 degrees, thus allowing for a variety of patient positions including prone, supine and decubitus. This is further supported by the cone shape of the manipulator, which precludes obstructions for the biopsy gun at all rotational angles (except for the attachment to the mounting arm). In Figure 1, an outline of a prostate is sketched below the sheath, indicating prone positioning of the patient. Needle angle adjustment of the steerable needle channel is controlled by turning the smaller diameter knob on the left of the manipulator. Turning the knob causes an internal rod in the center of the

62

A. Krieger et al.

manipulator axis to be translated forward and backward via a two stage cumulative screw mechanism. The push rod is connected to the steerable needle channel, thus rotating the needle channel about the hinge axis and controlling the needle angle. A narrow slot on the bottom of the endorectal sheath allows the needle to exit the sheath at an angle between 17.5 and 40 degrees. The mounting arm consists of two parts: a slide and rail assembly (Igus Inc., E. Province, RI) for linear motion into and out of the scanner bore with an integrated locking mechanism and a custom designed passive arm. The passive arm is comprised of a rigid plastic rod connected with spherical joints to the slide and the manipulator respectively. A locking mechanism is built into the rod to simultaneously immobilize both joints, once the manipulator is placed at its desired location. The mounting arm is designed to be sufficiently strong and rigid to practically preclude deflection of the manipulator, thus allowing an initial registration of the manipulator position to hold during an interventional procedure. The endorectal sheath with the hinge and needle channel are cleaned and sterilized before every procedure. Medical grade heat shrink (Tyco Electronics Corporation, Menlo Park, CA) is fitted around the sheath to keep it cleaner during a procedure. A click-in mechanism, comprised of a flat spring and a small nylon ball provides fast and easy assembly of the sterilized parts to the manipulator prior to a procedure. The presence of a strong magnetic field inside an MRI scanner precludes the use of any ferromagnetic materials. Nonmagnetic metals can create imaging artifact, caused by a disturbance of the magnetic field due to difference in susceptibility of the metal and surrounding objects, and need to be minimized. The manipulator is constructed mostly of plastic materials, foremost of Ultem (GE Plastics, Pittsfield, MA), selected for its structural stability, machinability and low cost. The endorectal sheath is built out of medical grade Ultem, since it may contact patient tissue. Only very small nonmagnetic metallic components are placed closed to the field of view (FOV) of the prostate: a brass needle channel, a phosphor bronze flat spring for the click in mechanism of the sheath, and an aluminum hinge axle. Additional brass and aluminum parts located in the mounting arm are spaced sufficiently from the FOV. Imaging studies revealed that the device did not cause visual artifacts at the FOV. Hybrid Tracking Method: The hybrid tracking method is comprised of a combination of passive tracking and joint encoders - an approach similar to that reported in [9]. At the beginning of an interventional procedure, the initial position of the device in scanner coordinates is obtained by automatically segmenting fiducial markers placed on the device in MRI images. From this initial position motion of the device along its DOFs is encoded with fiber-optical and manual encoders. For initial registration, an attachment is placed concentrically over the needle channel of the manipulator (Figure 2, left). The attachment contains two tubular MRI markers (Beekley Corp., Bristol, CT). Two additional markers are placed into the main axis of the manipulator. Instead of acquiring axial image sets along the axes, which would take several minutes, a thin slab of 1 mm x 1 mm x 1 mm isotropic sagittal turbo spin echo (TSE) proton density images


63

Fig. 2. Left: Photograph of manipulator during initial registration. An attachment is placed concentrically over the needle channel. The tube contains two tubular markers. Two additional markers are placed into the main axis of the manipulator. Right: Example of two binary reformatted MR images axial to a fiducial marker. The segmentation algorithm finds the best fitting circle center indicated by a big cross on both images. The algorithm is able to find the center, even when air bubbles in the marker on the left contaminate the image. Small crosses indicate the border of the marker.

in the plane of the markers is obtained. This reduces the imaged volume significantly and therefore reduces scan time of this high resolution image set to 2.5 minutes. In order to aid automatic segmentation of the markers, the sagittal images are reformatted using a custom targeting program as axial images along the main axis of the device and along the needle axis. The tubular markers appear on the reformatted axial images as circles. An algorithm was written based on the Hough transformation, which finds on each binary reformatted image the best fitting center of a circle with known diameter of the marker (Figure 2, right). This segmentation is very robust even on images containing air bubbles in the marker. Once both axes are calculated from the circle centers using a least square minimization, the 6-DOF position of the manipulator is defined. Rotation and needle angle change are redundantly encoded by MRI-compatible fiber-optic encoders and mechanical scales placed on the actuation knobs of the manipulator. The needle insertion depth is read manually using the scale on the needle. Although not present in our current design, it is possible to incorporate a translational optical encoder for the needle insertion. The fiber optic joint encoders consist of photoelectric sensors (Banner Engineering Corp., Minneapolis, Minnesota) placed in a box in the control room, adjacent to the shielded MRI scanner room. Each sensor is connected to two plastic optical fibers: one for sending of optical signal, and one for reception of optical signal. Only the plastic optical fibers are passed into the scanner room. Full MR compatibility of the joint encoding is achieved, since no electrical signal or power cables are passed into the scanner room. The optical fiber ends of each sensor are placed opposing each other through a code wheel for encoding rotation of the manipulator and through a code strip for encoding translation of the push rod, and thus indirectly encoding needle angle change. A two channel quadrature design with a third channel as index pulse is used for both encoders. Each sensor provides one channel, so six sensors are necessary to build the two encoders. Encoder

64

A. Krieger et al.

resolution for rotation of the manipulator is 0.25 degrees, and for needle angle less than 0.1 degrees at all needle angles. In our present design the resolution of the encoders is limited by the size of the core diameter (0.25 mm) of the plastic fiber, since the light is not columnated before passing through the code wheel. Targeting Program: The targeting program runs on a laptop computer located in the control room. The only data transfer between laptop and scanner computer are DICOM image transfers. The fiber optic encoders interface via a USB counter (USDigital, Vancouver, Washington) to the laptop computer. The targeting software displays the acquired MR images, provides the automatic segmentation for the initial registration of the manipulator, allows the physician to select targets for needle placements, provides targeting parameters for the placement of the needle, and tracks rotation and needle angle change provided by the encoders, while the manipulator is moved on target.

3

Experiments, Results, and Discussion

The system for MRI guided transrectal prostate interventions was tested in a phantom experiment on a 3T Philips Intera MRI scanner (Philips Medical Systems, Best, NL) using standard MR compatible biopsy needles and non artifact producing glass needles. The experimental setup is shown in Figure 1. Biopsy Needle Accuracies: The manipulator was placed in a prostate phantom and its initial position was registered. Twelve targets were selected within all areas of the prostate, from base to mid gland to apex, on T2 weighted axial TSE images (Figure 3, first row). For each target, the targeting program calculated the necessary targeting parameters for the needle placement. Rotation, needle angle and insertion depth to reach the target were displayed on a window which was projected onto a screen located next to the scanner. The phantom was pulled out of the MRI scanner on the scanner table, the physician rotated the manipulator, adjusted the needle angle and inserted the biopsy needle according to the displayed parameters. Since the fiber optic cables of our present prototype were too short to reach all the way from the control room into the scanner, this experiment was performed without the use of optical encoders. Instead, solely the mechanical scales on the manipulator were used to encode the rotation and needle angle. Compared to the respective resolution of the optical encoders of 0.25 degrees and 0.1 degrees, the mechanical scales feature slightly lower resolutions of 1.0 degrees and 0.5 degrees. The phantom was rolled back into the scanner to confirm the location of the needle on axial TSE proton density images which show the void created by the biopsy needle tip close to the target point (Figure 3, second row). The in-plane error for each of the twelve biopsies, defined as the distance of the target to the biopsy needle line was subsequently calculated to assess the accuracy of the system. The needle line was defined by finding the first and the last slice of the acquired confirmation volume, where the needle void is clearly visible. The center of the needle void on the first slice and the center of the void on the last slice define the needle line. The out of


65

Fig. 3. Targeting images, biopsy needle confirmation images, glass needle confirmation images and in plane errors for twelve biopsies of a prostate phantom. First and fourth row: Two targets (cross hairs) per image are selected on axial TSE T2-weighted images. The dark cross hair represents the active target. Second and fifth row: The biopsy needle tip void is visualized in an axial TSE proton density image. The desired target approximately matches the actual position of the needle. Third and sixth row: The glass needle tip void is visualized in an axial TSE proton density image. The void for the glass needle is much smaller than for the biopsy needle and closer to the selected target. Numbers indicate the in-plane needle targeting error for the needle placement.

plane error is not critical in biopsy procedures due to the length of the biopsy core and was not calculated. Hence, from the purpose of accuracy, there is no need for a more precise motorized needle insertion. The average in-plane error for the biopsy needles was 2.1 mm with a maximum error of 2.9 mm. Glass Needle Accuracies: The void created by the biopsy needle is mostly due to susceptibility artifact caused by the metallic needle. The void is not concentric around the biopsy needle and depends on the orientation of the needle to the direction of the main magnetic field in the scanner (B0), and the direction of the spatially encoding magnetic field gradients [10]. Consequently, center of needle voids do not necessarily correspond to actual needle centers. And since the same imaging sequence and similar orientation of the needle is used for all targets in a procedure, a systematic shift between needle void and actual needle might occur, which introduces a bias in the accuracy calculations. To explore this theory, every biopsy needle placement in the prostate phantom was followed by a placement of a glass needle to the same depth. The void created by the glass needle is

66

A. Krieger et al.

purely caused by a lack of protons in the glass compared to the surrounding tissue, and is thus artifact free and concentric to the needle. The location of the glass needle was again confirmed by acquiring axial TSE proton density images (Figure 3, third row). The average in-plane error for the glass needles was 1.3 mm with a maximum error of 1.7 mm, compared to 2.1 mm and 2.9 mm for the biopsy needles, which is sufficient to target the minimal clinically significant foci size of 1/2 cc [11]. Analyzing the error reveals an average shift between glass needle void location and biopsy needle void location of only 0.1 mm in the L-R direction, but 0.9 mm in the A-P direction. This corresponds to the direction of the frequency encoding gradient of the TSE imaging sequence and is consistent with the findings of [10]. The procedure time for six needle biopsies not including the glass needle insertion was measured at 45 minutes. In summary, we reported the results of preliminary phantom experiments to evaluate the feasibility of performing prostate interventions with the proposed system. The phantom experiments show adequate coverage of the prostate gland and demonstrate accurate and fast needle targeting of the complete clinical target volume. The errors and procedure time compare favorably to reported results (average error 1.8 mm and average procedure times of 76 minutes) that Krieger et al. achieved with the active tracking method in initial clinical trials [4]. The hybrid tracking method allows this system to be used on any MRI scanner without extensive systems integration and calibration. The two connections required are connection of the endorectal imaging coil to a scanner receiver channel and the DICOM image transfer between scanner computer and laptop computer running the targeting program. The rigid construction of mounting arm and manipulator, optimized manipulator mechanics, and use of fast actuated biopsy guns suggest that reported phantom accuracies of the proposed system translate well to real anatomical accuracies in clinical studies. Institutional review board (IRB) approvals were granted at two clinical sites. Initial clinical results will be reported at the conference.

References 1. Jemal, A., Siegel, R., Ward, E., Murray, T., Xu, J., Thun, M.J.: Cancer statistics, 2007. CA Cancer J. Clin. 57(1), 43–66 (2007) 2. Yu, K.K., Hricak, H.: Imaging prostate cancer. Radiol. Clin. North. Am. 38(1), 59–85 (2000) 3. Norberg, M., Egevad, L., Holmberg, L., Sparén, P., Norlén, B.J., Busch, C.: The sextant protocol for ultrasound-guided core biopsies of the prostate underestimates the presence of cancer. Urology 50(4), 562–566 (1997) 4. Terris, M.K.: Sensitivity and specificity of sextant biopsies in the detection of prostate cancer: preliminary report. Urology 54(3), 486–489 (1999) 5. Hata, N., Jinzaki, M., Kacher, D., Cormak, R., Gering, D., Nabavi, A., Silverman, S.G., D’Amico, A.V., Kikinis, R., Jolesz, F.A., Tempany, C.M.: Mr imaging-guided prostate biopsy with surgical navigation software: device validation and feasibility. Radiology 220(1), 263–268 (2001)


67

6. Susil, R.C., Camphausen, K., Choyke, P., McVeigh, E.R., Gustafson, G.S., Ning, H., Miller, R.W., Atalar, E., Coleman, C.N., Ménard, C.: System for prostate brachytherapy and biopsy in a standard 1.5 t mri scanner. Magn. Reson. Med. 52(3), 683–687 (2004) 7. Beyersdorff, D., Winkel, A., Hamm, B., Lenk, S., Loening, S.A., Taupitz, M.: Mr imaging-guided prostate biopsy with a closed mr unit at 1.5 t: initial results. Radiology 234(2), 576–581 (2005) 8. Krieger, A., Susil, R.C., Menard, C., Coleman, J.A., Fichtinger, G., Atalar, E., Whitcomb, L.L.: Design of a novel MRI compatible manipulator for image guided prostate interventions. IEEE Transactions on Biomedical Engineering 52(2), 306– 313 (2005) 9. Krieger, A., Metzger, G., Fichtinger, G., Atalar, E., Whitcomb, L.L.: A hybrid method for 6-DOF tracking of MRI-compatible robotic interventional devices. In: Proceedings - IEEE International Conference on Robotics and Automation, Orlando, FL, United States, vol. 2006, pp. 3844–3849. IEEE Computer Society Press, Los Alamitos (2006) 10. DiMaio, S.P., Kacher, D.F., Ellis, R.E., Fichtinger, G., Hata, N., Zientara, G.P., Panych, L.P., Kikinis, R., Jolesz, F.A.: Needle artifact localization in 3t mr images. Stud. Health. Technol. Inform. 119, 120–125 (2006) 11. Bak, J.B., Landas, S.K., Haas, G.P.: Characterization of prostate cancer missed by sextant biopsy. Clin. Prostate. Cancer 2(2), 115–118 (2003)

Thoracoscopic Surgical Navigation System for Cancer Localization in Collapsed Lung Based on Estimation of Lung Deformation Masahiko Nakamoto1 , Naoki Aburaya1, Yoshinobu Sato1 , Kozo Konishi2 , Ichiro Yoshino2 , Makoto Hashizume2 , and Shinichi Tamura1 1

Division of Image Analysis, Graduate School of Medicine, Osaka University, Japan 2 Graduate School of Medical Sciences, Kyushu University, Japan

Abstract. We have developed a thoracoscopic surgical navigation system for lung cancer localization. In our system, the thoracic cage and mediastinum are localized using rigid registration between the intraoperatively digitized surface points and the preoperative CT surface model, and then the lung deformation field is estimated using nonrigid registration between the registered and digitized point datasets on the collapsed lung surface and the preoperative CT lung surface model to predict cancer locations. In this paper, improved methods on key components of the system are investigated to realize clinically acceptable usability and accuracy. Firstly, we implement a non-contact surface digitizer under thoracoscopic control using an optically tracked laser pointer. Secondly, we establish a rigid registration protocol which minimizes the influence of the deformation in different patient’s positions by analyzing MR images of volunteers. These techniques were evaluated by in vitro and clinical experiments.

1

Introduction

The detection ratio of early small lung cancers has been improved by CT screening, and then resection of the small cancers by thoracoscopic surgery has recently become common as a minimally invasive technique. However, one problem is that localization of a small cancer often takes long time and sometimes even results in failure under thoracoscopic view. The lung is greatly deformed due to lung collapse by air suction to create a sufficient amount of workspace for surgical operation (Fig. 1). Thus the cancer position may change largely from its original position in a preoperative CT image. Furthermore, weak tactile feedback of surgical instruments makes the cancer localization difficult. Therefore, in order to narrow the extent of the existence possibility of a cancer in the collapsed lung, a system which predicts and indicates the cancer position during the surgery is highly desirable. To assist cancer localization, Shimada et al. developed a magnetic cancer tracking system [1]. In this system, a small magnetic marker is embedded near the tumor by CT-guided bronchoscopy just before the surgery, and then the N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 68–76, 2007. c Springer-Verlag Berlin Heidelberg 2007

Thoracoscopic Surgical Navigation System

69

Collapsed lung Visible surface

Workspace Cranial Mediastinum surface

Vertebral pleural surface Invisible surface of deeper anatomy Left Anterior

Fig. 1. Axial section of lung after collapse in the lateral position

Posterior

(a) Estimated lung shape (b) AR thoracoscopic imand cancer positions. age. Yellow circles: superimBlue points: actual po- posed cancers. sitions (gold standard). Red points: estimated positions. Fig. 2. Results of preliminary clinical experiment

tumor can be localized by tracking the embedded marker during the surgery. However, this approach requires an additional intervention procedure before the surgery. As an alternative approach that does not involve additional intervention, we have developed a surgical navigation system for cancer localization which estimates the collapsed lung deformation during the surgery [2]. In this system, the thoracic cage and mediastinum are localized using rigid registration between the digitized chest skin surface points and preoperative CT skin surface model, and then the lung deformation is estimated using nonrigid registration between the digitized and registered collapsed lung surface points and preoperative CT lung surface model. In our previous work [2], however, there are the following problems. (1) Physical contact of a long digitizing probe with the collapsed lung surface was necessary to acquire the 3D surface position data of the lung surface. (2) Difference in the patient’s position (supine during CT scanning and lateral during the surgery) was not considered in the rigid registration to localize the thoracic cage and mediastinum during the surgery. The former problem may cause risk of damaging the lung as well as degradation of positional accuracy due to surface deformation at a contact point or slight bend of the long probe. The latter may cause significant localization errors for the thoracic cage and mediastinum during the surgery due to skin deformation in different patient’s positions, which will finally affect cancer localization accuracy. In this paper, we describe improved methods which address the above mentioned problems. In order to solve the problems, we aim at the followings.

70

M. Nakamoto et al.

(1) Implementation and test of a non-contact surface digitizer that is compatible with thoracoscopy. (2) Establishment of the rigid registration protocol which minimizes the influence of the different patient’s positions. Previous studies investigated the use of laser systems for non-contact organ surface digitizing [3][4][5]. However, a dedicated endoscope in which a laser pointer is embedded, as described in [3], is not widely used, and a laser-scanner used in [5] is incompatible with thoracoscopy. In contrast, we combine a conventional laser pointer and thoracoscope both of which are tracked by an optical tracker so as to be widely available and compatible with thoracoscopy. To develop the rigid registration protocol, MR images of several volunteers in the supine and lateral positions are analyzed. The protocol is derived from the analysis results.

2 2.1

Methods System Overview

The thoracoscopic surgical navigation system consists of an optical 3D tracker (Polaris, Northern Digital Inc., Canada) , an oblique-viewing thoracoscope, a 3D position digitizer (i.e. stylus probe tracked by the optical 3D tracker) , a laser pointer (KOKUYO, IC-GREEN, Japan), and a PC (Xeon 3.0 GHz × 2, 2 GB memory). Optical markers are attached to the thoracoscope, 3D position digitizer, and laser pointer so that their position and orientation are measured by the optical tracker. We denote their position and orientation as Tscope , Tdigitizer and Tlaser , respectively. T is a 4 × 4 matrix representing rigid transformation defined by 3 × 3 rotation matrix R and translational 3D vector t. The oblique-viewing thoracoscope camera is calibrated by the method described in [6] beforehand. In this system [2], the thoracic cage and mediastinum are localized using ICP rigid registration between the digitized chest skin surface points and preoperative CT skin surface model, and then deformation field due to lung collapse is estimated by point-based nonrigid registration [7]. The preoperative CT image is deformed by the obtained deformation field, which is the continuous and smooth in the whole CT space, and then the collapsed lung shape and cancer position are estimated (Fig. 2(a)). The estimated cancer position is superimposed onto live thoracoscopic images, so that a surgeon can find a cancer from the neighborhood of the indicated position (Fig. 2(b)). In the preliminary clinical experiments, the estimation accuracy of the cancer positions were around 10 mm. The acquisition time of the digitized points was 5 minutes. Computation time for estimation of lung deformation was also 5 minutes.These results showed that potential usefulness of the system for narrowing the extent of the existence possibility of the cancer. Although the feasibility of our approach was confirmed, we also have found that accuracy was sometimes unstable (for examples, 20 mm or more), and thus the problems described in the previous section were clarified. 2.2

Digitizing Surface Points by Laser Pointer

To realize non-contact surface digitizing, we employed a commercially available laser pointer. While scanning the target surface using the laser pointer by freehand,


71

Optical axis of laser

Laser point

Detected point

Noise Optical markers

(a) Laser pointer.

Epipolar line

(b) Original image.

(c) Detected point.

Fig. 3. Detection of laser point from thoracoscopic image

the laser points on the surface are imaged by thoracoscope. Thoracoscopic images, Tlaser , and Tscope are recorded simultaneously during scanning, and then image processing for 3D coordinates measurement described below is performed in real-time. Figure 3 shows the appearance of the laser pointer and an example of laser point detection. We employ a green laser to obtain high contrast between the laser point and the organ surface. To detect the laser point region in the thoracoscopic image, color space conversion is performed and then the candidate regions are detected by p-tile thresholding. The center of gravity of each region is calculated, and then the region that is closest to the epipolar line is selected as the laser point. The 3D line passing through the focal point and the detected point, lview , is written as lview = sTscope ((px − cx )/fx , (py − cy )/fy , 1.0)T + tscope , where s is an arbitrary scalar, and (px , py ) is position of the detected point. (cx , cy ) and (fx , fy ) are image center and focal length, respectively. The 3D line of the laser, llaser , is written as llaser = sRlaser vlaser + Tlaser qlaser , where vlaser and qlaser are respectively the direction and position defining the laser line relative to the attached optical markers, which are obtained during calibration stage. The 3D position of the laser point is defined as the intersection point of lview and llaser . 2.3

Rigid Registration of Preoperative CT Model

Rigidity evaluation due to patient’s position change using MR images of volunteers. While the visible surface of the collapsed lung is digitized during surgery using the laser pointing system, subsequent nonrigid registration will be unstable without positional information on the invisible surface of deeper anatomy (invisible surface) attached to the mediastinum and the thoracic cage around the vertebra (see Fig. 1). In our previous system [2], the invisible surface is localized using rigid registration between actual patient and preoperative skin surface model assuming rigid relation between the invisible and skin surfaces. However, patient’s position changes from supine position during preoperative CT scanning to lateral position during surgery, and then the rigidity between the invisible and skin surfaces may not be kept after the position change.

72

M. Nakamoto et al.

We analyzed MR images of 6 volunteers to evaluate the rigidity. MR images of the same subject taken in lateral and supine positions were registered using regions around vertebral column by supposing that the thoracic cage is rigid and stable around the vertebral column in spite of the position change. Figure 4 shows axial and coronal sections of the registered images. Although misalignment over the skin, diaphragm, and mediastinal surfaces were around 10 mm or more due to deformation, misalignment over a wide range of backside of the thoracic cage as well as around the vertebral column (i.e. region enclosed with rectangle in Fig. 4(a)) was around 2 mm. As a result of observation of 6 subjects, the following findings were obtained: (1) A wide range of backside of the thoracic cage kept the rigidity with the invisible surface around the vertebral column (Hereafter, we call it the vertebral pleural surface). (2) The chest skin largely deformed due to the position change and did not keep rigidity with the invisible surface. (3) The median line on the sternum largely moved due to the position change but it was only along posterior-anterior direction in the median plane. Chest skin

Mediastinal surface Median lines Mediastinal surface

Median plane

Vertebral pleural surface

(a) Axial section.

Diaphragm

(b) Coronal section.

Fig. 4. Deformation caused by position change. Green: lateral position. Red: supine position.

Proposed registration protocol. Based on the findings described above, we derive the following rigid registration protocol. (1) Points on backside of the thoracic cage, which are intraoperatively acquired using the laser pointing system under thoracoscope, are registered to the preoperative CT lung surface. (2) Points on the skin along the median line, which are acquired using a 3D position digitizer, are registered to the preoperative CT median plane. Surface model of the thoracic cage Stc and the median plane Smp are reconstructed from patient’s CT image. The points on the skin along the median line {qi } were acquired and then digitized surface points on the thoracic cage {pi } were acquired after collapse under thoracoscope. ICP algorithm is performed by minimizing the following cost function:


E(Trigid ) =

M

|d(Stc , Trigid pi )| +

i=1

2

N

|d(Smp , Trigid qj )|2 ,

73

(1)

j=1

where Trigid is a rigid transformation from the patient space to the CT space. d(S, p) is a function representing the closest distance between a surface S and a 3D position p. Using estimated Trigid , the vertebral pleural surface is located.

3 3.1

Experimental Results Evaluation of Laser Surface Digitizing

Laboratory experiments. We compared accuracy of digitized surface points by the laser pointer with that by the conventional digitizing probe. The phantom was fixed in the training box, and then its surface points were acquired by the laser pointer and digitizing probe through a trocar under thoracoscopic control. The error was defined as an average distance between the digitized surface points and the gold standard surface. The gold standard surface was determined by ICP registration between densely acquired surface points and the surface model reconstructed from CT images of the phantom. The errors of the laser and probe digitizing were 3.6 ± 1.4 mm and 4.6 ± 2.0 mm, respectively, and thus the laser pointer was more accurate than the probe. Clinical experiments. We tested the laser pointing surface digitizer under thoracoscopic control for a real patient according to the IRB approved protocol. The conventional long probe were also employed to compare with the laser pointing digitizer. Using the non-contact digitizer, 90 points were acquired from 136 measurements. 21 measurements were failed to detect the laser points, and 15 measurements were rejected due to small parallax (less than 20 degrees) between the optical axis of the laser and the line of sight to the laser point. Average parallax was 34 degrees and acquisition time was around 4 minutes. Using the long probe, 53 points were acquired and acquisition time was around 3 minutes. Figure 5 shows distribution of acquired points. The extents of point datasets acquired by the two digitizers were comparable. 3.2

Simulation Experiments Using Volunteer MR Images to Validate Rigid Registration

The proposed rigid registration protocol was compared with intensity-based rigid registration and conventional ICP algorithm using the skin surface. The results of intensity-based method is regarded as ideal since rich information inside the body is available, which is unable to acquire without intraoperative MR or CT. Rigid registration of MR images between in the supine position at inspiration and in the lateral position at expiration was performed for six pairs of MR images by using the three protocols. Around 10 and 40 points were acquired from the median line and the backside of the thoracic cage, respectively. Registration error Ereg of estimated rigid transform Trigid was defined

74

M. Nakamoto et al.

14 12

Cranial

Error (mm)

10

Cranial

8 6 4 2

Anterior

Left

(a) Lateral view.

(b) Posterior-anterior view.

0

Intensity-based ICP (chest skin) method

ICP (proposed protocol)

Fig. 5. Results of clinical experiment for lung Fig. 6. Registration error of vertesurface digitizing. Red points: acquired by laser bral pleural surface pointer. Blue points: acquired by digitizing probe.

(a) Cranial-caudal view.

(c) Intensity-based.

(b) Lateral view.

(d) ICP (chest skin).

(e) ICP (proposed protocol).

Fig. 7. Results on accuracy evaluation for rigid registration. Blue and green points for rigid registration in the upper images are acquired from the median line and the backside of the thoracic cage, respectively. Lower images are axial sections of registered images in lateral position. Green: lateral position. Red: supine position.


75

as Ereg = 1/N N i=1 |d(S, Trigid qi )|, where {qi , i = 1, ..., N } is a point set acquired from the vertebral pleural surface in the lateral position, and S is the vertebral pleural surface in the supine position. As a result, the error of the proposed method was 2.3 ± 1.6 mm and it was comparable with the error of the intensity-based method (Fig. 6). The error of ICP algorithm using the skin was around 7 mm due to the large deformation caused by the position change. Figure 7 shows axial sections of the registered MR images. In the cases of the intensity-based and the proposed method, it was confirmed that misalignment on the vertebral pleural surface was sufficiently small.

4

Discussion and Conclusions

We have described improved methods for key components of our thoracoscopic surgical navigation system for cancer localization. We implemented a non-contact surface digitizer using a conventional laser pointer and thoracoscope. In the experiments, accuracy of the non-contact digitizer was better than that of the conventional long digitizing probe, and clinical feasibility was confirmed. As a result, the extent of measured points acquired by the non-contact digitizer was comparable to that of the conventional probe. According to the surgeon’s opinion, the non-contact digitizer was preferred since it allowed him to digitize lung surface without a special care for not damaging the lung by the conventional probe. We also established rigid registration protocol based on the evaluation using MR images of volunteers. In the simulation experiment, registration error of the proposed method was around 2 mm and it was comparable with that of the intensity-based method. Since the error of rigid registration affects accuracy of lung deformation estimation, the proposed method will improve overall accuracy of the system. Although evaluation of the system incorporating the non-contact digitizer and the proposed registration protocol currently have not been performed yet, improvements of the accuracy and usability of the system can be expected if they were employed. Future work includes validation study of the whole system incorporating the proposed methods and integration with biomechanical deformation model of the collapsed lung. Point datasets on the collapsed lung surface acquired by our techniques will utilized as constraints to estimate the biomechanical lung deformation. Our system can be used as a platform of the development and application of such biomechanical techniques.

References 1. Shimada, J., et al.: Intraoperative magnetic navigation system for thoracoscopic surgery and its application to partial resection of the pig lang. In: CARS 2004. Computer Assisted Radiology and Surgery: 18th International Congress and Exhibition, pp. 437–442 (2004) 2. Nakamoto, M., et al.: Estimation of intraoperative lung deformation for computer assisted thoracoscopic surgery. Int. J. Computer Assisted Radiology and Surgery 1(suppl. 1), 273–275 (2006)

76

M. Nakamoto et al.

3. Nakamura, Y., et al.: Laser-pointing endoscope system for natural 3D interface between robotic equipments and surgeons. Studies in health technology and informatics 81, 348–354 (2001) 4. Krupa, A., et al.: Autonomous 3-D positioning of surgical instruments in robotized laparoscopic surgery using visual servoing. IEEE Transactions on Robotics and Automation 19, 842–853 (2003) 5. Sinha, T.K., et al.: A method to track cortical surface deformations using a laser range scanner. IEEE Transactions on Medical Imaging 24, 767–781 (2005) 6. Yamaguchi, T., et al.: Development of camera model and calibration procedure for oblique-viewing endoscopes. Computer Aided Surgery 9, 203–214 (2004) 7. Chui, H., et al.: A unified non-rigid feature registration method for brain mapping. Medical Image Analysis 7, 113–130 (2003)

Clinical Evaluation of a Respiratory Gated Guidance System for Liver Punctures S.A. Nicolau1 , X. Pennec2 , L. Soler1 , and N. Ayache2 1

2

IRCAD-Hopital Civil, Virtual-surg, 1 Place de l’Hopital, 67091 Strasbourg Cedex {stephane.nicolau, luc.soler}@ircad.u-strasbg.fr INRIA Sophia, Epidaure, 2004 Rte des Lucioles, F-06902 Sophia-Antipolis Cedex

Abstract. We have previously proposed a computer guidance system for liver punctures designed for intubated (free breathing) patients. The lack of accuracy reported (1 cm) was mostly due to the breathing motion that was not taken into account. In this paper we modify our system to synchronise the guidance information on the expiratory phases of the patient and present an evaluation on 6 patients of our respiratory gated system. Firstly, we show how a specific choice of patient allows us to rigorously and passively evaluate the system accuracy. Secondly, we demonstrate that our system can provide a guidance information with an error below 5 mm during expiratory phases.

1

Introduction

CT/IRM guided liver puncture is a difficult gesture which can dramatically benefit from a computer guidance system [3,14,10,5]. Indeed, such systems can reduce the repetitive CT/MRI images needed for needle adjustment and the reinsertion attempts that lengthen the intervention duration and increase radiation exposure (when CT-guided). Moreover, it can improve the insertion accuracy that currently depends on the practitioner’s experience. In a previous work [9], we have introduced in the operating room a guiding system for radio-frequency thermal ablation (RFA) and showed that this system meets the sterility and cumbersomeness requirements. Then, the system accuracy was evaluated on patients with a passive protocol neglecting the breathing influence. The accuracy results around 1 cm were much larger that those obtained on a phantom (2 mm) [8](Wacker et. al. obtained an equivalent result on a freely breathing pig [14]). Indeed, liver displacement reaches 1 cm during shallow breathing [1,16]. A recent report shows that RFA ablation has to be performed on tumors which diameter is between 1 and 3 cm [11]. Thus, our radiologists consider that a guidance system has to provide an accuracy above 5 mm to avoid destroying too much healthy cells when the needle tip is not perfectly centered in the tumor.Consequently, to provide useful guidance information to the practitioner, we cannot neglect the breathing deformations. Several approaches are possible to take the breathing into account. Firstly, we can use the predictive model of N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 77–85, 2007. c Springer-Verlag Berlin Heidelberg 2007

78

S.A. Nicolau et al.

organ positions with respect to the breathing proposed by [4]. Unfortunately, it is not accurate enough for our application (error of prediction above 5 mm for the liver). Secondly we can synchronize the guidance system on a particular point of the breathing cycle i.e. the preoperative image and the guidance information are respectively acquired and provided at the same point of the respiratory cycle. This approach is motivated by several studies that evaluate the repositioning error of the liver between 1 and 2 mm [1,16,2,12,15]. Therefore, the cumulated error of the system components ( 3 mm) and the repositioning error ( 2 mm) should remain below 5 mm. This reasonable assumption has still not been demonstrated neither on animals nor patients: validation has been only performed on cadavers [3] or on living pigs without taking breathing into account [14]. In this paper, we report an in vivo accuracy evaluation of our system with a respiratory gating technique. After a presentation of the system principles, we explain how the choice of specific patients allows us to develop a riskless protocol to evaluate rigorously the system accuracy. Finally, we present the experimental results obtained on 6 patients and demonstrate that the system accuracy fits the clinical requirements when the guidance information is provided during expiratory phases.

2

System Components

In our setup, two jointly calibrated cameras are viewing the patient lying on the CT-table who is under general anesthesia and ventilated (70% of RFA are performed under general anesthesia in our local hospital). Radio-opaque markers with a ring shape are stuck on his abdominal skin and a black dot is printed inside each marker. Then, a preoperative CT acquisition is performed during an expiratory phase, the markers are removed and a 3D model of the patient (including his skin, liver, tumors and markers) is automatically obtained from the CT image (cf. top left Fig. 1) [13]. Then, this patient model is rigidly registered in the camera frame using radio-opaque markers, their position being extracted in both CT and video images. The marker extraction and matching is performed automatically and the registration is performed by minimisation of the Extended Projective Point Criterion (EPPC) (algorithmic details are further explained and validated in [7,6]). The needle position is also tracked in real-time by the cameras so that we can display on a screen its relative position with respect to the patient model to guide the practitioner (cf. right Fig. 1). The guidance information is provided only during the expiratory phases. These phases are automatically detected by the system using the reprojection error of CT markers in the video images. Indeed, this error computed in real-time is roughly sinusoidal and minimal during the expiration. We remind here the four error sources when the system is used by the practitioner. Three of them are due to the system only: needle tracking, patient registration and organ repositioning. The last error source is the ability of the practitioner to follow the guiding information provided by the system (we call it guidance error).

Clinical Evaluation of a Respiratory Gated AR System for Liver Punctures

79

Fig. 1. Illustration of the system principles

3

A Safe Evaluation Protocol with Specific Patients

Hepatic tumors sometimes need contrast agent to be injected in the patient to be visible in the CT modality. For these patients, the clinical protocol to target tumors in interventional CT is slightly different from the standard one. A preoperative CT acquisition of the abdomen is realized with contrast agent. To guide the needle, the practitioner performs a mental registration of interventional CT slices with the preoperative CT image (in which tumors are visible). When he thinks the needle is correctly positioned, a second CT acquisition with contrast agent of the patient abdomen is performed. This second CT acquisition allows the practitioner to check the needle position with respect to the tumor he targeted. The additional images available for these patients allow us to perform a passive evaluation of our system using the following data acquisition protocol: Experimental protocol Firstly, we stick homogeneously radio-opaque markers on the patient abdomen and a black dot is printed inside them. Then, a preoperative acquisition CT1 is realized in full expiration (it includes all the markers and the liver). The practitioner removes the markers and attaches to the needle a sterile pattern that allows its tracking. Then, he inserts the needle until he thinks he has correctly targeted the tumor. After the needle positioning, a stereoscopic video of the patient abdomen and needle is done during several breathing cycles. Finally, a second CT acquisition CT2 is done in full expiration, the needle remaining inside the patient (CT2 also includes the whole liver). This protocol does not change the information used by the practitioner to guide the needle: he realizes the intervention with his usual means (CT-slices) without any advice nor instruction from our system. From the acquired experimental data, we can not only evaluate the system accuracy but also check that the needle remains straight during the insertion and that the repositioning error of abdominal structures at expiratory phases is negligible. To perform these three studies, we realize the three following evaluation processes: Evaluation of the liver repositioning error (cf. Fig. 2) We extract the spine, liver and skin in both CT1 and CT2. Then, the spine from CT2 is rigidly registered on the spine in CT1 with the Iterative Closest Point

80

S.A. Nicolau et al.

algorithm and the computed transformation is applied to liver and skin from CT2. This registration allows us to compare the relative movement of liver and skin with respect to a common rigid structure. To quantify these movements, we compute the distance between the liver (resp. skin) surface in CT1 with the liver (resp. skin) surface extracted from CT2 and registered in CT1.

Fig. 2. To evaluate the repositioning error of liver and skin we firstly register the spines from CT1 and CT2. Then we apply the found rigid transformation to liver and skin surfaces and measure the distance between both surfaces. First half

Second half

Evaluation of the needle curvature (Fig. 3) alpha The needle in CT2 is extracted and we estimate Needle deflection orientations of the first and second half of its length. Then, we compare both orientations using the angular deviation α and the needle deFig. 3. Evaluation of the needle flection. curvature

Evaluation of the system accuracy (cf. Fig. 4) Liver and needle surfaces are extracted from CT2. The liver surface in CT2 is rigidly registered (using ICP) on the liver surface in CT1 and the computed transformation is applied to the needle extracted in CT2. This registration provides the final needle position in the CT1 image. Then, we register the patient model from CT1 (with the needle) in the camera reference frame using the video image of the patient at full expiration. Finally, we evaluate the euclidean distance between the needle tip tracked by the camera (at expiration phase) and the needle tip in CT1 registered in the camera frame. We call this distance system accuracy and emphasize it is an evaluation of the cumulated errors of the needle tracking, the patient model registration and the organ repositioning. It does not include the guidance error (defined in Sec. 2). Consequently, our experimental protocol allows us to evaluate all the error sources that only depend on the system and not on practitioner ability 1 . Alternatively, the measured error corresponds to the final system error if the needle insertion is robotized (in that case the guidance error is negligible). 1

In fact, we measure a slight over-estimation of the system error: the needle registration from CT2 to CT1 is not perfect (we check its high accuracy in Sec. 4).


81

Fig. 4. Illustration of the passive protocol to evaluate the system accuracy

4

Evaluation of the System on Six Clinical Cases

Six patients (5 males and 1 female, age between 50 and 60) have participated in our experiments (they signed an agreement form). They all had tumors the diagnosis of which led to a RF thermal ablation. Resolution of CT images was 1 × 1 × 2 mm3 . Below are presented the results obtained for the three experimental evaluations described in the previous section. Verification of the needle rigidity assumption. One can see in Tab. 1 that the needle deflection is not negligible in 30% of cases as it can reach 2.5 mm. Since the system assumes that the needle remains straight, the needle tip position provided by the system is systematically biased when there is an important deflection. Visual illustrations of a deflection are provided on Fig. 5. We are aware the practitioner sometimes bends the needle on purpose to avoid a critical structure. For all the reported cases, the practitioner estimated that this was Fig. 5. Lateral and not the case. Consequently, we have measured here the axial views of the needle (patient 2) uncontrollable bending of the needle. Table 1. Left table: Evaluation of the needle curvature after its positioning in the patient. Right table: Distance between the registered surfaces of spine, liver and skin.

Patient Patient Patient Patient Patient Patient

1 2 3 4 5 6

angular deviation needle alpha (o ) deflection (mm) 1.0 0.85 2.8 2.5 0.5 0.4 0.6 0.5 1.1 1.0 1.8 1.82

d(S1 ,S2 ) in mm Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6 Average

Spine 0.8 0.8 0.9 1.1 0.9 1.2 0.95

Liver 1.5 1.2 1.4 1.5 1.7 1.82 1.6

Skin 1.6 1.8 1.9 3.2 1.8 1.7 2.0

82

S.A. Nicolau et al.

Evaluation of the organ repositioning error. To quantify the distance between two registered surfaces S1 and S2 , we compute the average of the distance between each point on Si to the surface Sj : 2 2 Mi ∈S1 d(Mi , S2 ) + Pi ∈S2 d(Pi , S1 ) d(S1 , S2 ) = 2 · (card(S1 ) + card(S2 )) where the distance d(Mi , S) between a point Mi and a surface S is interpolated from the 3 closest points of Mi belonging to S. One can see in Tab. 1 (right) that the distance between liver surfaces is within 2 mm for each patient which is of the same magnitude as the segmentation uncertainty. To check that the measured distances are not due to a pure translation, we display the relative position of both surfaces. Fig. 6 (left columns) shows clearly that surfaces are closely interlaced for all patients. This means that the observed distance is essentially due to the segmentation error in the CT acquisitions and that the repositioning error of the liver is about 1 mm.

Fig. 6. Visual check of liver and skin repositioning errors on 3 patients (resp. left and right columns) . Two opposite views of registered surfaces are provided for each patient.

Oddly, distances between skin surfaces are not very low for each patient. A visual check (see right columns in Fig. 6) of registered surfaces shows that for these patients the skin of the lower part of the abdomen has moved between the two CT acquisitions. An inspection of both CT indicates that a gas movement in the stomach and bowels was responsible for this deformation. We highlight that this skin deformation highly disturbs the system if we take the radio-opaque markers on the deformed zone into account to compute the patient model registration. Indeed, the system implicitly assumes that the relative position of the liver w.r.t. the markers remains rigid during the intervention. Consequently, the skin deformation can lead to a wrong estimation of the liver position.


83

We notice that this phenomenon of gas movement essentially happened when the practitioner used the US probe. This means that the system should be carefully used if a US probe is manipulated. To avoid this problem, we can position the radio-opaque markers on the upper part of the abdomen only, which is a zone not influenced by gas movements. In the following we did not use radio-opaque markers on a deformed zone to evaluate the system accuracy. Influence of breathing on the system accuracy. During the 6 interventions, the needle and the patient were video tracked along several breathing cycles. In Tab. 2, one can read for each patient the system accuracy, the 3D/2D reprojection error of CT markers in the video images and the 3D/3D registration error between CT markers and markers reconstructed from video images. These values were averaged on expiratory phases that were video recorded. Additionally, we report in Fig. 7 a sample for patients 1 and 2 during 4 breathing cycles of the system accuracy, the 3D/2D and the 3D/3D registration errors.

Fig. 7. Sample of system accuracy and registration errors reported during several breathing cycles with patients 1 and 2

Results in Tab. 2 indicate clearly that for all patients the system accuracy during expiratory phases is between 4 and 5 mm. The two worst results have been obtained for patients whose abdominal zone has been deformed between the preoperative and control CT acquisitions. Indeed, in those cases, less markers could be used to compute the patient model registration. Note that including markers that had moved between the CT acquisitions in the registration computation leads to much worse accuracy (above 1 cm). For patients whose needle was bent, we have evaluated the system accuracy after having taken the observed curvature into account. This showed that if the rigidity assumption of the needle was true the system accuracy would be slightly better (about 0.5 mm). One can see in Fig.7 that RMS errors evolve cyclically, as expected, and are always minimal in expiration phases. The system accuracy also evolves cyclically but is not always minimal in expiration phases. Indeed, since the patient model registration is not perfect, the system can register the needle extracted from the CT at a position that corresponds to an intermediate phase of the breathing cycle (whereas it should be registered at expiratory position).

84

S.A. Nicolau et al.

Table 2. Average for each patient of the system error, 3D/2D and 3D/3D registration errors during expiration phases. The system provides an average guiding information during expiratory phases with an accuracy below 5 mm. Values in brackets correspond to the results obtained when the markers on an abdominal zone deformed by gas motion are used for the patient model registration. Values in square brackets correspond to the system accuracy re-evaluated after a compensation of the important needle curvature (only for patients 2 and 6).

Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6 Average

5

Number of RMS 3D/2D RMS 3D/3D System markers used (pixel) (mm) accuracy (mm) 15 1.3 1.5 4.0 13 1.0 1.7 4.2 [3.5] 6(15) 1.2 (2.2) 1.4 (2.5) 5.2 (14.5) 12 1.5 1.2 4.1 8(13) 0.9 (2.0) 1.5 (2.4) 4.8 (12.3) 14 1.2 1.2 4.3 [3.9] 11.5 1.18 1.44 4.3

Conclusion

We have developed a computer system to guide liver percutaneous punctures in interventional radiology. To tackle the breathing motion issue that induces a movement of the liver (above 1 cm), we propose to use a respiratory gating technique. We synchronize the preoperative CT acquisition and the guidance step with the expiratory phases of the patient. Then, we assume pseudo static conditions and rigidly register the patient model. To assess rigorously the system accuracy and the pseudo static assumption on real patients, we propose a passive protocol on carefully chosen patients that allows us to obtain a ground truth CT at the end of the needle insertion. Experimental results show firstly that the liver repositioning error is about 1 mm whereas it is sometimes much more important for the skin because of gas movement in the bowels. This phenomenon can dramatically decrease the system accuracy if markers on the deformed zone are used to compute the patient model registration. Therefore, to avoid this problem, markers have to be positioned only around the ribs. Secondly, we have evaluated that the needle curvature can cause a needle tracking error above 2 mm (although the practitioner thought it was not bent). Despite these uncertainties, we have finally showed that our system accuracy during the patient expiratory phases is about 4.5 mm, which fits the medical requirements. We investigate now the integration of an electromagnetic tracker in the current system so that we will be able to directly track the needle tip (although this is still a challenge due to ferromagnetic object presence in the operating room). Last but not least, a validation step including the needle manipulation by the practitioner is planned for next year.


85

References 1. Balter, J.M., et al.: Improvement of CT-based treatment-planning models of abdominals targets using static exhale imaging. IJROBP 41(4), 939–943 (1998) 2. Dawson, L., et al.: The reproducibility of organ position using active breathing control (ABC) during liver radiotherap. IJROBP 51, 1410–1421 (2001) 3. Fichtinger, G., et al.: Image overlay guidance for needle insertion in ct scanner. IEEE Transaction on Biomedical Engineering 52(8), 1415–1424 (2005) 4. Hostettler, A., Nicolau, S.A., Forest, C., Soler, L., Remond, Y.: Real time simulation of organ motions induced by breathing: First evaluation on patient data. In: Harders, M., Székely, G. (eds.) ISBMS 2006. LNCS, vol. 4072, pp. 9–18. Springer, Heidelberg (2006) 5. Mitschke, M., et al.: Interventions under video-augmented X-ray guidance: Application to needle placement. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) MICCAI 2000. LNCS, vol. 1935, pp. 858–868. Springer, Heidelberg (2000) 6. Nicolau, S., et al.: An augmented reality system to guide radio-frequency tumor ablation. Jour. of Computer Animation and Virtual World 16(1), 1–10 (2005) 7. Nicolau, S., Pennec, X., Soler, L., Ayache, N.: An accuracy certified augmented reality system for therapy guidance. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3023, pp. 79–91. Springer, Heidelberg (2004) 8. Nicolau, S., Schmid, J., Pennec, X., Soler, L., Ayache, N.: An augmented reality & virtuality interface for a puncture guidance system: Design and validation on an abdominal phantom. In: Yang, G.-Z., Jiang, T. (eds.) MIAR 2004. LNCS, vol. 3150, pp. 302–310. Springer, Heidelberg (2004) 9. Nicolau, S.A., Pennec, X., Soler, L., Ayache, N.: A complete augmented reality guidance system for liver punctures: First clinical evaluation. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 539–547. Springer, Heidelberg (2005) 10. Patriciu, A., et al.: Robotic assisted radio-frequency ablation of liver tumors:a randomized patient study. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 526–533. Springer, Heidelberg (2005) 11. Pereira, P.L.: Actual role of radiofrequency ablation of liver metastase. In: European Radiolology (February 15, 2007) 12. Remouchamps, V., et al.: Significant reductions in heart and lung doses using deep inspiration breath hold with active breathing control and intensity-modulated radiation therapy for patients treated with locoregional breast irradiation. IJROBP 55, 392–406 (2003) 13. Soler, L., et al.: Fully automatic anatomical, pathological, and functional segmentation from CT scans for hepatic surgery. Computer Aided Surgery 6(3) (2001) 14. Wacker, F., et al.: An augmented reality system for MR image-guided needle biopsy: Initial results in a swine model. Radiology 238(2), 497–504 (2006) 15. Wagman, R., et al.: Respiratory gating for liver tumors: use in dose escalation. Int. J. Radiation Oncology Biol. Phys. 55(3), 659–668 (2003) 16. Wong, J., et al.: The use of active breathing control (ABC) to reduce margin for breathing motion. Int. J. Radiation Oncology Biol. Phys. 44(4), 911–919 (1999)

Rapid Voxel Classification Methodology for Interactive 3D Medical Image Visualization Qi Zhang, Roy Eagleson, and Terry M. Peters Imaging Research Laboratories, Robarts Research Institute, Biomedical Engineering, University of Western Ontario, London, Ontario, N6A 5K8, Canada {qzhang, eagleson, tpeters}@imaging.robarts.ca Abstract. In many medical imaging scenarios, real-time high-quality anatomical data visualization and interaction is important to the physician for meaningful diagnosis 3D medical data and get timely feedback. Unfortunately, it is still difficult to achieve an optimized balance between real-time artifact-free medical image volume rendering and interactive data classification. In this paper, we present a new segment-based post color-attenuated classification algorithm to address this problem. In addition, we apply an efficient numerical integration computation technique and take advantage of the symmetric storage format of the color lookup table generation matrix. When implemented within our GPUbased volume raycasting system, the new classification technique is about 100 times faster than the unaccelerated pre-integrated classification approach, while achieving the similar or even superior quality volume rendered image. In addition, we propose an objective measure of artifacts in rendered medical image based on high-frequency spatial image content.

1

Introduction

The dramatically increased capabilities of computerized radiology equipment, such as CT or MRI, have made 3D and 4D (space and time) medical images ubiquitous in surgical planning, diagnosis and therapy. Direct volume rendering has proven to be an effective and flexible method for clinical dataset visualization [1]. However, in practice, the lack of an efficient strategy to map the scalar voxel value to the appropriate optical properties limits its wide applications in medicine [2]. The transfer function (TF) provides the mapping from scalar values to emitted radiant colors and extinction coefficients, thus rendering the scalar data visible and can isolate specific features in the rendered medical data. According to the sampling theorem, a continuous signal can be correctly reconstructed from its values at discrete sampling points with a sampling rate higher than the Nyquist frequency. The TF can either be applied directly to the discrete voxel points before the data interpolation step, or alternatively to the sampling points derived from the interpolation of the nearby voxel points, i.e., after the data interpolation. These processes are called pre- and post-classification respectively [3]. However, both algorithms introduce high spatial frequency artifacts N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 86–93, 2007. c Springer-Verlag Berlin Heidelberg 2007

Rapid Voxel Classification Methodology

0

1

sf

< < 1. So finally in (3), p(smi |Xm , θm ) is a constrained GMM, where p(smi |umj , vmj , σs ) is a constrained Gaussian: p(smi |umj , vmj , σs ) = s.t.

2.2

1 1

2π|Σmj | 2

1 −1 exp(− (smi − umj )T Σmj (smi − umj )) 2

min(eig(Σmj )) = σs , Σmj = f (vmj , σs ), and

σs2 ≤

1 vmj − umj 2 ≤ β · σs2 .(4) α

Priors

According to the generative model (1), p(Xm |Tm , X0 ) is a Gaussian distribution: p(Xm |Tm , X0 ) =

1 1 exp(− Xm − Tm (X0 )2 ). 2πσt 2σt

(5)

As to the transformations {Tm }, we assume them to be smooth, and we do not want any penalty on the rotation, translation and global shear, because we consider this is not the intrinsic variation of a shape. In this case the bending energy of Thin Plate Spline (TPS), Etps , can be utilized to construct the prior, as successfully applied in many previous works [6,9], by which the density function of Tm can be defined as p(Tm ) = Z1t exp(−λt Etps (Tm )). Then the total prior desnity function can be written as p(Xm , Tm , X0 ) =

1 exp −γ(Xm − Tm (X0 )2 + λEtps (Tm )) , Z

(6)

Shape Registration

813

where coefficient λ and γ are hyperparameters, and Z is a partition constant adopted to guarantee that p(Xm , X0 , Tm ) is a density function.

3

Optimization

The maximizing a posterior (MAP) problem is now formulated as: M

ˆ m }, {Tˆm }, X ˆ 0 ) = arg max ({θˆm }, {X

Nm

L

πmj pmj (smi |Xm , σs )p(Xm , Tm , X0 ).(7)

m=1 i=1 j=1

All the parameters, in both likelihood and prior items will be optimized together, or in other words, parameters for both representation and transformation models will be optimized simultaneously. Since the Gaussian mixture is involved, an EM algorithm is adopted for this task, where close-form solutions exist for πmj , {umj }, X0 and Tm , among which Tm is a regularized TPS [10]. There is no analytic solution for {vmi }, and they are optimized by gradient-based method in each maximization iteration. 3.1

Implementation

The proposed representation and transformation models both have a parameter that can naturally control how fine the models are, so we embed EM iteration in a coarse-to-fine scheme to achieve a more stable optimization. For representation model, it is σs , which represents the noise level of shape data that the constrained GMM can cope with; For deformation model it is λ, which controls how nonrigid Tm is. The implementation in this paper starts with great σsmax and λmax , then (k) gradually decrease them by certain ratios rσ and rλ respectively, until σs is (k) min less than σs . For each σs , the models are updated by the embedded EM algorithm, taking the result of previous step as the initial condition. (0) The very initial {Tm } are set to be identity transforms plus a translation between each shape centroid and their mean. This assumes that at the coarsest stage the representation of all shapes are the same except for a translation. The (0) initial {umj } are set to be evenly placed on a small circle around shape centroid. Besides, we set the initial covariance matrix of each Gaussian mixture to be isotropic, thus the equalprob of Gaussian becomes a circle, so as the possible (0) positions of vmj . Then we pick the rightmost point as vmj for all the mixture (k)

components. After first update, vmj will always be the ones resulted from EM (0)

algorithm and no selection is needed. The initial X0 is the mean of {Xm }. In all the experiments presented in this paper, λmax = Nm × M × σsmax , σsmax m is set to be the square of the size of the shape, and the final σsmin is set to be the mean square of distance between neighboring points. Ratio rσ and rλ are both (k) set to be 0.95. γ is difficult to decide and in this paper it is set to be 1/σs . For other parameters, α is not sensitive and α = 0.5; β decides how long the segments will be, and is the only parameter we adjust according to the data.

814

4 4.1

Y. Jiang et al.

Experimental Results Register 2D Shapes

We first demonstrate the registration results of SORT on 2D shapes with simple topologies. Typical landmark-sliding algorithms can also work on these shapes so a comparison can be conducted. SORT is compared with two of them. One is the MDL based algorithm implemented by Thodberg [8], and the other is arclength parameterization. In all experiments, Thodberg’s algorithm will run with 8 active nodes optimized over 40 passes, using 16, 32, or 64 landmarks (SORT will work with 8, 16 or 32 segments accordingly). In addition, a popular point cloud matching algorithm – Super Clustering-Matching (SCM) algorithm proposed by Chui [7], is also included for comparison. All algorithms are implemented using MATLAB 7.1, and run on an 1.66 GHz Intel Centrino CPU. Because our purpose for shape registration is to build shape models, we empoly the model generalization error [3] as the criterion for evaluation. In particular, the error adopted here is the fitting error between the original shape contour and the contour generated by the resultant model, which is more meaningful in practice than the distance error between landmarks points. To evaluate the results of SORT by this criterion, we take Xm = {(umj , vmj ), j = 1, . . . , L} as the “landmarks”, so the number of landmarks is twice the number of segments. Shape data under experiments include 9 synthetic bump boxes, 9 shapes of femur, and 9 silhouette profiles. All of them are obtained from Thodberg’s package [8] and widely tested in literatures. Fig. 2 shows the plain registration result for 9 bumpboxes and the variation of resulting shape model. The result is yielded by SORT using 8 segments. The equalprob ellipse of each segment is drawn on the shape (denoted by dense green dots), and the corresponding ones on different shapes have the same colors. The black and red dots on each segment denote {umj } and {vmj } respectively. The variation of resulting model shows that SORT has correctly captured the variation of bumpboxes. The registration process takes 37 seconds. The mean and standard deviation of shape generalization error for bumpboxes, are demonstrated in Fig. 3. They are compared with Thodberg’s algorithm, the

−2σ

2σ

mode 1

mode 2

mode 3

Fig. 2. Registration of 9 Bump boxes, using 8 segments. Left: Plain registration result; Right: the first three modes of variation.

Shape Registration 1.4

1.4

SORT Thod ARC SCM

1

0.8

Error

Error

1

0.6

0.2

0.2

0

2

4

6

8

0 −2

10

1

0.6

0.4

SORT Thod ARC SCM

1.2

0.8

0.4

0 −2

1.4

SORT Thod ARC SCM

1.2

Error

1.2

0.8

0.6

0.4

0.2

0

2

Modes

4

6

8

0 −2

10

0

2

Modes

1.4

1.2

1

4

6

8

10

Modes

1.4

SORT Thod ARC SCM

815

1.5

SORT Thod ARC SCM

1.2

1

SORT Thod ARC SCM

0.6

0.8

Error

Error

Error

1 0.8

0.6

0.5 0.4

0.4

0.2

0 −2

0.2

0

2

4

6

8

10

Modes

0 −2

0

2

4

Modes

6

8

10

0 −2

0

2

4

6

8

10

Modes

Fig. 3. Shape generalization errors on bump boxes. First row: From left to right, SORT uses 8, 16, and 32 segments,and other 3 algorithms use 16, 32, and 64 landmarks accordingly. Second row: Generalization error with noise of scale 0.1, 0.2, and 0.4 (from left to right). SORT uses 16 segments while other algorithms use 32 landmarks.

arc-length parameterization, and Chui’s SCM, denoted as “Thod”, “ARC” and “SCM” respectively in the figure. It is observed that SORT has considerable advantage when small number of segments is used for registration. Although SCM can find optimal transformations, its performance is not so good in terms of the shape generalization error. This is because the design of SCM has no intention to obtain an optimized representation of the original shapes. This is also true for most point cloud matching algorithms. Fig. 3 also shows the shape generalization error of registration under different scale of Gaussian noise. The scales are defined as the ratio between noise magnitude and mean distance among neighboring points of the shape. It is observed that the performance of SORT is obviously less affected by data noise. Similar results are also observed on Femur, and silhouette profiles. To demonstrate SORT’s capability of registering shapes of complicated topologies, which is difficult for landmark-sliding methods, a registration is conducted for shapes of 9 heart, each consisting of two chambers (shapes of multi-parts), and the results are given in Fig. 4. The registration process takes 173 seconds. 4.2

Register 3D Shapes

In the 3D space, the equalprob surfaces of Gaussian are ellipsoids, and the kernel for regularized TPS becomes φi (x) = x − X0i . Each segment is parameterized by 3 points (u, v, w), where u is still the center of the Gaussian, while (v, w) are located on the first and second major axes of its equalprob ellipsoid. The

816

Y. Jiang et al. −2σ

2σ

mode 1

mode 2

mode 3

Fig. 4. Registration of 9 heart chamber shapes. SORT uses 26 segments. Left: a shape consisting of 2 chambers extracted from a echocardiogram image; Right: first 3 modes of shape variation.

Fig. 5. Registration of 9 3D bumps. Left: Corresponding equalprob surfaces of segments on 4 bump shapes; Right: the shape variation (Surface shown here is interpolated from ends of the first two major axes of all the segments).

constraints for Gaussian are similar to 2D cases as in section 2.1, min(eig(Σmj )) 2 2 = σs , σs2 ≤ α1 vmj − umj ≤ β · σs2 , σs2 ≤ α1 wmj − umj ≤ β · σs2 , resulting a flattened equalprob ellipsoid, analogous to an elongated ellipse in 2D cases. But attention is needed on the ends of those open shapes, i.e. the boundaries of open surfaces. In our experiments, we handle this by registering the boundaries separately as a 3D curve, whose results are then merged to the surface registration results. Fig. 5 demonstrates the registration results on a group of synthesized 3D bumps. 12 segments are used for each surface, and 30 segments are used for each surface boundary. As seen, SORT performs very well to capture the only shape variation for this dataset.

5

Summary and Future Work

In this paper, shape registration is formulated as a Bayesian inference problem with a constrained GMM coupled by a regularized TPS based prior. This problem is solved by an algorithm called SORT. SORT basically is an EM algorithm embedded in a coarse-to-fine scheme. Extensive experimental results demonstrate that SORT has a number of advantages compared with the popular algorithms

Shape Registration

817

based on landmark-sliding. For future work, we plan to study some ways to improve the optimization, such as split and merge EM.

References 1. Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. John Wiley and Sons, West Sussex (1998) 2. Cootes, T.F., Taylor, C., Cooper, D., Graham, J.: Active shape models – their training and application. Comput Vis Image Underst 61, 38–59 (1995) 3. Davies, R.: Learning Shape: Optimal Models for Analysing Shape Variability. PhD thesis, University of Manchester (2002) 4. Meier, D., Fisher, E.: Parameter space warping: Shape-based correspondence between morphologically different objects. IEEE Trans. Med. Imaging 21(1), 31–47 (2002) 5. Huang, X., Paragios, N., Metaxas, D.N.: Shape registration in implicit spaces using information theory and free form deformations. IEEE Trans. Patt. Anal. Mach. Intell. 28(8), 1303–1318 (2006) 6. Bookstein, F.: Landmark methods for forms without landmarks: morphometrics of group differences in outline shape. Med. Image Anal. 1, 225–243 (1997) 7. Chui, H., Zhang, J., Rangarajan, A.: Unsupervised learning of an atlas from unlabeled point-sets. IEEE Trans. Patt. Anal. Mach. Intell 26, 160–173 (2004) 8. Thodberg, H.H.: Minimum description length shape and appearance models. In: Proc. IPMI, BMVA, pp. 51–62 (2003) 9. Richardson, T., Wang, S.: Shape correspondence using landmark sliding, insertion and deletion. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 435–442. Springer, Heidelberg (2005) 10. Wahba, G.: Spline models for observational data. Society for Industrial and Applied Mathematics, Philadelphia (1990)

Landmark Correspondence Optimization for Coupled Surfaces Lin Shi1,2 , Defeng Wang1,2 , Pheng Ann Heng1,2 , Tien-Tsin Wong1,2 , Winnie C.W. Chu3 , Benson H.Y. Yeung4 , and Jack C.Y. Cheng4 1

Department of Computer Science and Engineering {lshi,dfwang,pheng,ttwong}@cse.cuhk.edu.hk 2 Shun Hing Institute of Advanced Engineering 3 Department of Diagnostic Radiology and Organ Imaging [email protected] 4 Department of Orthopaedics and Traumatology, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China {byeung,jackcheng}@cuhk.edu.hk

Abstract. Volumetric layers are often encountered in medical images. Unlike solid structures, volumetric layers are characterized by double and nested bounding surfaces. It is expected that better statistical models can be built by utilizing the surface coupleness rather than simply applying the landmarking method on each of them separately. We propose an approach to optimizing the landmark correspondence on the coupled surfaces by minimizing the description length that incorporates local thickness gradient. The evaluations are performed on a set of 2-D synthetic close coupled contours and a set of real-world open surfaces, the skull vaults. Compared with performing landmarking separately on the coupled surfaces, the proposed method constructs models that have better generalization ability and specificity.

1

Introduction

Statistical shape analysis is attracting increasing research interests and efforts because of its wide application in model-based image segmentation and pathological changes detection. Landmark-based shape analysis methods, such as the active shape model, require labeling landmarks with anatomical equivalence. Although manual landmarking can generate acceptable results in 2-D, it is subjective, error-prone, and time-consuming, which limits its application in 3-D. Bookstein [1] proposed to optimize the positions of corresponding points by minimizing the bending energy between landmarks on two shapes when the landmarks are sliding on the shape boundary. The landmark correspondence problem can actually be solved in a principled way by being interpreted as an optimization problem. Kotcheff et al. [2] proposed to minimize the determinant of the covariance matrix, while Davies et al. [3] designed an objective function based on the minimum description length (MDL) principle that assumes simple descriptions generalize best. Different from landmarking methods that operate N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 818–825, 2007. c Springer-Verlag Berlin Heidelberg 2007

Landmark Correspondence Optimization for Coupled Surfaces

819

on an individual base, MDL determines the landmark positions via minimizing the description length of the information needed to transmit the training set, so that a compact description across the whole set can be derived with desired properties. Compared with manual labeling, SPHARM, and DetCov, MDL outperforms as it results in specific, generalized, and compact models [4]. Ericsson et al. [5] used the gradient descent strategy to improve the convergence speed of MDL, which makes MDL more practical in medical applications. Although MDL is recognized as the “optimal” method in landmark correspondence optimization, applying the MDL principle flexibly and creatively rather than following certain existing algorithm will achieve better results. Our insight is that the shape properties should be well-understood and exploited in designing the landmarking algorithm. For example, to find out the landmarks on shapes with meaningful curvature changes, the curvature information should be considered in the optimization [6]. Richardson et al. [7] deal with the landmarking problem for 2-D open curves by introducing a novel tailor-made method, which achieves better performance than the generic MDL.

(a)

(b)

(c)

Fig. 1. Examples of coupled-surface structures: (a) the skull; (b) the skull vault, which is the part above the red frame indicated in (a); (c) the cerebral cortex

Volumetric layers are a kind of commonly encountered shapes in medical images, such as the skin of internal organs, myocardium of the left ventricle, and the cerebral cortex. A open coupled-surface structure, i.e., the skull vault, and a closed coupled-surface structure, i.e., the cerebral cortex, are illustrated in Fig. 1. Because they contain double 3-D boundaries, automatic and accurate landmarking is of great importance in analyzing their shapes. However, existing landmarking techniques, including MDL, are designed for single-surface objects. Actually, the local thickness is hidden information, which reflects the correlation of the two surfaces and facilitates human perception of such coupled-surface shapes. Thus it is reasonable that the locations with consistent thickness changes are assigned with landmarks. In this paper, we demonstrate how the coupleness information can be properly incorporated in the description length to solve the automatic landmarking problem in coupled-surface shapes.

820

2 2.1

L. Shi et al.

Automatic Model Building for Coupled Surfaces Landmark Initialization

The training surfaces are parameterized for convenient landmarks manipulations. It is desired that when neighbouring parameterized landmarks are adjusted to the same direction, their corresponding points in the training shape move consistently. Thus the conformal mapping that preserves the local angles is preferred.

(a)

(d)

(b)

(e)

(c)

(f)

Fig. 2. Conformal mapping of the open and closed surfaces, and landmark initialization: (a) the outer skull vault surface, an open surface; (b) the conformal mapping of (a) to a unit disk; (c) uniform disk subdivision; (d) the GM/CSF interface, a closed surface; (e) the conformal mapping of (d) to a unit sphere; (f) uniform sphere subdivision

Mapping an open surface to a unit disk is achieved by minimizing the string energy of the mesh (1) E(W, Ω) = [v1 ,v2 ]∈E wv1 ,v2 Ω(v1 ) − Ω(v2 )2 , where Ω(v) is the map of vertex v. The weight wv1 ,v2 is determined via wv1 ,v2 = (tan α2 + tan β2 )/dist (v1 , v2 ), where α and β are the adjacent angles in the two triangles sharing the edge [v1 , v2 ], and dist (v1 , v2 ) is the Euclidean distance between v1 and v2 . Fig. 2 (a) and (b) give an outer skull vault mesh and its map on a unit disk. To map a closed mesh to a unit sphere, the string energy in equation (1) is still the objective to be minimized, but the weight is defined as wv1 ,v2 = 1 2 (cot μ + cot ν), where μ and ν are the opposite angles in the two triangles with


821

the common edge [v1 , v2 ]. A closed surface, i.e., the brain GM/CSF interface, and its map on a unit sphere are shown in Fig. 2 (d) and (e) respectively. After the mapping has been determined, we uniformly sample in the parameter domain and map the sample points back to the surface as the initial landmarks. The planar disk is subdivided recursively into small triangles, e.g., Fig. 2(c), and the vertices of those triangles are the sample points. Subdividing the sphere leads to a uniform sampling as Fig. 2(f) shows. 2.2

Landmark Correspondence Optimization Using MDL

Thickness Definition of Volumetric Layer. The thickness of a volumetric layer at a point on the bounding surface is the distance from that point to the opposite surface. There exist several definitions for the layer thickness, such as the closest thickness (Tclose ) and the normal thickness (Tnormal ) [8]. Tclose is the distance from a point on one surface to the closest point on the other. Tnormal is the distance from a point on one surface to the point on the other in the direction of the surface normal. To find a generic measure that performs reasonably on every type of layers is impractical. The layer thickness in this study is determined as the distance between each pair of corresponding points on the two surfaces with the same polar coordinate. This measure is named as the radial thickness (Tradial ). We illustrate the measures of Tclose , Tnormal , and Tradial on an axial plane of the skull boundary (see Fig.3). Different from Tclose and Tnormal that depend on the starting surface, the Tradial is unique and landmarks are grouped in pairs through this measurement. Description Length Minimization for Coupled-Surface Structures. The MDL is recognized as the “optimal” method for generating corresponding landmarks, since it is based on the philosophy that the simplest description generalizes best. Our point is that landmarks could have properties other than spatial locations, and these properties can also be considered to minimize the description length. Therefore, in our method, the coupled surfaces are treated as a master

Fig. 3. Different thickness definitions: (a) the coupled surfaces; (b) the closest thickness measure; (c) the normal thickness measure; (d) the proposed radial thickness measure

822

L. Shi et al.

surface and a supplementary surface. The information at each landmark in the master surface consists of both the spatial position and the thickness gradient at that landmark, i.e., [x, y, z, ξt ], where ξ is the parameter controlling the importance of the thickness gradient t . And the landmarks in the inner surface are obtained naturally through the thickness measurement. For the skull vault, we take the outer surface as the master surface because it is more dominant in determining the shape of the volumetric layer. In the cases that the inner surface is more important, the master surface can be switched to the inner surface. Actually, the shape of the supplementary surface is not discarded, as it is embeded in the “thickness” information. Once the landmark position is adjusted, the thickness at that particular landmark will be recomputed. We adopt a simplified version of the description length [6], 1 + log(λm /λcut ) if λm λcut (2) F = m Lm with Lm = λm /λcut if λm < λcut . Note that λm are the eigenvalues derived from the landmarks in the master surface. λcut can be determined by λcut = (σ/r)2 , where σ is the standard deviation of noise in the training data and r depends on the resolution of the images from which the training shapes are extracted. The landmark positions are adjusted by locally warping the parameterization inside Gaussian kernel regions. The magnitude of the adjustment is proportional to the distance to each kernel center. The optimization is implemented by the gradient descent strategy. Suppose matrix L contains landmarks on the training shapes as columns, k is the number of landmarks in each shape, and s is the number of shapes in the training set. Since each vertex on the mesh contains both spatial position and thickness gradient value at that point, the dimension 1 (L − L), where L is the matrix with of the matrix L is 4k × s. Let A = √s−1 all columns set to the mean shape x. Using the singular value decomposition (SVD), the matrix A can be written as A = UDV T . U and V are columnorthogonal matrices, and D is a diagonal matrix. Since the mesh to be analyzed in this study is 2-manifold, two variables (θ, φ) are involved in the disk or sphere parameter domain. Take the nth landmark of the j th sample for instance, we have the landmark movement (Δθ, Δφ) as follows, 4n ∂aij ∂Lm ∂F · ∂θnj = (3) Δθ = ∂θ m i=4n−3 ∂a nj ij ∂Lm 4n ∂aij ∂F Δφ = ∂φ · ∂φnj = i=4n−3 , (4) m ∂aij nj where ∂Lm = ∂aij

2uim vjm /dm 2dm uim vjm /λcut

if λm λcut . if λm < λcut

(5)

uim and vjm are the elements of the matrices U and √ V respectively. dm is the element of the diagonal matrix D, and it is equal to λm . The surface gradients ∂aij ∂aij ( ∂θnj , ∂φnj ) are estimated by the finite difference.


3

823

Experimental Evaluation and Comparison

The quality of landmark correspondence is evaluated by the performance of the resultant model. Given different number of modes M , the generalization ability is the ability to describe the object that is not included in the training set, because a good shape model should not be overfitted by training samples. Its error G(M ) is usually calculated as the averaged leave-one-out error. The specificity reflects if a model only generates samples similar to training shapes. Its error S(M ) can be estimated by the averaged distances between samples newly generated with the model and the closest training shape. In our experiment, 10,000 test samples are generated. The parameter σ is set to 0.3, r is 100, and ξ is 1.0. 3.1

Results on the Synthetic Dataset

A set of 50 samples of a simple 2-D shape with varying thickness values at different positions are generated. Fig. 4 shows the landmarking results of the proposed method (MDL-thickness) and the MDL performed on two boundaries separately (MDL-separate) on three of them. For each training shape, the number of landmarks on either the inner or the outer surface is set to 14. The results show that landmarks obtained by MDL-thickness are in pairs and are located in the regions where the thickness values reach the extrema. However, landmarks obtained by MDL-separate are equally spaced in the outer contour, while in the inner contour, they are located at positions with small spatial group changes. The MDL considering local curvature [6] can place the landmarks onto the “peaks” and “valleys” in the inner contour because large curvatures are

Fig. 4. Landmarking results on three training shapes in the synthetic dataset: (a) result of MDL-separate; (b) result of MDL-thickness

824

L. Shi et al.

detected there. Since the outer contour does not have any curvature change, the result on the outer contour will be the same as that from MDL-separate. Generalization errors and specificity errors of MDL-separate and MDL-thickness using different numbers of modes are plotted in Fig. 5 (a) and (b) respectively. It can be observed that both G(M ) and S(M ) of MDL-thickness are smaller than those of MDL-separate when various numbers of modes are chosen. 3.2

Evaluation on the Real Skull Vault Dataset

The skull volumes of 18 subjects were segmented from the head CT data collected in the Prince of Wales Hospital, Hong Kong. The field of view of the CT data is 512 × 512 and the voxel size is 0.49mm × 0.49mm × 0.63mm. The skull vault is the upper part of the skull and is an open coupled-surface structure. A total of 578 corresponding landmarks are determined using MDL-thickness and MDLseparate respectively. We plot the quality measures G(M ) and S(M ) of the models built with MDL-separate and MDL-thickness under different numbers of modes in Fig. 5 (c) and (d). It can be observed that both G(M ) and S(M ) of the model built with MDL-thickness are smaller than those built with the MDL-separate.

(a)

(b)

(c)

(d)

Fig. 5. The generalization error and specificity error of MDL-separate and MDLthickness on the synthetic dataset and the real skull vault dataset


4

825

Conclusion

This paper describes a generic automatic landmarking method for structures with coupled surfaces by minimizing the description length. In this method, the local thickness gradient is treated as an extra property of each landmark, and thus the positions with group-wise consistent thickness changes are implicitly favored. Once the landmark on one surface is determined, its counterpart on the other surface can be found directly. The optimization converges fast as the gradient descent method is used. The quality of the models constructed from our proposed method are evaluated and compared with those obtained by treating the coupled surfaces as independent. The evaluation results show the advantage of considering thickness information in landmarking volumetric layers.

Acknowledgement The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region (Project no. CUHK4453/06M) and CUHK Shun Hing Institute of Advanced Engineering. This work is also affiliated with the Virtual Reality, Visualization and Imaging Research Center at The Chinese University of Hong Kong as well as the Microsoft-CUHK Joint Laboratory for Human-Centric Computing and Interface Technologies.

References 1. Bookstein, F.L.: Landmark methods for forms without landmarks: morphometrics of group differences in outline shape. Medical Image Analysis 1(3), 225–244 (1997) 2. Kotcheff, A., Taylor, C.: Automatic construction of eigenshape models by direct optimization. Medical Image Analysis 2(4), 303–314 (1998) 3. Davies, R., Twining, C., Cootes, T., et al.: A minimum description length approach to statistical shape modelling. IEEE Trans. Med. Imaging 21, 525–537 (2002) 4. Styner, M., Rajamani, K., et al.: Evaluation of 3d correspondence methods for model building. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 63–75. Springer, Heidelberg (2003) 5. Ericsson, A., Astr¨ om, K.: Minimizing the description length using steepest descent. In: British Machine Vision Conference, Norwich, pp. 93–102 (2003) 6. Thodberg, H.H., Olafsdottir, H.: Adding curvature to minimum description length shape models. In: British Machine Vision Conference, Norwich, pp. 251–260 (2003) 7. Richardson, T., Wang, S.: Open-curve shape correspondence without endpoint correspondence. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 17–24. Springer, Heidelberg (2006) 8. MacDonald, D., Kabani, N., et al.: Automated 3-d extraction of inner and outer surfaces of cerebral cortex from MRI. NeuroImage 12(3), 340–356 (2000)

Mean Template for Tensor-Based Morphometry Using Deformation Tensors Natasha Leporé1 , Caroline Brun1 , Xavier Pennec2 , Yi-Yu Chou1 , Oscar L. Lopez3 , Howard J. Aizenstein4 , James T. Becker4, Arthur W. Toga1 , and Paul M. Thompson1 1

2

Laboratory of Neuro Imaging, UCLA, Los Angeles, CA 90095, USA Asclepios Research Project, INRIA Sophia-Antipolis, 2004 route des Lucioles 06902 Sophia-Antipolis Cedex, France 3 Department of Psychiatry, University of Pittsburgh, Pittsburgh, PA 15213 USA 4 Department of Neurology, University of Pittsburgh, Pittsburgh, PA 15213 USA

Abstract. Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In [14], it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is ’closest’ to all subjects’ anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework [1]. The control brain B that is already the closest to ’average’ is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling’s T 2 test on the deformation tensors. These results are compared to the ones found using the ’best’ control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the pvalues in maps of inter-group differences.

1

Introduction

Tensor-based morphometry (TBM) is an increasingly popular method to study differences in brain anatomy statistically [23],[5], [22]. In TBM, a non-linear registration algorithm is used to align a set of images to a common space, and a statistical analysis is typically performed on the Jacobian determinants (local N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 826–833, 2007. c Springer-Verlag Berlin Heidelberg 2007

Mean Template for Tensor-Based Morphometry Using Deformation Tensors

827

expansion factors) of the deformation fields generating the transformation. Most commonly, one of the control subjects’ images, or a high-resolution single subject MRI atlas [10], is selected as the reference to which all the other images are mapped. To avoid biases induced by the choosing a single individual as a template, methods for creating an average image using the entire set of controls have also been developed. For instance in [11], a mean template is defined by transforming one of the control images using the average of the displacement fields resulting from its registration to all other controls. A similar approach was also adopted in [9], where the average was taken with respect to both the deformation and the intensities of the reference images. Other investigators have advocated a more computationally intensive ’targetless’ normalization approach, in which all images in a group are matched to each other pairwise, and each image’s mean vector field so obtained is applied to it before averaging the deformed images across subjects [24], [22], [28], [27], [12]. Groupwise registration is increasingly common to avoid systematic confounding effects and bias associated with aligning images to a specific individual brain, which can arise when the geometry and intensities of the target image resemble some members of the population more √ than others. In [14], the deformation tensors J t J were used to perform statistics in TBM, where J is the local Jacobian matrix of the transformation. This method outperformed det J, the most commonly used scalar measure of deformation, for mapping the profile of brain atrophy associated with HIV/AIDS. Specifically, multivariate analysis of the local tensor, using a manifold version of the Hotelling T 2 test, was much more sensitive to group differences than det J. The determinants represent local volume differences across subjects, while the deformation tensors reflect local differences in shape, orientation, and volume. When statistics are performed on the deformation tensors in TBM, a consistent way to define the average image is as one that minimizes and appropriate norm on the deformation tensors generated using that image as a registration target. For example, when a set of control subjects’ images is mapped to a template, it is reasonable to expect the mean deformation tensor to be identically zero everywhere after log transformation, or, if that is not possible, at least having minimum mean-squared error in a relevant tensor norm. Here we develop an approach to achieve this, by using a log-Euclidean metric on the space of tensors; the regularizer then has a form that is consistent with the tensor statistics used ultimately for mapping systematic effects on anatomy. In related work on geodesic shooting [17] and large-deformation diffeomorphic metric mapping (LDDMM) [2], mean templates are defined that minimize the geodesic distance to a population of anatomies. These geodesic distances are Riemannian metrics formulated in terms of integrals of ||Lv||, where L is a self-adjoint (elliptic) differential operator regularizing the deformation, v is its velocity field, and ||.|| is a norm, such as the simple L2 norm or the Hα1 norm used in the Camassa-Holm equation for modeling solitons [29]. Lorenzen et al. [15] [16] generated a representative common template from a multimodality image set using large-deformation mappings and registration with the Kullback-Leibler

828

N. Leporé et al.

divergence. Gerig et al.[7] generalized the mean anatomical template estimation to accommodate repeated measures data, e.g. images collected longitudinally from a pediatric population. In this work, we set out to find a transformation ΦBA from an initial brain B selected from a set of control subjects, to an average brain A. The average brain image intensity is defined as IA = IB ◦ ΦBA . B is taken as the reference image, and we seek the transformation of its geometry that minimizes the bias on the deformation tensors: argminΦBA E(ΦBA ) where E(ΦBA ) is the total size of the deformation tensors E= d(Si , Id)2

(1)

(2)

i

Here the Si represent the square of the deformation tensors from image i, d(., .) is the distance, and Id is the identity. In practice, to make calculations easier, we actually compute the inverse transformation, ΦAB . (Note that this formulation could be extended to consider intensity matching as well, as in [15] [16] where the sum of an intensity matching energy and a deformation energy is minimized). The deformation tensors are constrained to be positive-definite matrices, and form a conical submanifold of the space of square matrices. An intrinsic definition of d(., .) is needed for (2). Recently, Arsigny et al. [1] presented a log-Euclidean framework to perform computations in this space. Distances are computed after applying the matrix logarithm transformation, which transports the deformation tensors to the tangent space at the origin, where simple matrix operations can be used. When log transforms are used, even on the scalar Jacobian determinant, several sources of bias are avoided in the resulting statistics (which can lead to skewness and non-zero mean even under the null hypothesis [13]). This method was used in [14] to compute statistics on the deformation tensors in TBM. In the log-Euclidean framework, the distance between two elements of the space S1 and S2 is given by d(S1 , S2 ) = || log S1 − log S2 ||, where ||.|| denotes a norm, and log is the matrix logarithm. Here we will use [1] d(S1 , S2 ) = (Trace(log S1 − log S2 )2 )1/2 . Taking into account (3), (2) becomes 2 2 E= || log Si || d x = T r(log Si )2 d2 x i

(3)

(4)

i

that is, the size of the Si given a transformation of the chosen image ΦAB . We used a fluid registration algorithm [6] to register the images. The code was accelerated using a convolution filter derived from the Green’s function of


829

the differential operator in the fluid equation [3] [8]. ΦAB was then computed using gradient descent. As our initial brain B, we selected the control subject for which (4) was minimal. In the next section, we describe our gradient descent algorithm. Our method is then applied to perform a TBM analysis of the corpus callosum in a group of 26 AIDS patients and 14 matched controls.

2

Method

A gradient descent method in the log-Euclidean framework was outlined in [19] and [20] for the log-Euclidean elasticity. Here we use the general philosophy described in those references. However, a major added complication is that our method requires two consecutive registrations, from A to B and from B to i. The transformation ΦAi (rA ) from A to image i at point rA is given as a function of the deformation fields D by [11] ΦAi (rA ) = ΦBi ◦ ΦAB (rA ) = rA + DAB (rA ) + DBi (rA + DAB (rA )) The value of Si from A to image i is thus given by Si (ΦAB ) = ∂α (ΦBi ◦ ΦAB )∂α (ΦBi ◦ ΦAB )t . α

Using Si (ΦAB + u) =

∂α (ΦBi ◦ (ΦAB + u))∂α (ΦBi ◦ (ΦAB + u))t

α

=

∂α (ΦBi ◦ ΦAB +

α

uk (∂k ΦBi ) ◦ ΦAB + ...)

k

∂α (ΦBi ◦ ΦAB +

uk (∂k ΦBi ) ◦ ΦAB + ...)t ,

k

we find the directional derivative of Si in the direction of the vector field u [∂α (ΦBi ◦ ΦAB )][∂α ( uk (∂k ΦBi ) ◦ ΦAB )]t ∂u Si (ΦAB ) = α

k

+[∂α ( uk (∂k ΦBi ) ◦ ΦAB )][∂α (ΦBi ◦ ΦAB )]t k

The directional derivative of the energy gradient for image i is then: 2 ∂u T r(log Si ) = 2 T r(log(Si )Si−1 ∂u Si ) [∂α (ΦBi ◦ ΦAB )][∂α ( uk (∂k ΦBi ) ◦ ΦAB )]t ) = 4 T r(Z α

+4

T r(Z

α

where Z ≡

log(Si )Si−1 .

k

[∂α ( uk (∂k ΦBi ) ◦ ΦAB )][∂α (ΦBi ◦ ΦAB )]t ) k

Integrating by parts, we finally obtain

830

N. Leporé et al.

∂u

T r([ ∂α (Z∂α (ΦBi ◦ ΦAB ))][ uk (∂k ΦBi ) ◦ ΦAB ]t )

uk (∂k ΦBi ) ◦ ΦAB ][ ∂α (Z∂α (ΦBi ◦ ΦAB ))]t ) T r([

T r(log Si ) = −4 2

−4

α

k

k

α

The total derivative term cancels as the image intensity and thus ΦAB is zero near enough to the boundary. This can be guaranteed in the general case by padding the image with zeros. Finally, we obtain the gradient of the energy for image i as ∂α (Z∂α (ΦBi ◦ ΦAB )) | (∇ΦBi ) ◦ ΦAB > . (5) ∇Ei = −4 < α

where < .|. > denotes the usual scalar product in R3 . 2.1

Numerical Implementation

As an initial condition for the gradient descent, we moved the chosen template B to the location of the average deformation field from B to all other controls. This definition of a ‘vector mean’ template has been adopted by others [11], but here we optimize it using a further deformation to yield a template with minimal energy in the multivariate log-Euclidean space. Using a finite difference scheme in the computation of the gradient yields poor results, as a small number of voxels with large gradient values can end up driving the computation, and in such cases most of the image will change very slowly. We remedied this problem using a multi-resolution scheme, for which all derivatives in (5) were computed through convolution with a Gaussian filter, for which the variance was reduced at each resolution step. To improve the speed of convergence, the positions were updated after the computation of the descent direction for each i. 2.2

Data

Twenty-six HIV/AIDS patients (age: 47.2 ± 9.8 years; 25M/1F; CD4+ T-cell count: 299.5 ± 175.7 per μl; log10 viral load: 2.57 ± 1.28 RNA copies per ml of blood plasma) and 14 HIV-seronegative controls (age: 37.6 ± 12.2 years; 8M/6F) underwent 3D T1-weighted MRI scanning; subjects and scans were the same as those analyzed in the cortical thickness study in [25], where more detailed neuropsychiatric data from the subjects is presented. All patients met Center for Disease Control criteria for AIDS, stage C and/or 3 (Center for Disease Control and Prevention, 1992), and none had HIV-associated dementia. All AIDS patients were eligible to participate, but those with a history of recent traumatic brain injury, CNS opportunistic infections, lymphoma, or stroke were excluded. All patients underwent a detailed neurobehavioral assessment within the 4 weeks before their MRI scan, involving a neurological examination, psychosocial interview, and neuropsychological testing, and were designated as having no,


831

mild, or moderate (coded as 0, 1, and 2 respectively) neuropsychological impairment based on a factor analysis of a broad inventory of motor and cognitive tests performed by a neuropsychologist [25]. All subjects received 3D spoiled gradient echo (SPGR) anatomical brain MRI scans (256x256x124 matrix, TR = 25 ms, TE = 5ms; 24-cm field of view; 1.5-mm slices, zero gap; flip angle = 40o ) as part of a comprehensive neurobehavioral evaluation. The MRI brain scan of each subject was co-registered with a 9parameter transformation to the ICBM53 average brain template, after removal of extracerebral tissues (e.g., scalp, meninges, brainstem and cerebellum). The corpus callosum of each subject was hand-traced [26], using an interactive segmentation software. The traces were treated as binary objects (1 within the CC, 0 outside), as we wished to evaluate anatomical differences in a setting where intensity was held constant (see Lorenzen et al. [15] [16], where a radiometric term based on information theory was included in the template estimation equations, but tensor statistics were not evaluated).

3

Results

The total energy was found to be much lower in the case of the mean template (EA = 3.027 × 103 vs EB = 3.794 × 103 ). T 2 statistics identifying group differences in our dataset are shown in Fig. 1a. The cumulative distribution function of the p-values is plotted in Fig. 1b against the p-values that would be expected under the null hypothesis, for both templates. For null distributions (i.e. no group difference detected), these are expected to fall along the x = y line, and larger deviations from that curve represent larger effect sizes. The registration to the average brain gives statistics similar to the one to one individual. Thus we do not sacrifice any of the signal by using our averaging procedure. Furthermore, the average template can be used to remove potential interaction between the 0

1 0.9

−0.5

0.8

−1

0.7 0.6

−1.5

0.5 0.4

−2

0.3

−2.5

0.2 0.1

−3

0

0

0.2

0.4

0.6

0.8

1

Fig. 1. Left: Voxelwise p-values computed from the Hotelling’s T 2 test on the deformation tensors for the average template. The scale shows values of log 10 (p). Right: Cumulative distribution of p-values vs the corresponding cumulative p-value that would be expected from a null distribution for the average shape and the best brain. Pink curve: average brain, blue curve: best individual brain. Dotted line: x = y curve (null distribution).

832

N. Leporé et al.

registration accuracy and diagnosis that can occur when using an individual brain as a registration target.

4

Conclusion

In this paper, we derive a new way to compute mean anatomical templates by minimizing a distance in the space of deformation tensors. The resulting templates may be used for TBM, in which statistical analyses are performed on the deformation tensors mapping individual brains to the target image [14]. Because the deformation distance to the template is smaller with a tensor-based mean template, there is a greater chance that intensity-based registrations of individual datasets will not settle in nonglobal minima that are far from the desired correspondence field. In neuroscientific studies, this could be helpful in detecting anatomical differences, for instance in groups of individuals with neurodegenerative diseases, or in designs where the power of treatment to counteract degeneration is evaluated. Two caveats are necessary regarding the interpretation of this data. First, strictly speaking we do not have ground truth regarding the extent and degree of atrophy or neurodegeneration in HIV/AIDS. So, although an approach that finds greater disease effect sizes is likely to be more accurate than one that fails to detect disease, it would be better to compare these models in a predictive design where ground truth regarding the dependent measure is known (i.e., morphometry predicting cognitive scores or future atrophic change). Second, it may be more appropriate to use the mean shape anatomical template derived here in conjunction with registration algorithms whose cost functions are explicitly based on the log-transformed deformation tensors, such as those found for instance in [4] and [19]. To do this, we are working on a unified registration and statistical analysis framework in which the regularizer, mean template, and voxel-based statistical analysis are all based on the same log-Euclidean metric.

References 1. Arsigny, V., et al.: Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Mag. Res. in Med. 56, 411–421 (2006) 2. Beg, M.F., et al.: Computing large deformation metric mappings via geodesic flow on diffeomorphisms. Int. J. of Comp. Vision 61, 139–157 (2005) 3. Bro-Nielsen, M., Gramkow, C.: Fast fluid registration of medical images. Visualization in Biomedical Computing, 267–276 (1996) 4. Brun, C., et al.: Comparison of Standard and Riemannian Elasticity for TensorBased Morphometry in HIV/AIDS. In: MICCAI workshop on Statistical Registration: Pair-wise and Group-wise Alignment and Atlas Formation (submitted, 2007) 5. Chiang, M.C., et al.: 3D pattern of brain atrophy in HIV/AIDS visualized using tensor-based morphometry. Neuroimage 34, 44–60 (2007) 6. Christensen, G.E., et al.: Deformable templates using large deformation kinematics. IEEE-TIP 5, 1435–1447 (1996) 7. Gerig, G., et al.: Computational anatomy to assess longitudinal trajectory of the brain. In: 3DPVT, pp. 1041–1047 (2006)


833

8. Gramkow, C.: Registration of 2D and 3D medical images, Master’s thesis, Danish Technical University, Copenhagen, Denmark (1996) 9. Guimond, et al.: Average brain models: a convergence study. Comp. Vis. and Im. Understanding 77, 192–210 (1999) 10. Kochunov, P., et al.: An optimized individual target brain in the Talairach coordinate system. Neuroimage 17, 922–927 (2003) 11. Kochunov, P., et al.: Regional spatial normalization: toward an optimal target. J. Comp. Assist. Tomogr. 25, 805–816 (2001) 12. Kochunov, P., et al.: Mapping structural differences of the corpus callosum in individuals with 18q deletions using targetless regional spatial normalization. Hum. Brain Map. 24, 325–331 (2005) 13. Leow, A.D., et al.: Statistical properties of Jacobian maps and inverse-consistent deformations in nonlinear image registration. IEEE-TMI 26, 822–832 (2007) 14. Leporé, N., et al.: Multivariate Statistics of the Jacobian Matrices in Tensor-Based Morphometry and their application to HIV/AIDS. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, Springer, Heidelberg (2006) 15. Lorenzen, P., et al.: Multi-class Posterior Atlas Formation via Unbiased KullbackLeibler Template Estimation. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 95–102. Springer, Heidelberg (2004) 16. Lorenzen, P., et al.: Multi-modal image set registration and atlas formation. Med. Imag. Analysis 10, 440–451 (2006) 17. Miller, M.I.: Computational anatomy: shape, growth and atrophy comparison via diffeomorphisms. Neuroimage 23(Suppl. 1), 19–33 (2004) 18. Nichols, T.E., Holmes, A.P.: Non parametric permutation tests for functional neuroimaging: a primer with examples. Hum. Brain Map. 15, 1–25 (2001) 19. Pennec, X., et al.: Riemannian elasticity: A statistical regularization framework for non-linear registration. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 943–950. Springer, Heidelberg (2005) 20. Pennec, X.: Left-invariant Riemannian elasticity: a distance on shape diffeomorphisms? In: MFCA, pp. 1–13 (2006) 21. Studholme, C., et al.: Detecting spatially consistent structural differences in Alzheimer’s and fronto-temporal dementia using deformation morphometry. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 41–48. Springer, Heidelberg (2001) 22. Studholme, C., Cardenas, V.: A template free approach to volumetric spatial normalization of brain anatomy. Patt. Recogn. Lett. 25, 1191–1202 (2004) 23. Thompson, P.M., et al.: Growth Patterns in the Developing Brain Detected By Using Continuum-Mechanical Tensor Maps. Nature 404, 190–193 (2000) 24. Thompson, P.M., et al.: Mathematical/Computational Challenges in Creating Population-Based Brain Atlases. Hum. Brain Map. 9, 81–89 (2000) 25. Thompson, P.M., et al.: Thinning of the cerebral cortex visualized in HIV/AIDS reflects CD4+ T-lymphocyte decline. Proc. Nat. Acad. Sci. 102, 15647–15652 (2005) 26. Thompson, P.M., et al.: 3D mapping of ventricular and corpus callosum abnormalities in HIV/AIDS. Neuroimage 31, 12–23 (2006) 27. Twining, C.J.: A unified information-theoretic approach to groupwise non-rigid registration and model building. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 190–193. Springer, Heidelberg (2005) 28. Woods, R.P.: Characterizing volume and surface deformation in an atlas framework: theory, applications and implementation. Neuroimage 18, 769–788 (2003) 29. Younes, L.: Jacobi fields in groups of diffeomorphisms and applications. Quar. J. of Appl. Math 65, 113–134 (2007)

Shape-Based Myocardial Contractility Analysis Using Multivariate Outlier Detection Karim Lekadir1, Niall Keenan2, Dudley Pennell2, and Guang-Zhong Yang1 1

Visual Information Processing, Department of Computing, Imperial College London, UK 2 Cardiovascular Magnetic Resonance Unit, Royal Brompton Hospital, London, UK

Abstract. This paper presents a new approach to regional myocardial contractility analysis based on inter-landmark motion (ILM) vectors and multivariate outlier detection. The proposed spatio-temporal representation is used to describe the coupled changes occurring at pairs of regions of the left ventricle, thus enabling the detection of geometrical and dynamic inconsistencies. Multivariate tolerance regions are derived from training samples to describe the variability within the normal population using the ILM vectors. For new left ventricular datasets, outlier detection enables the localization of extreme ILM observations and the corresponding myocardial abnormalities. The framework is validated on a relatively large sample of 50 subjects and the results show promise in localization and visualization of regional left ventricular dysfunctions.

1 Introduction Assessment of the left ventricle is important to the management of patients with cardiac disease. With increasing advances in imaging techniques, most modalities now offer routine 4D coverage of the heart, allowing both global and local assessment of left ventricular morphology and function. Several existing semi- and fully-automatic segmentation methods allow rapid and objective delineation of the left ventricle [1-3]. Extracting relevant and reliable indices of myocardial contractile abnormality, however, remains a complex task [4-7]. Global markers such as stroke volume and ejection fraction are widely used in clinical practice but they are not suitable for identifying local abnormalities. Alternative regional assessment based on wall thickening is problematic for a number of reasons. First, important information such as shape, size and endo-cardial displacement are not encoded for dysfunction analysis. Additionally, only end-diastole and end-systole differences are taken into account, whilst certain symptoms such as cardiac dys-synchronization are related to the entire cardiac cycle. The definition of normal ranges is a further challenge as significant overlap exists with abnormal values. Furthermore, local assessment methods do not consider the geometry and motion at other locations of the left ventricle to detect inconsistencies. For these reasons, visual assessment by expert observers remains the gold standard in routine clinical applications, but it is time consuming and can involve significant bias. The proposed method for myocardial abnormality localization is based on interlandmark motion (ILM) vectors, which represent the simultaneous endo- and epicardial changes occurring at two regions of the left ventricle over the entire cardiac N. Ayache, S. Ourselin, A. Maeder (Eds.): MICCAI 2007, Part II, LNCS 4792, pp. 834–841, 2007. © Springer-Verlag Berlin Heidelberg 2007

Shape-Based Myocardial Contractility Analysis Using Multivariate Outlier Detection

835

cycle. By combining pairs of locations of the left ventricle in the spatio-temporal representation, geometrical and dynamic inconsistencies can be identified efficiently, whilst the overlap between normal and abnormal values is reduced significantly. Additionally, ILM vectors can implicitly incorporate shape, size, thickness, and endo-cardial displacement for dysfunction analysis. To describe the variability within the normal population, multivariate tolerance regions are derived from training samples in a robust manner. For a given left ventricular dataset, an abnormality likelihood measure is estimated for each location from its associated ILM vectors and an iterative procedure enables the localization of myocardial abnormality. The method is validated with a population of 50 datasets containing normal and abnormal cases.

2 Methods 2.1 Inter-Landmark Motion (ILM) Vectors Conventional local assessment methods for abnormality localization consider each region of the left ventricle independently. Therefore, they do not take into account the global geometry and dynamics of the left ventricle in the analysis, nor in the definition of the normal ranges, thus causing significant overlap with abnormal values. To overcome these difficulties, this paper introduces inter-landmark motion (ILM) vectors, which describe the coupled motion and geometry over the entire cardiac cycle of pairs of myocardial locations (represented by landmark points). With this approach, each region is analyzed with respect to other locations of the left ventricle, allowing their coupled spatio-temporal relationships to be used for identifying geometrical or dynamic inconsistencies. Although the pairs of locations can be chosen for the entire left ventricle, it is more appropriate to restrict this to be within the same cross-section, where there is a high covariance between the landmarks. For each of the m points within the same cross-section, m − 1 ILM vectors can be derived. In the proposed framework, the required landmark-based representation of the myocardial boundaries is first obtained through delineation or segmentation. For each myocardial location (landmark), two rotational and translational invariant descriptors are extracted, i.e., the distances of the endo- and epi-cardial borders to a reference point on the same cross-section plane. The reference point is chosen as the center of the epi-cardial border as it is less susceptible to morphological variations. The invariance to scaling is not considered to allow the detection of size related abnormalities, such as dilatation. Each ILM vector, of dimension p = 4F , can be written as follows: T

v (Pi , Pj ) = (ai1, bi1,..., aiF , biF ,..., a j 1, bj 1,..., a jF , b jF )

(1)

where F is the number of frames in the cardiac cycle and a and b denote the endoand epi-cardial variables, respectively. The ILM vectors provide, in addition to size and thickness measures encapsulated by these variables, an implicit description of the shape of the myocardial borders.

836

K. Lekadir et al.

2.2 Multivariate Tolerance Regions In this work, the normal myocardial contractility properties are described using multivariate tolerance regions for each ILM vector. Given N training samples, a tolerance region TR in the p dimensional space can be described as:

TR = {v ∈ \ p | d (v, μ, Σ) < L}

(2)

where μ and Σ represent the location and scale of the multivariate distribution, d a distance measure to the center of the distribution and L a threshold that limits the size of the tolerance region to normal observations. The variability within the normal population can be well approximated by a multivariate normal distribution, in which case the location and scale in Eq. (1) are replaced by the mean observation v and the covariance matrix Sv , respectively. It was shown that an appropriate distance measure for multivariate normal tolerance regions is the Mahalanobis distance [8], i.e.,

d (v, v , Sv ) = (v − v )T Sv −1 (v − v )

(3)

In order to consider only the principle modes of variation, an eigen-decomposition of the covariance matrix can be applied. By rejecting the p − t noisy directions, the distance measure can be simplified to:

d (v, v , Sv ) =

t

∑ i =1

⎡U i (v − v ) ⎤ 2 i⎦ ⎣ where Sv = UEU T Ei

(4)

For the tolerance region limit L in Eq. (2), it was shown that it can be estimated from the critical values of the chi-square distribution as [10]:

L = χt2,(1−α )1 N

(5)

A training sample of normal subjects is used to capture the normal variability of myocardial contractility. In practice, however, extreme values of the ILM vectors may arise from some unexpected local abnormalities or due to errors in boundary delineation. This can considerably affect the calculation of the mean and covariance matrix. Therefore, a robust estimation of the tolerance region parameters is required. A natural robust estimator for the central observation of the distribution can be found by replacing the mean by the median vector, denoted as v * . A weighted estimation of the covariance can then be achieved in an iterative manner, where the robust covariance matrix Sv* at iteration t + 1 is calculated as: N

Sv* (t + 1) =

∑ w (v , v , S (t ))(v 2

i

*

* v

i

)(

− v * vi − v *

i =1

N

∑ ( i =1

)

w vi , v * , Sv* (t )

T

)

(6)

Shape-Based Myocardial Contractility Analysis Using Multivariate Outlier Detection

837

where w is a weight calculated from the observation, the median and the covariance matrix at previous iteration. The idea behind this formulation is to weight equally and heavily the observations that are close to the median and decrease the weights for observation further away. This procedure is repeated until the values of the weights do not change significantly. A definition of the weights can be written as follows:

(

w v, v * , S *

)

⎧⎪ 1 ⎪⎪ ⎪⎪ ⎛ ⎪ ⎜ d v, v * , S * − d0 = ⎪⎨ ⎪⎪exp ⎜⎜⎜− ⎜⎜⎜ 2σ02 ⎪⎪⎪ ⎜ ⎪⎪⎩ ⎝

((

)

(

)

if d v, v * , S * < d0 ⎞

) ⎟⎟⎟⎟ 2

⎟ ⎟⎟⎟ ⎠⎟

elsewhere

(7)

where d0 is a threshold calculated from the median d * and the robust standard deviation σ * of all distances [9], and σ0 specifies the decay rate for distances above the threshold, i.e.,:

d0 = d * + c1σ * (2 ≤ c1 ≤ 3) and σ0 = c2 σ * (0

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2007, 10 conf., part 2

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2007, 10 conf., part 1

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2002

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2002

Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2004, 7 conf

Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2004, 7 conf

Medical Image Computing and Computer-Assisted Intervention, Part III - MICCAI 2011

Medical Image Computing and Computer-Assisted Intervention, Part I - MICCAI 2011

Medical Image Computing and Computer-Assisted Intervention, Part II - MICCAI 201

Advances in Visual Computing, 3 conf., ISVC 2007, part 2

Agent Computing and Multi-Agent Systems, 10 conf., PRIMA 2007

Computing and Combinatorics, 13 conf., COCOON 2007

Affective Computing and Intelligent Interaction, 2 conf., ACII 2007

Advances in Grid and Pervasive Computing, 2 conf., GPC 2007

Advances in Visual Computing, 3 conf., ISVC 2007, part 1

Computer Algebra in Scientific Computing, 10 conf., CASC 2007

Medical Image Computing and Computer-Assisted Intervention MICCAI 2006: 9th International Conference, Copenhagen, Denmark, October 1-6, 2006, Proceedings,

Adaptive and Natural Computing Algorithms, 8 conf., ICANNGA 2007, part 2

Digital Image Processing - Part 2

Image Analysis, 15 conf., SCIA 2007

Ubiquitous Computing Systems, 4 conf., UCS 2007

UbiComp 2007.. Ubiquitous Computing, 9 conf

Pervasive Computing, 5 conf., PERVASIVE 2007

Advances in Multimedia Modeling, 13 conf., MMM 2007, Part 2

Computing and Combinatorics, 2 conf., COCOON '96

Medical Image Computing And Computer-assisted Intervention -- Miccai 2004: 7th International Conference Saint-malo, France, September 26-29, 2004, Pro ... s, Part One (Lecture Notes in Computer Science)

Medical Image Computing And Computer-assisted Intervention -- Miccai 2004: 7th International Conference Saint-malo, France, September 26-29, 2004, Pro ..., Part Two (Lecture Notes in Computer Science)

Dependable Computing, 3 conf., LADC 2007

Medical image computing and computer-assisted intervention - MICCAI 2009 : 12th international conference, London, UK, September 20-24, 2009 ; proceedings. Part II

Business Information Systems, 10 conf., BIS 2007

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2007, 10 conf., part 2

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2007, 10 conf., part 1

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2002

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2002

Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2004, 7 conf

Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2004, 7 conf

Medical Image Computing and Computer-Assisted Intervention, Part III - MICCAI 2011

Medical Image Computing and Computer-Assisted Intervention, Part I - MICCAI 2011

Medical Image Computing and Computer-Assisted Intervention, Part II - MICCAI 201

Advances in Visual Computing, 3 conf., ISVC 2007, part 2

Agent Computing and Multi-Agent Systems, 10 conf., PRIMA 2007

Computing and Combinatorics, 13 conf., COCOON 2007

Affective Computing and Intelligent Interaction, 2 conf., ACII 2007

Advances in Grid and Pervasive Computing, 2 conf., GPC 2007

Advances in Visual Computing, 3 conf., ISVC 2007, part 1

Computer Algebra in Scientific Computing, 10 conf., CASC 2007

Medical Image Computing and Computer-Assisted Intervention MICCAI 2006: 9th International Conference, Copenhagen, Denmark, October 1-6, 2006, Proceedings,

Adaptive and Natural Computing Algorithms, 8 conf., ICANNGA 2007, part 2

Digital Image Processing - Part 2

Image Analysis, 15 conf., SCIA 2007

Ubiquitous Computing Systems, 4 conf., UCS 2007

UbiComp 2007.. Ubiquitous Computing, 9 conf

Pervasive Computing, 5 conf., PERVASIVE 2007

Advances in Multimedia Modeling, 13 conf., MMM 2007, Part 2

Computing and Combinatorics, 2 conf., COCOON '96

Medical Image Computing And Computer-assisted Intervention -- Miccai 2004: 7th International Conference Saint-malo, France, September 26-29, 2004, Pro ... s, Part One (Lecture Notes in Computer Science)

Medical Image Computing And Computer-assisted Intervention -- Miccai 2004: 7th International Conference Saint-malo, France, September 26-29, 2004, Pro ..., Part Two (Lecture Notes in Computer Science)

Dependable Computing, 3 conf., LADC 2007

Medical image computing and computer-assisted intervention - MICCAI 2009 : 12th international conference, London, UK, September 20-24, 2009 ; proceedings. Part II

Business Information Systems, 10 conf., BIS 2007

Recommend Documents