Mathematics and Physics of
Emerging Biomedical Imaging

Committee on the Mathematics and Physics of
Emerging Dynamic Biomedical Imaging
Board on Mathematical Sciences
Board on Physics and Astronomy
Commission on Physical Sciences, Mathematics, and Applications
National Research Council
and
Board on Biobehavioral Sciences and Mental Disorders
Institute of Medicine

National Academy Press
Washington, D.C. 1996



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Mathematics and Physics of Emerging Biomedical Imaging Committee on the Mathematics and Physics of Emerging Dynamic Biomedical Imaging Board on Mathematical Sciences Board on Physics and Astronomy Commission on Physical Sciences, Mathematics, and Applications National Research Council and Board on Biobehavioral Sciences and Mental Disorders Institute of Medicine National Academy Press Washington, D.C. 1996

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Page ii NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. Support for this project was provided by the Advanced Research Projects Agency, the Department of Energy, and the National Institute of Mental Health. Library of Congress Catalog Card Number 95-72622 International Standard Book Number 0-309-05387-0 Copyright 1996 by the National Academy of Sciences. All rights reserved. Available from National Academy Press 2101 Constitution Avenue, NW Washington, DC 20418 Available on the Internet via the World Wide Web at the URL: http://www.nas.edu/ Printed in the United States of America COVER ILLUSTRATIONS: The upper figure was produced by rapid volumetric magnetic resonance imaging (MRI) after injection of a paramagnetic contrast agent and shows vessel anatomy, kidney perfusion, and ureters (bright). The contrast agent causes urine and blood to produce different magnetic resonance signals. (Illustration courtesy of George Holland, University of Pennsylvania and General Electric Medical Systems.) The lower illustration, an example of modern non-invasive computed tomography (CT), shows calcium deposits in the aorta (center of image) and the blood vessel anatomy. It was produced using rapid data collection via spiral CT with injected contrast material. (Illustration courtesy of Siemens Medical Systems.)

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Page iii COMMITTEE ON THE MATHEMATICS AND PHYSICS OF EMERGING DYNAMIC BIOMEDICAL IMAGING  THOMAS BUDINGER, Lawrence Berkeley National Laboratory, Co-chair FELIX WEHRLI, University of Pennsylvania Medical Center, Co-chair S. MORRIS BLUMENFELD, General Electric Medical Systems F. ALBERTO GRUNBAUM, University of California at Berkeley R. MARK HENKELMAN, University of Toronto PAUL C. LAUTERBUR, University of Illinois at Urbana-Champaign WILFRIED LOEFFLER, Siemens Medical Systems, Inc. FRANK NATTERER, University of Muenster SARAH JANE NELSON, University of California at San Francisco LAWRENCE SHEPP, AT&T Bell Laboratories ROBERT G. SHULMAN, Yale University BENJAMIN MING WAH TSUI, University of North Carolina at Chapel Hill SCOTT T. WEIDMAN, Senior Staff Officer, Board on Mathematical Sciences ROBERT L. RIEMER, Associate Director, Board on Physics and Astronomy CONSTANCE M. PECHURA, Director, Board on Biobehavioral Sciences and Mental Disorders

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Page iv BOARD ON MATHEMATICAL SCIENCES AVNER FRIEDMAN, University of Minnesota, Chair LOUIS AUSLANDER, City University of New York HYMAN BASS, Columbia University MARY ELLEN BOCK, Purdue University PETER E. CASTRO, Eastman Kodak Company FAN R.K. CHUNG, University of Pennsylvania R. DUNCAN LUCE, University of California at Irvine SUSAN M. MONTGOMERY, University of Southern California GEORGE L. NEMHAUSER, Georgia Institute of Technology ANIL NERODE, Cornell University INGRAM OLKIN, Stanford University RONALD F. PEIERLS, Brookhaven National Laboratory DONALD ST. P. RICHARDS, University of Virginia MARY F. WHEELER, Rice University WILLIAM P. ZIEMER, Indiana University Ex Officio Member JON R. KETTENRING, Bell Communications Research, Inc. Chair, Committee on Applied and Theoretical Statistics Staff JOHN R. TUCKER, Director SCOTT T. WEIDMAN, Senior Staff Officer (on loan from Board on Chemical Sciences and Technology) JACK ALEXANDER, Staff Officer RUTH E. O'BRIEN, Staff Associate BARBARA WRIGHT, Administrative Assistant

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Page v BOARD ON PHYSICS AND ASTRONOMY DAVID N. SCHRAMM, University of Chicago, Chair ROBERT C. DYNES, University of California at San Diego, Vice-chair LLOYD ARMSTRONG, University of Southern California DAVID H. AUSTON, Rice University IRA B. BERNSTEIN, Yale University PRAVEEN CHAUDHARI, IBM T.J. Watson Research Center SANDRA M. FABER, University of California at Santa Cruz HANS FRAUENFELDER, Los Alamos National Laboratory JEROME I. FRIEDMAN, Massachusetts Institute of Technology MARGARET J. GELLER, Harvard-Smithsonian Center for Astrophysics MARTHA P. HAYNES, Cornell University WILLIAM KLEMPERER, Harvard University ALBERT NARATH, Sandia National Laboratories JOSEPH M. PROUD, GTE Corporation ANTHONY C.S. READHEAD, California Institute of Technology ROBERT C. RICHARDSON, Cornell University JOHANNA STACHEL, State University of New York at Stony Brook DAVID T. WILKINSON, Princeton University Staff DONALD C. SHAPERO, Director ROBERT L. RIEMER, Associate Director DANIEL MORGAN, Staff Officer NATASHA CASEY, Program Assistant STEPHANIE Y. SMITH, Secretary

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Page vi COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS ROBERT J. HERMANN, United Technologies Corporation, Chair STEPHEN L. ADLER, Institute for Advanced Study PETER M. BANKS, Environmental Research Institute of Michigan SYLVIA T. CEYER, Massachusetts Institute of Technology L. LOUIS HEGEDUS, W.R. Grace & Company JOHN E. HOPCROFT, Cornell University RHONDA HUGHES, Bryn Mawr College SHIRLEY A. JACKSON, U.S. Nuclear Regulatory Commission KENNETH I. KELLERMANN, National Radio Astronomy Observatory KEN KENNEDY, Rice University THOMAS A. PRINCE, California Institute of Technology JEROME SACKS, National Institute of Statistical Sciences L.E. SCRIVEN, University of Minnesota LEON T. SILVER, California Institute of Technology CHARLES P. SLICHTER, University of Illinois at Urbana-Champaign ALVIN W. TRIVELPIECE, Oak Ridge National Laboratory SHMUEL WINOGRAD, IBM T.J. Watson Research Center CHARLES A. ZRAKET, MITRE Corporation (retired) NORMAN METZGER, Executive Director

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Page vii BOARD ON BIOBEHAVIORAL SCIENCES AND MENTAL DISORDERS JOSEPH T. COYLE, Harvard Medical School, Chair ELLEN FRANK, University of Pittsburgh School of Medicine, Vice-chair ALBERT BANDURA, Stanford University RICHARD J. BONNIE, University of Virginia WILLIAM E. BUNNEY, JR., University of California at Irvine GLEN R. ELLIOTT, University of California at San Francisco RONALD A. FELDMAN, Columbia University BEATRIX A. HAMBURG, William T. Grant Foundation JIMMIE HOLLAND, Memorial Sloan-Kettering Cancer Center PHILIP S. HOLZMAN, Harvard University SPERO M. MANSON, University of Colorado Health Sciences Center ROGER E. MEYER, George Washington University ROBERT MICHELS, Cornell University Medical College CHARLES P. O'BRIEN, University of Pennsylvania Medical Center STEVEN S. SHARFSTEIN, Sheppard and Enoch Pratt Hospital GARY L. TISCHLER, University of California at Los Angeles STEPHEN G. WAXMAN, Yale University Staff CONSTANCE M. PECHURA, Director TERRI SCANLAN, Administrative Assistant

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Page viii The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Harold Liebowitz is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce Alberts and Dr. Harold Liebowitz are chairman and vice chairman, respectively, of the National Research Council.

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Page ix PREFACE The Committee on the Mathematics and Physics of Emerging Dynamic Biomedical Imaging was constituted in 1993 and given the charge to "write a report that gives a survey of the emerging contributions of the mathematical sciences and physics to dynamic biomedical imaging and identifies and recommends specific mathematical sciences and physics research to accelerate the development and implementation of new medical imaging systems." At its first meeting, the committee discussed the frontiers of biomedical imaging that could profit from more involvement from physicists and mathematical scientists, outlined its proposed report, and identified individuals, listed below, who could supplement the committee's expertise in documenting these frontiers and the related research opportunities. At its subsequent two meetings, the committee drew on the large quantity of valuable drafts to generate the survey it envisioned. It is hoped that the present report will provide a readable introduction to emerging techniques of biomedical imaging for mathematical scientists and physicists and encourage some of them to apply their skills to the research challenges that will make these emerging techniques practical. The committee gratefully acknowledges the substantial contributions of the following people, who provided material for the committee to incorporate in its report:  Richard Albanese, Brooks Air Force Base Robert Alfano, City University of New York Simon Arridge, University College, London Randall Barbour, SUNY Health Science Center at Brooklyn Harrison Barrett, University of Arizona James Berryman, Lawrence Livermore National Laboratory Douglas P. Boyd, IMATRON-West Britton Chance, University of Pennsylvania Margaret Cheney, Rensselaer Polytechnic Institute Rolf Clack, University of Utah James G. Colsher, GE Medical Systems Robert Cox, Medical College of Wisconsin Michel Defrise, Vrije Universiteit

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Page x Charles L. Dumoulin, General Electric R&D Center Alan C. Evans, Montreal Neurological Institute Stuart Foster, University of Toronto C. Franzone, University of Pavia E.C. Frey, University of North Carolina at Chapel Hill Michael M. Graham, University of Washington Enrico Gratton, University of Illinois at Urbana-Champaign Peter J. Green, University of Bristol James F. Greenleaf, Mayo Clinic Grant T. Gullberg, University of Utah Semion Gutman, University of North Carolina at Charlotte E. Mark Haacke, Mallinckrodt Institute of Radiology Dennis M. Healy, Dartmouth College Manfried Hoke, University of Muenster Paul W. Hughett, Lawrence Berkeley National Laboratory James Hyde, Medical College of Wisconsin V. Isakov, Wichita State University Steven A. Johnson, University of Utah Valen E. Johnson, Duke University Willi A. Kalender, University of Erlangen-Nuremberg Linda Kaufman, AT&T Bell Laboratories Ronald Kikinis, Harvard Medical School Michael A. King, University of Massachusetts Medical School Michael Klibanov, University of North Carolina at Charlotte David Levin, University of Chicago Tom Lewellen, University of Washington Jorge Llacer, Lawrence Berkeley National Laboratory Bernd Luetkenhoener, University of Muenster Albert Macovski, Stanford University Ravi S. Menon, University of Western Ontario at London Michael I. Miller, Washington University Charles Mistretta, University of Wisconsin at Madison Adrian Nachman, University of Rochester Claude Nahmias, Chedoke-McMaster Hospitals William D. O'Brien, Jr., University of Illinois at Urbana-Champaign Matthew O'Donnell, University of Michigan John Ollinger, Washington University Arnulf Oppelt, Siemens Medical Engineering Group Walter W. Peppler, University of Wisconsin

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Page xi Stephen M. Pizer, University of North Carolina at Chapel Hill Jack Reid, Drexel University Joel G. Rogers, TRIUMF, University of British Columbia Yoram Rudy, Case Western Reserve University David Saloner, Veterans Affairs Medical Center, San Francisco Guenter Schwierz, Siemens Medical Engineering Group V. Sharafutdinov, Institute of Mathematics, Novosibirsk Gunnar Sparr, Lund Institute of Technology Terry Spinks, Hammersmith Hospital J. Sylvester, University of Washington Robert Turner, University of London Eugene Veklerov, Lawrence Berkeley Laboratory Robert Weisskoff, Massachusetts General Hospital The committee is also grateful to the six anonymous reviewers, whose comments strengthened this report considerably.

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Page xiii CONTENTS 1 INTRODUCTION AND SUMMARY 1   Plates 1.1 through 1.7 follow page 12.   2 X-RAY PROJECTION IMAGING 13   2.1 Introduction 13   2.2 Mammography 15   2.2.1 Scanning Methods 15   2.2.2 Area Detectors 16   2.3 Chest Radiography 18   2.3.1 Scanning Methods 18   2.3.2 Area Detectors 18   2.4 Digital Fluoroscopy 19   2.5 Portal Imaging 20   2.6 Research Opportunities 20   2.7 Suggested Reading 21 3 X-RAY COMPUTED TOMOGRAPHY 23   3.1 Introduction 23   3.1.1 History 23   3.1.2 Principle of Operation 24   3.2 Present Status of CT Instrumentation and Technology 26   3.2.1 X-Ray Tubes 26   3.2.2 Detector Systems 26   3.2.3 Image Artifacts 28   3.2.4 Quantitative CT 29   3.2.5 Requirements for High-Speed CT 30   3.3 Spiral CT 31   3.4 Electron Beam Techniques 32   3.5 Data Handling and Display Techniques 33   3.6 Research Opportunities 34   3.7 Suggested Reading 35 4 MAGNETIC RESONANCE IMAGING 37   4.1 Principles of Magnetic Resonance Imaging 38   4.2 Hardware 41   4.2.1 Magnet Systems: Current Status and Opportunities 41

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Page xiv   4.2.2 Pulsed-field MRI Systems 43   4.2.3 Radio-frequency Coils for MRI 45   4.2.4 Magnetic Field Gradients 48   4.2.5 Research Opportunities for MRI Hardware 53   4.2.6 Suggested Reading Related to MRI Hardware 54   4.3 Dynamic MR Image Reconstruction 56   4.3.1 Partial Fourier Reconstruction 56   4.3.2 Reduced Gibbs Ringing 58   4.3.3 High-speed K-space Coverage Techniques 60   4.3.4 Research Opportunities in Dynamic MR Image Reconstruction 61   4.3.5 Suggested Reading Related to Dynamic MR Image Reconstruction 61   4.4 Applications of Dynamic MRI 62   4.4.1 Blood Flow 62   4.4.2 Diffusion Imaging 65   4.4.3 Other Tissue Parameters 66   4.4.4 Functional Brain MRI 68   4.4.5 Multinuclear MRI 75   4.4.6 Microscopic Imaging 78   4.4.7 Research Opportunities Related to Applying Dynamic MRI 80   4.4.8 Suggested Reading on Applications of Dynamic MRI 83 5 SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY 89   5.1 Introduction 89   5.2 Physical and Instrumentation Factors That Affect SPECT Images 91   5.3 SPECT Instrumentation 92   5.3.1 SPECT System Designs 92   5.3.2 Special Collimators 93   5.3.3 New Radiation Detector Technologies 94   5.4 SPECT Image Reconstruction 96   5.4.1 The SPECT Reconstruction Problem 96   5.4.2 SPECT Image Reconstruction Methods 98   5.5 Research Opportunities 102   5.6 Suggested Reading 103 6 POSITRON EMISSION TOMOGRAPHY 105   6.1 Introduction 105   6.1.1 History 105   6.1.2 Applications 106

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Page xv   6.1.3 Principle of Operation 106   6.2 Current Status of PET Technology 108   6.2.1 y-Ray Detectors 108   6.2.2 Limitations of the Spatial Resolution 110   6.2.3 System Electronics 111   6.2.4 Data Correction and Reconstruction Algorithms 112   6.3 Three-Dimensional Acquisition and Reconstruction 114   6.3.1 Principle of Three-Dimensional Acquisition 114   6.3.2 Three-Dimensional Reconstruction 114   6.3.3 Scatter Correction in Three Dimensions 117   6.3.4 Attenuation Correction in Three Dimensions 118   6.4 Research Opportunities 119   6.5 Suggested Reading 119 7 ULTRASONICS 121   7.1 Introduction 121   7.2 Instrumentation 122   7.2.1 Transducers 122   7.2.2 Ultrasonic Beam Forming 123   7.2.3 Signal Processing 124   7.3 Scattering 125   7.4 Ultrasonic Tomography 127   7.5 Research Opportunities 128   7.6 Suggested Reading 129 8 ELECTRICAL SOURCE IMAGING 133   8.1 Introduction 133   8.2 Outline of ESI Reconstruction Methods 135   8.2.1 Forward Problem 136   8.2.2 Inverse Problem 137   8.2.3 Temporal Regularization 138   8.3 Research Problems and Opportunities 140   8.4 Suggested Reading 141 9 ELECTRICAL IMPEDANCE TOMOGRAPHY 143   9.1 Introduction 143   9.2 Comparison to Other Modalities 143   9.3 Present Status of EIT and Limitations 144   9.4 Research Opportunities 145

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Page xvi   9.5 Suggested Reading 146 10 MAGNETIC SOURCE IMAGING 147   10.1 Introduction 147   10.2 Mathematical Considerations 149   10.3 Source Models 150   10.4 Resolution 152   10.5 Summary 153   10.6 Research Opportunities 153   10.7 Suggested Reading 154 11 MEDICAL OPTICAL IMAGING 157   11.1 Introduction 157   11.2 Data Acquisition Strategies 158   11.3 Comparisons with Other Imaging Modalities 159   11.4 Possible Applications of Optical Tomography 161   11.5 Research Opportunities 162   11.6 Suggested Reading 163 12 IMAGE-GUIDED MINIMALLY INVASIVE DIAGNOSTIC AND THERAPEUTIC INTERVENTIONAL PROCEDURES 167   12.1 Therapeutic Intervention Experience with Different Imaging Modalities 168   12.1.1 X-Ray Imaging 168   12.1.2 Computed Tomography 168   12.1.3 Ultrasound 169   12.1.4 Endoscopy 170   12.1.5 Magnetic Resonance Imaging 170   12.2 The Roles of Imaging in Therapy 172   12.2.1 Planning 172   12.2.2 Guidance 173   12.2.3 Monitoring and Localization 175   12.2.4 Control 176   12.3 Thermal Surgery 177   12.3.1 Interstitial Laser Therapy 178   12.3.2 Cryotherapy 178   12.3.3 Focused Ultrasound 179   12.4 Research and Development Opportunities 182   12.5 Suggested Reading 185

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Page xvii 13 FRONTIERS OF IMAGE PROCESSING FOR MEDICINE 187   13.1 Image Segmentation 189   13.2 Computational Anatomy 190   13.3 Registration of Multimodality Images 191   13.4 Synthesis of Parametric Images 192   13.5 Data Visualization 193   13.6 Treatment Planning 194   13.7 Research Opportunities 195   13.8 Suggested Reading 196 14 A CROSS-CUTTING LOOK AT THE MATHEMATICS OF EMERGING BIOMEDICAL IMAGING 199   14.1 Mathematical Models for Particular Imaging Modalities 199   14.1.1 Transmission Computed Tomography 199   14.1.2 Emission Computed Tomography 202   14.1.3 Ultrasound Computed Tomography 205   14.1.4 Optical Tomography 207   14.1.5 Electrical Impedance Tomography 209   14.1.6 Magnetic Resonance Imaging 209   14.1.7 Vector Tomography 211   14.1.8 Tensor Tomography 212   14.1.9 Magnetic Source Imaging 213   14.1.10 Electrical Source Imaging 214   14.2 Forward Problems 215   14.3 Inverse Problems 215   14.4 Ill-Posedness and Regularization 217   14.4.1 The Tikhonov-Phillips Method 218   14.4.2 The Truncated Singular Value Decomposition 219   14.4.3 Iterative Methods 219   14.4.4 Regularization by Discretization 220   14.4.5 Maximum Entropy 220   14.5 Sampling 221   14.5.1 Sampling in Real Space 221   14.5.2 Sampling in Fourier Space 222   14.6 Priors and Side Information 222   14.7 Research Opportunities 224   14.8 Suggested Reading 226 INDEX 231

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