National Academies Press: OpenBook
Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
×

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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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.)

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Page viii Cite
Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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.

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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.

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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

Page xvii Cite
Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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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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Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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Page xvii Cite
Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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Suggested Citation:"FRONT MATTER." National Research Council. 1996. Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press. doi: 10.17226/5066.
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Next: 1 INTRODUCTION AND SUMMARY »
Mathematics and Physics of Emerging Biomedical Imaging Get This Book
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This cross-disciplinary book documents the key research challenges in the mathematical sciences and physics that could enable the economical development of novel biomedical imaging devices. It is hoped that the infusion of new insights from mathematical scientists and physicists will accelerate progress in imaging. Incorporating input from dozens of biomedical researchers who described what they perceived as key open problems of imaging that are amenable to attack by mathematical scientists and physicists, this book introduces the frontiers of biomedical imaging, especially the imaging of dynamic physiological functions, to the educated nonspecialist.

Ten imaging modalities are covered, from the well-established (e.g., CAT scanning, MRI) to the more speculative (e.g., electrical and magnetic source imaging). For each modality, mathematics and physics research challenges are identified and a short list of suggested reading offered. Two additional chapters offer visions of the next generation of surgical and interventional techniques and of image processing. A final chapter provides an overview of mathematical issues that cut across the various modalities.

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