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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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.
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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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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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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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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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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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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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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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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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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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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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CONTENTS
1 | INTRODUCTION AND SUMMARY | |
Plates 1.1 through 1.7 follow page 12. | ||
2 | X-RAY PROJECTION IMAGING | |
2.1 Introduction | ||
2.2 Mammography | ||
2.2.1 Scanning Methods | ||
2.2.2 Area Detectors | ||
2.3 Chest Radiography | ||
2.3.1 Scanning Methods | ||
2.3.2 Area Detectors | ||
2.4 Digital Fluoroscopy | ||
2.5 Portal Imaging | ||
2.6 Research Opportunities | ||
2.7 Suggested Reading | ||
3 | X-RAY COMPUTED TOMOGRAPHY | |
3.1 Introduction | ||
3.1.1 History | ||
3.1.2 Principle of Operation | ||
3.2 Present Status of CT Instrumentation and Technology | ||
3.2.1 X-Ray Tubes | ||
3.2.2 Detector Systems | ||
3.2.3 Image Artifacts | ||
3.2.4 Quantitative CT | ||
3.2.5 Requirements for High-Speed CT | ||
3.3 Spiral CT | ||
3.4 Electron Beam Techniques | ||
3.5 Data Handling and Display Techniques | ||
3.6 Research Opportunities | ||
3.7 Suggested Reading | ||
4 | MAGNETIC RESONANCE IMAGING | |
4.1 Principles of Magnetic Resonance Imaging | ||
4.2 Hardware | ||
4.2.1 Magnet Systems: Current Status and Opportunities |
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4.2.2 Pulsed-field MRI Systems | ||
4.2.3 Radio-frequency Coils for MRI | ||
4.2.4 Magnetic Field Gradients | ||
4.2.5 Research Opportunities for MRI Hardware | ||
4.2.6 Suggested Reading Related to MRI Hardware | ||
4.3 Dynamic MR Image Reconstruction | ||
4.3.1 Partial Fourier Reconstruction | ||
4.3.2 Reduced Gibbs Ringing | ||
4.3.3 High-speed K-space Coverage Techniques | ||
4.3.4 Research Opportunities in Dynamic MR Image Reconstruction | ||
4.3.5 Suggested Reading Related to Dynamic MR Image Reconstruction | ||
4.4 Applications of Dynamic MRI | ||
4.4.1 Blood Flow | ||
4.4.2 Diffusion Imaging | ||
4.4.3 Other Tissue Parameters | ||
4.4.4 Functional Brain MRI | ||
4.4.5 Multinuclear MRI | ||
4.4.6 Microscopic Imaging | ||
4.4.7 Research Opportunities Related to Applying Dynamic MRI | ||
4.4.8 Suggested Reading on Applications of Dynamic MRI | ||
5 | SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY | |
5.1 Introduction | ||
5.2 Physical and Instrumentation Factors That Affect SPECT Images | ||
5.3 SPECT Instrumentation | ||
5.3.1 SPECT System Designs | ||
5.3.2 Special Collimators | ||
5.3.3 New Radiation Detector Technologies | ||
5.4 SPECT Image Reconstruction | ||
5.4.1 The SPECT Reconstruction Problem | ||
5.4.2 SPECT Image Reconstruction Methods | ||
5.5 Research Opportunities | ||
5.6 Suggested Reading | ||
6 | POSITRON EMISSION TOMOGRAPHY | |
6.1 Introduction | ||
6.1.1 History | ||
6.1.2 Applications |
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6.1.3 Principle of Operation | ||
6.2 Current Status of PET Technology | ||
6.2.1 y-Ray Detectors | ||
6.2.2 Limitations of the Spatial Resolution | ||
6.2.3 System Electronics | ||
6.2.4 Data Correction and Reconstruction Algorithms | ||
6.3 Three-Dimensional Acquisition and Reconstruction | ||
6.3.1 Principle of Three-Dimensional Acquisition | ||
6.3.2 Three-Dimensional Reconstruction | ||
6.3.3 Scatter Correction in Three Dimensions | ||
6.3.4 Attenuation Correction in Three Dimensions | ||
6.4 Research Opportunities | ||
6.5 Suggested Reading | ||
7 | ULTRASONICS | |
7.1 Introduction | ||
7.2 Instrumentation | ||
7.2.1 Transducers | ||
7.2.2 Ultrasonic Beam Forming | ||
7.2.3 Signal Processing | ||
7.3 Scattering | ||
7.4 Ultrasonic Tomography | ||
7.5 Research Opportunities | ||
7.6 Suggested Reading | ||
8 | ELECTRICAL SOURCE IMAGING | |
8.1 Introduction | ||
8.2 Outline of ESI Reconstruction Methods | ||
8.2.1 Forward Problem | ||
8.2.2 Inverse Problem | ||
8.2.3 Temporal Regularization | ||
8.3 Research Problems and Opportunities | ||
8.4 Suggested Reading | ||
9 | ELECTRICAL IMPEDANCE TOMOGRAPHY | |
9.1 Introduction | ||
9.2 Comparison to Other Modalities | ||
9.3 Present Status of EIT and Limitations | ||
9.4 Research Opportunities |
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9.5 Suggested Reading | ||
10 | MAGNETIC SOURCE IMAGING | |
10.1 Introduction | ||
10.2 Mathematical Considerations | ||
10.3 Source Models | ||
10.4 Resolution | ||
10.5 Summary | ||
10.6 Research Opportunities | ||
10.7 Suggested Reading | ||
11 | MEDICAL OPTICAL IMAGING | |
11.1 Introduction | ||
11.2 Data Acquisition Strategies | ||
11.3 Comparisons with Other Imaging Modalities | ||
11.4 Possible Applications of Optical Tomography | ||
11.5 Research Opportunities | ||
11.6 Suggested Reading | ||
12 | IMAGE-GUIDED MINIMALLY INVASIVE DIAGNOSTIC AND THERAPEUTIC INTERVENTIONAL PROCEDURES | |
12.1 Therapeutic Intervention Experience with Different Imaging Modalities | ||
12.1.1 X-Ray Imaging | ||
12.1.2 Computed Tomography | ||
12.1.3 Ultrasound | ||
12.1.4 Endoscopy | ||
12.1.5 Magnetic Resonance Imaging | ||
12.2 The Roles of Imaging in Therapy | ||
12.2.1 Planning | ||
12.2.2 Guidance | ||
12.2.3 Monitoring and Localization | ||
12.2.4 Control | ||
12.3 Thermal Surgery | ||
12.3.1 Interstitial Laser Therapy | ||
12.3.2 Cryotherapy | ||
12.3.3 Focused Ultrasound | ||
12.4 Research and Development Opportunities | ||
12.5 Suggested Reading |
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13 | FRONTIERS OF IMAGE PROCESSING | |
13.1 Image Segmentation | ||
13.2 Computational Anatomy | ||
13.3 Registration of Multimodality Images | ||
13.4 Synthesis of Parametric Images | ||
13.5 Data Visualization | ||
13.6 Treatment Planning | ||
13.7 Research Opportunities | ||
13.8 Suggested Reading | ||
14 | A CROSS-CUTTING LOOK AT THE MATHEMATICS OF EMERGING BIOMEDICAL IMAGING | |
14.1 Mathematical Models for Particular Imaging Modalities | ||
14.1.1 Transmission Computed Tomography | ||
14.1.2 Emission Computed Tomography | ||
14.1.3 Ultrasound Computed Tomography | ||
14.1.4 Optical Tomography | ||
14.1.5 Electrical Impedance Tomography | ||
14.1.6 Magnetic Resonance Imaging | ||
14.1.7 Vector Tomography | ||
14.1.8 Tensor Tomography | ||
14.1.9 Magnetic Source Imaging | ||
14.1.10 Electrical Source Imaging | ||
14.2 Forward Problems | ||
14.3 Inverse Problems | ||
14.4 Ill-Posedness and Regularization | ||
14.4.1 The Tikhonov-Phillips Method | ||
14.4.2 The Truncated Singular Value Decomposition | ||
14.4.3 Iterative Methods | ||
14.4.4 Regularization by Discretization | ||
14.4.5 Maximum Entropy | ||
14.5 Sampling | ||
14.5.1 Sampling in Real Space | ||
14.5.2 Sampling in Fourier Space | ||
14.6 Priors and Side Information | ||
14.7 Research Opportunities | ||
14.8 Suggested Reading | ||
INDEX |