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  • PHYSICS in NUCLEAR MEDICINE

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  • PHYSICS in NUCLEAR MEDICINE

    FOURTH EDITION

    Simon R. Cherry, PhDProfessor, Departments of Biomedical Engineering and RadiologyDirector, Center for Molecular and Genomic ImagingUniversity of CaliforniaDavisDavis, California

    James A. Sorenson, PhDEmeritus Professor of Medical PhysicsDepartment of Medical PhysicsUniversity of WisconsinMadisonMadison, Wisconsin

    Michael E. Phelps, PhDNorton Simon ProfessorChief, Division of Nuclear MedicineChair, Department of Molecular and Medical PharmacologyDirector, Crump Institute for Molecular ImagingDavid Geffen School of MedicineUniversity of CaliforniaLos AngelesLos Angeles, California

  • Working together to grow libraries in developing countries

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    Physics in Nuclear Medicine ISBN: 978-1-4160-5198-5

    Copyright 2012, 2003, 1987, 1980 by Saunders, an imprint of Elsevier Inc.

    No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publishers permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions.

    This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

    NoticeKnowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary or appropriate. Readers are advised to check the most current information provided (i) on procedures featured or (ii) by the manufacturer of each product to be administered, to verify the recommended dose or formula, the method and duration of administration, and contraindications. It is the responsibility of practitioners, relying on their own experience and knowledge of their patients, to make diagnoses, to determine dosages and the best treatment for each individual patient, and to take all appropriate safety precautions. To the fullest extent of the law, neither the Publisher nor the authors assume any liability for any injury and/or damage to persons or property as a matter of products arising out of or related to any use of the material contained in this book.

    Library of Congress Cataloging-in-Publication Data

    Cherry, Simon R.Physics in nuclear medicine / Simon R. Cherry, James A. Sorenson, Michael E. Phelps. 4th ed. p. ; cm. Includes bibliographical references and index. ISBN 978-1-4160-5198-5 (hardback : alk. paper) 1. Medical physics. 2. Nuclear medicine. I. Sorenson, James A., 1938- II. Phelps, Michael E. III. Title. [DNLM: 1. Health Physics. 2. Nuclear Medicine. WN 110] R895.S58 2012 610.153dc23 2011021330

    Senior Content Strategist: Don ScholzContent Development Specialist: Lisa BarnesPublishing Services Manager: Anne AltepeterSenior Project Manager: Janaki Srinivasan KumarProject Manager: Cindy ThomsDesign Direction: Ellen Zanolle

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  • Preface

    Physics and instrumentation affect all of the subspecialty areas of nuclear medicine. Because of their fundamental importance, they usually are taught as a separate course in nuclear medicine training programs. This book is intended for use in such programs by physicians, technologists, and scientists who desire to become specialists in nuclear medicine and molecular imaging, as well as a reference source for physicians, scientists, and engineers in related fields.

    Although there have been substantial and remarkable changes in nuclear medicine, the goal of this book remains the same as it was for the first edition in 1980: to provide an introductory text for such courses, covering the physics and instrumentation of nuclear medicine in sufficient depth to be of permanent value to the trainee or student, but not at such depth as to be of interest only to the physics or instrumentation specialist. The fourth edition includes many recent advances, particularly in single-photon emission computed tomography (SPECT) and positron emission tomography (PET) imaging. As well, a new chapter is included on hybrid imaging techniques that combine the exceptional functional and physiologic imaging capabilities of SPECT and PET with the anatomically detailed techniques of computed tomography (CT) and magnetic resonance imaging (MRI). An introduction to CT scanning is also included in the new chapter.

    The fourth edition also marks the first use of color. We hope that this not only adds cosmetic appeal but also improves the clarity of our illustrations.

    The organization of this text proceeds from basic principles to more practi-cal aspects. After an introduction to nuclear medicine (Chapter 1), we provide a review of atomic and nuclear physics (Chapter 2) and basic principles of radioactivity and radioactive decay (Chapters 3 and 4). Radionuclide produc-tion methods are discussed in Chapter 5, followed by radiation interactions in Chapter 6. Basic principles of radiation detectors (Chapter 7), radiation-counting electronics (Chapter 8), and statistics (Chapter 9) are provided next.

    Following the first nine chapters, we move on to detailed discussions of nuclear medicine systems and applications. Pulse-height spectrometry, which plays an important role in many nuclear medicine procedures, is described in Chapter 10, followed by general problems in nuclear radiation counting in Chapter 11. Chapter 12 is devoted to specific types of nuclear radiation-counting instruments, for both in vivo and in vitro measurements.

    Chapters 13 through 20 cover topics in radionuclide imaging, beginning with a description of the principles and performance characteristics of gamma cameras (Chapters 13 and 14), which are still the workhorse of many nuclear medicine laboratories. We then discuss general concepts of image quality in nuclear medicine (Chapter 15), followed by an introduction to the basic con-cepts of reconstruction tomography (Chapter 16).

    The instrumentation for and practical implementation of reconstruction tomography are discussed for SPECT in Chapter 17 and for PET in Chapter 18. Hybrid imaging systems, as well as the basic principles of CT scanning, are covered in Chapter 19. Chapter 20 provides a summary of digital image processing techniques, which are important for all systems and applications.

    The imaging section of this text focuses primarily on instruments and tech-niques that now enjoy or appear to have the potential for achieving clinical

    v

  • vi Preface

    acceptance. However, nuclear medicine imaging has become increasingly important in the research environment. Therefore we have included some systems that are used for small-animal or other research purposes in these chapters.

    We then move on to basic concepts and some applications of tracer kinetic modeling (Chapter 21). Tracer kinetic modeling and its applications embody two of the most important strengths of nuclear medicine techniques: the ability to perform studies with minute (tracer) quantities of labeled molecules and the ability to extract quantitative biologic data from these studies. We describe the main assumptions and mathematical models used and present several examples of the application of these models for calculating physiologic, meta-bolic, and biochemical parameters

    The final two chapters address radiation dose and safety issues. Internal radiation dosimetry is presented in Chapter 22, and the final chapter presents an introduction to the problems of radiation safety and health physics (Chapter 23). We did not deal with more general problems in radiation biology, believing this topic to be of sufficient importance to warrant its own special treatment, as has been done already in several excellent books on the subject.

    Additional reading for more detailed infor mation is suggested at the end of each chapter. We also have included sample problems with solutions to illus-trate certain quantitative relationships and to demonstrate standard calcula-tions that are required in the practice of nuclear medicine. Systeme Internationale (SI) units are used throughout the text; however, traditional units still appear in a few places in the book, because these units remain in use in day-to-day practice in many laboratories. Appendix A provides a summary of conversion factors between SI and traditional units.

    Appendixes B, C, and D present tables of basic properties of elements and radionuclides, and of attenuation properties of some materials of basic rele-vance to nuclear medicine. Appendix E provides a summary of radiation dose estimates for a number of nuclear medicine procedures. Although much of this information now is available on the Internet, we believe that users of this text will find it useful to have a summary of the indicated quantities and param-eters conveniently available.

    Appendixes F and G provide more detailed discussions of Fourier trans-forms and convolutions, both of which are essential components of modern nuclear medicine imaging, especially reconstruction tomography. This is the only part of the book that makes extensive use of calculus.

    The fourth edition includes extensive revisions, and we are grateful to our many colleagues and friends who have assisted us with information, data, and figures. Particular gratitude is extended to Hendrik Pretorius, Donald Yapp, Jarek Glodo, Paul Kinahan, David Townsend, Richard Carson, Stephen Mather, and Freek Beekman. We also wish to thank readers who reported errors and inconsistencies in the third edition and brought these to our atten-tion. In particular, we recognize the contributions of Andrew Goertzen, Tim Turkington, Mark Madsen, Ing-Tsung Hsiao, Jyh Cheng Chen, Scott Metzler, Andrew Maidment, Lionel Zuckier, Jerrold Bushberg, Zongjian Cao, Marvin Friedman, and Fred Fahey. This feedback from our readers is critical in ensur-ing the highest level of accuracy in the text. Naturally, any mistakes that remain in this new edition are entirely our responsibility.

    We are grateful to Susie Helton (editorial assistance), and Robert Burnett and Simon Dvorak (graphics), at the University of CaliforniaDavis for their dedication to this project. We also appreciate the patience and efforts of the editorial staff at Elsevier, especially Lisa Barnes, Cindy Thoms, and Don Scholz. Finally, we thank our many colleagues who have used this book over the years and who have provided constructive feedback and suggestions for improvements that have helped to shape each new edition.

    Simon R. Cherry, James A. Sorenson, and Michael E. Phelps

  • vii

    CHAPTER 1 What Is Nuclear Medicine? 1 A. FUNDAMENTAL CONCEPTS 1 B. THE POWER OF NUCLEAR MEDICINE 1 C. HISTORICAL OVERVIEW 2 D. CURRENT PRACTICE OF NUCLEAR MEDICINE 4 E. THE ROLE OF PHYSICS IN NUCLEAR MEDICINE 6

    CHAPTER 2 Basic Atomic and Nuclear Physics 7 A. QUANTITIES AND UNITS 7

    1. Types of Quantities and Units 72. Mass and Energy Units 7

    B. RADIATION 8 C. ATOMS 9

    1. Composition and Structure 92. Electron Binding Energies and Energy Levels 93. Atomic Emissions 10

    D. THE NUCLEUS 131. Composition 132. Terminology and Notation 133. Nuclear Families 144. Forces and Energy Levels within the Nucleus 145. Nuclear Emissions 156. Nuclear Binding Energy 157. Characteristics of Stable Nuclei 16

    CHAPTER 3 Modes of Radioactive Decay 19 A. GENERAL CONCEPTS 19 B. CHEMISTRY AND RADIOACTIVITY 19 C. DECAY BY EMISSION 20 D. DECAY BY (, ) EMISSION 21 E. ISOMERIC TRANSITION AND INTERNAL CONVERSION 22 F. ELECTRON CAPTURE AND (EC, ) DECAY 24 G. POSITRON (+) AND (+, ) DECAY 25 H. COMPETITIVE + AND EC DECAY 26 I. DECAY BY EMISSION AND BY NUCLEAR FISSION 26 J. DECAY MODES AND THE LINE OF STABILITY 28 K. SOURCES OF INFORMATION ON RADIONUCLIDES 28

    CHAPTER 4 Decay of Radioactivity 31 A. ACTIVITY 31

    1. The Decay Constant 312. Definition and Units of Activity 31

    B. EXPONENTIAL DECAY 321. The Decay Factor 322. Half-Life 333. Average Lifetime 34

    Contents

  • viii Contents

    C. METHODS FOR DETERMINING DECAY FACTORS 341. Tables of Decay Factors 342. Pocket Calculators 353. Universal Decay Curve 35

    D. IMAGE-FRAME DECAY CORRECTIONS 35 E. SPECIFIC ACTIVITY 37 F. DECAY OF A MIXED RADIONUCLIDE SAMPLE 38 G. PARENT-DAUGHTER DECAY 39

    1. The Bateman Equations 392. Secular Equilibrium 403. Transient Equilibrium 414. No Equilibrium 41

    CHAPTER 5 Radionuclide and Radiopharmaceutical Production 43 A. REACTOR-PRODUCED RADIONUCLIDES 43

    1. Reactor Principles 432. Fission Fragments 443. Neutron Activation 45

    B. ACCELERATOR-PRODUCED RADIONUCLIDES 471. Charged-Particle Accelerators 472. Cyclotron Principles 473. Cyclotron-Produced Radionuclides 49

    C. RADIONUCLIDE GENERATORS 50 D. EQUATIONS FOR RADIONUCLIDE PRODUCTION 53

    1. Activation Cross-Sections 532. Activation Rates 543. Buildup and Decay of Activity 56

    E. RADIONUCLIDES FOR NUCLEAR MEDICINE 571. General Considerations 572. Specific Considerations 57

    F. RADIOPHARMACEUTICALS FOR CLINICAL APPLICATIONS 591. General Considerations 592. Labeling Strategies 593. Technetium-99m-Labeled Radiopharmaceuticals 604. Radiopharmaceuticals Labeled with Positron Emitters 605. Radiopharmaceuticals for Therapy Applications 616. Radiopharmaceuticals in Clinical Nuclear Medicine 61

    CHAPTER 6 Interaction of Radiation with Matter 63 A. INTERACTIONS OF CHARGED PARTICLES WITH MATTER 63

    1. Charged-Particle Interaction Mechanisms 632. Collisional Versus Radiation Losses 643. Charged-Particle Tracks 664. Deposition of Energy Along a Charged-Particle Track 675. The Cerenkov Effect 68

    B. CHARGED-PARTICLE RANGES 701. Alpha Particles 702. Beta Particles and Electrons 71

    C. PASSAGE OF HIGH-ENERGY PHOTONS THROUGH MATTER 741. Photon Interaction Mechanisms 742. The Photoelectric Effect 743. Compton Scattering 744. Pair Production 765. Coherent (Rayleigh) Scattering 776. Deposition of Photon Energy in Matter 77

    D. ATTENUATION OF PHOTON BEAMS 781. Attenuation Coefficients 782. Thick Absorbers, Narrow-Beam Geometry 793. Thick Absorbers, Broad-Beam Geometry 834. Polyenergetic Sources 84

  • Contents ix

    CHAPTER 7 Radiation Detectors 87 A. GAS-FILLED DETECTORS 87

    1. Basic Principles 872. Ionization Chambers 873. Proportional Counters 914. Geiger-Mller Counters 92

    B. SEMICONDUCTOR DETECTORS 96 C. SCINTILLATION DETECTORS 97

    1. Basic Principles 972. Photomultiplier Tubes 983. Photodiodes 994. Inorganic Scintillators 1005. Considerations in Choosing an Inorganic Scintillator 1036. Organic Scintillators 104

    CHAPTER 8 Electronic Instrumentation for Radiation Detection Systems 107 A. PREAMPLIFIERS 107 B. AMPLIFIERS 110

    1. Amplification and Pulse-Shaping Functions 1102. Resistor-Capacitor Shaping 1113. Baseline Shift and Pulse Pile-Up 112

    C. PULSE-HEIGHT ANALYZERS 1131. Basic Functions 1132. Single-Channel Analyzers 1133. Timing Methods 1144. Multichannel Analyzers 116

    D. TIME-TO-AMPLITUDE CONVERTERS 118 E. DIGITAL COUNTERS AND RATE METERS 119

    1. Scalers, Timers, and Counters 1192. Analog Rate Meters 120

    F. COINCIDENCE UNITS 121 G. HIGH-VOLTAGE POWER SUPPLIES 122 H. NUCLEAR INSTRUMENT MODULES 122 I. OSCILLOSCOPES 123

    1. Cathode Ray Tube 1232. Analog Oscilloscope 1243. Digital Oscilloscope 124

    CHAPTER 9 Nuclear Counting Statistics 125 A. TYPES OF MEASUREMENT ERROR 125 B. NUCLEAR COUNTING STATISTICS 126

    1. The Poisson Distribution 1262. The Standard Deviation 1283. The Gaussian Distribution 128

    C. PROPAGATION OF ERRORS 1281. Sums and Differences 1292. Constant Multipliers 1293. Products and Ratios 1294. More Complicated Combinations 129

    D. APPLICATIONS OF STATISTICAL ANALYSIS 1301. Effects of Averaging 1302. Counting Rates 1303. Significance of Differences Between Counting Measurements 1304. Effects of Background 1315. Minimum Detectable Activity 1316. Comparing Counting Systems 1327. Estimating Required Counting Times 1328. Optimal Division of Counting Times 133

  • x Contents

    E. STATISTICAL TESTS 1331. The 2 Test 1332. The t -Test 1353. Treatment of Outliers 1384. Linear Regression 139

    CHAPTER 10 Pulse-Height Spectrometry 141 A. BASIC PRINCIPLES 141 B. SPECTROMETRY WITH NaI(Tl) 142

    1. The Ideal Pulse-Height Spectrum 1422. The Actual Spectrum 1433. Effects of Detector Size 1454. Effects of Counting Rate 1465. General Effects of -Ray Energy 1476. Energy Linearity 1477. Energy Resolution 148

    C. SPECTROMETRY WITH OTHER DETECTORS 1511. Semiconductor Detector Spectrometers 1512. Liquid Scintillation Spectrometry 1523. Proportional Counter Spectrometers 153

    CHAPTER 11 Problems in Radiation Detection and Measurement 155 A. DETECTION EFFICIENCY 155

    1. Components of Detection Efficiency 1552. Geometric Efficiency 1563. Intrinsic Efficiency 1584. Energy-Selective Counting 1595. Some Complicating Factors 1606. Calibration Sources 164

    B. PROBLEMS IN THE DETECTION AND MEASUREMENT OF PARTICLES 166

    C. DEAD TIME 1681. Causes of Dead Time 1682. Mathematical Models 1683. Window Fraction Effects 1704. Dead Time Correction Methods 170

    D. QUALITY ASSURANCE FOR RADIATION MEASUREMENT SYSTEMS 171

    CHAPTER 12 Counting Systems 173 A. NaI(Tl) WELL COUNTER 173

    1. Detector Characteristics 173 2. Detection Efficiency 174 3. Sample Volume Effects 175 4. Assay of Absolute Activity 177 5. Shielding and Background 177 6. Energy Calibration 178 7. Multiple Radionuclide Source Counting 178 8. Dead Time 179 9. Automated Multiple-Sample Systems 17910. Applications 182

    B. COUNTING WITH CONVENTIONAL NaI(Tl) DETECTORS 182 1. Large Sample Volumes 182 2. Liquid and Gas Flow Counting 182

    C. LIQUID SCINTILLATION COUNTERS 182 1. General Characteristics 182 2. Pulse-Height Spectrometry 184 3. Counting Vials 184 4. Energy and Efficiency Calibration 185 5. Quench Corrections 185 6. Sample Preparation Techniques 187

  • Contents xi

    7. Cerenkov Counting 188 8. Liquid and Gas Flow Counting 188 9. Automated Multiple-Sample LS Counters 18810. Applications 189

    D. GAS-FILLED DETECTORS 189 1. Dose Calibrators 189 2. Gas Flow Counters 190

    E. SEMICONDUCTOR DETECTOR SYSTEMS 190 1. System Components 190 2. Applications 191

    F. IN VIVO COUNTING SYSTEMS 192 1. NaI(Tl) Probe Systems 192 2. Miniature -Ray and Probes for Surgical Use 192 3. Whole-Body Counters 194

    CHAPTER 13 The Gamma Camera: Basic Principles 195 A. GENERAL CONCEPTS OF RADIONUCLIDE IMAGING 195 B. BASIC PRINCIPLES OF THE GAMMA CAMERA 196

    1. System Components 1962. Detector System and Electronics 1973. Collimators 2014. Event Detection in a Gamma Camera 204

    C. TYPES OF GAMMA CAMERAS AND THEIR CLINICAL USES 206

    CHAPTER 14 The Gamma Camera: Performance Characteristics 209 A. BASIC PERFORMANCE CHARACTERISTICS 209

    1. Intrinsic Spatial Resolution 2092. Detection Efficiency 2113. Energy Resolution 2114. Performance at High Counting Rates 213

    B. DETECTOR LIMITATIONS: NONUNIFORMITY AND NONLINEARITY 2161. Image Nonlinearity 2162. Image Nonuniformity 2173. Nonuniformity Correction Techniques 2174. Gamma Camera Tuning 219

    C. DESIGN AND PERFORMANCE CHARACTERISTICS OF PARALLEL-HOLE COLLIMATORS 2201. Basic Limitations in Collimator Performance 2202. Septal Thickness 2203. Geometry of Collimator Holes 2224. System Resolution 225

    D. PERFORMANCE CHARACTERISTICS OF CONVERGING, DIVERGING, AND PINHOLE COLLIMATORS 225

    E. MEASUREMENTS OF GAMMA CAMERA PERFORMANCE 2281. Intrinsic Resolution 2292. System Resolution 2293. Spatial Linearity 2294. Uniformity 2305. Counting Rate Performance 2306. Energy Resolution 2317. System Sensitivity 231

    CHAPTER 15 Image Quality in Nuclear Medicine 233 A. BASIC METHODS FOR CHARACTERIZING AND EVALUATING

    IMAGE QUALITY 233 B. SPATIAL RESOLUTION 233

    1. Factors Affecting Spatial Resolution 2332. Methods for Evaluating Spatial Resolution 234

    C. CONTRAST 239

  • xii Contents

    D. NOISE 2431. Types of Image Noise 2432. Random Noise and Contrast-to-Noise Ratio 243

    E. OBSERVER PERFORMANCE STUDIES 2471. Contrast-Detail Studies 2472. Receiver Operating Characteristic Studies 248

    CHAPTER 16 Tomographic Reconstruction in Nuclear Medicine 253 A. GENERAL CONCEPTS, NOTATION, AND TERMINOLOGY 254 B. BACKPROJECTION AND FOURIER-BASED TECHNIQUES 256

    1. Simple Backprojection 2562. Direct Fourier Transform Reconstruction 2583. Filtered Backprojection 2604. Multislice Imaging 262

    C. IMAGE QUALITY IN FOURIER TRANSFORM AND FILTERED BACKPROJECTION TECHNIQUES 2631. Effects of Sampling on Image Quality 2632. Sampling Coverage and Consistency Requirements 2663. Noise Propagation, Signal-to-Noise Ratio, and Contrast-to-Noise

    Ratio 266 D. ITERATIVE RECONSTRUCTION ALGORITHMS 270

    1. General Concepts of Iterative Reconstruction 2702. Expectation-Maximization Reconstruction 272

    E. RECONSTRUCTION OF FAN-BEAM, CONE-BEAM AND PINHOLE SPECT DATA, AND 3-D PET DATA 2731. Reconstruction of Fan-Beam Data 2732. Reconstruction of Cone-Beam and Pinhole Data 2743. 3-D PET Reconstruction 275

    CHAPTER 17 Single Photon Emission Computed Tomography 279 A. SPECT SYSTEMS 279

    1. Gamma Camera SPECT Systems 2792. SPECT Systems for Brain Imaging 2803. SPECT Systems for Cardiac Imaging 2814. SPECT Systems for Small-Animal Imaging 283

    B. PRACTICAL IMPLEMENTATION OF SPECT 2851. Attenuation Effects and Conjugate Counting 2872. Attenuation Correction 2933. Transmission Scans and Attenuation Maps 2944. Scatter Correction 2965. Partial-Volume Effects 299

    C. PERFORMANCE CHARACTERISTICS OF SPECT SYSTEMS 2991. Spatial Resolution 3012. Volume Sensitivity 3013. Other Measurements of Performance 3024. Quality Assurance in SPECT 302

    D. APPLICATIONS OF SPECT 303

    CHAPTER 18 Positron Emission Tomography 307 A. BASIC PRINCIPLES OF PET IMAGING 307

    1. Annihilation Coincidence Detection 3072. Time-of-Flight PET 3093. Spatial Resolution: Detectors 3104. Spatial Resolution: Positron Physics 3125. Spatial Resolution: Depth-of-Interaction Effect 3166. Spatial Resolution: Sampling 3187. Spatial Resolution: Reconstruction Filters 3198. Sensitivity 3199. Event Types in Annihilation Coincidence Detection 322

  • Contents xiii

    B. PET DETECTOR AND SCANNER DESIGNS 3241. Block Detectors 3242. Modified Block Detectors 3253. Whole-Body PET Systems 3264. Specialized PET Scanners 3305. Small-Animal PET Scanners 331

    C. DATA ACQUISITION FOR PET 3321. Two-Dimensional Data Acquisition 3322. Three-Dimensional Data Acquisition 3323. Data Acquisition for Dynamic Studies and Whole-Body Scans 335

    D. DATA CORRECTIONS AND QUANTITATIVE ASPECTS OF PET 3351. Normalization 3352. Correction for Random Coincidences 3363. Correction for Scattered Radiation 3374. Attenuation Correction 3385. Dead Time Correction 3396. Absolute Quantification of PET Images 339

    E. PERFORMANCE CHARACTERISTICS OF PET SYSTEMS 340 F. CLINICAL AND RESEARCH APPLICATIONS OF PET 341

    CHAPTER 19 Hybrid Imaging: SPECT/CT and PET/CT 345 A. MOTIVATION FOR HYBRID SYSTEMS 345 B. X-RAY COMPUTED TOMOGRAPHY 346

    1. X-ray Tube 3462. X-ray Detectors 3473. X-ray CT Scanner 3484. CT Reconstruction 348

    C. SPECT/CT SYSTEMS 3501. Clinical SPECT/CT Scanners 3502. Small-Animal SPECT/CT Scanners 352

    D. PET/CT 3541. Clinical PET/CT Scanners 3542. Small-Animal PET/CT Scanners 356

    E. ATTENUATION AND SCATTER CORRECTION USING CT 3561. Computing Attenuation Correction Factors from CT Scans 3572. Possible Sources of Artifacts for CT-Based Attenuation Correction 3583. Scatter Correction 360

    F. HYBRID PET/MRI AND SPECT/MRI 360

    CHAPTER 20 Digital Image Processing in Nuclear Medicine 363 A. DIGITAL IMAGES 364

    1. Basic Characteristics and Terminology 3642. Spatial Resolution and Matrix Size 3653. Image Display 3674. Acquisition Modes 367

    B. DIGITAL IMAGE-PROCESSING TECHNIQUES 3691. Image Visualization 3692. Regions and Volumes of Interest 3723. Time-Activity Curves 3734. Image Smoothing 3735. Edge Detection and Segmentation 3736. Co-Registration of Images 375

    C. PROCESSING ENVIRONMENT 376

    CHAPTER 21 Tracer Kinetic Modeling 379 A. BASIC CONCEPTS 379 B. TRACERS AND COMPARTMENTS 380

    1. Definition of a Tracer 3802. Definition of a Compartment 3823. Distribution Volume and Partition Coefficient 382

  • xiv Contents

    4. Flux 3835. Rate Constants 3846. Steady State 385

    C. TRACER DELIVERY AND TRANSPORT 3861. Blood Flow, Extraction, and Clearance 3862. Transport 389

    D. FORMULATION OF A COMPARTMENTAL MODEL 390 E. EXAMPLES OF DYNAMIC IMAGING AND TRACER KINETIC

    MODELS 3921. Cardiac Function and Ejection Fraction 3922. Blood Flow Models 3923. Blood Flow: Trapped Radiotracers 3934. Blood Flow: Clearance Techniques 3945. Enzyme Kinetics: Glucose Metabolism 3966. Receptor Ligand Assays 401

    F. SUMMARY 403

    CHAPTER 22 Internal Radiation Dosimetry 407 A. RADIATION DOSE AND EQUIVALENT DOSE: QUANTITIES AND

    UNITS 407 B. CALCULATION OF RADIATION DOSE (MIRD METHOD) 408

    1. Basic Procedure and Some Practical Problems 4082. Cumulated Activity, A~ 4093. Equilibrium Absorbed Dose Constant, 4124. Absorbed Fraction, 4135. Specific Absorbed Fraction, , and the Dose Reciprocity Theorem 4146. Mean Dose per Cumulated Activity, S 4157. Whole-Body Dose and Effective Dose 4178. Limitations of the MIRD Method 424

    CHAPTER 23 Radiation Safety and Health Physics 427 A. QUANTITIES AND UNITS 428

    1. Dose-Modifying Factors 4282. Exposure and Air Kerma 428

    B. REGULATIONS PERTAINING TO THE USE OF RADIONUCLIDES 4311. Nuclear Regulatory Commission Licensing and Regulations 4312. Restricted and Unrestricted Areas 4313. Dose Limits 4314. Concentrations for Airborne Radioactivity in Restricted Areas 4325. Environmental Concentrations and Concentrations for Sewage

    Disposal 4326. Record-Keeping Requirements 4327. Recommendations of Advisory Bodies 433

    C. SAFE HANDLING OF RADIOACTIVE MATERIALS 4331. The ALARA Concept 4332. Reduction of Radiation Doses from External Sources 4343. Reduction of Radiation Doses from Internal Sources 4374. Laboratory Design 4385. Procedures for Handling Spills 438

    D. DISPOSAL OF RADIOACTIVE WASTE 439 E. RADIATION MONITORING 439

    1. Survey Meters and Laboratory Monitors 4392. Personnel Dosimeters 4403. Wipe Testing 441

    APPENDIX A Unit Conversions 443

    APPENDIX B Properties of the Naturally Occurring Elements 445

  • Contents xv

    APPENDIX C Decay Characteristics of Some Medically Important Radionuclides 449

    APPENDIX D Mass Attenuation Coefficients for Water, NaI(Tl), Bi4Ge3O12, Cd0.8Zn0.2Te, and Lead 476

    APPENDIX E Effective Dose Equivalent (mSv/MBq) and Radiation Absorbed Dose Estimates (mGy/MBq) to Adult Subjects from Selected Internally Administered Radiopharmaceuticals 478

    APPENDIX F The Fourier Transform 481A. THE FOURIER TRANSFORM: WHAT IT REPRESENTS 481B. CALCULATING FOURIER TRANSFORMS 481C. SOME PROPERTIES OF FOURIER TRANSFORMS 483D. SOME EXAMPLES OF FOURIER TRANSFORMS 486

    APPENDIX G Convolution 489

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  • Animations, Calculators, and Graphing Tools

    (Available online at expertconsult.com.)

    ANIMATIONS

    1. Emission of a characteristic x ray (Figure 2-4) 2. Emission of an Auger electron (Figure 2-5) 3. Internal conversion involving K-shell electron (Figure 3-5) 4. Positron emission and annihilation (Figure 3-7) 5. Positive ion cyclotron (Figure 5-3) 6. Ionization of an atom (Figure 6-1A) 7. Bremsstrahlung production (Figure 6-1B) 8. Photoelectric effect (Figure 6-11) 9. Compton scattering (Figure 6-12) 10. Pair production (Figure 6-14) 11. Basic principles of a gas-filled chamber (Figure 7-1) 12. Basic principles of a photomultiplier tube (Figure 7-13) 13. Scintillation detector (Figure 7-16) 14. Pulse-height spectrum (Figure 8-9 and Figure 10-2) 15. Gamma camera (Figure 13-1) 16. Sinogram formation and SPECT (Figure 16-4) 17. Backprojection (Figure 16-5)

    CALCULATORS

    1. Decay of activity (Equations 4-7 and 4-10) 2. Image-frame decay correction (Equations 4-15 and 4-16) 3. Carrier-free specific activity (Equations 4-21 to 4-23) 4. Cyclotron particle energy (Equation 5-12) 5. Compton scatter kinematics (Equations 6-11 and 6-12) 6. Photon absorption and transmission (Equation 6-22) 7. Effective atomic number (Equations 7-2 and 7-3) 8. Propagation of errors for sums and differences (Equation 9-12) 9. Solid angle calculation for a circular detector (Equation 11-7)10. Activity conversions (Appendix A)

    GRAPHING TOOLS

    1. Bateman equation (Equation 4-25) 2. Dead time models (Equations 11-16 and 11-18) 3. Resolution and sensitivity of a parallel-hole collimator (Equations 14-6

    and 14-7) 4. Resolution and sensitivity of a pinhole collimator (Equations 14-15 to

    14-18)

    xvii

    http://www.expertconsult.com

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  • PHYSICS in NUCLEAR MEDICINE

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  • 1chapter

    What Is Nuclear Medicine?

    A. FUNDAMENTALCONCEPTS

    The science and clinical practice of nuclearmedicine involvetheadministrationof traceamountsofcompoundslabeledwithradioac-tivity(radionuclides)thatareusedtoprovidediagnostic information in a wide range ofdisease states. Although radionuclides alsohave some therapeutic uses, with similarunderlying physics principles, this bookfocuses on the diagnostic uses of radionu-clidesinmodernmedicine.

    Initsmostbasicform,anuclearmedicinestudy involves injecting a compound, whichis labeled with a gamma-ray-emitting orpositron-emittingradionuclide,intothebody.Theradiolabeledcompoundiscalledaradio-pharmaceutical, or more commonly, a tracerorradiotracer.Whentheradionuclidedecays,gamma rays or high-energy photons areemitted.Theenergyofthesegammaraysorphotonsissuchthatasignificantnumbercanexit the body without being scattered orattenuated. An external, position-sensitivegamma-ray camera can detect the gammarays or photons and form an image of thedistribution of the radionuclide, and hencethe compound (including radiolabeled prod-uctsofreactionsofthatcompound)towhichitwasattached.

    There are two broad classes of nuclearmedicine imaging: single photon imaging[whichincludessinglephotonemissioncom-puted tomography (SPECT)] and positron imaging [positron emission tomography(PET)].Singlephotonimagingusesradionu-clides that decaybygamma-ray emission.Aplanarimageisobtainedbytakingapictureoftheradionuclidedistributioninthepatientfromoneparticularangle.Thisresultsinanimagewithlittledepthinformation,butwhichcanstillbediagnosticallyuseful(e.g.,inbone

    scans,wherethereisnotmuchtraceruptakeinthetissuelyingaboveandbelowthebones).For the tomographic mode of single photonimaging (SPECT), data are collected frommanyanglesaroundthepatient.Thisallowscross-sectional images of the distribution ofthe radionuclide to be reconstructed, thusprovidingthedepthinformationmissingfromplanarimaging.

    Positron imaging makes use of radio-nuclidesthatdecaybypositronemission.Theemitted positron has a very short lifetimeand,followingannihilationwithanelectron,simultaneously produces two high-energyphotonsthatsubsequentlyaredetectedbyanimaging camera. Once again, tomographicimages are formed by collecting data frommanyanglesaroundthepatient,resultinginPETimages.

    B. THEPOWEROFNUCLEARMEDICINE

    The power of nuclear medicine lies in itsability to provide exquisitely sensitive mea-suresofawiderangeofbiologicprocessesinthe body. Other medical imaging modalitiessuch as magnetic resonance imaging (MRI),x-ray imaging, and x-ray computed tomog-raphy (CT) provide outstanding anatomicimages but are limited in their ability toprovide biologic information. For example,magnetic resonance methods generally havea lower limit of detection in the millimolarconcentrationrange(61017moleculespermLtissue),whereasnuclearmedicinestudiesroutinely detect radiolabeled substances inthe nanomolar (6 1011 molecules per mLtissue) or picomolar (6 108 moleculespermLtissue)range.Thissensitivityadvan-tage,togetherwiththeever-growingselection

    1

  • 2 PhysicsinNuclearMedicine

    insidethehumanbodynoninvasivelyforthefirst time and was particularly useful fortheimagingofbone.Xrayssoonbecamethemethodofchoiceforproducingradiographsbecauseimagescouldbeobtainedmorequicklyandwithbettercontrastthanthoseprovidedbyradiumorothernaturallyoccurringradio-nuclides that were available at that time.Althoughthefieldofdiagnosticx-rayimagingrapidly gained acceptance, nuclearmedicinehadtoawaitfurtherdevelopments.

    Thebiologicfoundationsfornuclearmedi-cinewerelaiddownbetween1910and1945.In1913,GeorgdeHevesydevelopedtheprin-ciples of the tracer approach2 and was thefirst to apply them to a biologic system in1923,studyingtheabsorptionandtransloca-tion of radioactive lead nitrate in plants.3Thefirsthumanstudyemployingradioactivetracers was probably that of Blumgart andWeiss(1927),4whoinjectedanaqueoussolu-tionofradonintravenouslyandmeasuredthetransittimeofthebloodfromonearmtotheotherusingacloudchamberastheradiationdetector. Inthe1930s,withthe inventionofthe cyclotron by Lawrence (Fig. 1-1),5 itbecame possible to artificially produce newradionuclides,therebyextendingtherangeofbiologicprocessesthatcouldbestudied.Onceagain,deHevesywasattheforefrontofusingthesenewradionuclidestostudybiologicpro-cessesinplantsandinredbloodcells.Finally,at the end of the Second World War, thenuclearreactorfacilitiesthatweredevelopedas part of the Manhattan Project started tobe used for the production of radioactiveisotopes in quantities sufficient for medicalapplications.

    The1950ssawthedevelopmentoftechnol-ogythatallowedonetoobtainimagesofthedistribution of radionuclides in the humanbodyratherthanjustcountingatafewmea-surement points. Major milestones includedthedevelopmentoftherectilinearscannerin1951byBenedictCassen6 (Fig.1-2)and theAnger camera, the forerunner ofallmodernnuclear medicine single-photon imagingsystems,developedin1958byHalAnger(Fig.1-3).7 In 1951, the use of positron emittersand theadvantageous imagingproperties ofthese radionuclides also were described byWrennandcoworkers.8

    Untiltheearly1960s,thefledglingfieldofnuclear medicine primarily used 131I in thestudyanddiagnosisofthyroiddisordersandan assortment of other radionuclides thatwereindividuallysuitableforonlyafewspe-cific organs. The use of 99mTc for imaging in

    of radiolabeled compounds, allows nuclearmedicine studies to be targeted to the veryspecificbiologicprocessesunderlyingdisease.Examples of the diverse biologic processesthat can be measured by nuclear medicinetechniques include tissue perfusion, glucosemetabolism,thesomatostatinreceptorstatusoftumors,thedensityofdopaminereceptorsinthebrain,andgeneexpression.

    Because radiation detectors can easilydetectverytinyamountsofradioactivity,andbecauseradiochemistsareabletolabelcom-pounds with very high specific activity (alarge fraction of the injected molecules arelabeledwitharadioactiveatom),itispossibletoformhigh-qualityimagesevenwithnano-molar or picomolar concentrations of com-pounds.Thustraceamountsofacompound,typicallymanyordersofmagnitudebelowthemillimolartomicromolarconcentrationsthatgenerally are required for pharmacologiceffects, can be injected and followed safelyover time without perturbing the biologicsystem. Like CT, there is a small radiationdoseassociatedwithperformingnuclearmed-icinestudies,withspecificdosestothediffer-entorgansdependingontheradionuclide,aswellasthespatialandtemporaldistributionoftheparticularradiolabeledcompoundthatis being studied. The safe dose for humanstudiesisestablishedthroughcarefuldosim-etryforeverynewradiopharmaceuticalthatisapprovedforhumanuse.

    C. HISTORICALOVERVIEW

    Aswiththedevelopmentofanyfieldofscienceormedicine, thehistoryofnuclearmedicineis a complex topic, involving contributionsfromalargenumberofscientists,engineers,and physicians.A complete overview is wellbeyondthescopeofthisbook;however,afewhighlightsservetoplacethedevelopmentofnuclearmedicineinitsappropriatehistoricalcontext.

    The origins of nuclear medicine1 can betraced back to the last years of the 19thcenturyandthediscoveryofradioactivitybyHenri Becquerel (1896) and of radium byMarieCurie(1898).Thesedevelopmentscamecloseontheheelsofthediscoveryofxraysin1895byWilhelmRoentgen.Bothxraysandradium sources were quickly adopted formedicalapplicationsandwereusedtomakeshadow images in which the radiation wastransmittedthroughthebodyandontophoto-graphicplates.Thisallowedphysicianstosee

  • 1 WhatIsNuclearMedicine? 3

    FIGURE 1-1 Ernest O. Lawrencestanding next to the cyclotron heinvented at Berkeley, California.(From Myers WG, Wagner HN: Nuclear medicine: How it began. HospPract 9:103-113, 1974.)

    FIGURE1-2 Left,BenedictCassenwithhisrectilinearscanner(1951),asimplescintillationcounter(seeChapter7)thatscansbackandforthacrossthepatient.Right,Thyroidscansfromanearlyrectilinearscannerfollowingadmin-istration of 131I. The output of the scintillation counter controlled the movement of an ink pen to produce the firstnuclearmedicineimages.(Left, Courtesy William H. Blahd, MD; with permission of Radiology Centennial, Inc. Right, From Cassen B, Curtis L, Reed C, Libby R: Instrumentation for 131I use in medical studies. Nucleonics 9:46-50, 1951.)

  • 4 PhysicsinNuclearMedicine

    FIGURE1-3 Left,HalAngerwiththefirstgammacamerain1958.Right,99mTc-pertechnetatebrainscanofapatientwithgliomaatVanderbiltUniversityHospital(1971).Eachimagerepresentsadifferentviewofthehead.Thegliomaisindicatedbyanarrowinoneoftheviews.Inthe1960s,thiswastheonlynoninvasivetestthatcouldprovideimagesshowingpathologicconditionsinsidethehumanbrain.Thesestudiesplayedamajorroleinestablishingnuclearmedi-cineasanintegralpartofthediagnosticservicesinhospitals.(Left, From Myers WG: The Anger scintillation camera becomes of age. JNuclMed 20:565-567, 1979. Right, Courtesy Dennis D. Patton, MD, University of Arizona, Tucson, Arizona.)

    1964byPaulHarperandcolleagues9changedthis and was a major turning point for thedevelopmentofnuclearmedicine.Thegammarays emittedby 99mTc hadverygood proper-ties for imaging. It also proved to be veryflexible for labeling a wide variety of com-poundsthatcouldbeusedtostudyvirtuallyevery organ in the body. Equally important,itcouldbeproducedinarelativelylong-livedgenerator form,allowinghospitals tohaveareadily available supply of the radionuclide.Today,99mTcisthemostwidelyusedradionu-clideinnuclearmedicine.

    The final important development wasthemathematics to reconstruct tomographicimages from a set of angular views aroundthe patient. This revolutionized the wholefield of medical imaging (leading to CT,PET, SPECT and MRI) because it replacedthe two-dimensional representation of thethree-dimensional radioactivity distribution,with a true three-dimensional representa-tion. This allowed the development of PETby Phelps and colleagues10 and SPECT byKuhl and colleagues11 during the 1970s andmarked the start of the modern era ofnuclearmedicine.

    D. CURRENTPRACTICEOFNUCLEARMEDICINE

    Nuclearmedicineisusedforawidevarietyofdiagnostictests.Therewereroughly100dif-ferent diagnostic imaging procedures avail-able in 2006.* These procedures use manydifferent radiolabeled compounds, cover allthe major organ systems in the body, andprovide many different measures of biologicfunction. Table 1-1 lists some of the morecommonclinicalprocedures.

    Asof2008,more than 30 million nuclearmedicineimagingprocedureswereperformedonaglobalbasis.Therearemorethan20,000nuclearmedicinecamerascapableofimaginggamma-ray-emitting radionuclides installedin hospitals across the world. Even manysmallhospitalshavetheirownnuclearmedi-cineclinic.Therealsoweremorethan3,000PETscannersinstalledintheworldperform-ing on the order of 4 million procedures

    *Data courtesy Society of Nuclear Medicine, Reston,Virginia.Data courtesy Siemens Molecular Imaging, HoffmanEstates,Illinois.

  • 1 WhatIsNuclearMedicine? 5

    annually. The short half-lives of the mostcommonly used positron-emitting radionu-clides requireanonsiteaccelerator ordeliv-ery of PET radiopharmaceuticals fromregionalradiopharmacies.Tomeetthisneed,thereisnowaPETradiopharmacywithin100miles of approximately 90% of the hospitalbeds in the United States. The growth ofclinical PET has been driven by the utilityofametabolictracer, 18F-fluorodeoxyglucose,whichhaswidespreadapplicationsincancer,heartdisease,andneurologicdisorders.

    Onemajorparadigmshiftthathasoccurredsince the turn of the millennium has beentoward multimodality instrumentation. Vir-tuallyallPETscanners,andarapidlygrowingnumber of SPECT systems, are now inte-gratedwithaCTscannerincombinedPET/CT and SPECT/CT configurations. Thesesystemsenablethefacilecorrelationofstruc-ture (CT) and function (PET or SPECT),yielding better diagnostic insight in manyclinicalsituations.ThecombinationofnuclearmedicinescannerswithMRIsystemsalsoisunder investigation, and as of 2011, first

    commercial PET/MRI systems were beingdelivered.

    Inadditiontoitsclinicalrole,PET(andtoacertainextent,SPECT)continuestoplayamajor role in the biomedical research com-munity.PEThasbecomeanestablishedandpowerfulresearchtoolforquantitativelyandnoninvasivelymeasuringtheratesofbiologicprocesses, both in the healthy and diseasedstate. In this research environment, theradiolabeledcompoundsandclinicalnuclearmedicineassaysofthefuturearebeingdevel-oped.Inpreclinical,translationalandclinicalresearch, nuclear medicine has been at theforefrontindevelopingnewdiagnosticoppor-tunities in the field of molecular medicine,created by the merger of biology and medi-cine.Arapidgrowthisnowoccurring inthenumber and diversity of PET and SPECTmolecularimagingtracerstargetedtospecificproteinsandmolecularpathways implicatedindisease.Thesenuclearmedicinetechnolo-giesalsohavebeenembracedbythepharma-ceuticalandbiotechnologyindustriestoaidindrugdevelopmentandvalidation.

    TABLE 1-1 SELECTEDCLINICALNUCLEARMEDICINEPROCEDURES

    Radiopharmaceutical Imaging Measurement Examples of Clinical Use99mTc-MDP Planar Bonemetabolism Metastaticspreadofcancer,

    osteomyelitisvs.cellulitis99mTc-sestamibi(Cardiolite) SPECTor

    planarMyocardialperfusion Coronaryarterydisease

    99mTc-tetrofosmin(Myoview)201Tl-thallouschloride99mTc-MAG3 Planar Renalfunction Kidneydisease99mTc-DTPA99mTc-HMPAO(Ceretec) SPECT Cerebralbloodflow Neurologicdisorders99mTc-ECD SPECT Cerebralbloodflow Neurologicdisorders123I-sodiumiodide Planar Thyroidfunction Thyroiddisorders131I-sodiumiodide Thyroidcancer67Ga-galliumcitrate Planar Sequesteredintumors Tumorlocalization99mTc-macroaggregated

    albuminand133XegasPlanar Lungperfusion/

    ventilationPulmonaryembolism

    111In-labeledwhitebloodcells

    Planar Sitesofinfection Detectionofinflammation

    18F-fluorodeoxyglucose PET Glucosemetabolism Cancer,neurologicaldisorders,andmyocardialdiseases

    82Rb-rubidiumchloride PET Myocardialperfusion Coronaryarterydisease

    MDP, methylene diphosphonate; MAG3, mercapto-acetyl-triglycine; DTPA, diethylenetriaminepenta-acetic acid;HMPAO, hexamethylpropyleneamine oxime; ECD, ethyl-cysteine-dimer; SPECT, single photon emission computedtomography;PET,positronemissiontomography.

  • 6 PhysicsinNuclearMedicine

    5. Lawrence EO, Livingston MS: The production ofhigh-speed light ions without the use of high volt-ages.Phys Rev40:19-30,1932.

    6. CassenB,CurtisL,ReedC,LibbyR:Instrumenta-tionfor131Iuseinmedicalstudies.Nucleonics9:46-50,1951.

    7. AngerHO:Scintillationcamera.Rev Sci Instr29:27-33,1958.

    8. WrennFR,GoodML,HandlerP:Theuseofpositron-emitting radioisotopes for the localization of braintumors.Science113:525-527,1951.

    9. HarperPV,BeckR,CharlestonD,LathropKA:Opti-mization of a scanning method using technetium-99m.Nucleonics22:50-54,1964.

    10.PhelpsME,HoffmanEJ,MullaniNA,TerPogossianMM: Application of annihilation coincidence detec-tionoftransaxialreconstructiontomography.J Nucl Med16:210-215,1975.

    11. KuhlDE,EdwardsRQ,RicciAR,etal:TheMarkIVsystemforradionuclidecomputedtomographyofthebrain.Radiology121:405-413,1976.

    BIBLIOGRAPHYFor further details on the history of nuclear medicine, we recommend the following:

    MyersWG,WagnerHN:Nuclearmedicine:Howitbegan.Hosp Pract9(3):103-113,1974.

    NuttR:Thehistoryofpositronemissiontomography.Mol Imaging Biol4:11-26,2002.

    ThomasAMK,editor:The Invisible Light: One Hundred Years of Medical Radiology, Oxford, England, 1995,BlackwellScientific.

    WebbS:FromtheWatchingofShadows:TheOriginsofRadiological Tomography, Bristol, England, 1990,AdamHilger.

    Recommended texts that cover clinical nuclear medicine in detail are the following:

    EllP,GambhirS,editors:Nuclear Medicine in Clinical Diagnosis and Treatment, ed3,Edinburgh,Scotland,2004,ChurchillLivingstone.

    SandlerMP,ColemanRE,PattonJA,etal,editors:Diag-nostic Nuclear Medicine, ed 4, Baltimore, 2002, Wil-liams&Wilkins.

    SchiepersC, editor:Diagnostic Nuclear Medicine, ed2,NewYork,2006,Springer.

    VonSchulthessGK,editor:Molecular Anatomic Imaging: PET-CT and SPECT-CT Integrated Modality Imaging,ed 2, Philadelphia, 2006, Lippincott, Williams andWilkins.

    E. THEROLEOFPHYSICSINNUCLEARMEDICINE

    Although the physics underlying nuclearmedicine isnotchanging, the technology forproducingradioactivetracersandforobtain-ingimagesofthosetracerdistributionsmostcertainlyis.Wecanexpecttocontinueseeingmajor improvements in nuclear medicinetechnology, which will come from combiningadvancesindetectorandacceleratorphysics,electronics, signal processing, and computertechnology with the underlying physics ofnuclear medicine. Methods for accuratelyquantifyingtheconcentrationsofradiolabeledtracers in structures of interest, measuringbiologic processes, and then relaying thisinformation to the physician in a clinicallymeaningful and biologically relevant formatarealsoanimportantchallengeforthefuture.Refinement inthemodelsused indosimetrywillallowbettercharacterizationofradiationexposure and make nuclear medicine evensaferthanitalreadyis.Physicsthereforecon-tinues to play an important and continuingrole in providing high-quality, cost-effective,quantitative,reliable,andsafebiologicassaysinlivinghumans.

    REFERENCES 1. MouldRF:A Century of X-Rays and Radioactivity in

    Medicine,Bristol,1993,InstituteofPhysics. 2. deHevesyG:Radioelementsastracersinphysicsand

    chemistry.Chem News108:166,1913. 3. de Hevesy G: The absorption and translocation of

    lead by plants:A contribution to the application ofthemethodofradioactiveindicatorsintheinvestiga-tionofthechangeofsubstanceinplants.Biochem J17:439-445,1923.

    4. Blumgart HL, Weiss S: Studies on the velocity ofbloodflow.J Clin Invest4:15-31,1927.

  • 2chapter

    Basic Atomic and Nuclear Physics

    Radioactivityisaprocessinvolvingeventsinindividualatomsandnuclei.Beforediscuss-ing radioactivity, therefore, it is worthwhiletoreviewsomeofthebasicconceptsofatomicandnuclearphysics.

    A. QUANTITIESANDUNITS

    1. TypesofQuantitiesandUnitsPhysical properties and processes aredescribedintermsofquantitiessuchastimeand energy. These quantities are measuredin units such as seconds and joules. Thusa quantity describes what is measured,whereas a unit describes how much.

    Physical quantities are characterized asfundamental or derived. A base quantity isonethatstandsalone;thatis,noreferenceismadetootherquantitiesforitsdefinition.Usually, base quantities and their units aredefined with reference to standards kept atnationalorinternationallaboratories.Time(sorsec),distance(m),andmass(kg)areexam-plesofbasequantities.Derivedquantitiesaredefined in terms of combinations of basequantities.Energy(kgm2/sec2)isanexampleofaderivedquantity.

    Theinternationalscientificcommunityhasagreed to adopt so-called System Interna-tional(SI)unitsasthestandardforscientificcommunication. This system is based onsevenbasequantitiesinmetricunits,withallotherquantitiesandunitsderivedbyappro-priatedefinitionsfromthem.Thefourquanti-tiesofmass,length,timeandelectricalchargeare most relevant to nuclear medicine. Theuseofspeciallydefinedquantities(e.g.,atmo-spheres of barometric pressure) is specifi-cally discouraged. It is hoped that this will

    improvescientificcommunication,aswellaseliminate some of the more irrational units(e.g.,feetandpounds).Ausefuldiscussionofthe SI system, including definitions andvaluesofvariousunits,canbefoundinrefer-ence1.

    SIunitsortheirmetricsubunits(e.g.,cen-timetersandgrams)arethestandardforthistext; however, in some instances traditionalor other non-SI units are given as well (inparentheses).Thisisdonebecausesometra-ditionalunitsstillareusedintheday-to-daypractice of nuclear medicine (e.g., units ofactivityandabsorbeddose).Inotherinstances,SIunitsareunreasonablylarge(orsmall)fordescribingtheprocessesof interestandspe-ciallydefinedunitsaremoreconvenientandwidelyused.Thisisparticularlytrueforunitsof mass and energy, as discussed in the fol-lowingsection.

    2. MassandEnergyUnitsEvents occurring at the atomic level, suchas radioactive decay, involve amounts ofmass and energy that are very small whendescribed in SI or other conventional units.Therefore they often are described in termsofspeciallydefinedunitsthataremorecon-venient for the atomic scale.

    Thebasicunitofmassistheunified atomic mass unit,abbreviatedu.Oneuisdefinedasbeing equal to exactly 112 the mass of anunbound12Catom*atrestandinitsgroundstate.The conversion fromSImassunits tounifiedatomicmassunitsis1

    1 1 66054 10 27u kg= . (2-1)

    7

    *AtomicnotationisdiscussedinSectionD.2.

  • 8 PhysicsinNuclearMedicine

    2. Electromagnetic radiation, in whichenergyiscarriedbyoscillatingelectricaland magnetic fields traveling throughspaceatthespeedoflight.

    Radioactive decay processes, discussed inChapter3,resultintheemissionofradiationinbothoftheseforms.

    Thewavelength,,andfrequency,,oftheoscillatingfieldsofelectromagneticradiationarerelatedby:

    = c (2-3)

    wherecisthevelocityoflight.Mostofthemorefamiliartypesofelectro-

    magnetic radiation (e.g., visible light andradio waves) exhibit wavelike behavior intheir interactions with matter (e.g., diffrac-tionpatternsandtransmissionanddetectionofradiosignals).Insomecases,however,elec-tromagnetic radiation behaves as discretepacketsofenergy,calledphotons(alsocalledquanta).Thisisparticularlytrueforinterac-tions involving individual atoms. Photonshave no mass or electrical charge and alsotravelat thevelocity of light.These charac-teristics distinguish them from the formsof particulate radiation mentioned earlier.The energy of the photon E, in kiloelectronvolts, and the wavelength of its associatedelectromagnetic field (in nanometers) arerelatedby

    E( ) . ( )keV / nm= 1 24 (2-4)

    Figure2-1 illustratesthephotonenergiesfor different regions of the electromagneticspectrum.Notethatxraysandraysoccupythe highest-energy, shortest-wavelength endof the spectrum; x-ray and -ray photonshaveenergiesinthekeV-MeVrange,whereasvisible light photons, for example, have

    The universal mass unit often is called aDalton (Da) when expressing the masses oflargebiomolecules.Theunitsareequivalent(i.e., 1Da = 1u). Either unit is convenientfor expressing atomic or molecular masses,because a hydrogen atom has a mass ofapproximately1uor1Da.

    Thebasicunitofenergyistheelectron volt(eV). One eV is defined as the amount ofenergy acquired by an electron when it isacceleratedthroughanelectricalpotentialof1V.Basicmultiplesarethekiloelectronvolt(keV ) (1keV = 1000eV ) and the megaelec-tron volt (MeV ) (1MeV = 1000keV =1,000,000eV ).TheconversionfromSIenergyunitstotheelectronvoltis

    1 1 6022 10 19 2 2eV kg m /sec= . i (2-2)

    Mass m and energy E are related to eachotherbyEinsteinsequationE=mc2,inwhichc is the velocity of light (approximately 3 108m/secinvacuum).Accordingtothisequa-tion,1uofmassisequivalentto931.5MeVofenergy.

    Relationships between various units ofmassandenergyaresummarized inAppen-dixA.Universalmassunitsandelectronvoltsareverysmall,yet,asweshallsee,theyarequiteappropriatetotheatomicscale.

    B. RADIATION

    The term radiation refers to energy intransit. In nuclear medicine, we are inter-estedprincipallyinthefollowingtwospecificformsofradiation:

    1. Particulate radiation, consisting ofatomicorsubatomicparticles(electrons,protons, etc.) that carry energy in theformofkineticenergyofmassinmotion.

    FIGURE 2-1 Schematic representation of the different regions of the electromagnetic spectrum. Vis, visible light;UV,ultravioletlight.

    101 102 103 104 105 106 10 7 108 109 1010 1011 1012 101310 1

    Microwave

    Infrared

    Vis

    UV

    x rays

    Gamma raysRadio

    Wavelength (m)

    109 10

    1010

    1110

    12 1013

    1014 10

    1510

    1610

    1710

    18 1019

    1020

    102110

    8

    Frequency (Hz)

  • 2 BasicAtomicandNuclearPhysics 9

    Accordingtoclassicaltheory,orbitingelec-trons should slowly lose energy and spiralinto the nucleus, resulting in atomic col-lapse. This obviously is not what happens.The simple nuclear model therefore neededfurther refinement. This was provided byNiels Bohr in 1913, who presented a modelthathascometobeknownastheBohr atom.IntheBohratomthereisasetofstableelec-tronorbits,orshells,inwhichelectronscanexist indefinitelywithoutlossofenergy.Thediameters of these shells are determined byquantum numbers, which can have onlyintegervalues(n=1,2,3,).Theinnermostshell(n=1)iscalledtheKshell,thenexttheLshell(n=2),followedbytheMshell(n=3),Nshell(n=4),andsoforth.

    Each shell actually comprises a set oforbits, called substates, which differ slightlyfromoneanother.Eachshellhas2n1sub-states,inwhichnisthequantumnumberoftheshell.ThustheKshellhasonlyonesub-state;theLshellhasthreesubstates,labeledLI,LII,LIII;andsoforth.Figure2-2isasche-matic representation of the K, L, M, and Nshellsofanatom.

    The Bohr model of the atom was furtherrefinedwiththestatementofthePauli Exclu-sion Principlein1925.Accordingtothisprin-ciple,notwoorbitalelectronsinanatomcanmovewithexactlythesamemotion.Becauseof different possible electron spin orienta-tions, more than one electron can exist ineach substate; however, the number of elec-trons that can exist in any one shell or itssubstatesislimited.Forashellwithquantumnumbern,themaximumnumberofelectronsallowed is 2n2. Thus the K shell (n = 1) islimitedtotwoelectrons,theLshell(n=2)toeightelectrons,andsoforth.

    The Bohr model is actually an over-simplification.Accordingtomoderntheories,the orbital electrons do not move in precisecircular orbits but rather in impreciselydefinedregionsofspacearoundthenucleus,sometimes actually passing through thenucleus; however, the Bohr model is quiteadequateforthepurposesofthistext.

    2. ElectronBindingEnergiesandEnergyLevelsInthemoststableconfiguration,orbitalelec-tronsoccupytheinnermostshellsofanatom,where they are most tightly bound to thenucleus. For example, in carbon, which hasa total of six electrons, two electrons (themaximum number allowed) occupy the K

    energies of only a few electron volts. As aconsequenceoftheirhighenergiesandshortwavelengths,xraysandraysinteractwithmatter quite differently from other, morefamiliar types of electromagnetic radiation.These interactionsarediscussed indetail inChapter6.

    C. ATOMS

    1. CompositionandStructureAllmatteriscomposedofatoms.Anatomisthe smallest unit into which a chemicalelement can be broken down without losingitschemicalidentity.Atomscombinetoformmolecules and chemical compounds, whichin turn combine to form larger, macroscopicstructures.

    Theexistenceofatomswasfirstpostulatedon philosophical grounds by Ionian scholarsin the 5th century BC. The concept was for-malizedintoscientifictheoryearlyinthe19thcentury, owing largely to the work of thechemist, John Dalton, and his contempo-raries.Theexactstructureofatomswasnotknown,butatthattimetheywerebelievedtobe indivisible. Later in the century (1869),Mendeleev produced the first periodic table,anorderingofthechemicalelementsaccord-ingtotheweightsoftheiratomsandarrange-ment in a grid according to their chemicalproperties. For a time it was believed thatcompletionoftheperiodictablewouldrepre-sentthefinalstepinunderstandingthestruc-tureofmatter.

    Eventsofthelate19thandearly20thcen-turies,beginningwiththediscoveryofxraysby Roentgen (1895) and radioactivity byBecquerel(1896),revealedthatatomshadasubstructure of their own. In 1910, Ruther-ford presented experimental evidence indi-cating that atoms consisted of a massive,compact,positivelychargedcore,ornucleus,surrounded by a diffuse cloud of relativelylight,negativelychargedelectrons.Thismodelcame tobeknownas thenuclear atom.Thenumberofpositivechargesinthenucleusiscalledtheatomic numberof thenucleus (Z).Intheelectricallyneutralatom,thenumberof orbital electrons is sufficient to balanceexactlythenumberofpositivecharges,Z,inthe nucleus. The chemical properties of anatom are determined by orbital electrons;therefore the atomic number Z determinesthe chemical element to which the atombelongs. A listing of chemical elements andtheiratomicnumbersisgiveninAppendixB.

  • 10 PhysicsinNuclearMedicine

    Binding energies and energy differencesare sometimes displayed on an energy-level diagram.Figure2-3showssuchadiagramfortheKandLshellsoftheelementiodine.Thetop line represents an electron completelyseparated from the parent atom (unboundorfreeelectron).Thebottomlinerepresentsthemosttightlyboundelectrons,thatis,theKshell.Abovethisarelinesrepresentingsub-statesoftheLshell.(TheMshellandotherouter shell lines are just above the L shelllines.) The distance from the K shell to thetop level represents the K-shell bindingenergy for iodine (33.2keV). To move aK-shellelectrontotheLshellrequiresapprox-imately335=28keVofenergy.

    3. AtomicEmissionsWhenanelectronisremovedfromoneoftheinnershellsofanatom,anelectronfromanouter shell promptly moves in to fill thevacancyandenergyisreleasedintheprocess.Theenergyreleasedwhenanelectrondropsfrom an outer to an inner shell is exactlyequal to the difference in binding energiesbetween the two shells. The energy mayappearasaphotonofelectromagneticradia-tion(Fig.2-4).Electronbindingenergydiffer-ences have exact characteristic values fordifferentelements;thereforethephotonemis-sions are called characteristic radiation orcharacteristic x rays. The notation used to

    shell, and the four remaining electrons arefoundintheLshell.Electronscanbemovedtohighershellsor completelyremoved fromthe atom, but doing so requires an energyinputtoovercometheforcesofattractionthatbindtheelectrontothenucleus.Theenergymaybeprovided,forexample,byaparticleoraphotonstrikingtheatom.

    Theenergyrequiredtocompletelyremoveanelectronfromagivenshell inanatomiscalled the binding energy of that shell. It issymbolizedbythenotationKBfortheKshell,*LBfortheLshell(LIB,LIIB,LIIIBfortheLshellsubstates), and so forth. Binding energy isgreatestfortheinnermostshell,thatis,KB>LB>MB.Bindingenergyalsoincreaseswiththepositivecharge(atomicnumberZ)ofthenucleus, because a greater positive chargeexertsagreaterforceofattractiononanelec-tron.Thereforebindingenergiesaregreatestfor the heaviest elements. Values of K-shellbinding energies for the elements are listedinAppendixB.

    The energy required to move an electronfrom an inner to an outer shell is exactlyequal to the difference in binding energiesbetween the two shells. Thus the energyrequiredtomoveanelectronfromtheKshelltotheLshellinanatomisKBLB(withslightdifferencesfordifferentLshellsubstates).

    FIGURE2-2 SchematicrepresentationoftheBohrmodeloftheatom;n isthequantumnumberoftheshell.Eachshellhasmultiplesubstates,asdescribedinthetext.

    Nucleus

    K shelln = 1

    N shelln = 4

    M shelln = 3

    L shelln = 2

    *SometimesthenotationKabalsoisused.

  • 2 BasicAtomicandNuclearPhysics 11

    FIGURE2-3 Electronenergy-leveldiagramforan iodine atom. Vertical axis represents theenergyrequiredtoremoveorbitalelectronsfromdifferent shells (binding energy). Removing anelectron fromtheatom,orgoing froman inner(e.g.,K) toan outer (e.g.,L) shell, requiresanenergyinput,whereasanelectronmovingfromanoutertoaninnershellresultsintheemissionofenergyfromtheatom.

    Free electrons

    L shell

    45 keV

    33.2 keV

    Bin

    ding

    ene

    rgy

    K shell

    FIGURE 2-4 Emission of character-isticxraysoccurswhenorbital elec-tronsmovefromanoutershelltofillan inner-shell vacancy. (K x-rayemissionisillustrated.)

    K-shellvacancy

    Characteristicx ray

    Nucleus

    Electron

    K

    L

  • 12 PhysicsinNuclearMedicine

    characteristicradiation.TheprocessisshownschematicallyinFigure2-5.Theemittedelec-troniscalledanAuger electron.

    ThekineticenergyofanAugerelectronisequal to the difference between the bindingenergy of the shell containing the originalvacancyandthesumofthebindingenergiesofthetwoshellshavingvacanciesattheend.ThusthekineticenergyoftheAugerelectronemitted in Figure 2-5 is KB 2LB (ignoringsmalldifferencesinL-substateenergies).

    TwoorbitalvacanciesexistaftertheAugereffect occurs. These are filled by electronsfrom theother outer shells, resulting in theemissionofadditionalcharacteristicxraysorAugerelectrons.

    The number of vacancies that result inemissionofcharacteristicxraysversusAugerelectronsisdeterminedbyprobabilityvaluesthat depend on the specific element andorbitalshellinvolved.Theprobabilitythatavacancy will yield characteristic x rays iscalledthefluorescent yield,symbolizedbyKfortheKshell,LfortheLshell,andsoforth.Figure 2-6 is a graph of K versus Z. BothcharacteristicxraysandAugerelectronsareemittedbyallelements,butheavyelementsare more likely to emit x rays (large ),whereas light elements are more likely toemitelectrons(small).

    The notation used to identify the shellsinvolvedinAugerelectronemissioniseabc,inwhichaidentifiestheshellwiththeoriginalvacancy,b theshell fromwhichtheelectrondropped to fill the vacancy, and c the shellfromwhich theAugerelectron was emitted.

    identify characteristic x rays from variouselectron transitions is summarized in Table2-1. Note that some transitions are notallowed, owing to the selection rules ofquantummechanics.

    As an alternative to characteristic x-rayemission, the atom may undergo a processknown as the Auger (pronounced oh-zha)effect. In theAuger effect, an electron froman outer shell again fills the vacancy, butthe energy released in the process is trans-ferred to another orbital electron. This elec-tronthenisemittedfromtheatominsteadof

    FIGURE2-5 EmissionofanAugerelectronasanalternativetox-rayemission.Noxrayisemitted.

    K

    L

    K

    L

    Auger electron

    Nucleus

    TABLE 2-1 SOMENOTATIONUSEDFORCHARACTERISTICXRAYS

    Shell with Vacancy

    Shell from Which Filled Notation

    K LI Notallowed

    K LII K2

    K LIII K1

    K MI Notallowed

    K MII K3

    K MIII K1

    K NI Notallowed

    K NII,NIII K2

    LII MIV L1

    LIII MIV L2

    LIII MV L1

  • 2 BasicAtomicandNuclearPhysics 13

    FIGURE2-6 Fluorescentyield,K,orprobabilitythatanorbitalelectronshellvacancywillyieldcharacteristicxraysratherthanAugerelectrons,versusatomicnumberZoftheatom.(Data from Hubbell JH, Trehan PN, Singh N, et al: A review, bibliography, and tabulation of K, L, and higher atomic shell x-ray fluorescence yields. JPhysChemRefData 23:339-364, 1994.)

    Atomic number, Z10 20 30 40 50 60 70 80 90 100

    0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    Flu

    ores

    cent

    yie

    ld,

    K

    TABLE 2-2 BASICPROPERTIESOFNUCLEONSANDELECTRONS1

    Particle Charge*

    Mass

    u MeV

    Proton +1 1.007276 938.272

    Neutron 0 1.008665 939.565

    Electron 1 0.000549 0.511

    *One unit of charge is equivalent to 1.602 1019coulombs.

    Thustheelectronemitted inFigure2-5 isaKLL Auger electron, symbolized by eKLL. Inthe notation eKxx, the symbol x is inclusive,referringtoallAugerelectronsproducedfrominitialK-shellvacancies.

    D. THENUCLEUS

    1. CompositionThe atomic nucleus is composed of protonsand neutrons. Collectively, these particlesare known as nucleons. The properties ofnucleons and electrons are summarized inTable2-2.

    Nucleons are much more massive thanelectrons (by nearly a factor of 2000). Con-versely,nucleardiametersarevery small incomparison with atomic diameters (1013 vs.108cm). Thus it can be deduced that thedensity of nuclear matter is very high(1014g/cm3) and that the rest of the atom(electroncloud) ismostlyemptyspace.

    2. TerminologyandNotationAn atomic nucleus is characterized by thenumberofneutronsandprotons itcontains.Thenumberofprotonsdeterminestheatomic numberoftheatom,Z.Asmentionedearlier,this also determines the number of orbitalelectronsintheelectricallyneutralatomandtherefore the chemical element to which theatombelongs.

    Thetotalnumberofnucleons is themass number of the nucleus,A. The difference,A Z, is the neutron number, N. The massnumberAisapproximatelyequalto,butnotthesameas,theatomic weight(AW)usedinchemistry.Thelatteristheaverageweightofan atom of an element in its natural abun-dance(seeAppendixB).

    The notation now used to summarizeatomic and nuclear composition is ZA NX , inwhichX represents the chemical element towhich the atom belongs. For example, an

  • 14 PhysicsinNuclearMedicine

    4. ForcesandEnergyLevelswithintheNucleusNucleons within the nucleus are subject totwo kinds of forces. Repulsive coulombic orelectrical forces exist between positivelycharged protons. These are counteracted byverystrongforcesofattraction,callednuclear forces(sometimesalsocalledexchange forces),betweenanytwonucleons.Nuclearforcesareeffective only oververyshortdistances,andtheireffectsareseenonlywhennucleonsareveryclosetogether,astheyareinthenucleus.Nuclear forces hold the nucleus togetheragainst the repulsive coulombic forcesbetweenprotons.

    Nucleonsmoveaboutwithinthenucleusinaverycomplicatedwayundertheinfluenceoftheseforces.Onemodelofthenucleus,calledthe shell model, portrays the nucleons asmoving in orbits about one another in amanner similar to that of orbital electronsmovingaboutthenucleusintheBohratom.Onlyalimitednumberofmotionsareallowed,andthesearedeterminedbyasetofnuclearquantumnumbers.

    Themost stablearrangementofnucleonsis called the ground state. Other arrange-mentsof thenucleons fall intothe followingtwocategories:

    1. Excited states are arrangements thatare so unstable that they have only atransientexistencebeforetransformingintosomeotherstate.

    2. Metastable statesalsoareunstable,buttheyhaverelativelylonglifetimesbeforetransforming into another state. Thesealsoarecalledisomericstates.

    The dividing line for lifetimes betweenexcited and metastable states is approxi-mately 1012sec. This is not a long timeaccording to everyday standards, but it isrelatively long by nuclear standards. (TheprefixmetaderivesfromtheGreekwordforalmost.) Some metastable states are quitelong-lived; that is, they have average life-timesofseveralhours.Becauseofthis,meta-stablestatesareconsideredtohaveseparateidentities and are themselves classified asnuclides. Two nuclides that differ from oneanother in that one isametastable state oftheotherarecalledisomers.

    In nuclear notation, excited states areidentifiedbyanasterisk(AX*)andmetastablestates by the letter m (AmX or X-Am). Thus

    atom composed of 53 protons, 78 neutrons(andthus131nucleons),and53orbitalelec-trons represents the element iodine and issymbolizedby 53131 78I .Becausealliodineatomshaveatomicnumber53,theIandthe53are redundant and the 53 can be omitted.Theneutronnumber,78,canbeinferredfromthe difference, 131 53, so this also canbe omitted. Therefore a shortened but stillcomplete notation for this atom is 131I. Anacceptable alternative in terms of medicalterminology is I-131. Obsolete forms (some-times found in older texts) include I131, 131I,andI131.

    3. NuclearFamiliesNuclear species sometimes are grouped intofamilieshavingcertaincommoncharacteris-tics. A nuclide is characterized by an exactnuclear composition, including the massnumber A, atomic number Z, and arrange-ment of nucleons within the nucleus. To beclassifiedasanuclide,thespeciesmusthavea measurably long existence, which forcurrent technology means a lifetime greaterthan about 1012sec. For example, 12C, 16O,and131Iarenuclides.

    Figure 2-7 summarizes the notation usedfor identifying a particular nuclear species,as well as the terminology used for nuclearfamilies.Nuclidesthathavethesameatomicnumber Z are called isotopes. Thus 125I, 127I,and 131I are isotopes of the element iodine.Nuclides with the same mass number Aare isobars (e.g., 131I, 131Xe, and 131Cs).Nuclides with the same neutron number Nareisotones(e.g., 53131 78I , 54132 78Xe ,and 55133 78Cs ).Amnemonic device for remembering theserelationships is thatisotopeshavethesamenumberofprotons,isotonesthesamenumberof neutrons, and isobars the same massnumber(A).

    The notation AXm is sometimes used in Europe (e.g.,99Tcm).

    FIGURE 2-7 Notation and terminology for nuclearfamilies.

    isobars

    isotonesisotopes(Z = number of protons)

    XAZ N

  • 2 BasicAtomicandNuclearPhysics 15

    Photons of nuclear origin are called rays(gamma rays).Theenergydifferencebetweenthestates involved inthenucleartransitiondeterminesthe-rayenergy.Forexample,inFigure2-8atransitionfromthelevelmarked0.364MeVtothegroundstatewouldproducea 0.364-MeV ray. A transition from the0.364-MeVleveltothe0.080-MeVlevelwouldproducea0.284-MeVray.

    Asanalternative to emitting a ray, thenucleusmaytransfertheenergytoanorbitalelectron and emit the electron instead of aphoton.Thisprocess,whichissimilartotheAuger effect in x-ray emission (see SectionC.3,earlierinthischapter),iscalledinternal conversion.ItisdiscussedindetailinChapter3,SectionE.

    6. NuclearBindingEnergyWhenthemassofanatomiscomparedwiththesumofthemassesofitsindividualcom-ponents(protons,neutrons,andelectrons),italways is found to be less by some amount,m.Thismassdeficiency,expressedinenergyunits, is called thebinding energy EB of theatom:

    E mcB = 2 (2-5)

    For example, consider an atom of 12C. Thisatomiscomposedofsixprotons,sixelectrons,andsixneutrons,anditsmassisprecisely12u(by definition of the universal mass unit u).Thesumofthemassesofitscomponentsis

    electrons 60.000549u=0.003294uprotons 61.007276u=6.043656uneutrons 61.008665u=6.051990u

    total 12.098940u

    Thus m = 0.098940u. Because 1u =931.5MeV,thebindingenergyofa12Catomis0.098940931.5MeV=92.16MeV.

    Thebindingenergyistheminimumamountof energy required to overcome the forcesholdingtheatomtogethertoseparateitcom-pletelyintoitsindividualcomponents.Someofthisrepresentsthebindingenergyoforbitalelectrons,thatis,theenergyrequiredtostriptheorbitalelectronsawayfromthenucleus;however, comparison of the total bindingenergyofa12CatomwiththeK-shellbindingenergy of carbon (seeAppendix B) indicatesthat most of this energy is nuclear binding energy, that is, theenergy required to sepa-ratethenucleons.

    Nuclearprocessesthatresultinthereleaseofenergy(e.g.,-rayemission)alwaysincrease

    FIGURE 2-8 Partial nuclear energy-level diagram forthe 131Xe nucleus. The vertical axis represents energydifferencesbetweennuclearstates(orarrangementsofnucleons). Going up the scale requires energy input.Comingdownthescaleresultsintheemissionofnuclearenergy.Heavierlinesindicatemetastablestates.

    0.0

    0.1

    0.2

    Rel

    ativ

    e en

    ergy

    (M

    eV)

    0.3

    0.4

    0.5

    0.6

    0.70.722

    0.6670.637

    0.3640.341

    0.164 (Metastable)

    0.080

    Ground state

    0.8

    *Actually, these are the excited and metastable statesformedduringradioactivedecaybyemissionof131I(seeChapter3,SectionD,andAppendixC).

    99mTc (or Tc-99m) represents a metastablestateof99Tc,and99mTcand99Tcareisomers.

    Nuclear transitions between differentnucleon arrangements involve discrete andexactamountsofenergy,asdotherearrange-mentsoforbitalelectrons intheBohratom.A nuclear energy-level diagram is used toidentify the various excited and metastablestates of a nuclide and the energy relation-shipsamongthem.Figure2-8showsapartialdiagramfor131Xe.*Thebottomlinerepresentsthe ground state, and other lines representexcited or metastable states. Metastablestates usually are indicated by somewhatheavierlines.Theverticaldistancesbetweenlines are proportional to the energy differ-ences between levels. A transition from alower to a higher state requires an energyinputofsomesort,suchasaphotonorpar-ticle striking the nucleus. Transitions fromhighertolowerstatesresultinthereleaseofenergy,whichisgiventoemittedparticlesorphotons.

    5. NuclearEmissionsNuclear transformations can result in theemissionofparticles(primarilyelectronsorparticles)orphotonsofelectromagneticradia-tion.ThisisdiscussedindetailinChapter3.

  • 16 PhysicsinNuclearMedicine

    Afirstobservationisthattherearefavoredneutron-to-protonratiosamongthenaturallyoccurringnuclides.Theyareclusteredaroundanimaginarylinecalledtheline of stability.Forlightelements,thelinecorrespondstoNZ,thatis,approximatelyequalnumbersofprotonsandneutrons.Forheavyelements,itcorresponds to N 1.5Z, that is, approxi-mately50%moreneutronsthanprotons.Thelineofstabilityendsat209Bi(Z=83,N=126).Allheaviernuclidesareunstable.

    In general, there is a tendency towardinstability in atomic systems composed oflargenumbersofidenticalparticlesconfinedinasmallvolume.Thisexplainstheinstabil-ityofveryheavynuclei.Italsoexplainswhy,forlightelements,stabilityisfavoredbymoreorlessequalnumbersofneutronsandprotonsratherthangrosslyunequalnumbers.Amod-erate excess of neutrons is favored amongheavier elements because neutrons provideonly exchange forces (attraction), whereasprotonsprovidebothexchangeforcesandcou-lombicforces(repulsion).Exchangeforcesareeffective over very short distances and thusaffect only close neighbors in the nucleus,whereas the repulsive coulombic forces areeffective over much greater distances. Thus

    the binding energy of the nucleus. Thus anucleus emitting a 1-MeV ray would befound toweigh less (by the mass equivalentof 1MeV) after the ray was emitted thanbefore.Inessence,massisconvertedtoenergyintheprocess.

    7. CharacteristicsofStableNucleiNotallcombinationsofprotonsandneutronsproduce stable nuclei. Some are unstable,even in their ground states. An unstablenucleus emits particles or photons to trans-formitselfintoamorestablenucleus.Thisisthe process of radioactive disintegration orradioactive decay, discussed inChapter 3.Asurveyofthegeneralcharacteristicsofnatu-rallyoccurringstable nuclidesprovidescluestothefactorsthatcontributetonuclearinsta-bilityandthustoradioactivedecay.

    Figure2-9isaplotofthenuclidesfoundinnature,accordingtotheirneutronandprotonnumbers.Forexample,thenuclide 612Cisrep-resentedbyadotat thepointZ= 6,N= 6.Mostof thenaturallyoccurringnuclidesarestable;however,17verylong-livedbutunsta-ble(radioactive)nuclidesthatstillarepresentfrom the creation of the elements also areshown.

    FIGURE 2-9 Neutron number (N) versusatomic number (Z) for nuclides found innature. The boxed data points identify verylong-lived, naturally occurring unstable(radioactive) nuclides. The remainder arestable.Thenuclidesfoundinnatureareclus-teredaroundanimaginarylinecalledtheline of stability.NZforlightelements;N1.5Zforheavyelements.

    0 20 40 60 80 100Atomic number, Z

    0

    20

    40

    60

    80

    100

    120

    140

    160

    Neu

    tron

    num

    ber,

    N

    Isotones

    Isotopes

    Isobars

    N

    Z

  • 2 BasicAtomicandNuclearPhysics 17

    Thisreflectstheexistenceofseveralmodesofisobaric radioactive decay that permitnuclides to transform along isobaric linesuntilthemoststable isobarisreached.ThisisdiscussedindetailinChapter3.

    Onealsonotesamongthestablenuclidesatendencytofavorevennumbers.Forexample,thereare165stablenuclideswithbothevennumbersofprotonsandevennumbersofneu-trons.Examplesare 24 Heand 612C.Thereare109 even-odd stable nuclides, with evennumbersofprotonsandoddnumbersofneu-tronsorviceversa.Examplesare49Beand 511B.However,thereareonlyfourstableodd-oddnuclides:12H,36Li, 510B,and 714 N .Thestabilityofevennumbersreflectsthetendencyofnucleitoachievestablearrangementsbythepairingupofnucleonsinthenucleus.

    Anothermeasureofrelativenuclearstabil-ity is nuclear binding energy, because thisrepresentstheamountofenergyrequiredtobreakthenucleusupintoitsseparatecompo-nents. Obviously, the greater the number ofnucleons,thegreaterthetotalbindingenergy.Therefore a more meaningful parameter isthebinding energy per nucleon,EB/A.Highervalues of EB/A are indicators of greaternuclearstability.

    Figure2-10isagraphofEB/AversusAforthestablenuclides.Bindingenergyisgreat-est(8MeVpernucleon)fornuclidesofmassnumber A 60. It decreases slowly withincreasingA,indicatingthetendencytoward

    an excess of neutrons is required in heavynuclei to overcome the long-range repulsivecoulombic forces between a large number ofprotons.

    Nuclides that are not close to the line ofstability are likely to be unstable. Unstablenuclides lyingabove the lineof stabilityaresaid to be proton deficient, whereas thoselying below the line are neutron deficient.Unstablenuclidesgenerallyundergoradioac-tivedecayprocessesthattransformthemintonuclideslyingclosertothelineofstability,asdiscussedinChapter3.

    Figure 2-9 demonstrates that there oftenaremanystable isotopesofanelement. Iso-topesfallonverticallinesinthediagram.Forexample, therearetenstable isotopesof tin(Sn,Z=50)*.Theremayalsobeseveralstableisotones.Thesefallalonghorizontallines.Inrelatively few cases, however, is there morethan one stable isobar (isobars fall alongdescending 45-degree lines on the graph).

    FIGURE2-10 Bindingenergypernucleon(EB/A)versusmassnumber(A)forthestablenuclides.

    0 40 80 120 160 200Mass number, A

    0

    2

    4

    6

    8

    10

    Bin

    ding

    ene

    rgy

    per

    nucl

    eon,

    EB(M

    eV)/

    A

    *Althoughmostelementsymbolsaresimplyone-ortwo-letterabbreviationsoftheir(English)names,tensymbolsderive fromLatinorGreeknamesofmetalsknown formore than 2 millennia: antimony (stibium, Sb), copper(cuprum,Cu),gold (aurum,Au), iron(ferrum,Fe), lead(plumbum,Pb),mercury (hydrargyrum,Hg),potassium(kalium,K),silver(argentum,Ag),sodium(natrium,Na),and tin (stannum, Sn). The symbol for tungsten, W,derivesfromtheGermanwolfram,thenameitwasfirstgiveninmedievaltimes.

  • 18 PhysicsinNuclearMedicine

    instability for very heavy nuclides. Finally,thereareafewpeaksinthecurverepresent-ingverystablelightnuclides,including 24He,6

    12C, and 816O. Note that these are all even-evennuclides.

    REFERENCES1. National Institute of Standards and Technology

    (NIST): Fundamental Physics Constants. Availableat http://physics.nist.gov/cuu/Constants/index.html[accessedJuly4,2011].

    BIBLIOGRAPHYFundamentalquantitiesofphysicsandmathematics,aswellasconstantsandconversionfactors,canbefoundinreference1.

    Recommended texts for in-depth discussions of topics in atomic and nuclear physics are the following:

    Evans RD: The Atomic Nucleus, New York, 1972,McGraw-Hill.

    JelleyNA:Fundamentals of Nuclear Physics,NewYork,1990,CambridgeUniversityPress.

    Yang F, Hamilton JH: Modern Atomic and Nuclear Physics,NewYork,1996,McGraw-Hill.

    http://physics.nist.gov/cuu/Constants/index.html

  • 3chapter

    Modes of Radioactive Decay

    Radioactive decay is a process in which anunstablenucleustransformsintoamorestableone by emitting particles, photons, or both,releasingenergyintheprocess.Atomicelectronsmaybecomeinvolved insometypesofradioactivedecay,butitisbasicallyanuclearprocesscausedbynuclear instability.Inthischapterwediscussthegeneralcharacteristicsofvariousmodesofradioactivedecayandtheirgeneralimportanceinnuclearmedicine.

    A. GENERALCONCEPTS

    Itiscommonterminologytocallanunstableradioactivenucleustheparentandthemorestableproductnucleusthedaughter.Inmanycases, the daughter also is radioactive andundergoes further radioactive decay. Radioactivedecayisspontaneousinthattheexactmomentatwhichagivennucleuswilldecaycannotbepredicted,noris itaffectedtoanysignificantextentbyeventsoccurringoutsidethenucleus.

    Radioactivedecayresultsintheconversionof mass into energy. If all the products of aparticulardecayeventweregatheredtogetherand weighed, they would be found to weighless than the original radioactive atom.Usually,theenergyarisesfromtheconversionof nuclear mass, but in some decay modes,electronmassisconvertedintoenergyaswell.The total massenergy conversion amountis called the transition energy, sometimesdesignatedQ.*Mostofthisenergyisimpartedas kinetic energy to emitted particles or

    converted to photons, with a small (usuallyinsignificant)portiongivenaskineticenergyto the recoiling nucleus. Thus radioactivedecayresultsnotonlyinthetransformationofonenuclearspeciesintoanotherbutalsointhetransformationofmassintoenergy.

    Eachradioactivenuclidehasasetofcharacteristicproperties.Thesepropertiesincludethe mode of radioactive decay and type ofemissions, the transition energy, and theaveragelifetimeofanucleusoftheradionuclide before it undergoes radioactive decay.Becausethesebasicpropertiesarecharacteristicofthenuclide,itiscommontorefertoaradioactive species, such as 131I, as a radionuclide. The term radioisotope also is usedbut, strictly speaking, should be used onlywhenspecificallyidentifyingamemberofanisotopic family as radioactive; for example,131Iisaradioisotopeofiodine.

    B. CHEMISTRYANDRADIOACTIVITY

    Radioactivedecay isaprocess involvingprimarily the nucleus, whereas chemical reactionsinvolveprimarilytheoutermostorbitalelectronsof theatom.Thus the fact thatanatomhasaradioactivenucleusdoesnotaffectits chemical behavior and, conversely, thechemicalstateofanatomdoesnotaffectitsradioactive characteristics. For example, anatomoftheradionuclide131Iexhibitsthesamechemicalbehaviorasanatomof127I,thenaturallyoccurringstablenuclide,and131Ihasthesame radioactive characteristics whether itexistsasiodideion(I)orincorporatedintoa

    19

    *Sometextsandapplicationsconsideronlynuclearmass,rather than the mass of the entire atom (i.e., atomicmass), in the definitionof transition energy.Aswill beseen,theuseofatomicmassismoreappropriatefortheanalysis of radioactive decay becauseboth nuclear andnonnuclearmassareconvertedintoenergyinsomedecay

    modes.Aswell,energyoriginatingfromeithersourcecancontributetousableradiationortoradiationdosetothepatient.Foradetaileddiscussionofthetwomethodsfordefining transition energy, see Evans RD: The Atomic Nucleus.NewYork,1972,McGrawHill,pp117133.

  • 20 PhysicsinNuclearMedicine

    The electron (e) and the neutrino () areejectedfromthenucleusandcarryawaytheenergy released in the process as kineticenergy. The electron is called a particle.The neutrino is a particle havingno massorelectricalcharge.*Itundergoesvirtuallynointeractions with matter and therefore isessentially undetectable. Its only practicalconsequence is that it carries away some oftheenergyreleasedinthedecayprocess.

    Decayby emissionmayberepresentedinstandardnuclearnotationas

    ZA Z AX Y +1 (32)

    The parent radionuclide (X) and daughterproduct (Y)representdifferentchemicalelements because atomic number increases byone.Thusdecayresultsinatransmutationofelements.MassnumberAdoesnotchangebecause the totalnumberofnucleons in thenucleusdoesnotchange.Thisisthereforeanisobaricdecaymode, that is, theparentanddaughterareisobars(seeChapter2,SectionD.3).

    Radioactivedecayprocessesoftenarerepresentedbyadecay scheme diagram.Figure31showssuchadiagramfor14C,aradionuclide that decays solely by emission. Theline representing 14C (the parent) is drawnaboveandtotheleftofthelinerepresenting14N (the daughter). Decay is to the rightbecause atomic number increases by one(reading Z values from left to right). Theverticaldistancebetweenthelinesisproportionaltothetotalamountofenergyreleased,that is, the transition energy for the decayprocess(Q=0.156MeVfor14C).

    largeproteinmoleculeasaradioactivelabel.Independence of radioactive and chemicalproperties is of great significance in tracerstudies with radioactivitya radioactivetracer behaves in chemical and physiologicprocessesexactlythesameasitsstable,naturallyoccurringcounterpart,and,further,theradioactive properties of the tracer do notchange as it enters into chemical or physiologicprocesses.

    There are two minor exceptions to thesegeneralizations. The first is that chemicalbehavior can be affected by differences inatomicmass.Becausetherearealwaysmassdifferences between the radioactive and thestablemembersofanisotopicfamily(e.g.,131Iisheavierthan127I),theremayalsobechemicaldifferences.Thisiscalledtheisotope effect.Notethatthisisamasseffectandhasnothingtodowiththefactthatoneoftheisotopesisradioactive. The chemical differences aresmallunlesstherelativemassdifferencesarelarge, for example, 3H versus 1H. Althoughtheisotopeeffectisimportantinsomeexperiments, such as measurements of chemicalbondstrengths,itis,fortunately,ofnopracticalconsequenceinnuclearmedicine.

    Asecondexceptionisthattheaveragelifetimesofradionuclidesthatdecaybyprocessesinvolvingorbitalelectrons(e.g.,internalconversion, Section E, and electron capture,Section F) can be changed very slightly byalteringthechemical(orbitalelectron)stateofthe atom. The differences are so small thatthey cannot be detected except in elaboratenuclearphysicsexperimentsandagainareofnopracticalconsequenceinnuclearmedicine.

    C. DECAYBYEMISSION

    Radioactivedecaybyemissionisaprocessinwhich,essentially,aneutroninthenucleusistransformedintoaprotonandanelectron.Schematically,theprocessis n p e energy + + ++ (31)

    FIGURE 3-1 Decay scheme diagram for 14C, aemitter.Qisthetransitionenergy.Q = 0.156 MeV

    14C6

    14N7

    *Actually,inemissionanantineutrino, ,isemitted,whereasin+emissionandEC,aneutrino,,isemitted.Forsimplicity,nodistinction ismade inthistext.Also,evidencefromhighenergyphysicsexperimentssuggeststhatneutrinosmayindeedhaveaverysmallmass,butanexactvaluehasnotyetbeenassigned.

  • 3 ModesofRadioactiveDecay 21

    FIGURE3-2 Energyspectrum(numberemittedvs.energy)forparticlesemittedby14C.MaximumparticleenergyisQ,thetransitionenergy(seeFig.31).AverageenergyEis0.0497MeV,approximately 13( ) Emax.(Data courtesy Dr. Jongwha Chang, Korea Atomic Energy Research Institute.)

    0.00 0.04 0.08-particle energy (MeV)

    0.12 0.16 0.20

    E = 0.156 MeVmaxE = 0.0497 MeV

    Rel

    ativ

    e nu

    mbe

    r em

    itted

    (arb

    itrar

    y un

    its)

    Theenergyreleased indecay issharedbetweentheparticleandtheneutrino.Thissharingofenergyismoreorlessrandomfromonedecay to thenext.Figure32 shows thedistribution,orspectrum,ofparticleenergies resulting from the decay of 14C. Themaximumpossibleparticleenergy(i.e.,thetransition energy for the decay process) isdenotedbyEmax (0.156MeVfor

    14C).Fromthegraphitisapparentthattheparticleusuallyreceivessomethinglessthanhalfoftheavailableenergy.Onlyrarelydoes theparticlecarryawayalltheenergy