Physics in Nuclear Medicine

SIMON R. CHERRY, PH.D. Professor Department of Biomedical Engineering University of California-Davis Davis, California JAMES A. SORENSON, PH.D. Emeritus Professor of Medical Physics University of Wisconsin-Madison Madison, Wisconsin MICHAEL E. PHELPS, PH. D. Norton Simon Professor Chair, Department of Molecular and Medical Pharmacology Director, Center for Molecular Medicine Director, Crump Institute for Molecular Imaging David Geffen School of Medicine, UCLA Los Angeles, California Physics in Nuclear Medicine third edition SAUNDERS :4r : Imprint of Elsevier

What Is Nuclear Medicine? 1 G. Positron (R+) and (R+, ~,) Decay 25 A. Fundamental Concepts 1 H. Competitive R+ B. The and EC Decay Power of Nuclear Medicine 27 1 I, Decay by a Emission C. Historical Overview 2 and by Nuclear Fission 2'7 D. Current Practice of Nuclear J. Decay Medicine Modes and the Line of 3 E. Stability 28 The Role of Physics in Nuclear K. Sources of Medicine 6 Information on Radionuclides 30 Basic Atomic and Nuclear Physics 7 (1) Decay of Radioactivity 31 A. Quantities and Units 7 1. Types of Quantities and Units 7 A. Activity 31 2. Mass and Energy Units 7 1. The Decay Constant 31 B. Radiation 8 2. Definition and Units of Activity 31 C. Atoms 9 B. Exponential Decay 32 1. Composition and Structure 9 1. The Decay Factor 32 2. Electron Binding Energies and 2. Half-Life 33 Energy Levels 10 3. Average Lifetime 33 3. Atomic Emissions 11 C. Methods for Determining Decay D. The Nucleus 13 Factors 34 1. Composition 13 1. Tables of Decay Factors 34 2. Terminology and Notation 14 2. Pocket Calculators 35 3. Nuclear Families 14 3. Graphic Methods 35 4. Forces and Energy Levels within the D. Image-Frame Decay Corrections 36 Nucleus 14 E. Specific Activity 38 5. Nuclear Emissions 16 F. Decay of a Mixed Radionuclide 6. Nuclear Binding Energy 16 7. Characteristics of Stable Sample 40 Nuclei 16 G. Parent-Daughter Decay 41 1. The Bateman Equations 41 Modes of Radioactive 2. Secular Equilibrium 41 Decay 19 3. Transient Equilibrium 41 4. No Equilibrium 43 A. General Concepts 19 B. Chemistry and Radioactivity 19 C. Decay by R_ Emission 20 D. Decay by (0-,,y) Emission 22 Radionuclide and E. Isomeric Transition (IT) and Internal Radiopharmaceutical Conversion Production 45 (IC) 23 F. Electron Capture (EC) and (EC, y) A. Reactor-Produced Radionuclides 45 Decay 24 1. Reactor Principles 45

viii... PHYSICS IN NUCLEAR MEDICINE 2. Fission Fragments 46 3. Neutron Activation 48 B. Accelerator-Produced Radionuclides 49 1. Charged-Particle Accelerators 49 2. Cyclotron Principles 49 3. Cyclotron-Produced Radionuclides 51 C. Radionuclide Generators 52 D. Equations for Radionuclide Production 55 1. Activation Cross Sections 55 2. Activation Rates 55 3. Buildup and Decay of Activity 57 E. Radionuclides for Nuclear Medicine 58 1. General Considerations 58 2. Specific Considerations 59 F. Radiopharmaceutical Preparation 60 1. General Considerations 60 2. Labeling Strategies 61 3. Technetium 99m-Labeled Radiopharmaceuticals 62 4. Radiopharmaceuticals Labeled with Positron Emitters 62 5. Radiopharmaceuticals for Therapy Applications 62 6. Radiopharmaceuticals in Clinical Nuclear Medicine 63 Interaction of Radiation with Matter 65 A. Interactions of Charged Particles with Matter 65 1. Charged-Particle Interaction Mechanisms 65 2. Collisional Versus Radiation Losses 67 3. Charged-Particle Tracks 68 4. Deposition of Energy Along a Charged-Particle Track 69 5. The Cerenkov Effect 71 B. Charged-Particle Ranges 72 1. Alpha Particles 72 2. Beta Particles and Electrons 74 C. Passage of High-Energy Photons through Matter 76 1. Photon Interaction Mechanisms 76 2. The Photoelectric Effect 77 3. Compton Scattering 77 4. Pair Production 79 5. Coherent (Rayleigh) Scattering 80 6. Deposition of Photon Energy in Matter 80 D. Attenuation of Photon Beams 80 1. Attenuation Coefficients 80 2. Thick Absorbers, Narrow-Beam Geometry 84 3. Thick Absorbers, Broad-Beam Geometry 86 4. Polyenergetic Sources 88 Radiation Detectors 89 A. Gas-Filled Detectors 89 1. Basic Principles 89 2. Ionization Chambers 89 3. Proportional Counters 93 4. Geiger-Muller Counters 94 B. Semiconductor Detectors 98 C. Scintillation Detectors 100 1. Basic Principles 100 2. Photomultiplier Tubes 101 3. Inorganic Scintillators 103 4. Organic Liquid Scintillators 106 Electronic Instrumentation for Radiation Detection Systems 109 A. Preamplifiers 109 B. Amplifiers 112 1. Amplification and Pulse-Shaping Functions 112 2. Resistor-Capacitor Shaping 113 3. Baseline Shift and Pulse Pile-up 114 C. Pulse-Height Analyzers 115 1. Basic Functions 115 2. Single-Channel Analyzers 115 3. Timing Methods 117 4. Multichannel Analyzers 117 D. Time-to-Amplitude Converters 121 E. Digital Counters and Rate Meters 121 1. Scalers, Timers, and Counters 121 2. Analog Rate Meters 123 F. Coincidence Units 124 G. High-Voltage Power Supplies 125 H. Nuclear Instrument Modules 126 I. Cathode Ray Tube 126 1. Electron Gun 126 2. Deflection Plates 127 3. Phosphor-Coated Display Screens 128 4. Focus and Brightness Controls 128 5. Color Cathode Ray Tubes 128

J. Oscilloscopes 129 1. Semiconductor Detector K. Computer Monitors 129 Spectrometers 160 2. Liquid Scintillation Spectrometry 162 3. Proportional Counter Nuclear Counting Statistics 131 Spectrometers 163 A. Types of Measurement Error 131 B. Nuclear Counting Statistics 132 1. The Poisson Distribution 132 2. The Standard Deviation 134 3. The Gaussian Distribution 134 Problems in Radiation Detection and Measurement 165 A. Detection Efficiency 165 C. Propagation of Errors 135 1. Components of Detection 1. Sums and Differences 135 Efficiency 165 2. Constant Multipliers 135 2. Geometric Efficiency 166 3. Products and Ratios 136 3. Intrinsic Efficiency 168 4. More Complicated 4. Energy Selective Counting 169 Combinations 136 5. Some Complicating Factors 170 D. Applications of Statistical 6. Calibration Sources 175 Analysis 136 B. Problems in the Detection and 1. Effects of Averaging 136 Measurement of R Particles 176 2. Counting Rates 137 C. Dead Time 3. Significance of Differences 1. between Counting Causes of Dead Time 178 2. Measurements 137 Mathematical Models 179 4. Effects of Background 3. Window Fraction 137 Effects 181 5. Minimum 4. Dead Time Detectable Activity 138 Correction Methods 181 D. 6. Comparing Counting Quality Assurance for Radiation Systems 138 Measurement Systems 182 7. Estimating Required Counting Times 139 8. Optimal Division of Counting Times 140 Counting Systems 185 E. Statistical Tests 140 A. Nal(TI) Well Counter 185 1. The X2 Test 141 1. Detector Characteristics 185 2. The t-test 142 2. Detection Efficiency 186 3. Treatment of "Outliers" 145 3. Sample Volume Effects 188 Contents** e ix 4. Linear Regression 146 4. Assay of Absolute Activity 190 5. Shielding and Background 190 6. Energy Calibration 191 Pulse-Height Spectrometry 149 7. Multiple Radionuclide Source Counting 191 A. Basic Principles 149 8. Dead Time 192 B. Spectrometry with Nal(TI) 150 9. Automatic Multiple-Sample 1. The Ideal Pulse-Height Systems 192 Spectrum 150 10. Applications 195 2. The Actual Spectrum 151 B. Counting with Conventional Nal(TI) 3. Effects of Detector Size 154 Detectors 195 4. Effects of Counting Rate 155 1. Large Sample Volumes 195 5. General Effects of r-ray 2. Liquid and Gas Flow Energy 155 Counting 195 6. Energy Linearity 157 C. Liquid Scintillation Counters 196 7. Energy Resolution 157 1. General Characteristics 196 C. Spectrometry with Other 2. Pulse-Height Spectrometry 198 Detectors 160 3. Counting Vials 198

x.. * PHYSICS IN NUCLEAR MEDICINE 4. Energy and Efficiency Calibrations 199 5. Quench Corrections 199 6. Sample Preparation Techniques 201 7. Liquid and Gas Flow Counting 202 8. Automatic Multiple-Sample LS Counters 202 9. Applications 202 D. Gas-Filled Detectors 203 1. Dose Calibrators 203 2. Gas Flow Counters 204 E. Semiconductor Detector Systems 205 1. System Components 205 2. Applications 207 F. In Vivo Counting Systems 207 1. Nal(TI) Probe Systems 207 2. Miniature 7-Ray Probes for Surgical Use 207 3. Whole-Body Counters 210 The Gamma Camera : Basic Principles 211 C. D. E. 2. Image Nonuniformity 235 3. Nonuniformity Correction Techniques 236 4. Gamma Camera Tuning 238 Design and Performance Characteristics of Parallel-Hole Collimators 239 1. Basic Limitations in Collimator Performance 239 2. Spatal Thickness 239 3. Geometry of Collimator Holes 241 4. System Resolution 244 Performance Characteristics of Converging, Diverging, and Pinhole Collimators 245 Measurements of Gamma Camera Performance 247 1. Intrinsic Resolution 248 2. System Resolution 249 3. Spatial Linearity 249 4. Uniformity 249 5. Counting Rate Performance 250 6. Energy Resolution 250 7. System Sensitivity 250 A. General Concepts of Radionuclide Image Quality in Imaging 211 Nuclear Medicine 253 B. Basic Principles of the Gamma Camera 212 A. Basic Methods for Characterizing Components and Evaluating..-_ " _ and Q Electronics 213 B. Spatial Resolution 253 3. Collimators 218 1. Factors Affecting Spatial " " Gamma " - Camera 222 2. Methods for Evaluating Spatial C. Types of Gamma Cameras and Resolution 254 Their Clinical Uses 223 C. Contrast 259 -Noise 263 The Gamma Camera : Performance " - " Image Noise Random Noise "" Contrast-to-Noise Ratio 263 263 Characteristics 227 E. Observer Performance Studies 268 A. Basic Performance 1. Contrast-Detail (C-D) Studies 268 2. Receiver Operating Characteristic Characteristics 227 (ROC) Studies 270 1. Intrinsic Spatial Resolution 227 2. Detection Efficiency 229 3. Energy Resolution 230 Tomographic 4. Performance at High Counting Reconstruction Rates 231 in Nuclear Medicine B. 273 Detector Limitations : Nonuniformity and Nonlinearity 234 A. General Concepts, Notation, and 1. Image Nonlinearity 234 Terminology 274

B. Backprojection and Fourier-Based Positron Emission Techniques 276 Tomography 325 1. Simple Backprojection 276 2. Direct Fourier Transform A. Annihilation Coincidence Reconstruction 278 Detection 325 3. Filtered Backprojection 280 1. Basic Principles of Annihilation 4. Multislice Imaging 283 Coincidence Detection 325 C. Image Quality in Fourier Transform 2. Time-of-Flight PET 327 and Filtered Backprojection 3. Spatial Resolution : Detectors 328 4. Spatial Resolution : Positron Techniques 283 Physics 328 1. Effects of Sampling on Image 5. Spatial Resolution : Quality 283 Depth-of-Interaction Effect 334 2. Sampling Coverage and 6. Spatial Resolution : Sampling 336 Consistency Requirements 286 7. Spatial Resolution : 3. Noise Propagation, Signal-to-Noise Reconstruction Filters 336 Ratio, and Contrast-to-Noise 8. Sensitivity 337 Ratio 287 9. Event Types in Annihilation D. Iterative Reconstruction Coincidence Detection 340 Algorithms 291 B. PET Detector and Scanner 1. General Concepts of Iterative Designs 342 Reconstruction 291 1. Block Detectors 342 2. Expectation-Maximization 2. Modified Block Detectors 344 Reconstruction 293 3. Dedicated PET Systems 346 E. Reconstruction of Fan-Beam and 4. Gamma Camera Systems Cone-Beam Data 294 for PET 348 C. Data Acquisition for PET 350 1. Two-Dimensional Data Single Photon Emission Computed Tomography 299 Acquisition 350 2. Three-Dimensional Data Acquisition 351 3. Data Acquisition for Dynamic A. SPECT Systems 299 Studies and Whole-Body 1. Gamma Camera Scans 353 SPECT Systems 299 D. Data Corrections and 2. Advanced SPECT Systems 300 3. Combined Modality Systems 302 B. Practical Implementation Quantitative Aspects of PET 353 1. Normalization 353 2~ Correction for Random Coincidences 354 of SPECT 303 3. Correction for Scattered 1. Attenuation Effects Radiation 355 and Conjugate Counting 305 4. Attenuation Correction 355 2. Attenuation Correction 310 5. Dead Time Corrections 357 3. Transmission Scans and Attenuation 6. Absolute Quantification of Maps 313 PET Images 357 4. Scatter Corrections 315 E. Clinical and Research 5. Partial-Volume Effects 317 Applications of PET 358 Contents o o 9 xi C. Performance Characteristics of SPECT Systems 319 1. Spatial Resolution 319 2. Volume Sensitivity 320 Digital Image Processing in 3. Other Measurements of Nuclear Medicine 361 Performance 321 4. Quality Assurance in SPECT 321 A. Digital Images 362 D. Clinical Applications of 1. Basic Characteristics and SPECT 322 Terminology 362

xii. * * PHYSICS IN NUCLEAR MEDICINE 2. Spatial Resolution and Matrix Size 364 3. Image Display 365 4. Acquisition Modes 366 B. Digital Image-Processing Techniques 367 1. Image Visualization 367 2. Regions and Volumes of Interest 370 3. Time-Activity Curves 371 4. Image Smoothing 371 5. Edge Detection and Segmentation 371 6. Co-registration of Images 373 C. Processing Environment 375 Tracer Kinetic Modeling 377 A. Basic Concepts 377 B. Tracers and Compartments 378 1. Definition of a Tracer 378 2. Definition of a Compartment 380 3. Distribution Volume and Partition Coefficient 380 4. Flux 381 5. Rate Constants 382 6. Steady State 383 C. Tracer Delivery and Transport 385 1. Blood Flow, Extraction, and Clearance 385 2. Transport 387 D. Formulation of a Compartmental Model 388 E. Examples of Dynamic Imaging and Tracer Kinetic Models 391 1. Cardiac Function and Ejection Fraction 391 2. Blood Flow Models 392 3. Blood Flow : Trapped Radiotracers 392 4. Blood Flow : Clearance Techniques 394 5. Enzyme Kinetics : Glucose Metabolism 395 6. Receptor Ligand Assays 401 F. Summary 402 Internal Radiation Dosimetry 405 A. Radiation Dose and Equivalent Dose : Quantities and Units 405 B. Calculation of Radiation Dose (MIRD Method) 406 1. Basic Procedure and Some Practical Problems 406 2. Cumulated Activity, A 407 3. Equilibrium Absorbed Dose Constant, A 411 4. Absorbed Fraction, ~ 412 5. Specific Absorbed Fraction, (D, and the Dose Reciprocity Theorem 414 6. Mean Dose per Cumulated Activity, S 414 7. Whole-Body Dose, Effective Dose, and Effective Dose Equivalent 416 8. Limitations of the MIRD Method 417 Radiation Safety and Health Physics 427 A. Quantities and Units 428 1. Dose-Modifying Factors 428 2. Exposure and Air Kerma 428 B. Regulations Pertaining to the Use of Radionuclides 430 1. Nuclear Regulatory Commission Licensing and Regulations 430 2. Restricted and Unrestricted Areas 430 3. Dose Limits 431 4. Concentrations for Airborne Radioactivity in Restricted Areas 431 5. Environmental Concentrations and Concentrations for Sewage Disposal 431 6. Record-Keeping Requirements 432 7. Recommendations of Advisory Bodies 432 C. Safe Handling of Radioactive Materials 433 1. The ALARA Concept 433 2. Reduction of Radiation Doses from External Sources 433 3. Reduction of Radiation Doses from Internal Sources 436 4. Laboratory Design 437 5. Procedures for Handling Spills 438 D. Disposal of Radioactive Waste 439 E. Radiation Monitoring 439 1. Survey Meters and Laboratory Monitors 439

2. Personnel Dosimeters 440 3. Wipe Testing 440 Appendix A: Unit Conversions 443 Appendix 8: Properties of the Elements 444 Contents + s * Ail Appendix E: Effective Dose Equivalent (msv/mbq) and Radiation Absorbed Dose Estimates (mgy/mbq) to Adult Subjects from Selected Internally Administered Radiopharmaceuticals 480 Appendix C: Characteristics of Some Medically Appendix F: The Fourier Transform 483 Important A. The FT: What It Radionuclides Represents 483 447 B. Calculating FTs 484 Appendix D: Mass Attenuation C. Some Properties of FTs 485 Coefficients for Water, D. Some Examples of FTs 488 Sodium Iodide, BGO, CZT, Appendix G: Convolutions 493 and Lead 479 Index 499