Principles of Medical Imaging for Engineers : From Signals to Images

This introduction to medical imaging introduces all of the major medical imaging techniques in wide use in both medical practice and medical research, including Computed Tomography, Ultrasound, Positron Emission Tomography, Single Photon Emission Tomography and Magnetic Resonance Imaging. Principles of Medical Imaging for Engineers introduces fundamental concepts related to why we image and what we are seeking to achieve to get good images, such as the meaning of ‘contrast’ in the context of medical imaging. This introductory text separates the principles by which ‘signals’ are generated and the subsequent ‘reconstruction’ processes, to help illustrate that these are separate concepts and also highlight areas in which apparently different medical imaging methods share common theoretical principles. Exercises are provided in every chapter, so the student reader can test their knowledge and check against worked solutions and examples. The text considers firstly the underlying physical principles by which information about tissues within the body can be extracted in the form of signals, considering the major principles used: transmission, reflection, emission and resonance. Then, it goes on to explain how these signals can be converted into images, i.e., full 3D volumes, where appropriate showing how common methods of ‘reconstruction’ are shared by some imaging methods despite relying on different physics to generate the ‘signals’. Finally, it examines how medical imaging can be used to generate more than just pictures, but genuine quantitative measurements, and increasingly measurements of physiological processes, at every point within the 3D volume by methods such as the use of tracers and advanced dynamic acquisitions. Principles of Medical Imaging for Engineers will be of use to engineering and physical science students and graduate students with an interest in biomedical engineering, and to their lecturers. Preface 6 About This Book 8 Contents 9 From Signals ... 13 1 Introduction 14 1.1 What Is Medical Imaging? 14 1.2 Signals 15 1.3 Noise 16 1.4 Contrast 17 1.5 Electromagnetic Spectrum 18 2 Transmission—X-rays 20 2.1 Photon Interactions with Matter 20 2.1.1 Photoelectric Attenuation 21 2.1.2 Compton Scattering 22 2.1.3 Other Mechanisms 23 2.1.4 Attenuation Coefficient 23 2.2 Contrast 24 2.3 Background Signal 25 2.4 Anti-scatter Grids 27 2.5 The CT Number 27 3 Reflection—Ultrasound 30 3.1 Wave Propagation 31 3.2 Acoustic Impedance 33 3.3 Reflection and Refraction 34 3.4 Scattering 35 3.5 Absorption 36 3.6 Attenuation 36 3.7 Ultrasonic Contrast 37 3.8 Doppler Ultrasound 39 4 Emission—SPECT/PET 42 4.1 Radionuclides 42 4.1.1 Single-Photon Emission 43 4.1.2 Positron Emission 44 4.1.3 Radioactive Decay 45 4.2 Detection 45 4.2.1 Gamma Camera 45 4.2.2 Attenuation 46 4.2.3 Scatter 47 4.2.4 Deadtime 48 5 Resonance—Nuclear Magnetic Resonance 49 5.1 Microscopic Magnetization 50 5.2 Precession 51 5.3 Macroscopic Magnetization 52 5.4 Transverse Magnetization 54 5.5 RF Excitation 56 5.6 The Rotating Frame 57 5.7 Relaxation 58 5.7.1 Transverse Relaxation: T1 58 5.7.2 Longitudinal Relaxation: T2 59 5.8 The Bloch Equations 60 5.9 Spin Echoes and T2* 61 To Images ... 63 6 Imaging 64 6.1 Resolution 65 6.1.1 Pixels and Voxels 65 6.1.2 Line and Point Spread Functions 66 6.2 The General Image Formation Problem 66 6.3 The General Image Restoration Problem 68 6.4 A Revision of Frequency Analysis 70 6.4.1 Fourier in One Dimension 71 6.4.2 Fourier in Two Dimensions 72 6.4.3 2D FT in Polar Coordinates 73 6.5 Sampling 74 7 Timing-Based Reconstruction—Ultrasound 78 7.1 Converting Time to Depth 78 7.2 Ultrasound Beams and Pulse-Echoes 80 7.3 Scanning 83 7.4 Artefacts in Ultrasound 84 8 Back-Projection Reconstruction—CT and PET/SPECT 86 8.1 Projection: Computed Tomography 87 8.2 The Sinogram 89 8.3 Slice-Projection Theorem 90 8.4 Filtered Back-Projection 91 8.5 SPECT 93 8.6 PET 93 8.6.1 Randoms 94 8.6.2 Positron Range 95 9 Fourier Reconstruction—MRI 96 9.1 Gradients 96 9.2 Slice Selection 97 9.3 Frequency Encoding 99 9.4 Scanning k-Space 101 9.5 MRI Reconstruction 103 9.5.1 Field of View 103 9.5.2 k-Space Coverage and Resolution 104 9.5.3 The Effect of T2 Decay 106 9.6 More Advanced k-Space Trajectories 106 9.6.1 Partial Fourier 106 9.6.2 Non-Cartesian 107 9.6.3 3D k-Space 107 9.6.4 Compressed Sensing 108 10 Principles of Reconstruction 110 10.1 Analytic Reconstruction 110 10.2 Reconstruction as Cost Function Minimization 112 10.3 Iterative PET Reconstruction 114 10.4 Compressed Sensing MRI Reconstruction 116 And Beyond ... 118 11 Generating and Enhancing Contrast 119 11.1 Manipulating the Signal 120 11.1.1 MRI Relaxation Contrast 120 11.1.2 Diffusion 124 11.2 Contrast Agents 126 11.2.1 X-ray Contrast Agents 126 11.2.2 Ultrasound Contrast Agents 126 11.2.3 SPECT/PET Contrast Agents 127 11.2.4 MRI Contrast Agents 128 12 Beyond Contrast: Quantitative, Physiological and Functional Imaging 129 12.1 Quantitative Imaging 130 12.1.1 Transmission Methods 130 12.1.2 Reflection Methods 131 12.1.3 Emission Methods 131 12.1.4 Dynamic Data 132 12.1.5 Resonance Methods 133 12.2 Tracer Kinetics 133 12.2.1 The Arterial Input Function 134 12.2.2 The Tissue (Voxel) 135 12.2.3 A Simple Example: One-Compartment Model 135 12.2.4 The General Case: The Residue Function 136 12.2.5 Deconvolution Analysis 137 12.2.6 Signal Model 138 12.3 Perfusion Imaging 138 12.3.1 Static Perfusion Imaging 139 12.3.2 Semi-quantitative Dynamic Perfusion Imaging 139 12.3.3 Perfusion Kinetic Imaging 140 12.3.4 Perfusion CT 141 12.3.5 SPECT Perfusion 141 12.3.6 Tracer Perfusion MRI 141 12.3.7 Arterial Spin Labelling MRI 142 12.4 Oxygenation 145 12.5 Metabolic Imaging 146 12.5.1 Dynamic PET 146 12.5.2 MRI 148 Appendix A Exercise Solutions 149 A.1 Chapter 1 149 A.1.1 Exercise 1A 149 A.1.2 Exercise 1B 150 A.1.3 Exercise 1C 150 A.2 Chapter 2 151 A.2.1 Exercise 2A 151 A.2.2 Exercise 2B 151 A.2.3 Exercise 2C 152 A.2.4 Exercise 2D 152 A.3 Chapter 3 153 A.3.1 Exercise 3A 153 A.3.2 Exercise 3B 154 A.3.3 Exercise 3C 155 A.3.4 Exercise 3D 156 A.3.5 Exercise 3E 157 A.4 Chapter 4 157 A.4.1 Exercise 4A 157 A.4.2 Exercise 4B 158 A.5 Chapter 5 158 A.5.1 Exercise 5A 158 A.5.2 Exercise 5B 158 A.5.3 Exercise 5C 159 A.5.4 Exercise 5D 159 A.5.5 Exercise 5E 159 A.6 Chapter 6 160 A.6.1 Exercise 6A 160 A.6.2 Exercise 6B 160 A.6.3 Exercise 6C 161 A.6.4 Exercise 6D 162 A.7 Chapter 7 163 A.7.1 Exercise 7A 163 A.7.2 Exercise 7B 163 A.8 Chapter 8 163 A.8.1 Exercise 8A 163 A.8.2 Exercise 8B 164 A.9 Chapter 9 165 A.9.1 Exercise 9A 165 A.9.2 Exercise 9B 165 A.9.3 Exercise 9C 165 A.9.4 Exercise 9D 166 A.10 Chapter 10 166 A.10.1 Exercise 10A 166 A.10.2 Exercise 10B 167 A.11 Chapter 11 168 A.11.1 Exercise 11A 168 A.11.2 Exercise 11B 168 A.11.3 Exercise 11C 169 A.11.4 Exercise 11D 169 A.12 Chapter 12 170 A.12.1 Exercise 12A 170 A.12.2 Exercise 12B 170 A.12.3 Exercise 12C 171 A.12.4 Exercise 12D 172 A.12.5 Exercise 12E 173 Index 175 Front Matter ....Pages i-xiv Front Matter ....Pages 1-1 Introduction (Michael Chappell)....Pages 3-8 Transmission—X-rays (Michael Chappell)....Pages 9-18 Reflection—Ultrasound (Michael Chappell)....Pages 19-30 Emission—SPECT/PET (Michael Chappell)....Pages 31-37 Resonance—Nuclear Magnetic Resonance (Michael Chappell)....Pages 39-52 Front Matter ....Pages 53-53 Imaging (Michael Chappell)....Pages 55-68 Timing-Based Reconstruction—Ultrasound (Michael Chappell)....Pages 69-76 Back-Projection Reconstruction—CT and PET/SPECT (Michael Chappell)....Pages 77-86 Fourier Reconstruction—MRI (Michael Chappell)....Pages 87-100 Principles of Reconstruction (Michael Chappell)....Pages 101-108 Front Matter ....Pages 109-109 Generating and Enhancing Contrast (Michael Chappell)....Pages 111-120 Beyond Contrast: Quantitative, Physiological and Functional Imaging (Michael Chappell)....Pages 121-140 Back Matter ....Pages 141-169