Theory Of Quantitative Magnetic Resonance Imaging

by Hernan J Jara

Overview

qMRI is a rapidly evolving scientific field of high current interest because it has the potential of radically changing the clinical and research practices of magnetic resonance imaging (MRI). This focuses solely on the theoretical aspects of qMRI, which are treated and analyzed at three different spatial scales, specifically: i) the quantum physics scale of individual spins; ii) the semi-classical physics scale of spin packets; and iii) the imaging scale of voxels. Topics are presented paying particular attention to theoretical unification and mathematical uniformity.

Product Details

ISBN-13:	9789814295239
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	05/29/2013
Pages:	264
Product dimensions:	6.10(w) x 9.10(h) x 0.80(d)

Table of Contents

Preface xiii

A Introduction 1

A1 Historical Notes 1

A2 Image Processing 3

A3 Quantitative Imaging 4

A4 Book Organization 5

References 6

B Elements of Imaging Theory 7

B1 Introduction 7

B2 Imaging as a Mathematical Operation 7

B2.1 Spatial Encoding 7

B2.2 Spatial Localization: the Voxel Sensitivity Function 9

B2.3 Fourier Transform Imaging 10

B2.4 Noise 12

B3 Objective Measures of Image Quality 13

B3.1 Signal-to-Noise Ratio 13

B3.2 Spatial (Geometric) Resolution 14

B3.3 Contrast-to-Noise Ratio: Pixel Value Resolution 15

B3.4 Vulnerability to Artifacts (MRI) 16

B3.4.i Susceptibility artifacts 16

B3.4.ii Motion artifacts 17

B3.4.iii Chemical shift artifacts 18

B3.4.iv Truncation artifacts 18

B3.4.v Aliasing artifacts 18

References 19

C Physics of Quantitative MRI 21

C1 Introduction 21

C1.1 The Different Spatial Scales of qMRI Theory 21

C1.2 The Spatial Scale of the 'H Proton and the Water Molecule 22

C1.3 Spin Packets 23

C1.4 The Magnetic Fields of MRI 25

C2 The Quantum Physics Scale: Magnetic Moments 28

C2.1 Elements of Quantum Mechanics 28

C2.1.i The Language of Quantum Theory 28

C2.1.ii Postulates 28

C2.2 Solitary ¹H-Proton in a Static Magnetic Field 32

C2.2.i Stationary States: Longitudinal Zee man States 34

C2.2.ii Mixture States: Transverse Magnetic Dipole Moments 35

C2.2.iii The Transverse Spin State 37

C2.3 Solitary ¹H-Proton in a Time Dependent Magnetic Field 38

C2.3.i The Interaction Schrödinger Equation 38

C2.3.ii Magnetic Moment Dynamics: Differential and Integral Equations of Motion 39

C2.3.iii Integral Equations 40

C3 The Semi-Classical NMR Physics Scale: Magnetized Spin Packets 42

C3.1 Nuclear Magnetization of Spin Packets 42

C3.2 State of Thermal Equilibrium: Statistical Mechanics 43

C3.3 NMR Dynamics: The Bloch Equation 44

C3.4 The Transverse and Longitudinal Bloch Equations 47

C3.5 Bloch Theory: Assumptions and Limitations 48

C3.6 The Bloch-Torrey-Stejskal Equations: Kinetic Effects 49

C3.7 The Two-Pool Bloch-Torrey-Stejskal (BTS) Equations: Magnetization Exchange 50

C3.8 Relaxation by Magnetization Transfer 55

C3.9 The Spin-Lock Bloch Equations 56

C3.10 The Semi-Classical Classification Scheme of qNMR-Parameters 60

C4 Essential NMR Dynamics 62

C4.1 NMR Excitation: Flip Angle and Slice Selection 63

C4.1.i The Resonance Condition 66

C4.1.ii Slice Selection 67

C4.2 Inversion Recovery 69

C4.3 Magnetization Saturation in Repetitive Pulse Sequences 69

C4.4 Free Decay in the Presence of Magnetic Field Gradients: Effects of Diffusion 73

C4.5 rf-Refocuscd Decay: Spin-echoes 75

C4.6 Spin-echo: Effects of Anisotropic Diffusion and Flow 77

C5 The MR Imaging Scale: Voxels 79

C5.1 The MRI Pixel Value Equation: 3D-FT Imaging 79

C5.2 The MRI Pixel Value Equation: 2D-FT Imaging 83

C5.3 Pixel Value Equation: Exact Integral Form 84

C5.4 Voxel-Integrated Pixel Value Equation: Spin-echo 86

C5.5 Voxel-Integrated Pixel Value Equation: Gradient-Echo 87

C5.6 Classification of qMRI Parameters 89

C6 MRI Pulse Sequences 91

C6.1 Basic Concepts 91

C6.2 Pulse Sequence Classification 92

C6.3 Spatial Encoding Schemes (Scanning Techniques) 92

C6.4 Signal Types 93

C6.5 Data Acquisition Acceleration Techniques 94

C6.5.i Ultra-short TR Regime 94

C6.5.ii Medium-Short TR Regime 95

C6.5.iii Long TR Regime 96

C6.6 Modular Description of Pulse Sequences 98

C6.6.i Pre-Excitation Modules 100

C6.6.ii Post-Excitation Modules 102

References 103

D Elements of Relaxation Theory 107

D1 Introduction 107

D1.1 Relaxation Fundamentals 109

D1.2 Rate Equation Analysis: Two-Level Systems 110

D2 Spin Packet Quantum Mechanics 111

D2.1 Spin Packet Hamiltonian 111

D2.2 Random Field Relaxation: Local Field Equations 113

D2.3 The Bloch Equation Connection 115

D2.4 Random Field Relaxation 116

D2.5 Spectral Density 118

D2.6 Relaxation in Liquids: Kinetic Dipolar T₁ and T₂ Relaxation Mechanisms 118

D2.7 Relaxation by Paramagnetic Solutes 124

D2.8 Spin Locking 124

D3 Relaxation in Tissue 125

D3.1 Spatial Scalability and Exponentiality 125

D3.2 Empirical Tissue Relaxometry 126

References 127

E QMRI Theory 129

E1 Introduction 129

E2 qMRI Principles 129

E2.1 The Pixel Value Equation (Revisited) 131

E2.2 Association of qMRI Parameters with Weighting qCVs: Liquid Pool 132

E2.3 The Principle of Differential Weighting 133

E3 Parameter Specific qMRI Paradigms 135

E3.1 qMRI of the Proton Density: Un-weighting and Pixel Value Calibration 135

E3.2 qMRI of Diffusion and Perfusion: Intravoxel Incoherent Motion (IVIM) 138

E3.2.i Diffusion Tensor Imaging (DTI) 141

E3.2.ii Diffusion qMRI Pulse Sequences 144

E3.3 qMRI of Flow and Displacement 148

E3.4 qMRI of the Longitudinal Relaxation Time(T₁) 153

E3.4.i Inversion Recovery Techniques: qCV = TI 154

E3.4.ii Saturation Recovery Techniques: qCV = TR 159

E3.4.iii Variable Nutation Angle Techniques: qCV = FA 160

E3.4.iv Other Ti qMRI Techniques 162

E3.5 qMRI of the Transverse Relaxation Time (T₂) 163

E3.5.i Multi-SE (CPMG) Techniques: qCV = TE 163

E3.5.ii Steady State Free Precession Techniques: qCV = FA 167

E3.5.iii Fast Spin-echo Techniques: qCV = TE_eff 169

E3.6 qMRI of the Reduced Transverse Relaxation Time (T₂) 172

E3.7 qMRI of the Semisolid Pool 173

E3.7.i MT-Bloch Equations 175

E3.7.ii The Steady State 176

E3.7.iii The Bound Water Lineshape 178

E3.7.iv Model Parameters 180

E3.7.v Incidental MT Effects in 2D Multislice Imaging 182

E3.8 qMRI of Fat 183

E3.8.i Introduction 183

E3.8.ii Fat-Water Interference Phenomena 186

E3.9 qMRI of Temperature 189

E3.9.i Proton Resonance Frequency (PRF) 191

E3.9.ii Temperature Mapping via Proton Density 192

E3.9.iii Temperature Mapping via Diffusion Coefficient 192

E3.9.iv Temperature Mapping via T₁ 193

E3.10 Dynamic Differential Weighting 194

E3.10.i Time Dependent Pixel Value Equation 194

E3.10.ii Tracer Kinetics: non-diffusable tracers 196

E3.l0.iii Tracer Kinetics: diffusable tracer 198

E3.10.iv Arterial Spin Labeling (ASL) 199

References 203

F QMRI Processing 213

F1 Introduction 213

F2 Data Structure and Organization 213

F2.1 General Considerations: (Towards) Comprehensive qMRI 213

F2.2 Multispectral qMRI Pulse Sequences 216

F2.2.i IR-TrueFISP 216

F2.2.ii Mixed-TSE 219

F2.2.iii QRAPMASTER 222

F3 qMRI Algorithms 223

F3.1 Mapping Equations 223

F3.2 Model-Conforming Algorithms 224

F4 qMRI Map Quality 226

F4.1 Directly-Acquired Images: Image Quality 229

F4.2 Algorithm Fidelity and Nonlinearities 230

F4.3 B₀ Mapping Techniques 232

F4.4 B₁ Mapping Techniques 234

References 237

G Introduction to Applications of QMRI 241

G1 Introduction 241

G2 Image Synthesis: Virtual MRI Scanning 241

G3 Characterization of Organs and Tissue Types 244

G3.1 qMRI Space 244

G3.2 Segmentation 245

G3.3 Volumetry and qMRI Spectroscopy 246

References 248