A concise and complete introductory treatment of NMR and MRI
Essential Concepts in MRI delivers the first comprehensive look at magnetic resonance imaging with a practical focus on nuclear magnetic resonance spectroscopy applications. The book includes the essential components of MRI and NMR and is written for anyone new to the field of MRI who seeks to gain a complete understanding of all four essential components of MRI: physics theory, instrumentation, spectroscopy, and imaging.
Highly visual and including numerous full color figures that provide crucial graphical descriptions of key concepts discussed in the book, Essential Concepts in MRI includes discussions of quantitative and creative MRI, as well as spatial mapping in MRI and the effects of the field gradient and k-space imaging. The book also covers: - A thorough introduction to essential concepts in nuclear magnetic resonance, including classical descriptions of NMR and quantum mechanical descriptions of NMR - Comprehensive explorations of essential concepts in NMR instrumentation, including magnets, radio-frequency coils, transmitters, and receivers - Practical discussions of essential concepts in NMR spectroscopy, including simple 1D spectroscopy, double resonance, and dipolar interactions in two-spin systems - In-depth examinations of essential concepts in MRI, including the design of MRI pulse sequences and the elements of MRI instrumentation, with a special focus on quantitative MRI
Essential Concepts in MRI is a must-read reference for upper-level undergraduate and postgraduate students in the physical and medical sciences, especially radiology, MRI, and imaging courses. It is also essential for students and researchers in the biomedical sciences and engineering.
Table of Contents
Preface xi
Chapter 1 Introduction 1
1.1 Introduction 1
1.2 Major Steps in an NMR or MRI Experiment, and Two Conventions in Direction 2
1.3 Major Milestones in the History of NMR and MRI 4
1.4 The Organization for a One-semester Course 6
Part I Essential Concepts in NMR 9
Chapter 2 Classical Description of Magnetic Resonance 11
2.1 Fundamental Assumptions 11
2.2 Nuclear Magnetic Moment 12
2.3 The Time Evolution of Nuclear Magnetic Moment 15
2.4 Macroscopic Magnetization 16
2.5 Rotating Reference Frame 18
2.6 Spin Relaxation Processes 22
2.7 Bloch Equation 24
2.8 Fourier Transform and Spectral Line Shapes 25
2.9 CW NMR 28
2.10 Radio-frequency Pulses in NMR 29
2.11 FT NMR 30
2.12 Signal Detection in NMR 32
2.13 Phases of the NMR Signal 33
Chapter 3 Quantum Mechanical Description of Magnetic Resonance 37
3.1 Nuclear Magnetism 37
3.2 Energy Difference 39
3.3 Macroscopic Magnetization 40
3.4 Measurement of the X Component of Angular Momentum 41
3.5 Macroscopic Magnetization for Spin 1/2 42
3.6 Resonant Excitation 43
3.7 Mechanisms of Spin Relaxation 43
Chapter 4 Nuclear Interactions 51
4.1 Dipolar Interaction 51
4.2 Chemical Shift Interaction 54
4.3 Scalar Interaction 57
4.4 Quadrupole Interaction 61
4.5 Summary of Nuclear Interactions 61
Part II Essential Concepts in NMR Instrumentation 65
Chapter 5 Instrumentation 67
5.1 Magnets 67
5.2 Radio-frequency Coil, Its Resonant Circuitry, and the Probe 72
5.3 Frequency Management 75
5.4 Transmitter 76
5.5 Receiver 78
5.6 Pulse Programmer and Computer 78
5.7 Other Components 78
Chapter 6 NMR Experimental 81
6.1 Shimming 81
6.2 Preparing Samples 82
6.3 Pulse Sequences and FID 83
6.4 Digitization Rate and Digital Resolution 85
6.5 Dynamic Range 87
6.6 Phase Cycling 89
6.7 Data Accumulation 91
6.8 Pre-FFT Processing Techniques 92
6.9 Fast Fourier Transform 95
6.10 Post-FFT Processing 95
6.11 Signal-to-Noise Ratio 97
Chapter 7 Spin Manipulations by Pulse Sequences 101
7.1 Single Pulse: 90˚| X , 90˚| Y , 90˚| -x , 90˚| -y 101
7.2 Inversion Recovery Sequence, Saturation Recovery Sequence, and T1 Relaxation 103
7.3 Spin-Echo Sequence (Hahn Echo) and T2 Relaxation 106
7.4 CPMG Echo Train 110
7.5 Stimulated Echo Sequence 111
7.6 Spin-locking and T 1ρ Relaxation 112
7.7 How to Select the Delays in Relaxation Measurement 113
Part III Essential Concepts in NMR Spectroscopy 117
Chapter 8 First-order 1D Spectroscopy 119
8.1 Nomenclature of the Spin System 119
8.2 Peak Shift - the Effect of Chemical Shift 120
8.3 Peak Area - Reflecting the Number of Protons 122
8.4 Peak Splitting - the Consequence of J Coupling 122
8.5 Examples of 1D Spectra 128
Chapter 9 Advanced Topics in Spectroscopy 137
9.1 Double Resonance 137
9.2 Dipolar Interaction in a Two-spin System 141
9.3 Magic Angle 142
9.4 Chemical Exchange 143
9.5 Magnetization Transfer 144
9.6 Selective Polarization Inversion/ Transfer 146
9.7 Radiation Damping 147
Chapter 10 2D NMR Spectroscopy 151
10.1 Essence of 2D NMR Spectroscopy 151
10.2 COSY - Correlation Spectroscopy 153
10.3 J-resolved Spectroscopy 157
10.4 Examples of 2D NMR Spectroscopy 162
Part IV Essential Concepts in MRI 167
Chapter 11 Effect of the Field Gradient and k-space Imaging 169
11.1 Spatially Encoding Nuclear Spin Magnetization 170
11.2 k Space in MRI 173
11.3 Mapping of k Space 174
11.4 Gradient Echo 174
Chapter 12 Spatial Mapping in MRI 179
12.1 Slice Selection in 2D MRI 180
12.2 Reading a Graphical Imaging Sequence 186
12.3 2D Filtered Back-Projection Reconstruction 189
12.4 2D Fourier Imaging Reconstruction191
12.5 Sampling Patterns Between the Cartesian and Radial Grids 194
12.6 3D Imaging 196
12.7 Fast Imaging in MRI 198
12.8 Ultra-short Echo and ZTE MRI 202
12.9 MRI in Other Dimensions (4D, 1D, and One Voxel) 203
12.10 Resolution in MRI 206
Chapter 13 Imaging Instrumentation and Experiments 209
13.1 Shaped Pulses 209
13.2 The Gradient Units 211
13.3 Instrumentation Configurations for MRI 215
13.4 Imaging Parameters in MRI 217
13.5 Image Processing Software 219
13.6 Best Test Samples for MRI 219
Part V Quantitative and Creative MRI 223
Chapter 14 Image Contrast in MRI 225
14.1 Non-trivial Relationship Between Spin Density and Image Intensity 225
14.2 Image Contrast in MRI 227
14.3 How to Obtain Useful Information from Image Contrast? 229
14.4 Magnetization-prepared Sequences in Quantitative MRI 231
Chapter 15 Quantitative MRI 235
15.1 Quantitative Imaging of Velocity V and Molecular Diffusion D 235
15.2 Quantitative Imaging of Relaxation Times T1 , T2 , T1ρ 247
15.3 Quantitative Imaging of Chemical Shift δ 254
15.4 Secondary Image Contrasts in MRI259 15.5 Potential Issues and Practical Strategies in Quantitative MRI 264
Chapter 16 Advanced Topics in Quantitative MRI 275
16.1 Anisotropy and Tensor Properties in Quantitative MRI 277
16.2 Multi-Component Nature in Quantitative MRI 285
16.3 Quantitative Phase Information in the FID Data - SWI and QSM 288
16.4 Functional MRI (fMRI) 290
16.5 Optical Pumping and Hyperpolarization in MRI 290
Chapter 17 Reading the Binary Data 295
17.1 Formats of Data 295
17.2 Formats of Data Storage 296
17.3 Reading Unknown Binary Data 298
17.4 Examples of Specific Formats 301
Appendices 305
Appendix 1 Background in Mathematics 307
A1.1 Elementary Mathematics 307
A1.2 Fourier Transform 311
Appendix 2 Background in Quantum Mechanics 317
A2.1 Operators 317
A2.2 Expansion of a Wave Function 319
A2.3 Spin Operator I 320
A2.4 Raising and Lowering Operators I + and I - 320
A2.5 Spin-1/2 Operator (in the Formalism of Pauli’s Spin Matrices) 321
A2.6 Density Matrix Operator ρ 323
Appendix 3 Background in Electronics 325
A3.1 Ohm’s Law for DC and AC Circuits 325
A3.2 Electronics at Radio Frequency 327
Appendix 4 Sample Syllabi for a One-semester Course 329
Appendix 5 Homework Problems 331
Index 337
