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 Direction2
1.3 Major Milestones in the History of NMR and MRI 4
1.4 The Organization for a One-semester Course6
Part I Essential Concepts in NMR 9
Chapter 2 Classical Description of Magnetic Resonance11
2.1 Fundamental Assumptions11
2.2 Nuclear Magnetic Moment12
2.3 The Time Evolution of Nuclear Magnetic Moment15
2.4 Macroscopic Magnetization16
2.5 Rotating Reference Frame18
2.6 Spin Relaxation Processes22
2.7 Bloch Equation24
2.8 Fourier Transform and Spectral Line Shapes25
2.9 CW NMR28
2.10 Radio-frequency Pulses in NMR29
2.11 FT NMR30
2.12 Signal Detection in NMR32
2.13 Phases of the NMR Signal33
Chapter 3 Quantum Mechanical Description of Magnetic Resonance37
3.1 Nuclear Magnetism37
3.2 Energy Difference39
3.3 Macroscopic Magnetization40
3.4 Measurement of the x Component of Angular Momentum41
3.5 Macroscopic Magnetization for Spin 1/242
3.6 Resonant Excitation43
3.7 Mechanisms of Spin Relaxation43
Chapter 4 Nuclear Interactions51
4.1 Dipolar Interaction51
4.2 Chemical Shift Interaction54
4.3 Scalar Interaction57
4.4 Quadrupole Interaction61
4.5 Summary of Nuclear Interactions61
Part II Essential Concepts in NMR Instrumentation 65
Chapter 5 Instrumentation67
5.1 Magnets67
5.2 Radio-frequency Coil, Its Resonant Circuitry, and the Probe72
5.3 Frequency Management75
5.4 Transmitter76
5.5 Receiver78
5.6 Pulse Programmer and Computer78
5.7 Other Components78
Chapter 6 NMR Experimental81
6.1 Shimming81
6.2 Preparing Samples82
6.3 Pulse Sequences and FID83
6.4 Digitization Rate and Digital Resolution85
6.5 Dynamic Range87
6.6 Phase Cycling89
6.7 Data Accumulation91
6.8 Pre-FFT Processing Techniques92
6.9 Fast Fourier Transform95
6.10 Post-FFT Processing95
6.11 Signal-to-Noise Ratio97
Chapter 7 Spin Manipulations by Pulse Sequences101
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 T1ρ 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 Spectroscopy151
10.2 COSY – Correlation Spectroscopy153
10.3 J-resolved Spectroscopy157
10.4 Examples of 2D NMR Spectroscopy162
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 Magnetization170
11.2 k Space in MRI173
11.3 Mapping of k Space174
11.4 Gradient Echo174
Chapter 12 Spatial Mapping in MRI179
12.1 Slice Selection in 2D MRI180
12.2 Reading a Graphical Imaging Sequence186
12.3 2D Filtered Back-Projection Reconstruction189
12.4 2D Fourier Imaging Reconstruction191
12.5 Sampling Patterns Between the Cartesian and Radial Grids194
12.6 3D Imaging196
12.7 Fast Imaging in MRI198
12.8 Ultra-short Echo and ZTE MRI202
12.9 MRI in Other Dimensions (4D, 1D, and One Voxel)203
12.10 Resolution in MRI206
Chapter 13 Imaging Instrumentation and Experiments209
13.1 Shaped Pulses209
13.2 The Gradient Units211
13.3 Instrumentation Configurations for MRI215
13.4 Imaging Parameters in MRI217
13.5 Image Processing Software219
13.6 Best Test Samples for MRI219
Part V Quantitative and Creative MRI 223
Chapter 14 Image Contrast in MRI225
14.1 Non-trivial Relationship Between Spin Density and Image Intensity225
14.2 Image Contrast in MRI227
14.3 How to Obtain Useful Information from Image Contrast?229
14.4 Magnetization-prepared Sequences in Quantitative MRI231
Chapter 15 Quantitative MRI235
15.1 Quantitative Imaging of Velocity v and Molecular Diffusion D235
15.2 Quantitative Imaging of Relaxation Times T1, T2, T1ρ247
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 MRI264
Chapter 16 Advanced Topics in Quantitative MRI275
16.1 Anisotropy and Tensor Properties in Quantitative MRI277
16.2 Multi-Component Nature in Quantitative MRI285
16.3 Quantitative Phase Information in the FID Data – SWI and QSM288
16.4 Functional MRI (fMRI)290
16.5 Optical Pumping and Hyperpolarization in MRI290
Chapter 17 Reading the Binary Data295
17.1 Formats of Data295
17.2 Formats of Data Storage296
17.3 Reading Unknown Binary Data298
17.4 Examples of Specific Formats301
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
