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

Dettaglio

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