Preface ...................................................... xiii
List of Abbreviations and Symbols .............................. xv
1. Basic Principles ............................................ 1
1.1. Introduction .......................................... 1
1.2. Classical Description ................................. 2
1.3. Quantum Mechanical Description ........................ 4
1.4. Macroscopic Magnetization ............................. 6
1.5. Excitation ............................................ 8
1.6. Bloch Equations ...................................... 11
1.7. Fourier Transform NMR ................................ 14
1.8. Chemical Shift ....................................... 18
1.9. Digital Fourier Transform NMR ........................ 20
1.9.1. Multi-scan Principle ......................... 20
1.9.2. Time-domain Filtering ........................ 20
1.9.3. Analog-To-Digital Conversion ................. 22
1.9.4. Zero Filling ................................. 25
1.10. Spin-spin Coupling ................................... 26
1.10.1. Spectral Characteristics ..................... 30
1.11. T1 Relaxation ........................................ 33
1.12. T2 Relaxation and Spin-echoes ........................ 36
1.13. Exercises ............................................ 38
References ........................................... 41
2. In Vivo NMR Spectroscopy - Static Aspects .................. 43
2.1. Introduction ......................................... 43
2.2. Proton NMR Spectroscopy .............................. 43
2.2.1. Acetate (Ace) ................................ 45
2.2.2. N-Acetyl Aspartate (NAA) ..................... 45
2.2.1. N-Acetyl Aspartyl Glutamate (NAAG) ........... 52
2.2.4. Adenosine Triphosphate (ATP) ................. 52
2.2.5. Alanine (Ala) ................................ 53
2.2.6. γ-Aminobutyric Acid (GABA) ................... 54
2.2.7. Ascorbic Acid (Asc) .......................... 54
2.2.8. Aspartate (Asp) .............................. 55
2.2.9. Choline-containing Compounds (tCho) .......... 55
2.2.10. Creatine (Cr) and Phosphocreatine (PCr) ...... 57
2.2.11. Ethanolamine and Phosphorylethanolamine
(PE) ......................................... 58
2.2.12. Glucose (Glc) ................................ 59
2.2.13. Glutamate (Glu) .............................. 59
2.2.14. Glutamine (Gln) .............................. 61
2.2.15. Glutathione (GSH) ............................ 62
2.2.16. Glycerol ..................................... 62
2.2.17. Glycine ...................................... 63
2.2.18. Glycogen ..................................... 63
2.2.19. Histamine .................................... 64
2.2.20. Histidine .................................... 65
2.2.21. Homocarnosine ................................ 65
2.2.22. β-Hydroxybutyrate (BHB) ...................... 66
2.2.23. Myo-Inositol (mI) and scyllo-Inositol (sI) ... 66
2.2.24. Lactate (Lac) ................................ 67
2.2.25. Macromolecules ............................... 68
2.2.26. Phenylalanine ................................ 70
2.2.27. Pyruvate ..................................... 70
2.2.28. Serine ....................................... 71
2.2.29. Succinate .................................... 71
2.2.30. Taurine (Tau) ................................ 72
2.2.31. Threonine (Thr) .............................. 72
2.2.32. Tryptophan (Trp) ............................. 73
2.2.33. Tyrosine (Tyr) ............................... 73
2.2.34. Valine (Val) ................................. 74
2.2.35. Water ........................................ 74
2.2.36. Intra- and Extramyocellular Lipids
(IMCL and EMCL) .............................. 75
2.2.37. Deoxymyoglobin (DMb) ......................... 76
2.2.38. Citric Acid .................................. 77
2.2.39. Carnosine .................................... 78
2.3. Phosphorus-31 NMR Spectroscopy ....................... 78
2.3.1. Identification of Resonances ................. 79
2.3.2. Intracellular pH ............................. 80
2.4. Carbon-13 NMR Spectroscopy ........................... 82
2.4.1. Identification of Resonances ................. 82
2.5. Sodium-23 and Potassium-39 NMR Spectroscopy .......... 85
2.6. Fluorine-19 NMR Spectroscopy ......................... 89
2.6.1. Identification of Resonances ................. 89
2.6.2. Fluorinated Drags, Anaesthetics, and
Fluorodeoxyglucose Metabolism ................ 90
2.6.3. Fluorinated Probes ........................... 92
2.7. Exercises ............................................ 93
References ........................................... 95
3. In Vivo NMR Spectroscopy - Dynamic Aspects ................ 111
3.1. Introduction ........................................ 111
3.2. Relaxation .......................................... 112
3.2.1. General Principles of Dipolar Relaxation .... 112
3.2.2. Nuclear Overhauser Effect ................... 118
3.2.3. Alternative Relaxation Mechanisms ........... 119
3.2.4. In Vivo Relaxation .......................... 122
3.3. Magnetization Transfer .............................. 128
3.3.1. Creatine Kinase ............................. 130
3.3.2. Inversion Transfer .......................... 131
3.3.3. Saturation Transfer ......................... 131
3.3.4. ATpases ..................................... 134
3.3.5. Fast Magnetization Transfer Methods ......... 135
3.3.6. Off-resonance Magnetization Transfer ........ 136
3.3.7. Chemical Exchange Dependent Saturation
Transfer .................................... 141
3.4. Diffusion ........................................... 141
3.4.1. Principles of Diffusion ..................... 141
3.4.2. Diffusion and NMR ........................... 143
3.4.3. Anisotropic Diffusion ....................... 152
3.4.4. Restricted Diffusion ........................ 156
3.5. Dynamic Carbon-13 NMR Spectroscopy .................. 158
3.5.1. General Set-up .............................. 160
3.5.2. Metabolic Modeling .......................... 162
3.5.3. Substrates .................................. 166
3.5.4. Applications ................................ 171
3.6. Нуperpolarization ................................... 171
3.6.1. "Brute Force" Hyperpolarization ............. 172
3.6.2. Optical Pumping of Noble Gases .............. 173
3.6.3. Para-hydrogen-induced Polarization (PHIP) ... 175
3.6.4. Dynamic Nuclear Polarization ................ 177
3.7. Exercises ........................................... 179
References .......................................... 181
4. Magnetic Resonance Imaging ................................ 191
4.1. Introduction ........................................ 191
4.2. Magnetic Field Gradients ............................ 192
4.3. Slice Selection ..................................... 193
4.4. Frequency Encoding .................................. 195
4.5. Phase Encoding ...................................... 201
4.6. Spatial Frequency Space ............................. 202
4.7. Fast MRI Sequences .................................. 206
4.7.1. Echo-planar Imaging ......................... 208
4.8. Contrast in MRI ..................................... 212
4.8.1. Т1 and T2 Relaxation Mapping ................ 213
4.8.2. Fast T1 and T2 Relaxation Mapping ........... 214
4.8.3. Magnetic Field B0 Mapping ................... 216
4.8.4. Magnetic Field В1 Mapping ................... 218
4.8.5. Alternative Image Contrast Mechanisms ....... 219
4.8.6. Functional Imaging .......................... 220
4.9. Parallel MRI ........................................ 222
4.10. Exercises ........................................... 225
References .......................................... 229
5. Radiofrequency Pulses ..................................... 233
5.1. Introduction ........................................ 233
5.2. Square RF Pulses .................................... 233
5.3. Selective RF Pulses ................................. 239
5.3.1. Sine Pulses ................................. 239
5.3.2. Gaussian and Hermitian Pulses ............... 243
5.3.3. Multifrequency RF Pulses .................... 246
5.4. Pulse Optimization .................................. 247
5.4.1. Shinnar-Le Roux Algorithm ................... 248
5.5. DANTE RF Pulses ..................................... 254
5.6. Composite RF Pulses ................................. 255
5.7. Adiabatic RF Pulses ................................. 258
5.7.1. Rotating Frames of Reference ................ 259
5.7.2. Adiabatic Half and Full Passage Pulses ...... 262
5.7.3. Plane Rotations and Refocused Component ..... 268
5.7.4. Adiabatic Full Passage Refocusing ........... 269
5.7.5. Adiabatic Plane Rotation Pulses ............. 269
5.7.6. Variable Angle Adiabatic Plane Rotation
Pulse, BIR-4 ................................ 271
5.7.7. Modulation Functions ........................ 274
5.7.8. Offset-independent Adiabaticity ............. 275
5.8. Pulse Imperfections and Relaxation .................. 276
5.9. Power Deposition .................................... 280
5.10. Multidimensional RF Pulses .......................... 283
5.11. Spectral-spatial RF Pulses .......................... 289
5.12. Exercises ........................................... 290
References .......................................... 292
6. Single Volume Localization and Water Suppression .......... 297
6.1. Introduction ........................................ 297
6.2. Single Volume Localization .......................... 299
6.2.1. Image Selected In Vivo Spectroscopy
(ISIS) ...................................... 299
6.2.2. Chemical Shift Displacement ................. 302
6.2.3. Stimulated Echo Acquisition Mode (STEAM) .... 306
6.2.4. Point Resolved Spectroscopy (PRESS) ......... 310
6.2.5. Signal Dephasing with Magnetic Field
Gradients ................................... 311
6.2.6. Effects of Imperfect RF Pulses .............. 317
6.2.7. Localization by Adiabatic Selective
Refocusing (LASER) .......................... 320
6.2.8. Chemical Shift Displacement - Scalar-
coupled Spins ............................... 322
6.3. Water Suppression ................................... 325
6.3.1. Binomial and Related Pulse Sequences ........ 326
6.3.2. Frequency Selective Excitation .............. 333
6.3.3. Frequency Selective Refocusing .............. 337
6.3.4. Relaxation Based Methods .................... 338
6.3.5. Non-water-suppressed NMR Spectroscopy ....... 340
6.4. Exercises ........................................... 341
References .......................................... 344
7. Spectroscopic Imaging and Multivolume Localization ........ 349
7.1. Introduction ........................................ 349
7.2. Principles of Spectroscopic Imaging ................. 349
7.3. Spatial Resolution in MRSI .......................... 354
7.4. Temporal Resolution in MRSI ......................... 357
7.4.1. Conventional Methods ........................ 357
7.4.2. Methods Based on Fast MRI Sequences ......... 361
7.4.3. Methods Based on Prior Knowledge ............ 365
7.5. Lipid Suppression ................................... 367
7.5.1. Relaxation Based Methods .................... 368
7.5.2. Outer Volume Suppression and Volume
Pre-localization ............................ 368
7.5.3. Methods Utilizing Spatial Prior Knowledge ... 371
7.6. Spectroscopic Imaging Processing and Display ........ 373
7.7. Multivolume Localization ............................ 377
7.7.1. Hadamard Localization ....................... 378
7.7.2. Sequential Multivolume Localization ......... 380
7.8. Exercises ........................................... 382
References .......................................... 384
8. Spectral Editing and Two-dimensional NMR .................. 389
8.1. Introduction ........................................ 389
8.2. Scalar Evolution .................................... 390
8.3. J-difference Editing ................................ 392
8.4. Practical Considerations of J-difference Editing .... 397
8.5. Multiple Quantum Coherence Editing .................. 402
8.6. Heteronuclear Spectral Editing ...................... 407
8.7. Polarization Transfer - INEPT and DEPT .............. 409
8.8. Sensitivity ......................................... 414
8.9. Broadband Decoupling ................................ 416
8.10. Two-dimensional NMR Spectroscopy .................... 421
8.10.1. Correlation Spectroscopy (COSY) ............. 422
8.10.2. Spin-echo or J-resolved NMR ................. 432
8.10.3. Two-dimensional Exchange Spectroscopy ....... 434
8.11. Exercises ........................................... 438
References .......................................... 440
9. Spectral Quantification ................................... 445
9.1. Introduction ........................................ 445
9.2. Data Acquisition .................................... 446
9.3. Data Pre-processing ................................. 449
9.3.1. Phasing and Frequency Alignment ............. 450
9.3.2. Lineshape Correction ........................ 450
9.3.3. Removal of Residual Water ................... 451
9.3.4. Baseline Correction ......................... 453
9.4. Data Quantification ................................. 453
9.4.1. Time-and Frequency-domain Parameters ........ 454
9.4.2. Prior Knowledge ............................. 457
9.4.3. Spectral Fitting Algorithms ................. 460
9.4.4. Error Estimation ............................ 464
9.5. Data Calibration .................................... 466
9.5.1. Internal Concentration Reference ............ 470
9.5.2. External Concentration Reference ............ 472
9.5.3. Phantom Replacement External Concentration
Reference ................................... 473
9.6. Exercises ........................................... 473
References .......................................... 475
10. Hardware .................................................. 479
10.1. Introduction ........................................ 479
10.2. Magnets ............................................. 480
10.3. Magnetic Field Homogeneity .......................... 484
10.3.1. Origins and Effects of Magnetic Field
Inhomogeneity In Vivo ....................... 484
10.3.2. Active Shimming ............................. 489
10.3.3. Shimming Hardware ........................... 492
10.3.4. Manual Shimming ............................. 492
10.3.5. Magnetic Field Map Based Shimming ........... 494
10.3.6. Projection Based Shimming ................... 497
10.3.7. Dynamic Shim Updating (DSU) ................. 499
10.3.8. Passive Shimming ............................ 502
10.4. Magnetic Field Gradients ............................ 503
10.4.1. Eddy Currents ............................... 506
10.4.2. Pre-Emphasis ................................ 508
10.4.3. Active Shielding ............................ 512
10.5. Radiofrequency Coils ................................ 512
10.5.1. Resonant LCR Circuits ....................... 513
10.5.2. RF Coil Performance ......................... 519
10.5.3. Spatial Field Properties .................... 521
10.5.4. Principle of Reciprocity I .................. 526
10.5.5. Principle of Reciprocity II ................. 529
10.6. Radiofrequency Coil Types ........................... 530
10.6.1. Combined Transmit and Receive RF Coils ...... 531
10.6.2. Phased-array Coils .......................... 532
10.6.3. 1H-[13C] and 13C-[1H] RF Coils .............. 533
10.6.4. Cooled (Superconducting) RF Coils ........... 536
10.7. Complete MR System .................................. 536
10.7.1. RF Transmission ............................. 536
10.7.2. Signal Reception ............................ 537
10.7.3. Quadrature Detection ........................ 539
10.7.4. Dynamic Range ............................... 540
10.7.5. Gradient and Shim Systems ................... 541
10.8. Exercises ........................................... 542
References .......................................... 545
Appendix ...................................................... 549
Al. Matrix Calculations ................................... 549
A2. Trigonometric Equations ............................... 551
A3. Fourier Transformation ................................ 551
A3.1. Introduction .................................... 552
A3.2. Properties ...................................... 553
A3.3. Discrete Fourier Transformation ................. 554
A4. Product Operator Formalism ............................ 554
A4.1. Cartesian Product Operators ..................... 555
A4.2. Spherical Tensor Product Operators .............. 556
References .................................................... 559
Further Reading ............................................... 560
Index ......................................................... 563
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