In Vivo NMR Spectroscopy Principles and Techniques

Presents basic concepts, experimental methodology and data acquisition, and processing standards of in vivo NMR spectroscopy

This book covers, in detail, the technical and biophysical aspects of in vivo NMR techniques and includes novel developments in the field such as hyperpolarized NMR, dynamic ¹³C NMR, automated shimming, and parallel acquisitions. Most of the techniques are described from an educational point of view, yet it still retains the practical aspects appreciated by experimental NMR spectroscopists. In addition, each chapter concludes with a number of exercises designed to review, and often extend, the presented NMR principles and techniques.

The third edition of In Vivo NMR Spectroscopy: Principles and Techniques has been updated to include experimental detail on the developing area of hyperpolarization; a description of the semi-LASER sequence, which is now a method of choice; updated chemical shift data, including the addition of ³¹P data; a troubleshooting section on common problems related to shimming, water suppression, and quantification; recent developments in data acquisition and processing standards; and MatLab scripts on the accompanying website for helping readers calculate radiofrequency pulses.

• Provide an educational explanation and overview of in vivo NMR, while maintaining the practical aspects appreciated by experimental NMR spectroscopists
• Features more experimental methodology than the previous edition
• End-of-chapter exercises that help drive home the principles and techniques and offer a more in-depth exploration of quantitative MR equations
• Designed to be used in conjunction with a teaching course on the subject

In Vivo NMR Spectroscopy: Principles and Techniques, 3^rd Edition is aimed at all those involved in fundamental and/or diagnostic in vivo NMR, ranging from people working in dedicated in vivo NMR institutes, to radiologists in hospitals, researchers in high-resolution NMR and MRI, and in areas such as neurology, physiology, chemistry, and medical biology.

Robin A. de Graaf, PhD, is Professor at Yale University, School of Medicine, Department of Radiology and Biomedical Imaging, USA.

Preface xv

Abbreviations xvii

Supplementary Material xxiv

1 Basic Principles 1

1.1 Introduction 1

1.2 Classical Magnetic Moments 3

1.3 Nuclear Magnetization 5

1.4 Nuclear Induction 9

1.5 Rotating Frame of Reference 11

1.6 Transverse T2 and T2 * Relaxation 12

1.7 Bloch Equations 16

1.8 Fourier Transform NMR 17

1.9 Chemical Shift 20

1.10 Digital NMR 23

1.10.1 Analog‐to‐digital Conversion 23

1.10.2 Signal Averaging 25

1.10.3 Digital Fourier Transformation 25

1.10.4 Zero Filling 25

1.10.5 Apodization 26

1.11 Quantum Description of NMR 28

1.12 Scalar Coupling 30

1.13 Chemical and Magnetic Equivalence 33

Exercises 37

References 40

2 In Vivo NMR Spectroscopy – Static Aspects 43

2.1 Introduction 43

2.2 Proton NMR Spectroscopy 43

2.2.1 Acetate (Ace) 51

2.2.2 N‐Acetyl Aspartate (NAA) 52

2.2.3 N‐Acetyl Aspartyl Glutamate (NAAG) 53

2.2.4 Adenosine Triphosphate (ATP) 54

2.2.5 Alanine (Ala) 55

2.2.6 γ‐Aminobutyric Acid (GABA) 56

2.2.7 Ascorbic Acid (Asc) 57

2.2.8 Aspartic Acid (Asp) 58

2.2.9 Branched‐chain Amino Acids (Isoleucine, Leucine, and Valine) 58

2.2.10 Choline‐containing Compounds (tCho) 59

2.2.11 Creatine (Cr) and Phosphocreatine (PCr) 61

2.2.12 Ethanol 62

2.2.13 Ethanolamine (EA) and Phosphorylethanolamine (PE) 63

2.2.14 Glucose (Glc) 63

2.2.15 Glutamate (Glu) 64

2.2.16 Glutamine (Gln) 65

2.2.17 Glutathione (GSH) 66

2.2.18 Glycerol 67

2.2.19 Glycine 68

2.2.20 Glycogen 68

2.2.21 Histidine 69

2.2.22 Homocarnosine 70

2.2.23 β‐Hydoxybutyrate (BHB) 70

2.2.24 2‐Hydroxyglutarate (2HG) 71

2.2.25 myo‐Inositol (mI) and scyllo‐Inositol (sI) 72

2.2.26 Lactate (Lac) 73

2.2.27 Macromolecules 74

2.2.28 Nicotinamide Adenine Dinucleotide (NAD+) 76

2.2.29 Phenylalanine 76

2.2.30 Pyruvate 77

2.2.31 Serine 78

2.2.32 Succinate 79

2.2.33 Taurine (Tau) 79

2.2.34 Threonine (Thr) 80

2.2.35 Tryptophan (Trp) 80

2.2.36 Tyrosine (Tyr) 80

2.2.37 Water 81

2.2.38 Non‐cerebral Metabolites 82

2.2.39 Carnitine and Acetyl‐carnitine 82

2.2.40 Carnosine 84

2.2.41 Citric Acid 86

2.2.42 Deoxymyoglobin (DMb) 87

2.2.43 Lipids 87

2.2.44 Spermine and Polyamines 89

2.3 Phosphorus‐31 NMR Spectroscopy 90

2.3.1 Chemical Shifts 90

2.3.2 Intracellular pH 92

2.4 Carbon‐13 NMR Spectroscopy 93

2.4.1 Chemical Shifts 93

2.5 Sodium‐23 NMR Spectroscopy 96

2.6 Fluorine‐19 NMR Spectroscopy 102

2.7 In vivo NMR on Other Non‐proton Nuclei 104

Exercises 106

References 108

3 In Vivo NMR Spectroscopy – Dynamic Aspects 129

3.1 Introduction 129

3.2 Relaxation 129

3.2.1 General Principles of Dipolar Relaxation 129

3.2.2 Nuclear Overhauser Effect 133

3.2.3 Alternative Relaxation Mechanisms 134

3.2.4 Effects of T1 Relaxation 137

3.2.5 Effects of T2 Relaxation 138

3.2.6 Measurement of T1 and T2 Relaxation 141

3.2.6.1 T1 Relaxation 141

3.2.6.2 Inversion Recovery 141

3.2.6.3 Saturation Recovery 142

3.2.6.4 Variable Nutation Angle 142

3.2.6.5 MR Fingerprinting 143

3.2.6.6 T2 Relaxation 143

3.2.7 In Vivo Relaxation 144

3.3 Magnetization Transfer 147

3.3.1 Principles of MT 149

3.3.2 MT Methods 150

3.3.3 Multiple Exchange Reactions 152

3.3.4 MT Contrast 152

3.3.5 Chemical Exchange Saturation Transfer (CEST) 156

3.4 Diffusion 160

3.4.1 Principles of Diffusion 160

3.4.2 Diffusion and NMR 160

3.4.3 Anisotropic Diffusion 169

3.4.4 Restricted Diffusion 173

3.5 Dynamic NMR of Isotopically‐Enriched Substrates 175

3.5.1 General Principles and Setup 177

3.5.2 Metabolic Modeling 177

3.5.3 Thermally Polarized Dynamic 13C NMR Spectroscopy 184

3.5.3.1 [1‐13C]‐Glucose and [1,6‐13C2]‐Glucose 184

3.5.3.2 [2‐13C]‐Glucose 185

3.5.3.3 [U‐13C6]‐Glucose 187

3.5.3.4 [2‐13C]‐Acetate 187

3.5.4 Hyperpolarized Dynamic 13C NMR Spectroscopy 189

3.5.4.1 Brute Force Hyperpolarization 189

3.5.4.2 Optical Pumping of Noble Gases 190

3.5.4.3 Parahydrogen‐induced Polarization (PHIP) 191

3.5.4.4 Signal Amplification by Reversible Exchange (SABRE) 193

3.5.4.5 Dynamic Nuclear Polarization (DNP) 193

3.5.5 Deuterium Metabolic Imaging (DMI) 196

Exercises 197

References199

4 Magnetic Resonance Imaging 211

4.1 Introduction 211

4.2 Magnetic Field Gradients 211

4.3 Slice Selection 212

4.4 Frequency Encoding 215

4.4.1 Principle 215

4.4.2 Echo Formation 216

4.5 Phase Encoding 219

4.6 Spatial Frequency Space 221

4.7 Fast MRI Sequences 225

4.7.1 Reduced TR Methods 225

4.7.2 Rapid k‐Space Traversal 226

4.7.3 Parallel MRI 229

4.7.3.1 SENSE 230

4.7.3.2 GRAPPA 233

4.8 Contrast in MRI 234

4.8.1 T1 and T2 Relaxation Mapping 236

4.8.2 Magnetic Field B0 Mapping 239

4.8.3 Magnetic Field B1 Mapping 241

4.8.4 Alternative Image Contrast Mechanisms 242

4.8.5 Functional MRI 243

Exercises 245

References 249

5 Radiofrequency Pulses 253

5.1 Introduction 253

5.2 Square RF Pulses 253

5.3 Selective RF Pulses 259

5.3.1 Fourier‐transform‐based RF Pulses 260

5.3.2 RF Pulse Characteristics 262

5.3.3 Optimized RF Pulses 266

5.3.4 Multifrequency RF Pulses 269

5.4 Composite RF Pulses 271

5.5 Adiabatic RF Pulses 273

5.5.1 Rotating Frame of Reference 275

5.5.2 Adiabatic Condition 276

5.5.3 Modulation Functions 278

5.5.4 AFP Refocusing 280

5.5.5 Adiabatic Plane Rotation of Arbitrary Nutation Angle 282

5.6 Multidimensional RF Pulses 284

5.7 Spectral–Spatial RF Pulses 284

Exercises 286

References 288

6 Single Volume Localization and Water Suppression 293

6.1 Introduction 293

6.2 Single‐volume Localization 294

6.2.1 Image Selected In Vivo Spectroscopy (ISIS) 295

6.2.2 Chemical Shift Displacement 297

6.2.3 Coherence Selection 301

6.2.3.1 Phase Cycling 302

6.2.3.2 Magnetic Field Gradients 302

6.2.4 STimulated Echo Acquisition Mode (STEAM) 304

6.2.5 Point Resolved Spectroscopy (PRESS) 307

6.2.6 Signal Dephasing with Magnetic Field Gradients 309

6.2.7 Localization by Adiabatic Selective Refocusing (LASER) 314

6.3 Water Suppression 317

6.3.1 Binomial and Related Pulse Sequences 318

6.3.2 Frequency‐Selective Excitation 321

6.3.3 Frequency‐Selective Refocusing 323

6.3.4 Relaxation‐Based Methods 323

6.3.5 Non‐water‐suppressed NMR Spectroscopy 326

Exercises 327

References 330

7 Spectroscopic Imaging and Multivolume Localization 335

7.1 Introduction 335

7.2 Principles of MRSI 335

7.3 k‐Space Description of MRSI 338

7.4 Spatial Resolution in MRSI 339

7.5 Temporal Resolution in MRSI 341

7.5.1 Conventional Methods 343

7.5.1.1 Circular and Spherical k‐Space Sampling 343

7.5.1.2 k‐Space Apodization During Acquisition 343

7.5.1.3 Zoom MRSI 345

7.5.2 Methods Based on Fast MRI 346

7.5.2.1 Echo‐planar Spectroscopic Imaging (EPSI) 346

7.5.2.2 Spiral MRSI 349

7.5.2.3 Parallel MRSI 350

7.5.3 Methods Based on Prior Knowledge 351

7.6 Lipid Suppression 353

7.6.1 Relaxation‐based Methods 353

7.6.2 Inner Volume Selection and Volume Prelocalization 355

7.6.3 Outer Volume Suppression (OVS) 357

7.7 MR Spectroscopic Image Processing and Display 360

7.8 Multivolume Localization 364

7.8.1 Hadamard Localization 365

7.8.2 Sequential Multivolume Localization 366

Exercises 368

References370

8 Spectral Editing and 2D NMR 375

8.1 Introduction 375

8.2 Quantitative Descriptions of NMR 375

8.2.1 Density Matrix Formalism 376

8.2.2 Classical Vector Model 377

8.2.3 Correlated Vector Model 378

8.2.4 Product Operator Formalism 379

8.3 Scalar Evolution 380

8.4 J‐Difference Editing 384

8.4.1 Principle 384

8.4.2 Practical Considerations 385

8.4.3 GABA, 2HG, and Lactate 389

8.5 Multiple Quantum Coherence Editing 395

8.6 Spectral Editing Alternatives 400

8.7 Heteronuclear Spectral Editing 402

8.7.1 Proton‐observed, Carbon‐edited (POCE) MRS 402

8.7.2 Polarization Transfer – INEPT and DEPT 407

8.8 Broadband Decoupling 410

8.9 Sensitivity 414

8.10 Two‐dimensional NMR Spectroscopy 415

8.10.1 Correlation Spectroscopy (COSY) 416

8.10.2 J‐resolved Spectroscopy (JRES) 422

8.10.3 In vivo 2D NMR Methods 424

Exercises 429

References 432

9 Spectral Quantification 439

9.1 Introduction 439

9.2 Data Acquisition 440

9.2.1 Magnetic Field Homogeneity 440

9.2.2 Spatial Localization 442

9.2.3 Water Suppression 442

9.2.4 Sensitivity 442

9.3 Data Preprocessing 443

9.3.1 Phased‐array Coil Combination 443

9.3.2 Phasing and Frequency Alignment 444

9.3.3 Line‐shape Correction 444

9.3.4 Removal of Residual Water 444

9.3.5 Baseline Correction 446

9.4 Data Quantification 447

9.4.1 Time‐ and Frequency‐domain Parameters 447

9.4.2 Prior Knowledge 450

9.4.3 Spectral Fitting Algorithms 453

9.4.4 Error Estimation 457

9.5 Data Calibration 460

9.5.1 Partial Saturation 461

9.5.2 Nuclear Overhauser Effects 462

9.5.3 Transverse Relaxation 462

9.5.4 Diffusion 462

9.5.5 Scalar Coupling 462

9.5.6 Localization 463

9.5.7 Frequency‐dependent Amplitude‐ and Phase Distortions 463

9.5.8 NMR Visibility 463

9.5.9 Internal Concentration Reference 464

9.5.10 External Concentration Reference 466

9.5.11 Phantom Replacement Concentration Reference 466

Exercises 467

References 469

10 Hardware 473

10.1 Introduction 473

10.2 Magnets 473

10.3 Magnetic Field Homogeneity 478

10.3.1 Origins of Magnetic Field Inhomogeneity 478

10.3.2 Effects of Magnetic Field Inhomogeneity 482

10.3.3 Principles of Spherical Harmonic Shimming 485

10.3.4 Practical Spherical Harmonic Shimming 489

10.3.5 Alternative Shimming Strategies 491

10.4 Magnetic Field Gradients 493

10.4.1 Eddy Currents 498

10.4.2 Preemphasis 499

10.4.3 Active Shielding 503

10.5 Radiofrequency (RF) Coils 503

10.5.1 Electrical Circuit Analysis 503

10.5.2 RF Coil Performance 509

10.5.3 Spatial Field Properties 510

10.5.3.1 Longitudinal Magnetic Fields 512

10.5.3.2 Transverse Magnetic Fields 513

10.5.4 Principle of Reciprocity 514

10.5.4.1 Electromagnetic Wave Propagation 515

10.5.5 Parallel Transmission 517

10.5.6 RF Power and Specific Absorption Rate (SAR) 519

10.5.7 Specialized RF Coils 520

10.5.7.1 Combined Transmit and Receive RF Coils 521

10.5.7.2 Phased‐Array Coils 522

10.5.7.3 1H‐[13C] and 13C‐[1H] RF Coils 522

10.5.7.4 Cooled and Superconducting RF Coils 525

10.6 Complete MR System 526

10.6.1 RF Transmission 526

10.6.2 Signal Reception 527

10.6.3 Quadrature Detection 528

10.6.4 Dynamic Range 529

10.6.5 Gradient and Shim Systems 530

Exercises 531

References 534

Appendix A 541

A.1 Matrix Calculations 541

A.2 Trigonometric Equations 543

A.3 Fourier Transformation 543

A.3.1 Introduction 543

A.3.2 Properties 544

A.3.2.1 Linearity 544

A.3.2.2 Time and Frequency Shifting 544

A.3.2.3 Scaling 545

A.3.2.4 Convolution 545

A.3.3 Discrete Fourier Transformation 545

A.4 Product Operator Formalism 546

A.4.1 Cartesian Product Operators 546

A.4.2 Shift (Lowering and Raising) Operators 548

References 550

Further Reading 551

Index 553

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