Essential Concepts in MRI

Yang Xia, PhD, is Distinguished Professor of Physics in the Department of Physics at Oakland University, USA. Dr. Xia is a Fellow of the American Physical Society, the International Society for Magnetic Resonance in Medicine, and the American Institute for Medical and Biological Engineering.

• Preface xiChapter 1 Introduction 11.1 Introduction 11.2 Major Steps in an NMR or MRI Experiment, and Two Conventions in Direction 21.3 Major Milestones in the History of NMR and MRI 41.4 The Organization for a One-semester Course 6Part I Essential Concepts in NMR 9Chapter 2 Classical Description of Magnetic Resonance 112.1 Fundamental Assumptions 112.2 Nuclear Magnetic Moment 122.3 The Time Evolution of Nuclear Magnetic Moment 152.4 Macroscopic Magnetization 162.5 Rotating Reference Frame 182.6 Spin Relaxation Processes 222.7 Bloch Equation 242.8 Fourier Transform and Spectral Line Shapes 252.9 CW NMR 282.10 Radio-frequency Pulses in NMR 292.11 FT NMR 302.12 Signal Detection in NMR 322.13 Phases of the NMR Signal 33Chapter 3 Quantum Mechanical Description of Magnetic Resonance 373.1 Nuclear Magnetism 373.2 Energy Difference 393.3 Macroscopic Magnetization 403.4 Measurement of the X Component of Angular Momentum 413.5 Macroscopic Magnetization for Spin 1/2 423.6 Resonant Excitation 433.7 Mechanisms of Spin Relaxation 43Chapter 4 Nuclear Interactions 514.1 Dipolar Interaction 514.2 Chemical Shift Interaction 544.3 Scalar Interaction 574.4 Quadrupole Interaction 614.5 Summary of Nuclear Interactions 61Part II Essential Concepts in NMR Instrumentation 65Chapter 5 Instrumentation 675.1 Magnets 675.2 Radio-frequency Coil, Its Resonant Circuitry, and the Probe 725.3 Frequency Management 755.4 Transmitter 765.5 Receiver 785.6 Pulse Programmer and Computer 785.7 Other Components 78Chapter 6 NMR Experimental 816.1 Shimming 816.2 Preparing Samples 826.3 Pulse Sequences and FID 836.4 Digitization Rate and Digital Resolution 856.5 Dynamic Range 876.6 Phase Cycling 896.7 Data Accumulation 916.8 Pre-FFT Processing Techniques 926.9 Fast Fourier Transform 956.10 Post-FFT Processing 956.11 Signal-to-Noise Ratio 97Chapter 7 Spin Manipulations by Pulse Sequences 1017.1 Single Pulse: 90˚| X , 90˚| Y , 90˚| -x , 90˚| -y 1017.2 Inversion Recovery Sequence, Saturation Recovery Sequence, and T1 Relaxation 1037.3 Spin-Echo Sequence (Hahn Echo) and T2 Relaxation 1067.4 CPMG Echo Train 1107.5 Stimulated Echo Sequence 1117.6 Spin-locking and T 1ρ Relaxation 1127.7 How to Select the Delays in Relaxation Measurement 113Part III Essential Concepts in NMR Spectroscopy 117Chapter 8 First-order 1D Spectroscopy 1198.1 Nomenclature of the Spin System 1198.2 Peak Shift – the Effect of Chemical Shift 1208.3 Peak Area – Reflecting the Number of Protons 1228.4 Peak Splitting – the Consequence of J Coupling 1228.5 Examples of 1D Spectra 128Chapter 9 Advanced Topics in Spectroscopy 1379.1 Double Resonance 1379.2 Dipolar Interaction in a Two-spin System 1419.3 Magic Angle 1429.4 Chemical Exchange 1439.5 Magnetization Transfer 1449.6 Selective Polarization Inversion/ Transfer 1469.7 Radiation Damping 147Chapter 10 2D NMR Spectroscopy 15110.1 Essence of 2D NMR Spectroscopy 15110.2 COSY – Correlation Spectroscopy 15310.3 J-resolved Spectroscopy 15710.4 Examples of 2D NMR Spectroscopy 162Part IV Essential Concepts in MRI 167Chapter 11 Effect of the Field Gradient and k-space Imaging 16911.1 Spatially Encoding Nuclear Spin Magnetization 17011.2 k Space in MRI 17311.3 Mapping of k Space 17411.4 Gradient Echo 174Chapter 12 Spatial Mapping in MRI 17912.1 Slice Selection in 2D MRI 18012.2 Reading a Graphical Imaging Sequence 18612.3 2D Filtered Back-Projection Reconstruction 18912.4 2D Fourier Imaging Reconstruction19112.5 Sampling Patterns Between the Cartesian and Radial Grids 19412.6 3D Imaging 19612.7 Fast Imaging in MRI 19812.8 Ultra-short Echo and ZTE MRI 20212.9 MRI in Other Dimensions (4D, 1D, and One Voxel) 20312.10 Resolution in MRI 206Chapter 13 Imaging Instrumentation and Experiments 20913.1 Shaped Pulses 20913.2 The Gradient Units 21113.3 Instrumentation Configurations for MRI 21513.4 Imaging Parameters in MRI 21713.5 Image Processing Software 21913.6 Best Test Samples for MRI 219Part V Quantitative and Creative MRI 223Chapter 14 Image Contrast in MRI 22514.1 Non-trivial Relationship Between Spin Density and Image Intensity 22514.2 Image Contrast in MRI 22714.3 How to Obtain Useful Information from Image Contrast? 22914.4 Magnetization-prepared Sequences in Quantitative MRI 231Chapter 15 Quantitative MRI 23515.1 Quantitative Imaging of Velocity V and Molecular Diffusion D 23515.2 Quantitative Imaging of Relaxation Times T1 , T2 , T1ρ 24715.3 Quantitative Imaging of Chemical Shift δ 25415.4 Secondary Image Contrasts in MRI259 15.5 Potential Issues and Practical Strategies in Quantitative MRI 264Chapter 16 Advanced Topics in Quantitative MRI 27516.1 Anisotropy and Tensor Properties in Quantitative MRI 27716.2 Multi-Component Nature in Quantitative MRI 28516.3 Quantitative Phase Information in the FID Data – SWI and QSM 28816.4 Functional MRI (fMRI) 29016.5 Optical Pumping and Hyperpolarization in MRI 290Chapter 17 Reading the Binary Data 29517.1 Formats of Data 29517.2 Formats of Data Storage 29617.3 Reading Unknown Binary Data 29817.4 Examples of Specific Formats 301Appendices 305Appendix 1 Background in Mathematics 307A1.1 Elementary Mathematics 307A1.2 Fourier Transform 311Appendix 2 Background in Quantum Mechanics 317A2.1 Operators 317A2.2 Expansion of a Wave Function 319A2.3 Spin Operator I 320A2.4 Raising and Lowering Operators I + and I - 320A2.5 Spin-1/2 Operator (in the Formalism of Pauli’s Spin Matrices) 321A2.6 Density Matrix Operator ρ 323Appendix 3 Background in Electronics 325A3.1 Ohm’s Law for DC and AC Circuits 325A3.2 Electronics at Radio Frequency 327Appendix 4 Sample Syllabi for a One-semester Course 329Appendix 5 Homework Problems 331Index 337