Yang Xia - Essential Concepts in MRI

10 Part IV Essential Concepts in MRI Chapter 11 Effect of the Field Gradient and k-space Imaging 11.1 Spatially Encoding Nuclear Spin Magnetization11.2 k Space in MRI11.3 Mapping of k Space11.4 Gradient Echo Chapter 12 Spatial Mapping in MRI 12.1 Slice Selection in 2D MRI12.2 Reading a Graphical Imaging Sequence12.3 2D Filtered Back-Projection Reconstruction12.4 2D Fourier Imaging Reconstruction12.5 Sampling Patterns Between the Cartesian and Radial Grids12.6 3D Imaging12.7 Fast Imaging in MRI12.8 Ultra-short Echo and ZTE MRI12.9 MRI in Other Dimensions (4D, 1D, and One Voxel)12.10 Resolution in MRI Chapter 13 Imaging Instrumentation and Experiments 13.1 Shaped Pulses13.2 The Gradient Units13.3 Instrumentation Configurations for MRI13.4 Imaging Parameters in MRI13.5 Image Processing Software13.6 Best Test Samples for MRI

11 Part V Quantitative and Creative MRI Chapter 14 Image Contrast in MRI 14.1 Non-trivial Relationship Between Spin Density and Image Intensity14.2 Image Contrast in MRI14.3 How to Obtain Useful Information from Image Contrast?14.4 Magnetization-prepared Sequences in Quantitative MRI Chapter 15 Quantitative MRI 15.1 Quantitative Imaging of Velocity v and Molecular Diffusion D 15.2 Quantitative Imaging of Relaxation Times T1 , T2 , T 1ρ15.3 Quantitative Imaging of Chemical Shift δ15.4 Secondary Image Contrasts in MRI 25915.5 Potential Issues and Practical Strategies in Quantitative MRI Chapter 16 Advanced Topics in Quantitative MRI 16.1 Anisotropy and Tensor Properties in Quantitative MRI16.2 Multi-Component Nature in Quantitative MRI16.3 Quantitative Phase Information in the FID Data – SWI and QSM16.4 Functional MRI (fMRI)16.5 Optical Pumping and Hyperpolarization in MRI Chapter 17 Reading the Binary Data 17.1 Formats of Data17.2 Formats of Data Storage17.3 Reading Unknown Binary Data17.4 Examples of Specific Formats

12 Appendices Appendix 1 Background in Mathematics A1.1 Elementary Mathematics A1.2 Fourier Transform Appendix 2 Background in Quantum Mechanics A2.1 Operators A2.2 Expansion of a Wave Function A2.3 Spin Operator I A2.4 Raising and Lowering Operators I+ and I- A2.5 Spin-1/2 Operator (in the Formalism of Pauli’s Spin Matrices) A2.6 Density Matrix Operator ρ Appendix 3 Background in Electronics A3.1 Ohm’s Law for DC and AC Circuits A3.2 Electronics at Radio Frequency Appendix 4 Sample Syllabi for a One-semester Course Appendix 5 Homework Problems

13 Index

14 End User License Agreement

1 Chapter 1Figure 1.1 The resonance phenomenon,...Figure 1.2 The B 0direction in NMR and MRI....Figure 1.3 The positive directions of rotations in...Figure 1.4 The first NMR spectrum of ethanol...Figure 1.5 The first proton NMR image of two tubes of...Figure 1.6 Major conceptual components of NMR and MRI.

2 Chapter 2Figure 2.1 (a) Moving charges at velocity...Figure 2.2 The application of an external magnetic...Figure 2.4 (a) A single nucleus in an external magnetic...Figure 2.5 Two counter-rotating fields (right)...Figure 2.6 (a) A magnetic moment µ...Figure 2.7 In the rotating frame that has...Figure 2.8 Motion of the magnetization in the...Figure 2.9 The motion of the longitudinal magnetization...Figure 2.10 The motion of the magnitude...Figure 2.11 Two equivalent functions...Figure 2.12 Comparison between a Lorentzian and...Figure 2.13 Fourier transform of (a) a hard...Figure 2.14 (a) and (b) The time-domain NMR...Figure 2.15 (a) A vector Mrotates in...

3 Chapter 3Figure 3.1 The quantities in a spin-1/2...Figure 3.2 (a) A precise value of the Zeeman...Figure 3.3 Schematic power spectra of the...Figure 3.4 Schematic log/log trends of relaxation...

4 Chapter 4Figure 4.1 (a) A nuclear spin behaves...Figure 4.2 The application of the external...Figure 4.3 The introduction of the chemical...Figure 4.4 TMS is commonly used as the...Figure 4.5 The scalar interaction arises via...Figure 4.6 The influences of the chemical shift...Figure 4.7 The effect of the J -coupling constant...Figure 4.8 A schematic summary of the...

5 Chapter 5Figure 5.1 A block diagram for an NMR...Figure 5.2 A cut-open vertical-bore...Figure 5.3 Halbach magnet configurations....Figure 5.4 Shimming patterns that make the...Figure 5.5 Basic configurations of rf coils,...Figure 5.6 The rf coil and two capacitors form...Figure 5.7 An NMR spectrometer, where all six...Figure 5.8 The imperfections in the leading and...

6 Chapter 6Figure 6.1 (a) A slightly off-resonance FID...Figure 6.2 (a) A text file for a simple...Figure 6.3 Consequences of under-sampling....Figure 6.4 A spectrum of the ethanol’s triplet....Figure 6.5 The issue of dynamic range in signal...Figure 6.6 Basic relationships in phase cycling,...Figure 6.7 CYCLOPS phase cycling. The size of...Figure 6.8 Improvement of SNR by data accumulation....Figure 6.9 (a) The FID has a finite and constant...Figure 6.10 Sensitivity enhancement by filtering...Figure 6.11 Zero-filling the time-domain data...Figure 6.12 The effect of the zeroth-order phase shift...Figure 6.13 The first-order phase shift...Figure 6.14 Estimation of the SNR from a spectrum...

7 Chapter 7Figure 7.1 (a) A pulse sequence with a...Figure 7.2 The magnetization vectors and...Figure 7.3 (a) An inversion recovery pulse sequence....Figure 7.4 (a) A saturation recovery pulse sequence....Figure 7.5 The cover of the November 1953 issue of...Figure 7.6 Two versions of the spin-echo sequence, which...Figure 7.7 (a) CPMG sequence, which can have a...Figure 7.8 (a) Stimulated echo sequence....Figure 7.9 (a) The T 1ρ...Figure 7.10 Two ways to sample an exponential...

8 Chapter 8Figure 8.1 Fundamental relationships among the...Figure 8.2 A low-resolution spectrum of...Figure 8.3 Schematic line patterns of a two...Figure 8.4 Schematic line patterns of the A...Figure 8.5 Schematic line patterns of the A...Figure 8.6 The full 1H NMR spectrum of...Figure 8.7a 1H spectrum of styrene, where...Figure 8.7b 13C spectrum of styrene when...Figure 8.7c 13C spectrum of styrene when...Figure 8.8 1H NMR spectrum of ethyl acetate,...Figure 8.9 1H NMR spectrum of quinoline....

9 Chapter 9Figure 9.1 Pulse sequences for double-resonance...Figure 9.2 Schematic of homonuclear decoupling,...Figure 9.3 13C NMR spectra of quinoline...Figure 9.4 13C NMR spectra of quinoline dissolved...Figure 9.5 The rate of chemical exchange,...Figure 9.6 (a) Two resonant peaks represent two...Figure 9.7 Magnetization transfer can be used to...Figure 9.8 Numerical illustrations for selective...Figure 9.9 Comparison of two CH 2resonant peaks...

10 Chapter 10Figure 10.1 A schematic illustration of...Figure 10.2 (a) 2D heteronuclear COSY sequence,...Figure 10.3 An energy-level diagram for a heteronuclear...Figure 10.4 A schematic 2D heteronuclear COSY spectrum,...Figure 10.5 A conceptual pulse sequence for 2D homonuclear...Figure 10.6 A schematic 2D homonuclear COSY spectrum,...Figure 10.7 (a) A conceptual pulse sequence for 2D...Figure 10.8 (a) The general pulse sequence for 2D...Figure 10.9 (a) The general pulse sequence for 2D...Figure 10.10a 2D homonuclear 1H COSY...Figure 10.10b The AMX peaks in the 2D homonuclear...Figure 10.11a 2D heteronuclear 13C J-resolvedFigure 10.11b The enlarged spectra of the individual...

11 Chapter 11Figure 11.1 1D profiles of a tube of water....Figure 11.2 Spatially encoding the nuclear...Figure 11.3 Components of the 3D field gradient,...Figure 11.4 Insignificant effect of the field gradient...Figure 11.5 Moving around in 2D kspace,...Figure 11.6 (a) Covering the first quadrant in kFigure 11.7 Four non-standard 2D mapping...Figure 11.8 The dephasing and re-phasing by a...