Оглавление
Yang Xia. Essential Concepts in MRI
Essential Concepts in MRI. Physics, Instrumentation, Spectroscopy, and Imaging
Contents
List of Illustrations
List of Tables
Guide
Pages
Preface
1 Introduction. 1.1 INTRODUCTION
1.2 MAJOR STEPS IN AN NMR OR MRI EXPERIMENT, AND TWO CONVENTIONS IN DIRECTION
1.3 MAJOR MILESTONES IN THE HISTORY OF NMR AND MRI
1.4 THE ORGANIZATION FOR A ONE-SEMESTER COURSE
References
2 Classical Description of Magnetic Resonance. 2.1 FUNDAMENTAL ASSUMPTIONS
2.2 NUCLEAR MAGNETIC MOMENT
2.3 THE TIME EVOLUTION OF NUCLEAR MAGNETIC MOMENT
2.4 MACROSCOPIC MAGNETIZATION
2.5 ROTATING REFERENCE FRAME
2.6 SPIN RELAXATION PROCESSES
2.7 BLOCH EQUATION
2.8 FOURIER TRANSFORM AND SPECTRAL LINE SHAPES
2.8.1 Fourier Transform
2.8.2 Spectral Line Shapes – Lorentzian and Gaussian
2.9 CW NMR
2.10 RADIO-FREQUENCY PULSES IN NMR
2.11 FT NMR
2.12 SIGNAL DETECTION IN NMR
2.13 PHASES OF THE NMR SIGNAL
References
Notes
3 Quantum Mechanical Description of Magnetic Resonance
3.1 NUCLEAR MAGNETISM
3.2 ENERGY DIFFERENCE
3.3 MACROSCOPIC MAGNETIZATION
3.4 MEASUREMENT OF THE X COMPONENT OF ANGULAR MOMENTUM
3.5 MACROSCOPIC MAGNETIZATION FOR SPIN 1/2
3.6 RESONANT EXCITATION
3.7 MECHANISMS OF SPIN RELAXATION
3.7.1 Relaxation Mechanism in Terms of Quantum Transitions
3.7.2 Relaxation Mechanisms in the Random Field Model
References
Notes
4 Nuclear Interactions
4.1 DIPOLAR INTERACTION
4.2 CHEMICAL SHIFT INTERACTION
4.3 SCALAR INTERACTION
4.4 QUADRUPOLE INTERACTION
4.5 SUMMARY OF NUCLEAR INTERACTIONS
References
5 Instrumentation
5.1 MAGNETS
5.1.1 Electromagnet
5.1.2 Superconducting Magnet
5.1.3 Permanent Magnet
5.1.4 Ways to Make the Magnetic Field Uniform
5.2 RADIO-FREQUENCY COIL, ITS RESONANT CIRCUITRY, AND THE PROBE
5.2.1 Rf Coil Configurations
5.2.2 Rf Resonant Circuit and the Switching Between Transmitter and Receiver
5.2.3 Probe
5.3 FREQUENCY MANAGEMENT
5.4 TRANSMITTER
5.5 RECEIVER
5.6 PULSE PROGRAMMER AND COMPUTER
5.7 OTHER COMPONENTS
References
6 NMR Experimental
6.1 SHIMMING
6.2 PREPARING SAMPLES
6.3 PULSE SEQUENCES AND FID
6.4 DIGITIZATION RATE AND DIGITAL RESOLUTION
6.5 DYNAMIC RANGE
6.6 PHASE CYCLING
6.7 DATA ACCUMULATION
6.8 PRE-FFT PROCESSING TECHNIQUES
6.9 FAST FOURIER TRANSFORM
6.10 POST-FFT PROCESSING
6.11 SIGNAL-TO-NOISE RATIO
References
Notes
7 Spin Manipulations by Pulse Sequences
7.1 SINGLE PULSE: 90˚Ix, 90˚Iy, 90˚I-x, 90˚I-y
7.2 INVERSION RECOVERY SEQUENCE, SATURATION RECOVERY SEQUENCE, AND T1 RELAXATION
7.3 SPIN-ECHO SEQUENCE (HAHN ECHO) AND T2 RELAXATION
7.4 CPMG ECHO TRAIN
7.5 STIMULATED ECHO SEQUENCE
7.6 SPIN-LOCKING AND T1ρ RELAXATION
7.7 HOW TO SELECT THE DELAYS IN RELAXATION MEASUREMENT
References
8 First-order 1D Spectroscopy
8.1 NOMENCLATURE OF THE SPIN SYSTEM
8.2 PEAK SHIFT – THE EFFECT OF CHEMICAL SHIFT
8.3 PEAK AREA – REFLECTING THE NUMBER OF PROTONS
8.4 PEAK SPLITTING – THE CONSEQUENCE OF J COUPLING
8.4.1 Characteristics of J Coupling Constant and the Coupled Spectrum
8.4.2 Basis Product Functions
8.4.3 Two-spin AX Systems
8.4.4 Three-spin AMX Systems
8.4.5 Coupled with Identical Spins in AXN Systems
8.5 EXAMPLES OF 1D SPECTRA
8.5.1 Ethanol
8.5.2 Styrene and 2,3,4,5,6-pentafluorostyrene
8.5.3 Ethyl Acetate
8.5.4 Quinoline
References
9 Advanced Topics in Spectroscopy
9.1 DOUBLE RESONANCE
9.1.1 Homonuclear Decoupling
9.1.2 Heteronuclear Decoupling
9.2 DIPOLAR INTERACTION IN A TWO-SPIN SYSTEM
9.3 MAGIC ANGLE
9.4 CHEMICAL EXCHANGE
9.5 MAGNETIZATION TRANSFER
9.6 SELECTIVE POLARIZATION INVERSION/TRANSFER
9.7 RADIATION DAMPING
References
10 2D NMR Spectroscopy
10.1 ESSENCE OF 2D NMR SPECTROSCOPY
10.1.1 The Second Dimension
10.1.2 Coupled Spins
10.1.3 Classification
10.2 COSY – CORRELATION SPECTROSCOPY
10.2.1 2D Heteronuclear COSY
10.2.2 2D Homonuclear COSY
10.3 J-RESOLVED SPECTROSCOPY
10.3.1 Basic Pulse Sequences
10.3.2 2D Heteronuclear J-resolved Spectroscopy
10.3.3 2D Homonuclear J-resolved Spectroscopy
10.4 EXAMPLES OF 2D NMR SPECTROSCOPY. 10.4.1 Homonuclear COSY of Styrene
10.4.2 Heteronuclear J-resolved Spectroscopy of Styrene
References
11 Effect of the Field Gradient and k-space Imaging
11.1 SPATIALLY ENCODING NUCLEAR SPIN MAGNETIZATION
11.2 k SPACE IN MRI
11.3 MAPPING OF k SPACE
11.4 GRADIENT ECHO
References
12 Spatial Mapping in MRI
12.1 SLICE SELECTION IN 2D MRI
12.1.1 Graphical Description of 2D Slice Selection
12.1.2 Mathematic Description of 2D Slice Selection
12.1.3 Sequences and Parameters in 2D Slice Selection
12.2 READING A GRAPHICAL IMAGING SEQUENCE
12.3 2D FILTERED BACK-PROJECTION RECONSTRUCTION
12.4 2D FOURIER IMAGING RECONSTRUCTION
12.5 SAMPLING PATTERNS BETWEEN THE CARTESIAN AND RADIAL GRIDS
12.5.1 Sampling Density
12.5.2 Echo Time
12.5.3 Re-gridding
12.6 3D IMAGING
12.7 FAST IMAGING IN MRI
12.7.1 Fast MRI with Fully Sampled k Space
12.7.2 Compressed Sensing Technique
12.8 ULTRA-SHORT ECHO AND ZTE MRI
12.9 MRI IN OTHER DIMENSIONS (4D, 1D, AND ONE VOXEL)
12.10 RESOLUTION IN MRI
References
13 Imaging Instrumentation and Experiments
13.1 SHAPED PULSES
13.2 THE GRADIENT UNITS
13.2.1 Gradient Power Supplies
13.2.2 Gradient Coils
13.2.3 Eddy Current Reduction
13.3 INSTRUMENTATION CONFIGURATIONS FOR MRI
13.4 IMAGING PARAMETERS IN MRI
13.4.1 Imaging Resolution and Data Size
13.4.2 Parameters that Relate to the Experimental Time
13.4.3 SNR in MRI
13.4.4 Fundamental Constraints in MRI
13.5 IMAGE PROCESSING SOFTWARE
13.6 BEST TEST SAMPLES FOR MRI
References
14 Image Contrast in MRI
14.1 NON-TRIVIAL RELATIONSHIP BETWEEN SPIN DENSITY AND IMAGE INTENSITY
14.2 IMAGE CONTRAST IN MRI
14.3 HOW TO OBTAIN USEFUL INFORMATION FROM IMAGE CONTRAST?
14.3.1 Qualitative Approach to Extract Image Contrast
14.3.2 Quantitative Approaches to Extract Image Contrast
14.4 MAGNETIZATION-PREPARED SEQUENCES IN QUANTITATIVE MRI
References
15 Quantitative MRI
15.1 QUANTITATIVE IMAGING OF VELOCITY V AND MOLECULAR DIFFUSION D
15.1.1 PGSE Sequence
15.1.2 q-Space Imaging
15.1.3 Imaging Fluid Flow
15.1.4 Imaging Molecular Diffusion
15.2 QUANTITATIVE IMAGING OF RELAXATION TIMES T1, T2, T1ρ
15.2.1 Magic Angle Effect and Relaxation Anisotropy
15.2.2 T1 Relaxation Time
15.2.3 T2 Relaxation Time
15.2.4 T1ρ Relaxation Time
15.3 QUANTITATIVE IMAGING OF CHEMICAL SHIFT δ
15.4 SECONDARY IMAGE CONTRASTS IN MRI
15.4.1 Susceptibility
15.4.2 BOLD
15.4.3 Temperature
15.4.4 The Use of Contrast Agents
15.5 POTENTIAL ISSUES AND PRACTICAL STRATEGIES IN QUANTITATIVE MRI
15.5.1 How Quantitative Is This Quantitative Result?
15.5.2 Issues and Strategies in Discrete Fourier Transform
15.5.3 Issues and Strategies in Least-squares Fitting
References
16 Advanced Topics in Quantitative MRI
16.1 ANISOTROPY AND TENSOR PROPERTIES IN QUANTITATIVE MRI
16.1.1 Anisotropy and T2 Anisotropy
16.1.2 Dispersion and T1ρ Dispersion
16.1.3 Tensor and Diffusion Tensor Imaging
16.1.4 Kurtosis and Diffusion Kurtosis Imaging
16.2 MULTI-COMPONENT NATURE IN QUANTITATIVE MRI
16.3 QUANTITATIVE PHASE INFORMATION IN THE FID DATA – SWI AND QSM
16.4 FUNCTIONAL MRI (fMRI)
16.5 OPTICAL PUMPING AND HYPERPOLARIZATION IN MRI
References
17 Reading the Binary Data
17.1 FORMATS OF DATA
17.2 FORMATS OF DATA STORAGE
17.3 READING UNKNOWN BINARY DATA
17.4 EXAMPLES OF SPECIFIC FORMATS
17.4.1 Bruker Pre-clinical MRI Systems
17.4.2 Bruker NMR Spectroscopy Systems
Appendices
Appendix 1 Background in Mathematics. A1.1 ELEMENTARY MATHEMATICS
A1.1.1 Scalars and Vectors
A1.1.2 Dot and Cross Products in Vector Analysis
A1.1.3 Complex Numbers
A1.1.4 Taylor Expansions
A1.1.5 Matrix and Operations
A1.2 FOURIER TRANSFORM
A1.2.1 Definitions
A1.2.2 Convolution Theorem
A1.2.3 Digital Fourier Transform
References
Appendix 2 Background in Quantum Mechanics
A2.1 OPERATORS
Example
A2.2 EXPANSION OF A WAVE FUNCTION
A2.3 SPIN OPERATOR I
A2.4 RAISING AND LOWERING OPERATORS I+ AND I–
Example
A2.5 SPIN-1/2 OPERATOR (IN THE FORMALISM OF PAULI’S SPIN MATRICES)
Example
A2.6 DENSITY MATRIX OPERATOR r
Some Properties of r:
Example
Reference
Appendix 3 Background in Electronics
A3.1 OHM’S LAW FOR DC AND AC CIRCUITS
A3.2 ELECTRONICS AT RADIO FREQUENCY
A3.2.1 The Frequency Dependency of Wavelength
A3.2.2 The Skin Effect
A3.2.3 Concepts of Transmission Line in rf Electronics
References
Appendix 4 Sample Syllabi for a One-semester Course
Four Schedules for Syllabi
Appendix 5 Homework Problems
SAMPLE PROBLEMS FOR PART 1 ESSENTIAL CONCEPTS IN NMR
SAMPLE PROBLEMS FOR PART 2 ESSENTIAL CONCEPTS IN NMR INSTRUMENTATION
SAMPLE PROBLEMS FOR PART 3 ESSENTIAL CONCEPTS IN NMR SPECTROSCOPY
SAMPLE PROBLEMS FOR PART 4 ESSENTIAL CONCEPTS IN MRI
SAMPLE PROBLEMS FOR PART 5 QUANTITATIVE AND CREATIVE MRI
Index
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