Thoroughly revised, updated and expanded, the second edition of Magnetic Resonance Imaging: Physical Principles and Sequence Design remains the preeminent text in its field. Using consistent nomenclature and mathematical notations throughout all the chapters, this new edition carefully explains the physical principles of magnetic resonance imaging design and implementation. In addition, detailed figures and MR images enable readers to better grasp core concepts, methods, and applications.
Magnetic Resonance Imaging, Second Edition begins with an introduction to fundamental principles, with coverage of magnetization, relaxation, quantum mechanics, signal detection and acquisition, Fourier imaging, image reconstruction, contrast, signal, and noise. The second part of the text explores MRI methods and applications, including fast imaging, water-fat separation, steady state gradient echo imaging, echo planar imaging, diffusion-weighted imaging, and induced magnetism. Lastly, the text discusses important hardware issues and parallel imaging.
Readers familiar with the first edition will find much new material, including:
- New chapter dedicated to parallel imaging
- New sections examining off-resonance excitation principles, contrast optimization in fast steady-state incoherent imaging, and efficient lower-dimension analogues for discrete Fourier transforms in echo planar imaging applications
- Enhanced sections pertaining to Fourier transforms, filter effects on image resolution, and Bloch equation solutions when both rf pulse and slice select gradient fields are present
- Valuable improvements throughout with respect to equations, formulas, and text
- New and updated problems to test further the readers' grasp of core concepts
Three appendices at the end of the text offer review material for basic electromagnetism and statistics as well as a list of acquisition parameters for the images in the book.
Acclaimed by both students and instructors, the second edition of Magnetic Resonance Imaging offers the most comprehensive and approachable introduction to the physics and the applications of magnetic resonance imaging.
Table of Contents
Foreword to the Second Edition xvii
Foreword to the First ~ Edition xxi
Preface to the Second Edition xxvii
Preface to the First Edition xxix
Acknowledgements xxx
Acknowledgements to the First Edition xxxi
1 Magnetic Resonance Imaging: A Preview 1
1.1 Magnetic Resonance Imaging: The Name 1
1.2 The Origin of Magnetic Resonance Imaging 2
1.3 A Brief Overview of MRI Concepts 3
2 Classical Response of a Single Nucleus to a Magnetic Field 19
2.1 Magnetic Moment in the Presence of a Magnetic Field 20
2.2 Magnetic Moment with Spin: Equation of Motion 25
2.3 Precession Solution: Phase 29
3 Rotating Reference Frames and Resonance 37
3.1 Rotating Reference Frames 38
3.2 The Rotating Frame for an RF Field 41
3.3 Resonance Condition and the RF Pulse 44
4 Magnetization, Relaxation, and the Bloch Equation 53
4.1 Magnetization Vector 53
4.2 Spin-Lattice Interaction and Regrowth Solution 54
4.3 Spin-Spin Interaction and Transverse Decay 57
4.4 Bloch Equation and Static-Field Solutions 60
4.5 The Combination of Static and RF Fields 62
5 The Quantum Mechanical Basis of Precession and Excitation 67
5.1 Discrete Angular Momentum and Energy 68
5.2 Quantum Operators and the Schrödinger Equation 72
5.3 Quantum Derivation of Precession 77
5.4 Quantum Derivation of RF Spin Tipping 80
6 The Quantum Mechanical Basis of Thermal Equilibrium and Longitudinal Relaxation 85
6.1 Boltzmann Equilibrium Values 86
6.2 Quantum Basis of Longitudinal Relaxation 89
6.3 The RF Field 92
7 Signal Detection Concepts 95
7.1 Faraday Induction 96
7.2 The MRI Signal and the Principle of Reciprocity 99
7.3 Signal from Precessing Magnetization 101
7.4 Dependence on System Parameters 107
8 Introductory Signal Acquisition Methods: Free Induction Decay, Spin Echoes, Inversion Recovery, and Spectroscopy 113
8.1 Free Induction Decay and T∗ 2 114
8.2 The Spin Echo and T2 Measurements 120
8.3 Repeated RF Pulse Structures 126
8.4 Inversion Recovery and T1 Measurements 131
8.5 Spectroscopy and Chemical Shift 136
9 One-Dimensional Fourier Imaging, k-Space and Gradient Echoes 141
9.1 Signal and Effective Spin Density 142
9.2 Frequency Encoding and the Fourier Transform 144
9.3 Simple Two-Spin Example 147
9.4 Gradient Echo and k-Space Diagrams 151
9.5 Gradient Directionality and Nonlinearity 162
10 Multi-Dimensional Fourier Imaging and Slice Excitation 165
10.1 Imaging in More Dimensions 166
10.2 Slice Selection with Boxcar Excitations 175
10.3 2D Imaging and k-Space 184
10.4 3D Volume Imaging 194
10.5 Chemical Shift Imaging 197
11 The Continuous and Discrete Fourier Transforms 207
11.1 The Continuous Fourier Transform 208
11.2 Continuous Transform Properties and Phase Imaging 209
11.3 Fourier Transform Pairs 220
11.4 The Discrete Fourier Transform 223
11.5 Discrete Transform Properties 225
12 Sampling and Aliasing in Image Reconstruction 229
12.1 Infinite Sampling, Aliasing, and the Nyquist Criterion 230
12.2 Finite Sampling, Image Reconstruction, and the Discrete Fourier Transform 237
12.3 RF Coils, Noise, and Filtering 245
12.4 Nonuniform Sampling 250
13 Filtering and Resolution in Fourier Transform Image Reconstruction 261
13.1 Review of Fourier Transform Image Reconstruction 262
13.2 Filters and Point Spread Functions 264
13.3 Gibbs Ringing 267
13.4 Spatial Resolution in MRI 272
13.5 Hanning Filter and T∗2 Decay Effects 281
13.6 Zero Filled Interpolation, Sub-Voxel Fourier Transform Shift Concepts, and Point Spread Function Effects 283
13.7 Partial Fourier Imaging and Reconstruction 286
13.8 Digital Truncation 293
14 Projection Reconstruction of Images 297
14.1 Radial k-Space Coverage 298
14.2 Sampling Radial k-Space and Nyquist Limits 302
14.3 Projections and the Radon Transform 308
14.4 Methods of Projection Reconstruction with Radial Coverage 310
14.5 Three-Dimensional Radial k-Space Coverage 317
14.6 Radial Coverage Versus Cartesian k-Space Coverage 320
15 Signal, Contrast, and Noise 325
15.1 Signal and Noise 326
15.2 SNR Dependence on Imaging Parameters 334
15.3 Contrast, Contrast-to-Noise, and Visibility 342
15.4 Contrast Mechanisms in MRI and Contrast Maximization 345
15.5 Contrast Enhancement with T1-Shortening Agents 358
15.6 Partial Volume Effects, CNR, and Resolution 363
15.7 SNR in Magnitude and Phase Images 365
15.8 SNR as a Function of Field Strength 368
16 A Closer Look at Radiofrequency Pulses 375
16.1 Relating RF Fields and Measured Spin Density 376
16.2 Implementing Slice Selection 381
16.3 Calibrating the RF Field 383
16.4 Solutions of the Bloch Equations 387
16.5 Spatially Varying RF Excitation 393
16.6 RF Pulse Characteristics: Flip Angle and RF Power 400
16.7 Spin Tagging 405
17 Water/Fat Separation Techniques 413
17.1 The Effect of Chemical Shift in Imaging 413
17.2 Selective Excitation and Tissue Nulling 420
17.3 Multiple Point Water/Fat Separation Methods 428
18 Fast Imaging in the Steady State 447
18.1 Short-TR, Spoiled, Gradient Echo Imaging 448
18.2 Short-TR, Coherent, Gradient Echo Imaging 468
18.3 SSFP Signal Formation Mechanisms 481
18.4 Understanding Spoiling Mechanisms 498
19 Segmented k-Space and Echo Planar Imaging 511
19.1 Reducing Scan Times 512
19.2 Segmented k-Space: Phase Encoding Multiple k-Space Lines per RF Excitation for Gradient Echo Imaging 514
19.3 Echo Planar Imaging (EPI) 522
19.4 Alternate Forms of Conventional EPI 530
19.5 Artifacts and Phase Correction 543
19.6 Spiral Forms of EPI 549
19.7 An Overview of EPI Properties 556
19.8 Phase Encoding Between Spin Echoes and Segmented Acquisition 560
19.9 Mansfield 2D to 1D Transformation Insight 563
20 Magnetic Field Inhomogeneity Effects and T∗2 Dephasing 569
20.1 Image Distortion Due to Field Effects 570
20.2 Echo Shifting Due to Field Inhomogeneities in Gradient Echo Imaging 580
20.3 Methods for Minimizing Distortion and Echo Shifting Artifacts 587
20.4 Empirical T∗2 603
20.5 Predicting T∗2 for Random Susceptibility Producing Structures 611
20.6 Correcting Geometric Distortion 615
21 Random Walks, Relaxation, and Diffusion 619
21.1 Simple Model for Intrinsic T2 620
21.2 Simple Model for Diffusion 622
21.3 Carr-Purcell Mechanism 624
21.4 Meiboom-Gill Improvement 626
21.5 The Bloch-Torrey Equation 628
21.6 Some Practical Examples of Diffusion Imaging 632
22 Spin Density, T1 and T2 Quantification Methods in MR Imaging 637
22.1 Simplistic Estimates of ρ0, T1 T2 638
22.2 Estimating T1 and T2 from Signal Ratio Measurements 640
22.3 Estimating T1 and T2 from Multiple Signal Measurements 647
22.4 Other Methods for Spin Density and T1 Estimation 649
22.5 Practical Issues Related to T1 and T2 Measurements 657
22.6 Calibration Materials for Relaxation Time Measurements 665
23 Motion Artifacts and Flow Compensation 669
23.1 Effects on Spin Phase from Motion along the Read Direction 670
23.2 Velocity Compensation along the Read and Slice Select Directions 675
23.3 Ghosting Due to Periodic Motion 683
23.4 Velocity Compensation along Phase Encoding Directions 688
23.5 Maximum Intensity Projection 698
24 MR Angiography and Flow Quantification 701
24.1 Inflow or Time-of-Flight (TOF) Effects 702
24.2 TOF Contrast, Contrast Agents, and Spin Density/T∗2 -Weighting 711
24.3 Phase Contrast and Velocity Quantification 719
24.4 Flow Quantification 730
25 Magnetic Properties of Tissues: Theory and Measurement 739
25.1 Paramagnetism, Diamagnetism, and Ferromagnetism 740
25.2 Permeability and Susceptibility: The →H Field 744
25.3 Objects in External Fields: The Lorentz Sphere 745
25.4 Susceptibility Imaging 755
25.5 Brain Functional MRI and the BOLD Phenomenon 760
25.6 Signal Behavior in the Presence of Deoxygenated Blood 766
26 Sequence Design, Artifacts, and Nomenclature 779
26.1 Sequence Design and Imaging Parameters 780
26.2 Early Spin Echo Imaging Sequences 785
26.3 Fast Short TR Imaging Sequences 791
26.4 Imaging Tricks and Image Artifacts 798
26.5 Sequence Adjectives and Nomenclature 812
27 Introduction to MRI Coils and Magnets 823
27.1 The Circular Loop as an Example 824
27.2 The Main Magnet Coil 827
27.3 Linearly Varying Field Gradients 838
27.4 RF Transmit and Receive Coils 846
28 Parallel Imaging 859
28.1 Coil Signals, Their Images, and a One-Dimensional Test Case 860
28.2 Parallel Imaging with an x-Space Approach 865
28.3 Parallel Imaging with a k-Space Approach 873
28.4 Noise and the g-Factor 885
28.5 Additional Topics in Acquisition and Reconstruction 888
A Electromagnetic Principles: A Brief Overview 893
A.1 Maxwell's Equations 894
A.2 Faraday's Law of Induction 894
A.3 Electromagnetic Forces 895
A.4 Dipoles in an Electromagnetic Field 896
A.5 Formulas for Electromagnetic Energy 896
A.6 Static Magnetic Field Calculations 897
B Statistics 899
B.1 Accuracy Versus Precision 899
B.1.1 Mean and Standard Deviation 900
B.2 The Gaussian Probability Distribution 901
B.2.1 Probability Distribution 901
B.2.2 z-Score 901
B.2.3 Quoting Errors and Confidence Intervals 902
B.3 Type I and Type II Errors 902
B.4 Sum over Several Random Variables 904
B.4.1 Multiple Noise Sources 905
B.5 Rayleigh Distribution 906
B.6 Experimental Validation of Noise Distributions 907
B.6.1 Histogram Analysis 907
B.6.2 Mean and Standard Deviation 909
C Imaging Parameters to Accompany Figures 913
Index 923
