Magnetic Resonance Imaging

Robert W. Brown, Ph.D.Institute Professor and Distinguished University ProfessorCase Western Reserve University, Cleveland, Ohio, USAHis research group efforts have resulted in over 200 published papers and abstracts, and his former students hold at least 150 patents (eight co-authored by him) and he has done important work in radiation physics, MRI, PET, CT, electromagnetics, inverse methods, mechanical and thermal modeling, nonlinear dynamics, EEG, MEG, sensors, and physics education, as well as a professional-life-long involvement in elementary particle physics and cosmology.Yu-Chung N. Cheng, Ph.D.Associate Professor of RadiologyWayne State University, Detroit, Michigan, USAE. Mark Haacke, Ph.D.Professor of Radiology, Wayne State University, Detroit, Michigan, USAProfessor of Physics, Case Western Reserve University, Cleveland, Ohio, USAAdjunct Professor of Radiology, Loma Linda University, Loma Linda, California, USAAdjunct Professor of Radiology, McMaster University, Hamilton, Ontario, CanadaDistinguished Foreign Professor, Northeastern University, Shenyang, Liaoning, ChinaDirector of The Magnetic Resonance Imaging Institute for Biomedical Research and Professor of Radiology, Department of Biomedical Engineering, Wayne State University. Dr. Haacke has two decades of experience teaching courses in physics, mathematics and statistics.Michael R. Thompson, Ph.D.Principal Scientist, Toshiba Medical Research Institute,Cleveland, Ohio, USARamesh Venkatesan, D.Sc.Manager, MR Applications EngineeringWipro GE Healthcare Pvt. Ltd., Bangalore, Karnataka, India

• Foreword to the Second Edition xvii Foreword to the First ~ Edition xxi Preface to the Second Edition xxviiPreface to the First Edition xxixAcknowledgements xxxAcknowledgements to the First Edition xxxi 1 Magnetic Resonance Imaging: A Preview 11.1 Magnetic Resonance Imaging: The Name 11.2 The Origin of Magnetic Resonance Imaging 21.3 A Brief Overview of MRI Concepts 32 Classical Response of a Single Nucleus to a Magnetic Field 192.1 Magnetic Moment in the Presence of a Magnetic Field 202.2 Magnetic Moment with Spin: Equation of Motion 252.3 Precession Solution: Phase 293 Rotating Reference Frames and Resonance 373.1 Rotating Reference Frames 383.2 The Rotating Frame for an RF Field 413.3 Resonance Condition and the RF Pulse 444 Magnetization, Relaxation, and the Bloch Equation 534.1 Magnetization Vector 534.2 Spin-Lattice Interaction and Regrowth Solution 544.3 Spin-Spin Interaction and Transverse Decay 574.4 Bloch Equation and Static-Field Solutions 604.5 The Combination of Static and RF Fields 625 The Quantum Mechanical Basis of Precession and Excitation 675.1 Discrete Angular Momentum and Energy 685.2 Quantum Operators and the Schrödinger Equation 725.3 Quantum Derivation of Precession 775.4 Quantum Derivation of RF Spin Tipping 80 6 The Quantum Mechanical Basis of Thermal Equilibrium and Longitudinal Relaxation 856.1 Boltzmann Equilibrium Values 866.2 Quantum Basis of Longitudinal Relaxation  896.3 The RF Field 927 Signal Detection Concepts 957.1 Faraday Induction 967.2 The MRI Signal and the Principle of Reciprocity 997.3 Signal from Precessing Magnetization 1017.4 Dependence on System Parameters 1078 Introductory Signal Acquisition Methods: Free Induction Decay, Spin Echoes, Inversion Recovery, and Spectroscopy 113 8.1 Free Induction Decay and T∗ 2 1148.2 The Spin Echo and T2 Measurements 1208.3 Repeated RF Pulse Structures 1268.4 Inversion Recovery and T1 Measurements 1318.5 Spectroscopy and Chemical Shift 1369 One-Dimensional Fourier Imaging, k-Space and Gradient Echoes 1419.1 Signal and Effective Spin Density 1429.2 Frequency Encoding and the Fourier Transform 1449.3 Simple Two-Spin Example 1479.4 Gradient Echo and k-Space Diagrams 1519.5 Gradient Directionality and Nonlinearity 16210 Multi-Dimensional Fourier Imaging and Slice Excitation 16510.1 Imaging in More Dimensions 16610.2 Slice Selection with Boxcar Excitations 17510.3 2D Imaging and k-Space 18410.4 3D Volume Imaging 19410.5 Chemical Shift Imaging 19711 The Continuous and Discrete Fourier Transforms 20711.1 The Continuous Fourier Transform 20811.2 Continuous Transform Properties and Phase Imaging 20911.3 Fourier Transform Pairs 22011.4 The Discrete Fourier Transform 22311.5 Discrete Transform Properties 22512 Sampling and Aliasing in Image Reconstruction 22912.1 Infinite Sampling, Aliasing, and the Nyquist Criterion 23012.2 Finite Sampling, Image Reconstruction, and the Discrete Fourier Transform 23712.3 RF Coils, Noise, and Filtering 24512.4 Nonuniform Sampling 25013 Filtering and Resolution in Fourier Transform Image Reconstruction 26113.1 Review of Fourier Transform Image Reconstruction 26213.2 Filters and Point Spread Functions 26413.3 Gibbs Ringing 26713.4 Spatial Resolution in MRI 27213.5 Hanning Filter and T∗2 Decay Effects 28113.6 Zero Filled Interpolation, Sub-Voxel Fourier Transform Shift Concepts, and Point Spread Function Effects 28313.7 Partial Fourier Imaging and Reconstruction 28613.8 Digital Truncation 29314 Projection Reconstruction of Images 29714.1 Radial k-Space Coverage 29814.2 Sampling Radial k-Space and Nyquist Limits 30214.3 Projections and the Radon Transform 30814.4 Methods of Projection Reconstruction with Radial Coverage 31014.5 Three-Dimensional Radial k-Space Coverage 31714.6 Radial Coverage Versus Cartesian k-Space Coverage 32015 Signal, Contrast, and Noise 32515.1 Signal and Noise 32615.2 SNR Dependence on Imaging Parameters 33415.3 Contrast, Contrast-to-Noise, and Visibility 34215.4 Contrast Mechanisms in MRI and Contrast Maximization 34515.5 Contrast Enhancement with T1-Shortening Agents 35815.6 Partial Volume Effects, CNR, and Resolution 36315.7 SNR in Magnitude and Phase Images 36515.8 SNR as a Function of Field Strength 36816 A Closer Look at Radiofrequency Pulses 37516.1 Relating RF Fields and Measured Spin Density 37616.2 Implementing Slice Selection 38116.3 Calibrating the RF Field 38316.4 Solutions of the Bloch Equations 38716.5 Spatially Varying RF Excitation 39316.6 RF Pulse Characteristics: Flip Angle and RF Power 40016.7 Spin Tagging 40517 Water/Fat Separation Techniques 41317.1 The Effect of Chemical Shift in Imaging 41317.2 Selective Excitation and Tissue Nulling 42017.3 Multiple Point Water/Fat Separation Methods 42818 Fast Imaging in the Steady State 44718.1 Short-TR, Spoiled, Gradient Echo Imaging 44818.2 Short-TR, Coherent, Gradient Echo Imaging 46818.3 SSFP Signal Formation Mechanisms 48118.4 Understanding Spoiling Mechanisms 49819 Segmented k-Space and Echo Planar Imaging 51119.1 Reducing Scan Times 51219.2 Segmented k-Space: Phase Encoding Multiple k-Space Lines per RF Excitation for Gradient Echo Imaging 51419.3 Echo Planar Imaging (EPI) 52219.4 Alternate Forms of Conventional EPI 53019.5 Artifacts and Phase Correction 54319.6 Spiral Forms of EPI 54919.7 An Overview of EPI Properties 55619.8 Phase Encoding Between Spin Echoes and Segmented Acquisition 56019.9 Mansfield 2D to 1D Transformation Insight 56320 Magnetic Field Inhomogeneity Effects and T∗2 Dephasing 56920.1 Image Distortion Due to Field Effects 57020.2 Echo Shifting Due to Field Inhomogeneities in Gradient Echo Imaging 58020.3 Methods for Minimizing Distortion and Echo Shifting Artifacts 58720.4 Empirical T∗2 60320.5 Predicting T∗2 for Random Susceptibility Producing Structures 61120.6 Correcting Geometric Distortion 61521 Random Walks, Relaxation, and Diffusion 61921.1 Simple Model for Intrinsic T2 62021.2 Simple Model for Diffusion 62221.3 Carr-Purcell Mechanism 62421.4 Meiboom-Gill Improvement 62621.5 The Bloch-Torrey Equation 62821.6 Some Practical Examples of Diffusion Imaging 63222 Spin Density, T1 and T2 Quantification Methods in MR Imaging 63722.1 Simplistic Estimates of ρ0, T1 T2 63822.2 Estimating T1 and T2 from Signal Ratio Measurements 64022.3 Estimating T1 and T2 from Multiple Signal Measurements 64722.4 Other Methods for Spin Density and T1 Estimation 64922.5 Practical Issues Related to T1 and T2 Measurements 65722.6 Calibration Materials for Relaxation Time Measurements 66523 Motion Artifacts and Flow Compensation 66923.1 Effects on Spin Phase from Motion along the Read Direction 67023.2 Velocity Compensation along the Read and Slice Select Directions 67523.3 Ghosting Due to Periodic Motion 68323.4 Velocity Compensation along Phase Encoding Directions 68823.5 Maximum Intensity Projection 69824 MR Angiography and Flow Quantification 70124.1 Inflow or Time-of-Flight (TOF) Effects 70224.2 TOF Contrast, Contrast Agents, and Spin Density/T∗2 -Weighting 71124.3 Phase Contrast and Velocity Quantification 71924.4 Flow Quantification 73025 Magnetic Properties of Tissues: Theory and Measurement 73925.1 Paramagnetism, Diamagnetism, and Ferromagnetism 74025.2 Permeability and Susceptibility: The →H Field 74425.3 Objects in External Fields: The Lorentz Sphere 74525.4 Susceptibility Imaging 75525.5 Brain Functional MRI and the BOLD Phenomenon 760 25.6 Signal Behavior in the Presence of Deoxygenated Blood 76626 Sequence Design, Artifacts, and Nomenclature 77926.1 Sequence Design and Imaging Parameters 78026.2 Early Spin Echo Imaging Sequences 78526.3 Fast Short TR Imaging Sequences 79126.4 Imaging Tricks and Image Artifacts 79826.5 Sequence Adjectives and Nomenclature 81227 Introduction to MRI Coils and Magnets 82327.1 The Circular Loop as an Example 82427.2 The Main Magnet Coil 82727.3 Linearly Varying Field Gradients 83827.4 RF Transmit and Receive Coils 84628 Parallel Imaging 85928.1 Coil Signals, Their Images, and a One-Dimensional Test Case 86028.2 Parallel Imaging with an x-Space Approach 86528.3 Parallel Imaging with a k-Space Approach 87328.4 Noise and the g-Factor 88528.5 Additional Topics in Acquisition and Reconstruction 888A Electromagnetic Principles: A Brief Overview 893A.1 Maxwell's Equations 894A.2 Faraday's Law of Induction 894A.3 Electromagnetic Forces 895A.4 Dipoles in an Electromagnetic Field 896A.5 Formulas for Electromagnetic Energy 896A.6 Static Magnetic Field Calculations 897B Statistics 899B.1 Accuracy Versus Precision 899B.1.1 Mean and Standard Deviation 900B.2 The Gaussian Probability Distribution 901B.2.1 Probability Distribution 901B.2.2 z-Score 901B.2.3 Quoting Errors and Confidence Intervals 902B.3 Type I and Type II Errors 902B.4 Sum over Several Random Variables 904B.4.1 Multiple Noise Sources 905B.5 Rayleigh Distribution 906B.6 Experimental Validation of Noise Distributions 907B.6.1 Histogram Analysis 907B.6.2 Mean and Standard Deviation 909C Imaging Parameters to Accompany Figures 913Index 923