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New edition explores contemporary MRI principles and practices 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…mehr
New edition explores contemporary MRI principles and practices 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.
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Robert W. Brown, Ph.D. Institute Professor and Distinguished University Professor Case Western Reserve University, Cleveland, Ohio, USA His 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 Radiology Wayne State University, Detroit, Michigan, USA E. Mark Haacke, Ph.D. Professor of Radiology, Wayne State University, Detroit, Michigan, USA Professor of Physics, Case Western Reserve University, Cleveland, Ohio, USA Adjunct Professor of Radiology, Loma Linda University, Loma Linda, California, USA Adjunct Professor of Radiology, McMaster University, Hamilton, Ontario, Canada Distinguished Foreign Professor, Northeastern University, Shenyang, Liaoning, China Director 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, USA Ramesh Venkatesan, D.Sc. Manager, MR Applications Engineering Wipro GE Healthcare Pvt. Ltd., Bangalore, Karnataka, India
Inhaltsangabe
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 rho0, 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
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 rho0, 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
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