Electromagnetic Analysis and Design in

This book presents a comprehensive treatment of electromagnetic analysis and design of three critical devices for an MRI system - the magnet, gradient coils, and radiofrequency (RF) coils. Electromagnetic Analysis and Design in Magnetic Resonance Imaging is unique in its detailed examination of the analysis and design of the hardware for an MRI system. It takes an engineering perspective to serve the many scientists and engineers in this rapidly expanding field.Chapters present:o an introduction to MRIo basic concepts of electromagnetics, including Helmholtz and Maxwell coils, inductance calculation, and magnetic fields produced by special cylindrical and spherical surface currentso principles for the analysis and design of gradient coils, including discrete wires and the target field methodo analysis of RF coils based on the equivalent lumped-circuit model as well as an analysis based on the integral equation formulationo survey of special purpose RF coilso analytical and numerical methods for the analysis of electromagnetic fields in biological objectsWith the continued, active development of MRI instrumentation, Electromagnetic Analysis and Design in Magnetic Resonance Imaging presents an excellent, logically organized text - an indispensable resource for engineers, physicists, and graduate students working in the field of MRI.

Preface

v

(2)

About the Author

vii

(2)

Acknowledgments

ix

(2)

Contents

xi

1 Introduction to Magnetic Resonance Imaging

1

(38)

1.1 Introduction

1

(2)

1.2 Physical Principles of Nuclear Magnetic Resonance

3

(18)

1.2.1 Property of Spin

3

(2)

1.2.2 Behavior of Nuclei in an External Magnetic Field

5

(3)

1.2.3 Bulk Magnetization

8

(2)

1.2.4 Effects of a Radiofrequency Pulse

10

(6)

1.2.5 Phenomenological Relaxation--the Bloch Equations

16

(2)

1.2.6 Physical Origins of Relaxation

18

(3)

1.3 Hardware of Magnetic Resonance Imaging

21

(6)

1.3.1 The Main Magnet

21

(2)

1.3.2 The Gradient Coils

23

(1)

1.3.3 The Transmitter

24

(1)

1.3.4 The RF Coils

25

(1)

1.3.5 The Receiver

26

(1)

1.4 Basic Pulse Sequences and Imaging Methods

27

(9)

1.4.1 RF Pulse Sequences

27

(5)

1.4.2 Basic Imaging Methods

32

(4)

References

36

(3)

2 Basic Electromagnetic Theory

39

(40)

2.1 Introduction

39

(1)

2.2 Brief Review of Vector Analysis

39

(2)

2.3 Magnetostatic Fields in Free Space

41

(6)

2.4 Helmholtz and Maxwell Coils

47

(3)

2.5 Boundary Conditions for Magnetostatic Fields

50

(2)

2.6 Magnetostatic Fields in Source-Free Regions

52

(2)

2.7 Magnetostatic Fields Produced by Cylindrical and Spherical Surface Currents

54

(3)

2.8 Inductance Calculation

57

(4)

2.9 Time-Varying Electromagnetic Fields

61

(2)

2.10 Time-Harmonic Fields

63

(1)

2.A Divergence, Curl, Gradient, and Laplacian Operations

64

(1)

2.B Associated Legendre Polynomials

65

(3)

2.C Magnetic Field Produced by a Spherical Surface Current

68

(3)

2.D Computer Program for Inductance Calculation

71

(3)

Problems

74

(2)

References

76

(3)

3 Analysis and Design of Gradient Coils

79

(58)

3.1 Introduction

79

(1)

3.2 Effect of Coil's Inductance

80

(3)

3.3 Figure of Merit

83

(1)

3.4 Gradient Coils Made of Discrete Wires

83

(10)

3.4.1 Longitudinal Gradient

83

(4)

3.4.2 Transverse Gradients

87

(6)

3.5 Magnetic Field Produced by a Cylindrical Surface Current

93

(5)

3.6 Target Field Method

98

(10)

3.7 Shielded Gradient Coils

108

(5)

3.8 Minimization of Inductance and Power Dissipation

113

(5)

3.9 Planar Gradient Coils

118

(8)

3.9.1 Magnetic Field Produced by a Planar Surface Current

118

(3)

3.9.2 Target Field Method

121

(1)

3.9.3 Shielded Planar Coils

122

(1)

3.9.4 Minimization of Inductance and Power Dissipation

123

(3)

3.A Modified Bessel Functions

126

(4)

3.B Alternative Derivation of Equation (3.66)

130

(1)

Problems

131

(2)

References

133

(4)

4 Analysis and Design of RF Coils

137

(74)

4.1 Introduction

137

(2)

4.2 Concepts of Resonance and Reciprocity

139

(5)

4.3 Equivalent Circuit Analysis

144

(20)

4.3.1 A Simple Example

144

(2)

4.3.2 Highpass Birdcage Coil

146

(3)

4.3.3 Lowpass Birdcage Coil

149

(6)

4.3.4 Hybrid Birdcage Coil

155

(2)

4.3.5 Open Coils

157

(7)

4.4 Analysis of RF Shields

164

(11)

4.4.1 Analysis Using Image Method

165

(5)

4.4.2 Improving Field Homogeneity Using End-Caps

170

(2)

4.4.3 Design of RF Shield

172

(3)

4.5 Field Inhomogeneity of Birdcage Coils

175

(6)

4.6 Method of Moments Analysis

181

(10)

4.6.1 Unshielded Coil

181

(4)

4.6.2 Shielded Coil

185

(1)

4.6.3 Numerical Simulation

186

(5)

4.7 Miscellaneous Topics

191

(11)

4.7.1 Brief History of Birdcage Coils

191

(3)

4.7.2 Quadrature Coils

194

(1)

4.7.3 Double-Tuned Coils

195

(2)

4.7.4 Surface Coils

197

(1)

4.7.5 Phased Arrays

198

(1)

4.7.6 Unicoil Concept and Design

198

(4)

Problems

202

(3)

References

205

(6)

5 RF Fields in Biological Objects

211

(62)

5.1 Introduction

211

(2)

5.2 Analytical Methods

213

(6)

5.2.1 Two-Dimensional Example

213

(3)

5.2.2 Three-Dimensional Example

216

(3)

5.3 Two-Dimensional Numerical Analysis

219

(21)

5.3.1 Finite Difference Method

219

(5)

5.3.2 Finite Element Method

224

(2)

5.3.3 Numerical Simulations

226

(14)

5.4 Three-Dimensional Numerical Analysis

240

(15)

5.4.1 Finite-Difference Time-Domain Method

240

(4)

5.4.2 Method of Moments

244

(7)

5.4.3 Numerical Simulations

251

(4)

5.A Bessel Functions

255

(8)

5.B Spherical Bessel Functions

263

(3)

Problems

266

(1)

References

267

(6)

A About the Software

273

(6)

A.1 Introduction

273

(1)

A.2 RF Coil Analysis

274

(1)

A.3 RF Field Analysis

275

(4)

Index

279

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Electromagnetic Analysis and Design in Magnetic Resonance Imaging

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Table of Contents

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