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1 | (10) |
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1.1 MPI in the Context of Medical Imaging |
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1 | (2) |
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1.2 Historical Perspective |
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3 | (5) |
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1.3 Structure of the Book |
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8 | (3) |
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2 How Magnetic Particle Imaging Works |
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11 | (60) |
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11 | (1) |
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12 | (13) |
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2.2.1 Particle Concentration |
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12 | (2) |
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2.2.2 Particle Magnetization |
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14 | (4) |
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2.2.3 Derivative of the Magnetization Characteristic |
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18 | (2) |
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2.2.4 Mean Magnetic Moment |
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20 | (1) |
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2.2.5 Particle Size Distribution |
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21 | (1) |
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22 | (3) |
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2.3 Signal Generation and Acquisition |
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25 | (11) |
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25 | (3) |
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2.3.2 Direct Coupling of Excitation Field |
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28 | (1) |
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29 | (3) |
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32 | (3) |
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2.3.5 Excitation Frequency and Field Strength |
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35 | (1) |
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2.4 Spatial Encoding: Selection Field |
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36 | (4) |
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36 | (2) |
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2.4.2 Sampling of Volumes |
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38 | (1) |
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2.4.3 Properties of the Selection Field |
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39 | (1) |
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2.5 Performance Upgrade: Drive Field |
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40 | (18) |
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2.5.1 Moving the Field-Free Point |
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40 | (1) |
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2.5.2 How to Move the Field-Free Point Nonmechanically |
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41 | (1) |
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2.5.3 Drive-Field Waveform |
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42 | (2) |
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44 | (3) |
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2.5.5 Convolution with the FFP Kernel |
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47 | (2) |
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49 | (9) |
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2.6 Performance Upgrade: Focus Field |
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58 | (3) |
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2.6.1 Limitations of the Drive Field |
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59 | (1) |
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2.6.2 Scanning Large Volumes Using the Focus Field |
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59 | (2) |
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61 | (10) |
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61 | (7) |
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2.7.2 Sensitivity and Temporal Resolution |
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68 | (1) |
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69 | (2) |
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3 How to Build an MPI Scanner |
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71 | (26) |
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71 | (1) |
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3.2 Magnetic Field Generation |
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71 | (10) |
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3.2.1 Electromagnetic Coils |
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72 | (1) |
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3.2.2 Soft-Magnetic Iron Cores |
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72 | (1) |
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73 | (1) |
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3.2.4 Skin Effect and Litz Wire |
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74 | (2) |
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3.2.5 Generating Homogeneous Magnetic Fields |
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76 | (2) |
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3.2.6 Generating Magnetic Gradient Fields |
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78 | (3) |
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3.3 Generic MPI Coil Configuration |
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81 | (5) |
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3.3.1 Generating the Selection and Focus Field |
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82 | (1) |
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3.3.2 Generating the Drive Field |
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83 | (1) |
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3.3.3 Receiving the Particle Magnetization |
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84 | (1) |
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85 | (1) |
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3.4 Generic MPI Signal Chain |
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86 | (11) |
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87 | (2) |
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3.4.2 Overview of the 3D Signal Chain |
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89 | (1) |
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90 | (3) |
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93 | (4) |
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4 Prior to Reconstruction - The System Function |
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97 | (30) |
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97 | (1) |
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4.2 Signal Equation in Time Space |
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97 | (2) |
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4.3 Signal Equation in Frequency Space |
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99 | (2) |
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99 | (1) |
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4.3.2 Energy of the System Function |
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100 | (1) |
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4.3.3 Spatial Structure of the System Function |
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100 | (1) |
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101 | (4) |
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102 | (1) |
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102 | (3) |
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105 | (8) |
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4.5.1 Spatial Structure of the 2D System Function |
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105 | (2) |
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4.5.2 Energy of the 2D System Function |
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107 | (1) |
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4.5.3 Nonlinear Frequency Mixing |
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108 | (3) |
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4.5.4 Similarity to Tensor Products of Chebyshev Polynomials |
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111 | (1) |
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112 | (1) |
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113 | (1) |
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4.7 Discrete Signal Equation |
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113 | (5) |
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113 | (2) |
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115 | (1) |
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4.7.3 Discretization of the Signal Equation |
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116 | (2) |
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4.8 How to Determine the System Function |
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118 | (9) |
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4.8.1 Measurement-Based Approach |
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119 | (3) |
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4.8.2 Model-Based Approach |
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122 | (1) |
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4.8.3 Comparison of Measured and Modeled System Functions |
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123 | (4) |
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5 From Data to Images: Reconstruction |
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127 | (22) |
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127 | (1) |
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5.2 Least-Squares Solution |
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128 | (3) |
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5.2.1 Statistical Motivation |
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129 | (1) |
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5.2.2 Weighted Least-Squares Solution |
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130 | (1) |
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5.3 Discrete Ill-Posed Problems |
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131 | (1) |
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5.4 Regularization Methods |
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132 | (7) |
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5.4.1 Singular Value Decomposition |
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133 | (2) |
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5.4.2 Choice of the Regularization Parameter |
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135 | (2) |
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5.4.3 Complexity Analysis |
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137 | (2) |
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139 | (1) |
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5.5 Choosing the Weighting Matrix |
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139 | (2) |
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140 | (1) |
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5.5.2 Row Normalization Weights |
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140 | (1) |
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5.5.3 Removing Noisy Frequency Components |
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140 | (1) |
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141 | (8) |
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5.6.1 Conjugate Gradient Normal Residual |
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142 | (2) |
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144 | (1) |
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5.6.3 Regularization by Stopping the Iteration Process |
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145 | (1) |
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5.6.4 Convergence Speed of Iterative Solvers |
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146 | (1) |
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5.6.5 Physical Constraints |
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147 | (2) |
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6 Special System Topologies |
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149 | (22) |
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149 | (1) |
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149 | (8) |
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150 | (3) |
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6.2.2 Multidimensional Imaging |
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153 | (2) |
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155 | (2) |
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6.3 Field-Free Line Imaging |
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157 | (12) |
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6.3.1 Static Field-Free Line Imaging |
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161 | (4) |
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6.3.2 Dynamic Field-Free Line Imaging |
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165 | (4) |
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6.4 MPI/MRI Hybrid Systems |
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169 | (2) |
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7 Putting MPI to Use: Applications |
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171 | (6) |
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171 | (1) |
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171 | (3) |
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7.3 Oncology, Sentinel Lymph Node Imaging, and Hyperthermia |
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174 | (1) |
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7.4 Cell Labeling and Tracking |
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175 | (1) |
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7.4.1 Red Blood Cell Labeling |
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175 | (1) |
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175 | (1) |
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7.5 Gastrointestinal and Lung Imaging |
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176 | (1) |
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A Fundamentals of Electromagnetism |
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177 | (14) |
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177 | (1) |
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177 | (5) |
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A.2.1 Constitutive Relations |
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179 | (1) |
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180 | (1) |
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A.2.3 Quasi-static Approximation |
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181 | (1) |
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A.2.4 Time-Independent Current Distribution |
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182 | (1) |
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182 | (4) |
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A.3.1 Magnetic Vector Potential |
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183 | (2) |
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185 | (1) |
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185 | (1) |
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A.4 Electromagnetic Induction |
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186 | (5) |
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187 | (1) |
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188 | (1) |
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188 | (1) |
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189 | (2) |
References |
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191 | (8) |
Index |
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199 | |