Modeling & Imaging of Bioelectrical Activity (eBook)

Bin He, PhD., is a leading figure in the field of bioelectric engineering. An internationally recognized scientist with numerous publications, Dr. He has served as the President of the International Society of Bioelectromagnetism and as an Associate or Guest Editor for nine international journals in the field of biomedical engineering. Dr. Bin He is currently Professor of Bioengineering at the University of Minnesota.

PREFACE 6
Table of Contents 
9 
1 FROM CELLULAR ELECTROPHYSIOLOGY TO ELECTROCARDIOGRAPHY 
15 
INTRODUCTION 15
1.1 THE ONE-CELL MODEL 17
1.1.1 VOLTAGE GATING ION CHANNEL KINETICS (HODGKIN-HUXLEY FORMAUSM) 
17 
1.1.2 MODELING THE CARDIAC ACTION POTENTIAL 21
1.1.2.1 Classical models of the cardiac actionpotential 
22 
1.1.2.2 Modern models of cardiac action potentials 
23 
1.1.3 MODELING PATHOLOGIC ACTION POTENTIALS 24
1.1.3.1 Myocardial ischemia 25
1.1.3.2 Early afterdepolarizations (EADs) and delayed afterdepolarizations (DADs) 
28 
1.1.3.3 Long-QT syndrome 29
1.2 NETWORK MODELS 31
1.2.1 CELL-CELL COUPLING AND LINEAR CABLE THEORY 31
1.2.2 MULTIDIMENSIONAL NETWORKS 32
1.2.3 RECONSTRUCTION OF THE LOCAL EXTRACELLULAR ELECTROGRAM (FORWARD PROBLEM) 
34 
1.2.4 MODELING PATHOLOGY IN CELLULAR NETWORKS 37
1.2.4.1 Myocardial ischemia 38
1.2.4.2 EADs in 1D and 2D networks 39
1.2.4.3 The ionic basis of spiralwaves andfibrillation 
41 
1.2.4.4 Cell-networks in Long-QT Syndrome 43
1.3 MODELING PATHOLOGY IN THREE-DIMENSIONAL AND WHOLE HEART MODELS 
43 
1.3.1 MYOCARDIAL ISCHEMIA 45
1.3.2 PREEXCITATION STUDIES 45
1.3.3 HYPERTROPHIC CARDIOMYOPATHY 48
1.3.4 DRUG INTEGRATION IN THREE-DIMENSIONAL WHOLE HEART MODELS 
49 
1.3.5 GENETIC INTEGRATION IN THREE-DIMENSIONAL WHOLE HEART MODELS 
49 
1.4 DISCUSSION 50
REFERENCES 52
2 THE FORWARD PROBLEM OF ELECTROCARDIOGRAPHY: THEORETICAL UNDERPINNINGS AND APPLICATIONS 
57 
2.1 INTRODUCTION 57
2.2 DIPOLE SOURCE REPRESENTATIONS 58
2.2.1 FUNDAMENTAL EQUATIONS 58
2.2.2 THE BIDOMAIN MYOCARDIUM 60
2.2.2.1 Equations for an Isotropic Bidomain-the Uniform Dipole Layer 61
2.2.2.2 Equations for an Anisotropic Bidomain-the Oblique Dipole Layer 64
2.3 TORSO GEOMETRYREPRESENTATIONS 67
2.4 SOLUTION METHODOLOGIES FOR THEFORWARD PROBLEM 67
2.4.1 SURFACE METHODS 68
2.4.1.1 Solutions from Equivalent Dipoles 68
2.4.1.2 Solutionsfrom Epicardial Potentials 71
2.4.2 VOLUME METHODS 72
2.4.2.1 Finite-Difference Method 72
2.4.2.2 Finite-Element Method 72
2.4.2.3 Finite-Volume Method 74
2.4.3 COMBINATION METHODS 75
2.5 APPUCATIONS OF THE FORWARD PROBLEM 75
2.5.1 COMPUTER HEART MODELS 76
2.5.1.1 Determining the Excitation Pattern of the Heart 
76 
2.5.1.2 Calculating Torso and/or Epicardial Potentials 
78 
2.5.2 EFFECTS OF TORSO CONDUCTIVITY INHOMOGENEITIES 84
2.5.3 DEFIBRILLATION 86
2.6 FUTURE TRENDS 89
ACKNOWLEDGMENT 89
REFERENCES 89
3 WHOLE HEART MODELING AND COMPUTER SIMULATION 
95 
3.1 INTRODUCTION 95
3.2 METHODOLOGY IN 3D WHOLE HEART MODELING 96
3.2.1 HEART-TORSO GEOMETRY MODELING 96
3.2.2 INCLUSION OFSPECIALIZED CONDUCTION SYSTEM 97
3.2.3 INCORPORATING ROTATING FIBER DIRECTIONS 99
3.2.4 ACTIONPOTENTIALS AND ELECTROPHYSIOLOGIC PROPERTIES 103
3.2.5 PROPAGATION MODELS 108
3.2.5.1 Propagation model of Huygens' type 
109 
3.2.5.2 Propagation of Hodgkin-Huxley type 
112 
3.2.5.3 Propagation using Fitzllugh-Nagumo model 114
3.2.6 CARDIAC ELECTRIC SOURCES AND SURFACE ECG POTENTIALS 114
3.3 COMPUTER SIMULATIONS AND APPliCATIONS 117
3.3.1 SIMULATION OF THE NORMAL ELECTROCARDIOGRAM 117
3.3.2 SIMULATION OF ST-T WAVES IN PATHOLOGIC CONDITIONS 121
3.3.3 SIMULATION OF MYOCARDIAL INFARCTION 122
3.3.4 SIMULATION OF PACE MAPPING 124
3.3.5 SPIRAL WAVES-A NEW HYPOTHESIS OF VENTRICULAR FIBRILLATION 
124 
3.3.6 SIMULATION OF ANTIARRHYTHMICDRUG EFFECT 124
3.4 DISCUSSION 125
REFERENCES 128
4 HEART SURFAC EELECTROCARDIOGRAPHIC INVERSE SOLUTIONS 
133 
4.1 INTRODUCTION 133
4.1.1 THE RATIONALE FOR IMAGING CARDIAC ELECTRICAL FUNCTION 134
4.1.2 A HISTORICAL PERSPECTIVE 134
Microscopic: Action Potential 134
Macroscopic: Electrocardiogram 135
4.1.3 NOTATION AND CONVENTIONS 137
4.2 THE BASIC MODEL AND SOURCE FORMULATIONS 137
4.3 HEARTSURFACE INVERSE PROBLEMS METHODOLOGY 142
4.3.1 SOLUTION NONUNIQUENESS AND INSTABILITY 143
4.3.2 LINEAR ESTIMATIONAND REGULARIZATION 146
4.3.3 STOCHASTIC PROCESSES AND TIME SERIES OF INVERSE PROBLEMS 149
4.4 EPICARDIAL POTENTIAL IMAGING 152
4.4.1 STATISTICAL REGULARIZATION 152
4.4.2 TIKHONOV REGULARIZATIONAND ITS MODIFICATIONS 153
4.4.3 TRUNCATION SCHEMES 155
4.4.4 SPECIFIC CONSTRAINTS IN REGULARIZATION 156
4.4.5 NONLINEAR REGULARIZATIONMETHODOLOGY 157
4.4.6 ANAUGMENTED SOURCE FORMULATION 157
4.4.7 DIFFERENTMETHODS FOR REGULARIZATION PARAMETER SELECTION 
157 
4.4.8 THE BODY SURFACE LAPLACIANAPPROACH 158
4.4.9 SPATIOTEMPORAL REGULARIZATION 159
4.4.10 RECENTIN VITRO AND IN VIVO WORK 160
4.5 ENDOCARDIAL POTENTIAL IMAGING 161
4.6 IMAGING FEATURES OF THE ACTION POTENTIAL 163
4.6.1 MYOCARDIAL ACTIVATION IMAGING 163
4.6.2 IMAGING OTHER FEATURES OF THE ACTION POTENTIAL 168
4.7 DISCUSSION 169
REFERENCES 170
5 THREE-DIMENSIONAL ELECTROCARDIOGRAPHIC TOMOGRAPHIC IMAGING 
175 
5.1 INTRODUCTION 175
5.2 THREE-DIMENSIONAL MYOCARDIAL DIPOLE SOURCE IMAGING 176
5.2.1 EQUIVALENT MOVING DIPOLE MODEL 176
5.2.2 EQUIVALENT DIPOLE DISTRIBUTION MODEL 177
5.2.3 INVERSE ESTIMATION OF 3D DIPOLE DISTRIBUTION 177
5.2.4 NUMERICAL EXAMPLE OF 3D MYOCARDIAL DIPOLE SOURCE IMAGING 
179 
5.3 THREE-DIMENSIONAL MYOCARDIAL ACTIVATION IMAGING 181
5.3.1 OUTLlNE OF THE HEART-MODEL BASED 3D ACTlVATION TIME IMAGING APPROACH 
181 
5.3.2 COMPUTER HEART EXCITATION MODEL 182
5.3.3 PRELIMINARY CLASSIFICATION SYSTEM 183
5.3.4 NONLINEAR OPTIMIZATION SYSTEM 184
5.3.5 COMPUTER SIMULATION 185
5.3.6 DISCUSSION 188
5.4 THREE-DIMENSIONAL MYOCARDIAL TRANSMEMBRANE POTENTIAL IMAGING 
189 
5.5 DISCUSSION 192
ACKNOWLEDGEMENT 193
REFERENCES 194
6 BODYSURFACE LAPLACIAN MAPPING OF BIOELECTRIC SOURCES 
197 
6.1 INTRODUCTION 197
6.1.1 HIGH-RESOLUTION ECG AND EEG 197
6.1.2 BIOPHYSICAL BACKGROUND OF THE SURFACE LAPLACIAN 198
6.2 SURFACE LAPLACIAN ESTIMATION TECHNIQUES 200
6.2.1 LOCAL LAPLACIAN ESTIMATES 200
6.2.2 GLOBAL LAPLACIAN ESTIMATES 202
6.2.2.1 Spline interpolation of the surface geometry 
202 
6.2.2.2 Spline interpolation of the surface potential distribution 
203 
6.2.2.3 Determination of the spline parameters 
203 
6.2.3 SURFACE LAPLACIAN BASED INVERSE PROBLEM 204
6.3 SURFACE LAPLACIAN IMAGING OF HEART ELECTRICAL ACTIVITY 
206 
6.3.1 HIGH-RESOLUTION LAPLACIAN ECG MAPPING 206
6.3.2 PERFORMANCE EVALUATION OF THE SPLINE LAPLACIAN ECG 207
6.3.2.1 Effects of noise 
207 
6.3.2.2 Effects of number of recording electrodes 
208 
6.3.2.3 Effects of regularization 
209 
6.3.2.4 Simulationin a realistic geometry heart-torso model 210
6.3.2.5 Spline Laplacian ECG mapping in Humans 211
6.3.3 SURFACE LAPLACIAN BASED EPICARDIAL INVERSE PROBLEM 213
6.4 SURFACE LAPLACIAN IMAGING OF BRAIN ELECTRICAL ACTIVITY 
214 
6.4.1 HIGH-RESOLUTION LAPLACIAN EEG MAPPING 214
6.4.2 PERFORMANCE EVALUATION OF THE SPLINE LAPLACIAN EEG 214
6.4.2.1 Effects of noise 
214 
6.4.2.2 Effects of number of recording electrodes 
215 
6.4.2.3 Effects of regularization 
216 
6.4.2.4 Simulation in a realistic geometry head model 218
6.4.2.5 Surface Laplacian imaging of visual evoked potential activity 
218 
6.4.3 SURFACE LAPLACIAN BASED CORTICAL IMAGING 220
6.5 DISCUSSION 222
ACKNOWLEDGEMENT 223
REFERENCES 223
7 NEUROMAGNETIC SOURCE RECONSTRUCTION AND INVERSE MODELING 
227 
7.1 INTRODUCTION 227
7.2 BRIEFSUMMARY OFNEUROMAGNETOMETER HARDWARE 
228 
7.3 FORWARD MODELING 229
7.3.1 DEFINITIONS 229
7.3.2 ESTIMATION OF THE SENSOR LEAD FlEW 230
7.3.3 LOW-RANK SIGNALS AND THEIR PROPERTIES 233
7.4 SPATIAL FILTER FORMULATION AND NON-ADAPTIVE SPATIAL FILTER TECHNIQUES 
235 
7.4.1 SPATIAL FILTER FORMULATION 235
7.4.2 RESOLUTION KERNEL 236
7.4.3 NON-ADAPTIVE SPATIAL FILTER 236
Minimum norm spatialfilter 236
Least-squares-based interpretation of the minimum-normmethods 
238 
7.4.4 NOISE GAIN AND WEIGHT NORMALIZATION 
239 
7.5 ADAPTIVE SPATIAL FILTER TECHNIQUES 240
7.5.1 SCALAR MINIMUM-VARIANCE-BASED BEAMFORMER TECHNIQUES 240
7.5.2 EXTENSION TO EIGENSPACE-PROJECTION BEAMFORMER 241
7.5.3 COMPARISON BETWEEN MINIMUM-VARIANCE AND EIGENSPACE BEAMFORMER TECHNIQUES 
242 
7.5.4 VECTOR-TYPE ADAPTIVE SPATIAL FILTER 244
Problem of virtual source correlation 
244 
A vector-extended minimum-variance beamformer 
244 
Vector-extended Borgiotti-Kaplan beamformer 245
Extension to eigenspace-projection vector beamformer 
246 
7.6 NUMERICAL EXPERIMENTS: RESOLUTION KERNEL COMPARISON BETWEENADAPTIVEAND NON-ADAPTIVE SPATIAL FILTERS 
246 
7.6.1 RESOLUTION KERNEL FOR THE MINIMUM-NORM SPATIAL FILTER 246
7.6.2 RESOLUTION KERNEL FOR THE MINIMUM-VARIANCE ADAPTIVE SPATIAL FILTER 
248 
7.7 NUMERICAL EXPERIMENTS: EVALUATION OF ADAPTIVE BEAMFORMER PERFORMANCE 
249 
7.7.1 DATA GENERATION AND RECONSTRUCTION CONDITION 
249 
7.7.2 RESULTS FROM MINIMUM-VARIANCE VECTOR BEAMFORMER 252
7.7.3 RESULTS FROM THE VECTOR-EXTENDED BORGIOTT/-KAPLAN BEAMFORMER 
252 
7.7.4 RESULTS FROM THE EIGENSPACE PROJECTED VECTOR-EXTENDED BORGIOTTI- KAPLAN BEAMFORMER 
252 
7.8 APPLICATION OF ADAPTIVE SPATIAL FILTER TECHNIQUE TO MEG DATA 
257 
7.8.1 APPLICATION TO AUDITORY-SOMATOSENSORY COMBINED RESPONSE 257
7.8.2 APPLICATION TO SOMATOSENSORY RESPONSE: HIGH-RESOLUTION IMAGING EXPERIMENTS 
259 
ACKNOWLEDGMENTS 260
REFERENCES 261
8 MULTIMODAL IMAGING FROM NEUROELECTROMAGNETIC AND FUNCTIONAL MAGNETIC RESONANCE RECORDINGS 
265 
8.1 INTRODUCTION 265
8.2 GENERALITIES ON FUNCTIONAL MAGNETIC RESONANCE IMAGING 
266 
8.2.1 BLOCK-DESIGN AND EVENT-RELATED fMRI 268
8.3 INVERSE TECHNIQUES 268
8.3.1 ACQUISITION OF VOLUME CONDUCTOR GEOMETRY 269
8.3.2 DIPOLELOCALIZATION TECHNIQUES 270
8.3.3 CORTICAL IMAGING 271
8.3.4 DISTRIBUTED LINEAR INVERSE ESTIMATION 273
8.4 MULTIMODAL INTEGRATION OF EEG, MEG AND FMRI DATA 275
8.4.1 VISIBLE AND INVISIBLE SOURCES 275
8.4.2 EXPERIMENTAL DESIGNAND CO-REGISTRATION ISSUES 276
8.4.2.a Experimental design 276
8.4.2.b Co-registration 
277 
8.4.3 INTEGRATION OF EEG AND MEG DATA 277
8.4.4 FUNCTIONAL HEMODYNAMIC COUPLING AND INVERSE ESTIMATION OF SOURCE ACTIVITY 
281 
8.4.4.a Multimodal integration of EEG/MEG and fMRI data with dipole localization techniques 
281 
8.4.4.b Multimodal integration of EEG/MEG and fMRI data with distributed model by using diagonal source metric 
284 
8.4.4.c Multimodal integration of EEG/MEG and fMRI data with distributed model by using full source metric 
285 
8.4.4.d Application of the multimodal EEG-fMRI integration techniques to the estimation of sources of self-paced movements 
286 
8.5 DISCUSSION 289
ACKNOWLEDGMENTS 290
REFERENCES 290
9 THE ELECTRICAL CONDUCTIVITY OF LIVING TISSUE: A PARAMETER IN THE BIOELECTRICAL INVERSE PROBLEM 
295 
9.1 INTRODUCTION 295
9.1.1 SCOPE OF THISCHAPTER 296
9.1.2 AMBIGUITY OF THE EFFECTIVE CONDUCTIVITY 297
9.1.3 MEASURING THE EFFECTIVE CONDUCTIVITY 298
9.1.4 TEMPERATURE DEPENDENCE 301
9.1.5 FREQUENCY DEPENDENCE 301
9.1.5.1 Impact of the frequency dependence on the EEG 
303 
9.2 MODELS OF HUMAN TISSUE 303
9.2.1 COMPOSITES OF HUMAN TISSUE 303
9.2.1.1 Cells 303
9.2.1.2 Volume fraction occupied by cells 305
9.2.1.3 The extracellular fluid 
305 
9.2.2 CONDUCTIVITIES OF COMPOSITES OF HUMAN TISSUE 306
9.2.2.1 Effective conductivity of a sphericalcell 
307 
9.2.2.2 Effective conductivity of a cylindrical cell 
308 
9.2.2.3 Conductivity of extracellular fluid 
309 
9.2.3 MAXWELL'S MIXTURE EQUATION 310
9.2.3.1 A dilute solution of spheres 
311 
9.2.3.1.a. Blood 313
9.2.4 ARCHIE'S LAW 314
9.2.4.1 Ellipsoidal particles with the sameorientation 
315 
9.2.4.1.a. Fat 315
9.2.4.1.b. Skeletal muscles 315
9.2.4.1.c. Cardiac tissue 316
9.2.4.2 Randomly orientated ellipsoidal particles 
317 
9.2.4.2.a. Blood 318
9.2.4.3 Cells of different shape 
319 
9.2.4.3.a. Gray matter 
319 
9.2.4.4 Clustered cells 320
9.2.4.4.a. Blood 320
9.2.4.4.b. Liver 320
9.3 LAYERED STRUCTURES 321
9.3.1 THE SCALP 321
9.3.2 THE SKULL 322
9.3.3 A LAYER OF SKELETAL MUSCLE 324
9.4 COMPARTMENTS 325
9.4.1 USING IMPLANTED ELECTRODES 325
9.4.2 COMBINING MEASUREMENTS OF THE POTENTIAL AND THE MAGNETIC FlEW 
326 
9.4.3 ESTIMATION OF THE EQUIVALENT CONDUCTIVITY USING IMPEDANCE TOMOGRAPHY 
326 
9.5 UPPER AND LOWER BOUNDS 327
9.5.1 WHITE MATTER 328
9.5.2 THE FETUS 328
9.6 DISCUSSION 330
REFERENCES 330
INDEX 335