Contents

	
SYMBOLS AND UNITS, xv
ABBREVIATIONS, xxi
PHYSICAL CONSTANTS, xxiii

1. Introduction, 3
	1.1	The Concept of Bioelectromagnetism, 3
	1.2	Subdivisions of Bioelectromagnetism, 4
		1.2.1	Division on a theoretical basis, 4
		1.2.2	Division on an anatomical basis, 7
		1.2.3	Organization of this textbook, 7
	1.3	Importance of Bioelectromagnetism, 10
	1.4	Short History of Bioelectromagnetism, 11
		1.4.1	The first written documents and first experiments in bioelectromagnetism, 11
		1.4.2	Electric and magnetic stimulation, 12
		1.4.3	Detection of bioelectric activity, 16
		1.4.4	Modern electrophysiological studies of neural cells, 20
		1.4.5	Bioelectromagnetism, 21
		1.4.6	Theoretical contributions to bioelectromagnetism, 23
		1.4.7	Summary of the history of bioelectromagnetism, 24
	1.5	Nobel Prizes in Bioelectromagnetism, 25


I   ANATOMICAL AND PHYSIOLOGICAL BASIS OF BIOELECTROMAGNETISM
2. Nerve and Muscle Cells, 33
	2.1	Introduction, 33
	2.2	Nerve Cell, 33
		2.2.1	The main parts of the nerve cell, 33
		2.2.2	The cell membrane, 34
		2.2.3	The synapse, 36
	2.3	Muscle Cell, 36
	2.4	Bioelectric Function of the Nerve Cell, 37
	2.5	Excitability of Nerve Cell, 38
	2.6	The Generation of the Activation, 39
	2.7	Concepts Associated wth the Activation Process, 39
	2.8	Conduction of the Nerve Impulse in an Axon, 42

3. Subthreshold Membrane Phenomena, 44
	3.1	Introduction, 44
	3.2	Nernst Equation, 45
		3.2.1	Electric potential and electric field, 45
		3.2.2	Diffusion, 46
		3.2.3	Nernst-Planck equation, 46
		3.2.4	Nernst potential, 47
	3.3	Origin of the Resting Voltage, 50
	3.4	Membrane with Multi-ion Permeability, 51
		3.4.1	Donnan equilibrium, 51
		3.4.2	The value of the resting-voltage Goldman-Hodgkin-Katz equation, 51
		3.4.3	The reversal voltage, 54
	3.5	Ion Flow Through the Membrane, 54
		3.5.1	Factors affecting ion transport through the membrane, 54
		3.5.2	Membrane ion flow in a cat motoneuron, 54
		3.5.3	Na-K pump, 55
		3.5.4	Graphical illustration of the membrane ion flow, 56
	3.6	Cable Equation of the Axon, 56
		3.6.1	Cable model of the axon, 56
		3.6.2	The steady-state response, 58
		3.6.3	Stimulation with a step-current impulse, 59
	3.7	Strength-Duration Relation, 62

4. Active Behavior of the Membrane, 66 
	4.1	Introduction, 66
	4.2	Voltage-clamp Method, 66
		4.2.1	Goal of the voltage-clamp measurement, 66
		4.2.2	Space clamp, 68
		4.2.3	Voltage clamp, 69
	4.3	Examples of Results Obtained with the Voltage-Clamp Method, 70
		4.3.1	Voltage clamp to sodium Nernst voltage, 70
		4.3.2	Altering the ion concentrations, 71
		4.3.3	Blocking of ionic channels with pharmaceuticals, 73
	4.4	Hodgkin-Huxley Membrane Model, 74
		4.4.1	Introduction, 74
		4.4.2	Total membrane current and its components, 74
		4.4.3	Potassium conductance, 77
		4.4.4	Sodium conductance, 81
		4.4.5	Hodgkin-Huxley equations, 85
		4.4.6	Propagating nerve impulse, 85
		4.4.7	Properties of the Hodgkin-Huxley model, 89
		4.4.8	The quality of the Hodgkin-Huxley model, 92
	4.5	Patch-clamp Method, 93
		4.5.1	Introduction, 93
		4.5.2	Patch clamp measurement techniques, 94
		4.5.3	Applications of the patch-clamp method, 96
	4.6	Modern Understanding of the Ionic Channels, 97
		4.6.1	Introduction, 97
		4.6.2	Single-channel behavior, 99
		4.6.3	The ionic channel, 99
		4.6.4	Channel structure: Biophysical studies, 99
		4.6.5	Channel structure: Studies in molecular genetics, 102
		4.6.6	Channel structure: Imaging methods, 103
		4.6.7	Ionic conductance based on single-channel conductance, 103

5. Synapse, Reseptor Cells, and Brain, 106
	5.1	Introduction, 106
	5.2	Synapses, 107
		5.2.1	Structure and function of the synapse, 107
		5.2.2	Excitatory and inhibitory synapses, 108
		5.2.3	Reflex arc, 109
		5.2.4	Electric model of the synapse, 109
	5.3	Receptor Cells, 111
		5.3.1	Introduction, 111
		5.3.2	Various types of receptor cells, 111
		5.3.3	The Pacinian corpuscle, 113
	5.4	Anatomy and Physiology of the Brain, 113
		5.4.1	Introduction, 113
		5.4.2	Brain anatomy, 114
		5.4.3	Brain function, 116
	5.5	Cranial Nerves, 117

6. The Heart, 
	6.1	Anatomy and Physiology of the Heart, 119
		6.1.1	Location of the heart, 119
		6.1.2	The anatomy of the heart, 119
	6.2	Electric Activation of the Heart, 121
		6.2.1	Cardiac muscle cell, 121
		6.2.2	The conduction system of the heart, 122
	6.3	The Genesis of the Electrocardiogram, 124
		6.3.1	Activation currents in cardiac tissue, 124
		6.3.2	Depolarization wave, 126
		6.3.3	Repolarization wave, 128

II   BIOELECTRIC SOURCES AND CONDUCTORS AND THEIR MODELING 
7. Volume Source and Volume Conductor, 133
	7.1	The Concepts of Volume Source and Volume Conductor, 133
	7.2	Bioelectric Source and its Electric Field, 134
		7.2.1	Definition of the preconditions, 134
		7.2.2	Volume source in a homogeneous volume conductor, 134
		7.2.3	Volume source in an inhomogeneous volume conductor, 135
		7.2.4	Quasistatic conditions, 136
	7.3	The Concept of Modeling, 136
		7.3.1	The purpose of modeling, 136
		7.3.2	Basic models of the volume source, 137
		7.3.3	Basic models of the volume conductor, 139
	7.4	The Humand Body as a Volume Conductor, 140
		7.4.1	Tissue resistivities, 140
		7.4.2	Modeling the head, 141
		7.4.3	Modeling the thorax, 142
	7.5	Forward and Inverse Problem, 143
		7.5.1	Forward problem, 143
		7.5.2	Inverse problem, 143
		7.5.3	Solvability of the inverse problem, 143
		7.5.4	Possible approaches to the solution of the inverse problem, 144
		7.5.5	Summary, 146

8. Source-field Models, 148
	8.1	Introduction, 148
	8.2	Source Models, 148
		8.2.1	Monopole, 148
		8.2.2	Dipole, 149
		8.2.3	Single isolated fiber: transmembrane current source, 151
		8.2.4	Discussion of transmembrane current source, 152
	8.3	Equivalent Volume Source Density, 152
		8.3.1	Equivalent monopole density, 152
		8.3.2	Equivalent dipole density, 153
		8.3.3	Lumped equivalent sources: Tripole model, 153
		8.3.4	Mathematical basis for double-layer source (uniform bundle), 153
	8.4	Rigorous Formulation, 155
		8.4.1	Field of a single cell of arbitrary shape, 155
		8.4.2	Field of an isolated cylindrical fiber, 156
	8.5	Mathematical Basis for Macroscopic Volume Source Density (Flow Source Density), 156 
	          and Impressed Current Density, 158
	8.6	Summary of the Source-field Models, 158

	
9. Bidomain Model of Multicellular Volume Conductors, 159
	9.1	Introduction, 159
	9.2	Cardiac Muscle Considered as a Continuum, 159
	9.3	Mathematical Description of the Bidomain and Anisotropy, 161
	9.4	One-Dimensional Cable: A One-Dimensional Bidomain, 162
	9.5	Solution for Point-Current Source in a Three-Dimensional, Isotropic Bidomain, 164
	9.6	Four-Electrode Impedance Method Applied to an Isotropic Bidomain, 167

	
10. Electronic Neuron Models, 169
	10.1 Introduction, 169
		10.1.1	Electronic modeling of excitable tissue, 169
		10.1.2	Neurocomputers, 170
	10.2 Classification of Neuron Models, 171
	10.3 Models Describing the Function of the Membrane, 171
		10.3.1	The Lewis membrane model, 171
		10.3.2	The Roy membrane model, 173
	10.4 Models Describing the Cell as an Independent Unit, 174
		10.4.1	The Lewis neuron model, 174
		10.4.2	The Harmon neuron model, 176
	10.5 A Model Describing the Propagation of Action Pulse in Axon, 179
	10.6 Integrated Circuit Realizations, 180


III   THEORETICAL METHODS IN BIOELECTROMAGNETISM
11. Theoretical Methods for Analyzing Volume Sources and Volume Conductors, 185
	11.1 Introduction, 185
	11.2 Solid-Angle Theorem, 185
		11.2.1	Inhomogeneous double layer, 185
		11.2.2	Uniform double layer, 187
	11.3 Miller-Geselowitz Model, 188
	11.4 Lead Vector, 190
		11.4.1	Definition of the lead vector, 190
		11.4.2	Extending the concept of lead vector, 191
		11.4.3	Example of lead vector applications: Einthoven, Frank, and Burger triangles, 192
	11.5 Image Surface, 195
		11.5.1	The definition of the image surface, 195
		11.5.2	Points located inside the volume conductor, 198
		11.5.3	Points located inside the image surface, 198
		11.5.4	Application of the image surface to the synthesis of leads, 199
		11.5.5	Image surface of homogeneous human torso, 200
		11.5.6	Recent image-surface studies, 200
	11.6 Lead Field, 201
		11.6.1	Concepts used in connection with lead fields, 201
		11.6.2	Definition of the lead field, 202
		11.6.3	Reciprocity theorem: the historical approach, 206
		11.6.4	Lead field theory: the historical approach, 208
		11.6.5	Field-theoretic proof of the reciprocity theorem, 210
		11.6.6	Summary of the lead field theory equations, 212
		11.6.7	Ideal lead field of a lead detecting the equivalent electric dipole of a volume source, 214
		11.6.8	Application of lead field theory to the Einthoven limb leads, 215
		11.6.9	Synthesization of the ideal lead field for the detection of the electric dipole moment of a volume source, 216
		11.6.10	Special properties of electric lead fields, 219
		11.6.11	Relationship between the image surface and the lead field, 219
	11.7 Gabor-Nelson Theorem, 221
		11.7.1	Determination of the dipole moment, 221
		11.7.2 	The location of the equivalent dipole, 223
	11.8 Summary of the Theoretical Methods for Analyzing Volume Sources and Volume Conductors, 224

12. Theory of Biomagnetic Measurements, 227
	12.1 Biomagnetic Field, 227
	12.2 Nature of the Biomagnetic Sources, 228
	12.3 Reciprocity Theorem for Magnetic Fields, 230
		12.3.1	The form of the magnetic lead field, 230
		12.3.2	The source of the magnetic field, 233
		12.3.3	Summary of the lead field theoretical equations for electric and magnetic measurements, 234
	12.4 The Magnetic Dipole Moment of a Volume Source, 235
	12.5 Ideal Lead Field of a Lead Detecting the Equivalent Magnetic Dipole of a Volume Source, 236
	12.6 Synthetization of the Ideal Lead Field for the Detection of the Magnetic Dipole Moment of a Volume Source, 237
	12.7 Comparison of the Lead Fields of Ideal Leads for Detecting the Electric and the Magnetic Dipole Moments of a Volume Source, 240
		12.7.1	The bipolar lead system for detecting the electric dipole moment, 240
		12.7.2	The bipolar lead system for detecting the magnetic dipole moment, 240
	12.8 The Radial and Tangential Sensitivities of the Lead Systems Detecting the Electric and Magnetic Dipole Moments of a Volume Source, 242
		12.8.1	Sensitivity of the electric lead, 242
		12.8.2	Sensitivity of the magnetic lead, 243
	12.9 Special Properties of the Magnetic Lead Fields, 243
	12.10 The Independence of Bioelectric and Biomagnetic Fields and Measurements, 244
		12.10.1	Independence of flow and vortex sources, 244
		12.10.2	Lead field theoretic explanation of the independence of bioelectric and biomagnetic fields and measurements, 246
	12.11 Sensitivity Distribution of Basic Magnetic Leads, 247
		12.11.1	The equations for calculating the sensitivity distribution of basic magnetic leads, 247
		12.11.2	Lead field current density of a unipolar lead of a single-coil magnetometer, 251
		12.11.3	The effect of the distal coil, 252
		12.11.4	Lead field current density of a bipolar lead, 253

IV   ELECTRIC AND MAGNETIC MEASUREMENT OF THE ELECTRIC ACTIVITY OF NEURAL TISSUE
13 Electroencephalography ,257
	13.1 Introduction, 257
	13.2 The brain as a Bioelectric Generator, 257
	13.3 EEG Lead Systems, 258
	13.4 Sensitivity Distribution of EEG Electrodes, 260
	13.5 The Behavior of the EEG Signal, 263
	13.6 The Basic Principles of EEG Diagnosis, 264
	
14. Magnetoencephalography, 265
	14.1 The Brain as a Biomagnetic Generator, 265
	14.2 Sensitivity Distribution of MEG-Leads, 266
		14.2.1	Sensitivity calculation method, 266
		14.2.2	Single-coil magnetometer, 267
		14.2.3	Planar gradiometer, 268
	14.3 Comparison of the EEG and MEG Half-Sensitivity Volumes, 270
	14.4 Summary, 272

V   ELECTRIC AND MAGNETIC MEASUREMENT OF THE ELECTRIC ACTIVITY OF THE HEART
15. 12-Lead ECG System, 277
	15.1 Limb Leads, 277
	15.2 ECG Signal, 278
		15.2.1	The signal produced by the activation front, 278
		15.2.2	Formation of the ECG signal, 280
	15.3 Wilson Central Terminal, 284
	15.4 Goldberger Augmented Leads, 285
	15.5 Precordial Leads, 186
	15.6 Modifications of the 12-Lead System, 286
	15.7 The Information Content of the 12-Lead System, 288

16. Vectorcardiographic Lead Systems, 290
	16.1 Introduction, 290
	16.2 Uncorrected Vectorcardiographic Lead Systems, 292
		16.2.1	Monocardiogram by Mann, 292
		16.2.2	Lead systems based on rectangular body axes, 292
		16.2.3	Akulinichev VCG lead systems, 293
	16.3 Corrected Vectorcardiographic Lead Systems, 296
		16.3.1	Frank lead system, 296
		16.3.2	McFee-Parungao lead system, 299
		16.3.3	SVEC III lead system, 300
		16.3.4	Fischmann-Barber-Weiss lead system, 302
		16.3.5	Nelson lead system, 302
	16.4 Discussion of Vectorcardiographic Leads, 303
		16.4.1	The interchangeability of vectorcardiographic systems, 303
		16.4.2	Properties of various vectorcardiographic lead systems, 304

17. Other ECG Lead Systems, 307
	17.1 Moving Dipole, 307
	17.2 Multiple Dipoles, 307
	17.3 Multipole, 308
	17.4 Summary of theECG Lead Systems, 309

18. Distortion Factors in the ECG, 313
	18.1 Introduction, 313
	18.2 Effect of the Inhomogeneity of the Thorax, 313
	18.3 Brody Effect, 314
		18.3.1	Description of the Brody effect, 314
		18.3.2	Effect of the ventricular volume,314
		18.3.3	Effect of the blood resistivity, 316
		18.3.4	Integrated effects (model studies), 316
	18.4 Effect of Respiration, 316
	18.5 Effect of Electrode Location, 318

19. The Basis of ECG Diagnosis, 320
	19.1 Principle of the ECG Diagnosis, 320
		19.1.1	On the possible solutions to the cardiac inverse problem, 320
		19.1.2	Bioelectric principles in ECG diagnosis, 321
	19.2 Applications of ECG Diagnosis, 321
	19.3 Determination of the Electric Axis of the Heart, 322
	19.4 Cardiac Rhythm Diagnosis, 323
		19.4.1	Differentiating the P, QRS. and T waves, 323
		19.4.2	Supraventricular rhythms, 323
		19.4.3	Ventricular arrhythmias, 326
	19.5 Disorders in the Activation Sequence, 328
		19.5.1	Atrioventricular conduction variations, 328
		19.5.2	Bundle-branch block, 328
		19.5.3	Wolff-Parkinson-White syndrome, 331
	19.6 Increase in Wall Thickness or Size of Atria and Ventricles, 332
		19.6.1	Definition, 332
		19.6.2	Atrial hypertrophy, 332
		19.6.3	Ventricular hypertrophy, 334
	19.7 Myocardial Ischemia and Infarction, 334

20. Magnetocardiography, 336
	20.1 Introduction, 336
	20.2 Basic Methods in Magnetocardiography, 336
		20.2.1	Measurement of the equivalent magnetic dipole, 336
		20.2.2	The magnetic field-mapping method, 337
		20.2.3	Other methods of magnetocardiography, 338
	20.3 Methods for Detecting the Magnetic Heart Vector, 339
		20.3.1	The source and conductor models and the basic form of the lead system for measuring the magnetic dipole, 339
		20.3.2	Baule-McFee lead system, 339
		20.3.3	XYZ lead system, 341
		20.3.4	ABC lead system, 342
		20.3.5	Unipositional lead system, 342
	20.4 Sensitivity Distribution of Basic MCG Leads, 346
		20.4.1	Heart- and thorax models and the magnetometer, 346
		20.4.2	Unipolar measurement, 346
		20.4.3	Bipolar measurement, 348
	20.5 Generation of the MCG Signal from the Electric Activation of the Heart, 348
	20.6 ECG-MCG Relationship, 353
	20.7 Clinical Application of Magneocardiography, 354
		20.7.1	Advantages of magnetocardiography, 354
		20.7.2	Disadvantages of magnetocardiography, 356
		20.7.3	Clinical application, 356
		20.7.4	Basis for the increase in diagnostic performance by biomagnetic measurement, 358
		20.7.5	General conclusions on magnetocardiography, 358

VI   ELECTRIC AND MAGNETIC STIMULATION OF NEURAL TISSUE
21. Functional Electric Stimulation, 363
	21.1 Introduction, 363
	21.2 Simulation of Excitation of a Myelinated Fiber, 363
	21.3 Stimulation of an Unmyelinated Axon, 368
	21.4 Muscle Recruitment, 370
	21.5 Electrode-Tissue Interface, 372
	21.6 Electrode Materials and Shapes, 373

22. Magnetic Stimulation of Neural Tissue, 375
	22.1 Introduction, 375
	22.2 The Design of Stimulator Coils, 376
	22.3 Current Distribution in Magnetic Stimulation, 377
	22.4 Stimulus Pulse, 379
	22.5 Activation of Excitable Tissue by Time-Varying Magnetic Fields, 379
	22.6 Application Areas of Magnetic Stimulation of Neural Tissue, 380

VII   ELECTRIC AND MAGNETIC STIMULATION OF THE HEART
23. Cardiac Pacing, 385
	23.1 Stimulation of Cardiac Muscle, 385
	23.2 Indications for Cardiac Pacing, 385
	23.3 Cardiac Pacemaker, 386
		23.3.1	Pacemaker principles, 386
		23.3.2	Control of impulses, 386
		23.3.3	Dual chamber multiprogrammable, 387
		23.3.4	Rate modulation, 388
		23.3.5	Anti-tachycardia/fibrillation, 388
	23.4 Site of Stimulation, 389
	23.5 Excitation Parameters and Configuration, 389
	23.6 Implantable Energy Sources, 391
	23.7 Electrodes, 391
	23.8 Magnetic Stimulation of Cardiac Muscle

24. Cardiac Defibrillation, 393
	24.1 Introduction, 393
	24.2 Mechanism of Defibrillation, 393
		24.2.1	Reentry, 393
		24.2.2	Reentry with and without anatomic obstacles, 395
	24.3 Theories of Defibrillation, 396
		24.3.1	Introduction, 396
		24.3.2	Critical mass hypothesis, 397
		24.3.3	One-dimensional activation/defibrillation model, 398
	24.4 Defibrillation Devices, 400

VIII   MEASUREMENT OF THE INTRINSIC ELECTRIC PROPERTIES OF BIOLOGICAL TISSUES
25. Impedance Pletysmography, 405
	25.1 Introduction, 405
	25.2 Bioelectric Basis of Impedance Plethysmograpy, 405
		25.2.1	Relationship between the principles of impedance measurement and bioelectric signal measurement, 405
		25.2.2	Tissue impedance, 407
	25.3 Impedance Cardiography, 408
		25.3.1 	Measurement of the impedance of the thorax, 408
		25.3.2 	Simplified model of the impedance of the thorax, 409
		25.3.3 	Determining changes in blood volume in the thorax, 410
		25.3.4	Determining the stroke volume, 410
		25.3.5	Discussion of the stroke volume calculation method, 411
	25.4 The Origin of Impedance Signal in Impedance Cardiography, 412
		25.4.1	Model studies, 412
		25.4.2	Animal and human studies, 412
		25.4.3	Determining the systolic time intervals from the impedance, 413
		25.4.4	The effect of the electrodes, 414
		25.4.5	Accuracy of the impedance cardiography, 414
	25.5 Other Applications of Impedance Plethysmography, 416
		25.5.1	Peripheral blood flow, 416
		25.5.2	Cerebral blood flow, 416
		25.5.3	Intrathoracic fluid volume, 417
		25.5.4	Determination of body composition, 417
		25.5.5	Other applications, 417
	25.6 Discussion, 417

26. Impedance Tomography, 420
	26.1 Introduction, 420
	26.2 Impedance Measurement Methods, 421
		26.2.1	Electric measurement of the impedance, 421
		26.2.2	Electromagnetic measurement of the electric impedance, 424
	26.3 Image Reconstruction, 426

27 The Electrodermal Response, 428
	27.1 Introduction, 428
	27.2 Physiology of the Skin, 428
	27.3 Electrodermal Measures, 430
	27.4 Measurement Sites and Characteristic Signals, 430
	27.5 Theory of EDR, 432
	27.6 Applications, 434

IX   OTHER BIOELECTROMAGNETIC PHENOMENA
28. The Electric Signals Originating in the Eye, 437
	28.1 Introduction, 437
	28.2 The Anatomy and Physiology of the Eye and its Neural Pathways, 437
		28.2.1	The major components of the eye, 437
		28.2.2	The retina, 438
	28.3 Electro-Oculogram, 440
		28.3.1	Introduction, 440
		28.3.2	Saccadic response, 440
		28.3.3	Nystagmography, 441
	28.4 Electroretinogram, 442
		28.4.1	Introduction, 442
		28.4.2	The volume conductor influence on the ERG, 444
		28.4.3	Ragnar Granit contribution, 446

APPENDIXES
A.   Consistent System of Rectangular and Spherical Coordinates for Electrocardiology and Magnetocardiology, 449
	A.1 Introduction, 449
	A.2 Requirements for a Consistent System of Coordinates, 450
	A.3 Alignment of the Coordinate System with the Body, 450
	A.4 Consistent Spherical Coordinate System, 451
		A.4.1	 Mathematically consistent spherical polar coordinate system, 451
		A.4.2	 Illustrative spherical coordinate system, 452
	A.5 Comparison of the Consistent Coordinate System and the AHA-System, 452
	A.6 Rectangular ABC-Coordinates, 453

B.   The Application of Maxwell's Equations in Bioelectromagnetism, 455
	B.1 Introduction, 455
	B.2 Maxwell's Equations Under Free Space Conditions, 455
	B.3 Maxwell's Equations for Finite Conducting Media, 456
	B.4 Simplification of Maxwell's Equations in Physiological Preparations, 457
		B.4.1	 Frequency limit, 457
		B.4.2	 Size limitation, 457
		B.4.3	 Volume conductor impedance, 457
	B.5 Magnetic Vector Potential and Electric Scalar Potential in the Region Outside the Sources, 458
	B.6 Stimulation with Electric and Magnetic Fields, 460
		B.6.1	Stimulation with electric field, 460
		B.6.2	Stimulation with magnetic field, 460
	B.7 Simplified Maxwell's Equations in Physiological Preparations in the Region Outside the Sources, 461
	
NAME INDEX, 463

SUBJECT INDEX, 471