There has been a continuous controversy whether the
presence of electromagnetic fields pertaining to the
non-ionizing part of the spectrum in the environment
could be associated with health risk. The biological
effects of electromagnetic fields are appreciably de-
pendent on actual intensity and frequency, therefore a
rough classification is often related to low frequency
(LF) and high frequency (HF) exposures. Consequently,
an assessment of distribution of the fields induced in bi-
ological bodies is crucial to study the related biological
effects.
The present book aims to provide necessary infor-
mation regarding computational models in electromag-
netic and thermal dosimetry.
Chapter 1 provides general considerations of human
exposure to electromagnetic fields, while some basics of
computational electromagnetics are given in Chapter 2.
Chapter 3 deals with theoretical and experimental
procedures on incident field dosimetry covering LF and
HF electromagnetic interference (EMI) sources.
Simplified (canonical) models of the human body
are presented in Chapter 4.
The central part of the book is given in Chapters 5
and 6, in which realistic models of the human body at
LF and HF exposures based on Finite Element Method
(FEM) and Boundary Element method (BEM), hybrid
FEM/BEM and Method of Moments (MoM) are given.
Furthermore, biomedical applications of electromag-
netic fields are given in Chapter 7. Therefore, in addition
to unwanted human exposure to LF and HF sources,
of particular interest are also some biomedical applica-
tions of electromagnetic fields.
Finally, some useful mathematical details are avail-
able in Appendices A to F.
Rigorous theoretical background accompanied with
mathematical details of various formulations and re-
lated solution methods being used throughout the book
are presented.
The book includes many illustrative computational
examples arising from realistic exposure scenarios and
a reference list at the end of each chapter.
The intention of the present book is to provide not
only useful description of our own expertise concerning
bioelectromagnetics, but also to give updated informa-
tion on some of the latest advances in this area.
We hope that this book will be useful material for
undergraduate, graduate and postdoc students, as well
as engineers in the industry, to learn about advanced
computational models in electromagnetic and thermal
dosimetry and to tackle some problems arising from re-
alistic exposure scenarios.
We also think that the book could be used for var-
ious university courses involving bioelectromagnetics
and computational dosimetry.
The book requires a general background in electrical
engineering, involving some topics in basic electromag-
netics. Fundamental concepts in bioelectromagnetics as
well as numerical modeling principles are given in this
book. Thus, the book is convenient for students, special-
ists, researchers and engineers.
To sum up, we are glad we have managed to compose
this material stemming from more than two decades
of rather intensive research in bioelectromagnetics. Of
course, there are many rather challenging problems we
would like to tackle in the future, such as stochastic bio-
electromagnetics.
Author(s): Dragan Poljak, Mario Cvetkovic
Publisher: Academic Press
Year: 2019
Language: English
Pages: 269
Cover......Page 1
Human Interaction
with Electromagnetic
Fields:
Computational Models in
Dosimetry......Page 4
Copyright
......Page 5
Dedication
......Page 6
About the authors......Page 7
Preface......Page 8
1.1 General Considerations......Page 9
1.1.1.2 Time-Varying Fields......Page 10
1.1.3 Biomedical Applications of Electromagnetics Fields......Page 11
1.2.1.1 Coupling to Static Magnetic Fields......Page 12
1.2.2.3 Absorption of Energy From Electromagnetic Radiation......Page 13
1.2.3.1 Biological Effects of Static Magnetic Fields......Page 14
1.2.3.2 Biological Effects of LF Fields......Page 15
1.2.3.3 Biological Effects of HF Radiation......Page 16
1.3.1 EMF Standards......Page 17
1.3.2 ICNIRP Guidelines......Page 20
1.3.3 IEEE Standards......Page 23
1.3.4 Directive 2013/35/EU......Page 25
1.4.1 Exposure to LF Fields......Page 26
References......Page 27
2.1.2 Maxwell's Equations - Differential and Integral Form......Page 29
2.1.4 Conservation of Electromagnetic Energy - Poynting Theorem......Page 31
2.1.5 Electromagnetic Wave Equations......Page 32
2.1.6 Electromagnetic Potentials......Page 33
2.1.7 Plane Wave Propagation......Page 34
2.1.8 Radiation and Hertz Dipole......Page 35
2.1.9.1 Radiation Power Density......Page 36
2.1.9.4 Input Impedance, Radiation and Loss Resistance......Page 37
2.1.10 Dipole Antennas......Page 38
2.1.11 Pocklington Integro-Differential Equation for a Straight Thin Wire......Page 39
2.2 Introduction to Numerical Methods in Electromagnetics......Page 41
2.2.1 Weighted Residual Approach......Page 42
2.2.1.1 Fundamental Lemma of Variational Calculus......Page 43
2.2.2 The Finite Element Method (FEM)......Page 44
2.2.2.2 One-Dimensional FEM......Page 45
2.2.2.4 Computational Example: 1D Problem......Page 47
2.2.2.5 Two-Dimensional FEM......Page 48
2.2.2.6 The Weak Formulation for Generalized Helmholtz Equation......Page 50
2.2.2.7 Computation of Fluxes on the Domain Boundary......Page 51
2.2.2.9 Three-Dimensional Elements......Page 52
2.2.3.1 Integral Equation Formulation......Page 53
2.2.3.3 Constant Boundary Elements......Page 55
2.2.3.4 Linear and Quadratic Elements......Page 56
2.2.4 Numerical Solution of Integral Equations Over Unknown Sources......Page 57
References......Page 59
3.1.1 Fields Generated by Power Lines......Page 61
3.1.1.1 The Electric Field......Page 62
3.1.1.2 The Magnetic Field......Page 65
3.1.2.1 The Electric Field......Page 67
3.1.2.2 The Magnetic Field......Page 70
3.1.3 Assessment of Circular Current Density Induced in the Body......Page 71
3.1.4.1 Measurement of LF Electric Fields......Page 73
3.1.4.2 Measurement of LF Magnetic Fields......Page 74
3.1.4.3 Comparison of Calculated and Experimental Results......Page 75
3.2 Assessment of High Frequency Electromagnetic Fields......Page 77
3.2.1 Fields Radiated by Power Line Communication (PLC) Systems......Page 78
3.2.2 Fields in the Vicinity of RFID Loop Antennas......Page 79
3.2.3 Radiation From Base Station Antennas......Page 80
3.2.3.1 Near Field Analysis: Assessment of Power Density......Page 83
3.2.3.2 Far Field Analysis: Calculation of Power Density and Electric Field......Page 84
3.2.3.3 Some Computational Examples......Page 85
3.2.3.4 Some Measured Results......Page 86
3.2.3.5 Far Field Analysis: Presence of a Lossy Ground and Layered Medium......Page 87
3.2.3.6 Accurate Numerical Modeling of Radio Base Station Antenna Systems......Page 93
References......Page 96
4.1 Parallelepiped Model of the Human Body......Page 98
4.3.1 Pocklington Equation Formulation for LF Exposures......Page 99
4.3.2 Numerical Solution of the Pocklington Equation......Page 100
4.3.3 Analytical Modeling of the Human Body - Hallén Equation for LF and HF Exposures......Page 102
4.3.5 Numerical Solution Via Method of Moments (MoM)......Page 104
4.3.6.1 LF Exposures......Page 105
4.3.6.2 HF Exposures......Page 108
4.4.1 Time Domain Formulation......Page 110
4.4.2 Numerical Solution of the Time Domain Hallén Integral Equation......Page 111
4.4.3.2 Root-Mean-Square Value of the Transient Current......Page 114
4.4.3.4 Total Absorbed Energy......Page 115
4.4.3.5 The Specific Absorption......Page 116
4.4.4 Numerical Results......Page 117
4.5.1 Theoretical Background......Page 119
4.5.2 Solution of the Transmission Line Equations in the Frequency Domain......Page 121
4.5.3.1 Single Cylinder Model......Page 123
4.5.3.3 Human Exposure to High Frequency (HF) Radiation......Page 124
References......Page 128
5.1 Parameters for Quantifying LF Exposures......Page 130
5.2 Human Head Exposed to Electrostatic Field......Page 131
5.2.1 Finite Element Solution......Page 132
5.2.2 Boundary Element Solution......Page 133
5.2.3 Computational Examples......Page 134
5.3 Whole Body Exposed to LF Fields......Page 137
5.3.1 Quasi-Static Formulation......Page 138
5.3.2 Multi-Domain Model of the Human Body......Page 139
5.3.3 Realistic Model of the Human Body - No Arms......Page 141
5.3.4 Realistic Model of the Human Body - Arms Included......Page 142
5.3.5 Pregnant Woman/Fetus Exposed to ELF Electric Field......Page 144
References......Page 148
6.1.1 Surface Integral Equation Formulation......Page 151
6.1.1.1 Numerical Solution Using Method of Moments......Page 153
6.1.2 Tensor Volume Integral Equation......Page 154
6.1.3 Hybrid Finite Element/Boundary Element Approach......Page 156
6.1.4.1 Model of the Human Eye......Page 158
6.1.4.2 Human Eye Exposed to Plane Wave......Page 159
6.1.4.3 Compound Versus Extracted Eye Models......Page 160
6.1.5 The Brain Exposure......Page 163
6.1.5.2 Human Brain Exposed to Plane Wave......Page 164
6.1.5.3 Child Brain Exposed to Plane Wave......Page 167
6.1.6 The Human Head Exposure......Page 174
6.1.6.1 Brain Dosimetry Comparison......Page 176
6.1.7 The Whole Body Exposure......Page 178
6.2 Thermal Dosimetry Procedures......Page 183
6.2.1.2 Heat Conduction Equation......Page 184
6.2.1.4 Pennes' Equation......Page 186
6.2.2 Finite Element Solution......Page 187
6.2.3 Boundary Element Solution......Page 188
6.2.4.1 Thermal Dosimetry for the Homogeneous Human Brain Model......Page 190
6.2.4.2 Temperature Increase in the Human Eye......Page 195
6.2.4.3 Temperature Rise in Compound and Extracted Eye Models......Page 196
6.2.4.4 Thermal Response of the Human Body......Page 199
References......Page 201
7.1.1 Modeling TMS......Page 205
7.1.1.1 Surface Integral Equation Based Formulation for TMS......Page 206
7.1.2.1 TMS for Pediatric Population......Page 208
7.1.2.2 Brain Tissue Parameters......Page 209
7.1.3.1 Electric Field Due to Various TMS Coils......Page 210
7.1.3.2 Current Density......Page 211
7.1.3.3 Magnetic Flux Density......Page 212
7.1.3.4 Pediatric Models Using Adult Brain Parameters......Page 215
7.1.3.5 Pediatric Models Using Age-Dependent Brain Parameters......Page 216
7.2.1 Nerve Fiber Models......Page 219
7.2.1.1 Nerve Fiber Antenna Model......Page 221
7.2.2 Passive Nerve Fiber......Page 222
7.2.3 Active Nerve Fiber......Page 223
7.2.4.1 Numerical Results for Passive Nerve Fiber......Page 224
7.2.4.2 Numerical Results for Active Nerve Fiber......Page 225
7.3 Laser Radiation......Page 226
7.3.1 Laser-Eye Interaction......Page 227
7.3.2 Tissue Optical Parameters......Page 228
7.3.3 Model of the Human Eye......Page 229
7.3.4 Laser Source Modeling......Page 230
7.3.5 Heat Transfer in the Human Eye......Page 231
7.3.6 Numerical Solution of the Heat Transfer......Page 233
7.3.7.1 Steady-State Temperature Distribution......Page 234
7.3.7.2 Nd:YAG 1064 nm Laser......Page 235
7.3.7.3 Ho:YAG 2090 nm Laser......Page 236
7.3.7.4 694.3 nm Ruby Laser......Page 238
7.3.7.6 Nd:YLF 1053 nm Laser......Page 239
References......Page 240
APPENDIX
A The Generalized Symmetric Form of Maxwell's Equations......Page 246
APPENDIX
B A Note on Integral Equations......Page 248
C.1 Scalar Green's Function......Page 250
C.2 Scalar Helmholtz Equation Solution......Page 251
References......Page 252
D.2 On the Use of Green's Second Identity......Page 253
D.3 Region Around Singularity......Page 255
D.6 Application of the Equivalence Principle......Page 256
References......Page 258
E.2 Vector Identities......Page 259
E.4 Recursive Formulas Including Position Vector and/or Scalar 3-Dimensional Free-Space Green's Function......Page 260
F.2 Shape Functions Over Tetrahedra......Page 261
F.3 Solution of Characteristic Integrals......Page 262
References......Page 263
Index......Page 264
Back Cover......Page 269
