ABSTRACT
CONTENTS 10.1 Introduction ..................................................................................................................... 294
10.1.1 Induced Field Intensity and Dosimetric Quantities.................................... 295 10.1.2 Characterizing EMFs ........................................................................................ 296
10.2 Planar Tissue Models ..................................................................................................... 297 10.2.1 Thick or Semi-Infinite Layers.......................................................................... 297 10.2.2 Multiple Layers ................................................................................................. 301
10.3 Bodies of Revolution ...................................................................................................... 304 10.3.1 Spherical Models............................................................................................... 304 10.3.2 Prolate Spheroidal Models .............................................................................. 308
10.4 Anatomically Based Models ......................................................................................... 311 10.4.1 Brief Survey of Numerical Methods.............................................................. 311
10.4.1.1 Quasi-Static Impedance Method ................................................... 311 10.4.1.2 Volume Integral Equation MoM ................................................... 312 10.4.1.3 SMoM................................................................................................. 313 10.4.1.4 FEM .................................................................................................... 314 10.4.1.5 FDTD Method................................................................................... 314
10.4.2 Human Bodies Exposed to EMFs................................................................... 318 10.4.2.1 Realistic Models of the Human Body........................................... 318 10.4.2.2 Currents Induced in the Human Body
by Low-Frequency EMFs................................................................ 319 10.4.2.3 Absorption in Human Bodies Exposed
to Far Field of RF Sources .............................................................. 327 10.4.2.4 Human Exposure to the Field Radiated
by Transceiver Base-Station Antennas ......................................... 335 10.4.2.5 Coupling of Transient EM Pulses into the Human Body ......... 340 10.4.2.6 Absorption in the Head of Cellular Phone Users ...................... 343
10.5 Temperature Elevations Induced in Biological Tissues by EM Power Absorption.............................................................................................. 348 10.5.1 Introduction ....................................................................................................... 348 10.5.2 Bio-Heat Equation............................................................................................. 348
10.5.2.1 Initial Conditions ............................................................................. 350 10.5.2.2 Boundary Conditions ...................................................................... 350
10.5.3 Thermoregulatory Responses ......................................................................... 351 10.5.4 Numerical Methods for Solving the Thermal Problem.............................. 353
10.5.4.1 Explicit Finite Difference Formulation......................................... 353 10.5.4.2 ADI Formulation.............................................................................. 355
to EM Fields ...................... 357 10.5.5.1 Temperature Increments in the Human Body Exposed
to the Far Field of Radiating RF Sources ..................................... 357 10.5.5.2 Temperature Increments in the Head of a
Cellular Telephone User ................................................................. 359 10.6 Thermal Therapeutic Applications of Microwave Energy ...................................... 361
10.6.1 Ablation for Cardiac Arrhythmias................................................................. 362 10.6.2 Ablation for Endometrial Disorders .............................................................. 363 10.6.3 Microwave Interstitial Hyperthermia for Cancer Treatment .................... 364
10.7 Concluding Remarks...................................................................................................... 366 Acknowledgment....................................................................................................................... 368 References ................................................................................................................................... 368
Electromagnetic energy at both high and low-frequencies can be transmitted into biological materials through the use of antennas or applicators. Antennas launch the electromagnetic energy into the medium. They serve to couple the generating source of electromagnetic energy into the medium, which surrounds it. The spatial distribution of electromagnetic energy from an antenna is directional and varies with distance from the antenna. At distances sufficiently far from an antenna, so that local field distribution changes predictably and varies mostly with distance, the region is called a far field or radiation zone. In the near field or near zone close to the antenna, the electromagnetic energy distribution varies as a function of both angle and distance. Moreover, the behavior of electromagnetic fields (EMFs) and their coupling and interaction with biological systems are very different, depending on whether they are in the near or far zone. In fact, these differences constitute the major variances between radio frequency (RF) and low-frequency energy deposition into biological systems. As shown in subsequent sections, the induction of electric and magnetic fields, deposition of electromagnetic power, absorption of electromagnetic energy, and their penetration into tissue, all are functions of the source and its frequency or wavelength. In general, when considering the interaction of EMFs with biological systems, it is necessary to account for the frequency or wavelength and its relationship to the physical dimensions of the body. In addition, the interaction of EMFs with biological systems is characterized by the
electromagnetic properties of tissue media, specifically, dielectric permittivity. Biological materials have magnetic permeability values close to that of free space and are independent of frequency. In a medium such as biological tissue with a finite electrical conductivity s, a conduction current, J ¼ sE, can be induced to flow, giving rise to energy loss by joule heating. Clearly, fields must be coupled into tissues, and energy must be deposited or absorbed in the biological systems, regardless of the mechanism that is accountable for an effect, for the system to respond in some manner. Thus, to achieve any biological response, the electric field, magnetic field, or EMF that is exerting its influence must be quantified and correlated with the observed phenomenon. The purpose of this chapter is to present an account of electromagnetic interactions in
biological media, with special emphasis on the energy coupling and distribution characteristics in models of biological structures. Such information is essential for analyzing the interrelationships among various observed biological effects, for separating known and substantiated effects from those that are speculative and unsubstantiated, for assessing
and for extracting diagnostic information from field effects. There exist a wide variety of methods for quantifying fields in biological bodies. The
extent of computer usage varies, depending on the specific information sought and the complexity of tissue geometry. This chapter outlines a number of techniques that have been successfully employed to analyze the propagation and absorption characteristics of electromagnetic energy in tissue structures. There are two general approaches: one involves extensive use of analytical development and the other relies more heavily on numerical formulation. Analytical computations are most suited for calculation of the distribution of absorbed energy in simplified tissue geometries such as plane slabs, cylinders, and spheroids, whereas numerical methods offer the opportunity of analyzing the coupling of electromagnetic energy to animal and human bodies, which is difficult, if not impossible, to approach analytically. The advantages and limitations of various methods for field computations, along with representative results, are provided in this chapter. In some cases, for additional details, the reader is referred to previous editions of this handbook [1,2]. This chapter will begin with a brief introduction to the concepts of induced field and power deposition and the characteristics of field intensities and dosimetric quantities.
