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5
Propagation and Absorption in Tissue Media

The propagation of electromagnetic waves in biological materials is governed by the dielectric constant, conductivity, source configuration, and the geometrical factors that describe the tissue structure. These parameters also determine the quantity of energy a given biological body extracts from the propagating wave. When the radius of curvature of the body surface is large compared to the wavelength and beam width of the impinging radiation, planar tissue models may be used to estimate the absorbed energy and its distribution inside the body. Otherwise, the absorbed energy will be dictated by the size of the body, the curvature of its surface, the ratio of body size to wavelength, and the source characteristics. The purpose of this chapter is to present a concise account of electromagnetic wave propagation 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 therapeutic effectiveness of electromagnetic waves, and for extracting diagnostic information from field effects. It should be noted that the whole-body absorption of electromagnetic energy by humans and laboratory animals is of interest because it is related to the energy required to alter the thermoregulatory system of the exposed subject, and because it may serve as an index for extrapolating experimental results to human exposures. The distribution of absorbed electromagnetic waves within an irradiated body is important because it relates to specific responses of the body, because it facilitates understanding of phenomena, and because it contributes to definition of mechanisms of interaction.
137

S. M. Michaelson et al., Biological Effects and Health Implications of Radiofrequency Radiation ? Springer Science+Business Media New York 1987

138

CHAPTER 5

5.1. PLANAR TISSUE GEOMETRIES

5. 1. 1. Reflection and Transmission

The fate of plane waves at a planar tissue interface depends on the frequency, polarization, and angle of incidence of the wave, and on the dielectric constant and conductivity of the tissue. For a linearly polarized plane wave impinging normallyon a boundary separating two semiinfinite media, the reftection and transmission coefficients are respectively given by equations (2.55) and (2.56). When the dielectric properties of the media are approximately equal, there is no reftection and the transmission is maximum. In contrast, there is complete reftection if the second medium is perfectly conductive. Table 5-1 summarizes the magnitude of the reftection coefficient at the boundary separating various tissues. The fraction of normal incident power reftected by the discontinuity is given by R 2 ? Clearly, about one-haH of the incident power is reftected at these boundaries. Further, the reftection coefficients for tissue-tissue interfaces range from a low of about 5 for muscle-blood to high of about 50 for bone-biological ftuid interfaces. This suggests that the closer the dielectric properties on both sides of the interface, the smaller is the power reftection. The fraction of transmitted power is related to the power transmission coefficient (1 - R 2 ). It is readily apparent from Table 5-1 that the transmitted power at air-tissue interfaces is quite substantial at radio and microwave frequencies. Moreover, Fig. 5-1 shows that the power transmission coefficient is highly frequency dependent, especially at lower frequencies, while the transmitted power for an air-fat interface is about twice as great as for an air-muscle boundary (about 40% at 1 GHz); it is nearly the same as that for a fat-muscle interface. Clearly, power transmission is highest when the dielectric properties of the adjacent media are similar. As the transmitted wave propagates in the tissue medium, energy is extracted from the wave and absorbed by the medium. This absorption will result in a progressive reduction of the wave's power density as it advances in the tissue. This reduction is quantified by the depth of penetration 6, which is the distance in which the power density decreases by a factor of e- 2 ? Table 5-2 presents the calculated depth of penetration in selected tissues using typical dielectric constants and conductivities provided in Chapter 4. A graphical representation of penetration depth versus frequency for blood, muscle, and fat is given in Fig. 5-2. It is seen that 6 is frequency dependent and takes on different values for different tissues. In particular, the penetration depth for fat and bone is nearly five times greater than for higher-water-content tissues, and has values that range from a few millimeters to several centimeters.


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