Heating of spherical versus realistic models of human and infrahuman heads by electromagnetic waves

Abstract

A numerical method based on a tensor integral equation has been employed to quantify the induced EM heating in realistic models of the human and infrahuman head. The head consists of a brain of realistic shape and eyes that are surrounded by a bony structure. The numerical method has also been used to determine the induced EM heating in spherical models of human and infrahuman heads and brains. The EM heating induced in the brain of the realistic model is lower than that induced in the brain of the spherical model. The bony stucture of the skull tends to attenuate heating of the brain, including the eyes. within realistic models of heads that contain simulated brains of realistic shape, and eyes that are surrounded by bony structures. To handle the irregular geometries, the only potent method is a numerical technique aided by a highspeed computer. We have employed a numerical technique called the "tensor-integral-equation method" [Livesay and Chen, 1974; Guru and Chen, 1976], which was developed by our group, to solve the problem. The accuracy of our numerical method was checked by comparing the numerical results on a homogeneous sphere with the corresponding results obtained from the exact solution of Mie theory [Stratton, 1941 ]. The tensor-integral-equation (TIE) method as defined for this paper is outlined briefly. If a finite biological body of arbitrary shape, with permittivity e(r), conductivity of o(r) and permeability t•o, is irradiated in free space by an electromagnetic wave with an electric field E'(r), the total induced electric field E(r) inside the body can be deter-mined from the following tensor integral equation: [1 + [r(r)/3jCoeollE(r) -PV Iv r(r')E(r') ß G (r,r)dV • = E'(r) (1) where •(r) = o(r) + jc0[e(r) -eo], eo is the free-space permittivity, the P V symbol means the principal value of the integral, G (r,r') is the free-space tensor Green's function, and V is the body volume. If the body is partitioned into N subvolumes or cells, and E(r) and •(r) are assumed to be constant within each cell, equation (1) can be transformed into 3N simultaneous equations for Ex, Ey and E, at the centers of N cells by the point-matching method. These simultaneous equations can be written into matrix form as (2) The [G] matrix is a 3N x 3N matrix, while [E] and [E'] are 3N column matrices expressing the total electric field and the incident electric field at the centers of N cells. The elements of the [G] matrix have been evaluated by Livesay and Chen [1974]. Therefore, with the known incident electric field E'(r), the total induced electric field E(r) inside the 0048-6604/79/1112-S009501.00 51

Brain temperature measurements in rats: A comparison of microwave and ambient temperature exposures

“…Lin et a1 [1973] predicted nonuniform energy deposition at 2450 MHz in spheres with radii between 0.9 and 5.0 cm, and the 1975 study by Kritikos and Schwan also predicted, at 2450 MHz, an area of high energy deposition in the center of a sphere with radii between 0.8 and 5.5 cm. Ohlsson and Risman [1978] with both calculations and experimental work showed that core heating is most pronounced in spheres with diameters between 2.0 and 3.5 cm at 2450 MHz. Block models of man by Rukspollmuang and Chen [1979] and Hagmann et a1 [ 19791 also predict nonuniform energy deposition during microwave exposure. As with the spherical models, these models were for heads with diameters much larger than that of the rat.…”

An efficient integral equation based dosimetry model of the human brain

“…First, the equivalent electric and magnetic currents J and M in (11) are expanded in terms of a linear combination of known basis functions f n and g n , respectively…”

“…Throughout the seventies there has been some effort in development of the dosimetry model of the human body. Surface integral equation approach was used to set up the axially simetrical model of the body [8], [9], while for more complex geometries volume integral equation was used [10], [11]. Unfortunately, the latter approach leads to a mathematically more complex tensor integral equations, which was one of the reason why earlier researchers preferred more simpler differential equation based approach.…”