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

An implantable electric field probe with an interference‐free lead wire system was constructed at a nominal cost for the purpose of measuring the induced electric fields in a phantom model of man irradiated by waves of various frequencies. The probe consisted of a short dipole loaded with a zero‐bias microwave diode, and the interference‐free lead wires were constructed with two series of lumped resistors of 3 k Ω. Characteristics of the probe were checked first by measuring the induced electric fields in irradiated, electrically small cubes filled with phantom material. The measured results were in good agreement with theoretical results obtained from the tensor integral equation method. A phantom model of man was constructed with thin Plexiglas filled with phantom material. The model was irradiated by 500‐ to 3000‐MHz em waves in a microwave anechoic chamber. Induced electric fields were probed over 28 locations in one side of the model. The distribution of the measured electric fields was compared with the distribution of theoretical results obtained numerically from the tensor integral equation methods. A qualitative agreement was obtained between experiment and theory. It was found that the agreement between experiment and theory tended to deteriorate at lower frequencies. The reason for this discrepancy is explained.