A mathematical comparison of two models of the electrical properties of biological tissues

The purpose of this paper is to compare two models of the electrical properties of tissue, which may be used to relate the effective conductivity to the volume fraction f of cells in the tissue. Both models assume that tissue comprises spherical cells, which behave electrically as dipoles. The first model, developed by Hanai, describes the tissue as a concentrated suspension of weakly conducting spheres in a conducting medium, with each sphere experiencing a uniform mean field. The second approach, developed by Chiew and Glandt, explicitly describes the effect of a random but statistically homogeneous cell structure on the average field and magnitude of the dipole interaction. The two analyses are identical to first order in f, but differ in the way in which the interactions between the dipoles are accounted for. The model developed by Chiew and Glandt appears to offer a more robust theoretical framework for describing the electrical properties of tissue. The comparison aims to contribute to an improved understanding of the relationship between the electrical properties and spatial structure of tissue.