Electrical analogues for tissues

Abstract

The equations of Maxwell and Reyleigh for the electrical resistance of suspensions of spheres and cylinders have been widely used to calculate the volume concentration of nonconducting cells in several tissues. The assumptions made in the derivations of these equations are not valid over at least part of the concentration range from 50 to 100% so that such calculations are without analytical basis. Approximations for uniform, uniformly separated, space filling figures and for randomly oriented, uniform and uniformly distributed, conducting planes show that each of the equations is correct for volume concentrations approaching 100%. Analogue measurements were made with conducting paper for circular cylinders in square and hexagonal arrays and with an electrolytic tank for spheres in simple and face centered cubic arrays. The available theories are not entirely satisfactory. Similar measurements were made for a square array of square cylinders and a hexagonal array of hexagonal cylinders and for a cubic array of cubes and a hexagonal array of tetrakaidecahedra. In all cases it was found that the measured volume concentrations agreed with those given by the simple Rayleigh and Maxwell equations, to within the experimental accuracies of about 1%, over all of the concentration ranges measured from 30% or less to 90% or more. These analogue calculations thus provide a basis for the use of the equations over the entire range.