Using a Spread Sheet Program to Model the Interaction of Low-Frequency Electric Fields with Inhomogeneous, Irregularly Shaped Objects

Abstract

This paper describes the use of an ordinary business spread sheet program to calculate, using a two-stage finite difference method, the electric fields and current densities produced inside irregularly shaped models of the upper arm and forearm. The limb interiors are inhomogeneous, being represented as realistic cross-sections of bone and muscle.

A spread sheet forms a two-dimensional array. Each cell of the sheet can correspond to a physical element of space. Equations entered into the cells then represent the relationships among the potentials of the corresponding spatial elements.

The model is validated for a two-layer, lossy dielectric cylinder. Good agreement is obtained between the numerical and analytical solutions in this case except near the boundaries of the outer layer. The electric field within the limb depends on the shape and orientation of the limb relative to the applied field. The flow of current around the less conductive bones in the forearm can be observed.