Optimal design of concentric electrodes for functional electrical stimulation in multilayered isotropic tissues

Abstract

We present an analytical approach to determining the nerve activation induced in multiple, layered, isotropic tissues by an unconventional planar concentric ring electrode geometry and assess the applicability of such electrodes for skin surface Functional Electrical Stimulation (FES). We model this problem using Laplace’s equation in a semi-infinite domain of piecewise constant conductivity subject to appropriate interface and surface boundary conditions given by the complete electrode model. This system of equations is solved by means of Hankel Transforms to determine the spatial potential distribution. In this paper, for simplicity, we present the detailed mathematical formulation for a three-layer medium, and we include the results of the numerical simulations obtained for a four-layered realistic tissue model consisting of skin, fat, muscle and bone. The approach can be easily extended to more layers. Different sets of tissue layer thicknesses were considered, corresponding to three standard categories of patient physical build. The results show that for each of these sets, the electrode design can be optimized to maximize the activating function at different depths and reduce the peaks of high current density that occur at the electrode edges. The impact of the thickness of the fat layer on the activating function is also highlighted.