Approximate complex electrical potential distribution in the monodomain model with unequal conductivity and relative permittivity anisotropy ratios

Abstract

Objective: Electrical conductivity and relative permittivity are properties that indicate muscle health and they have different values parallel and perpendicular to the direction of the myofiber, a concept known as anisotropy. When the intrinsic electrical properties of muscle have ratios of anisotropy that are different then there is no analytical solution that can describe the electrical potential distribution in the tissue. Approach: Here, we present approximate analytical solutions to monodomain equations with unequal anisotropy ratios. For this, we base our analysis on perturbation theory where the electrical potential is approximated by the sum of the zeroth- and first-order terms of an infinite series. Main results: The validity of the approach is confirmed using experimental data for healthy and diseased muscle available online. Significance: A better understanding of electrical potential distribution in anisotropic skeletal muscle tissue will allow the development of improved diagnostic tools for neuromuscular diseases.