Calculation of Electric Potentials Generated by a Dipole Source in an Elliptical Conducting Cylinder of a Finite Length

In this paper we present an analytical method for computation of electric potential of the point current dipole, placed inside homogeneous conducting elliptical cylinder. We use elliptical cylinder as a model of human torso. Current dipole is a model for current sources in the heart. So we solve the forward electrocardiographic problem. We calculate electric potential maps on the body surface by two methods: Analytical and numerical. An analytical method is based on equations involving Mathieu functions. Calculation of such functions is performed by usage of Mathieu functions toolbox, developed by authors of the current work in the Scilab computer language. A numerical approach is based on the finite element method (FEM). After the comparison of the potential distributions obtained by two methods we can see that the results are very close for various sets of source and medium parameters. In this article, an analytical method has been implemented for calculating the electric potentials created by a current dipole in an elliptical conducting cylinder of finite length. The convergence of the used series is shown, as well as the convergence of the solution during the transformation of an elliptic cylinder into a circular cylinder. The presented materials illustrate one of the possible applications of the Mathieu functions.