Electric field and potential calculation for a bioelectric current dipole in an ellipsoid

摘要

Computer-based modelling in ellipsoidal geometry can be useful in electroencephalography and gastrography due to the resemblance of the human brain and stomach to an ellipsoid. Both theoretically and computationally, the bioelectric current dipole model is important for the study of electrical activity in these two organs. Computing the electric potential phi and electric field E due to a current dipole located in an ellipsoid requires truncated series expansions involving ellipsoidal harmonics E-n(m), which are the products of Lame functions. A theoretical model for this has appeared in the literature only for expansions of order 2 in E-n(m); however, this may be insufficient in forward electrogastrography, while an analogous situation is encountered in some geodetic problems where similar expansions are required. In this paper, vie propose a generalized model for computing phi and E numerically using harmonic expansions of arbitrary order and degree. The implementation of such a procedure involves finding roots of Lame polynomials of degree 5 or higher using an optimization technique for solving nonlinear systems of equations. This process can allow one to make a knowledgeable decision concerning the optimal expansion size required for the physical problem under investigation without compromising the overall accuracy of the computation.