Numerical Methods for Bioelectromagnetic Field Computations

To compute the bioelectric and/or biomagnetic forward and inverse solutions, digitized models of the associated volume conductor are required. For computational reasons, the surfaces that separate regions of different conductivity must first be tesselated with a covering set of polygons, such as triangles or quadrilaterals. Hence, a method for a compact and continuous representation of anatomical surfaces is introduced. The method is based on a combined second order surface and double Fourier series approximation. This method is compared to another approach using the surface harmonic expansion. Both methods provide an accurate and efficient parameterization of conductivity interfaces and can be practically applied to the automatic reconstruction of individualized boundary element head and torso volume conductor models necessary for bioelectromagentic forward and inverse computations. The double Fourier series representation introduced for modeling the volume conductor is then applied to solve the bioelectric forward problem using two-dimensional discrete Fourier transforamtion. The method is used to compute the electric potential on a spherical conducting medium generated by an eccentric dipole. The result is compared to both an anlytic solution and the results gained from applying the boundary element method.