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The objective of this paper is the application of two-dimensional discrete Fourier transformation for solving the integral equation of the bioelectric forward problem. Therefore, the potential, the source term, and the integral equation kernel are assumed to be sampled at evenly spaced intervals. Thus the continuous functions of the problem domain can be expressed by their two-dimensional discrete Fourier transform in the spatial frequency domain. The method is applied to compute the surface potential generated by an eccentric dipole in a homogeneous spherical conducting medium. The integral equation for the potential is solved in the spatial frequency domain and the value of the potential at the sampling points is obtained from inverse Fourier transformation. The solution of the presented method is compared to both, an analytic solution and a solution gained from applying the boundary element method. Isoparametric quadrilateral boundary elements are used for modeling the spherical volume conductor in the boundary element solution, while in the two-dimensional Fourier transformation method the volume conductor is represented by a parametric boundary surface approximation.

biomedizinische technik

Two-Dimensional Fourier Representation Used in the Bioelectric Forward Problem - Zweidimensionale Fourier-Darstellung, angewandt im bioelektrischen Vorwärtsproblem