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We describe a 3-D boundary element method (BEM) solution to the electrical impedance tomography (EIT) problem. The long-term goal is to use EIT to reconstruct a conductivity map to be used in the inverse problem of electrocardiography. The principle advantage of a BEM solution to EIT is that it imposes the assumption that the internal organ conductivities are piecewise constant in the volume. This dramatically decreases the number of unknowns. The forward problem of EIT, as we approach it here, is to compute the potentials at electrodes on the body surface, given a set of current patterns injected by those same electrodes and a known conductivity map. We present the application of EIT-specific boundary conditions on the BEM equations and report simulations illustrating the effect of some internal inhomogeneities on the EIT forward solution.