Electrical impedance tomography using a 3-D boundary element inverse solution

In this paper, we describe a 3-D boundary element method (BEM) solution to the forward and inverse problems of electrical impedance tomography (EIT). Our target application is to use EIT to reconstruct a conductivity map to be used in the inverse problem of electrocardiography. However the method is quite general, subject to the restriction that the geometry must be known and only the conductivities need to be reconstructed. 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, which dramatically decreases the number of unknowns. It appears that our formulation of the inverse problem leads to a stable minimization problem.