The transfer matrix for epicardial potential in a piece-wise homogeneous thorax model: the boundary element formulation

In epicardial potential imaging, the epicardial potential is reconstructed computationally from the measured body surface potential. The transfer function that relates the heart and body surface potentials is commonly constructed with some point-collocation-weighted boundary element technique, assuming an electrically homogeneous volume conductor. This assumption causes modeling errors. In this study, the system of surface integral equations that describes the relationship between the heart and body surface potentials is thoroughly derived in a piece-wise homogeneous volume conductor. The equations are discretized with the method of weighted residuals, enabling the use of Galerkin weighting in the numerical solution of the equations. The construction of the transfer matrix is described in detail for constant and linear collocation and Galerkin methods, and the resulting forward transfer matrices are validated via simple numerical simulations. The linear Galerkin method is found to generate the smallest errors. The presented method increases the accuracy of the forward-computed body surface potential and thus prepares the way for more accurate inverse reconstructions of epicardial potential.