Comparison of regularization techniques for the reconstruction of transmembrane potentials in the heart

Computer simulations to reconstruct the transmembrane potential distribution were performed for an anisotropic finite element model of the heart. Transmembrane potential was reconstructed in the form of 3D patches. Test patterns generated with a cellular automaton were used. Tikhonov 0-order and 2-order reconstruction techniques were compared. Tikhonov 2-order regularization was shown to deliver better solutions; this is demonstrated by the inspection of the source space of the inverse problem and by the comparison of the correlation coefficients between the reconstructed and original distributions. Time information was incorporated into the regularization.