Solving the Inverse Problem of Electrocardiography on the Endocardium Using a Single Layer Source

The inverse problem of electrocardiography consists in reconstructing cardiac electrical activity from given body surface electrocardiographic measurements. Despite tremendous progress in the field over the last decades, the solution of this problem in terms of electrical potentials on both epi- and the endocardial heart surfaces with acceptable accuracy remains challenging. This paper presents a novel numerical approach aimed at improving the solution quality on the endocardium. Our method exploits the solution representation in the form of electrical single layer densities on the myocardial surface. We demonstrate that this representation brings twofold benefits: first, the inverse problem can be solved for the physiologically meaningful single layer densities. Secondly, a conventional transfer matrix for electrical potentials can be split into two parts, one of which turned out to posess regularizing properties leading to improved endocardial reconstructions. The method was tested in-silico for ventricular pacings utilizing realistic CT-based heart and torso geometries. The proposed approach provided more accurate solution on the ventricular endocardium compared to the conventional potential-based solutions with Tikhonov regularization of the 0th, 1st, and 2nd orders. Furthermore, we show a uniform spatio-temporal behavior of the single layer densities over the heart surface, which could be conveniently employed in the regularization procedure.