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

Abstract

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.

Noninvasive epi-endocardial electrocardiographic imaging of ventricular septal pacing

“…Кроме того, необходимо учитывать положение МЖП, фактически скрытой свободными стенками желудочков сердца. Используемые в настоящее время алгоритмы были подробно описаны ранее и протестированы на различных данных, однако они не позволяли решить данную проблему [5,6].…”

“…Для дальнейших расчетов проводился экспорт трехмерных полигональных моделей в формате VTK и исходных записей многоканальной ЭКГ в специальном текстовом формате из программного обеспечения «Amycard 01C». Вначале применялся итеративный алгоритм решения обратной задачи в терминах потенциала простого слоя (ESL-iterative) с последующей визуализацией изопотенциальных карт [5]. Затем для расчета исходных данных использовался новый алгоритм, основанный на комбинации методов векторного анализа и кратчайшего пути нахождения наиболее правдоподобного центра зоны ранней активации фокусных источников (FRA-V) c последующей визуализацией вероятностных корреляционных карт [8].…”

Single-Layer Based Algorithms for Solving the Inverse Problem of ECG

“…The classical BEM approach to the forward ECG problem results in the following system of linear equations connecting electrical potentials u l and their normal derivatives q l on the surfaces Γ l (l = 0, 1) [1,3]:…”

“…One of the consequences of this ill-posedness is solution's ambiguity making reconstruction of endocardial sources extremely challenging. With this respect, the equivalent single layer (ESL) source model was recently introduced and shown to improve ECGI accuracy on the endocardium using three simulated cases of ectopic ventricular excitation [1].…”

“…In the present work, we propose two alternative numerical formulations of the ESL-based inverse problem and introduce a combined approach, resulting in four distinct ECGI algorithms. Furthermore, we quantitatively assess performance of these approaches for the in silico data used in [1] and clinical pacing data from [2].…”