Local regularization of endocardial and epicardial surfaces for better localization of ectopic beats in the inverse problem of ECG

The problem of non-invasively finding cardiac electrical sources from body surface potential maps (BSPM) is ill-posed. A standard Tikhonov regularization approach to the problem produces a solution biased toward the electrodes and thus to the left ventricular epicardium, which limits its potential to reconstruct endocardial sources. In this work we consider a transmembrane voltages based inverse problem of ECG for the identification of extrasystole origins from simulated BSPM. With use of a pair of heart wall epicardial/endocardial extrasystoles and a pair of septal ectopic foci we demonstrate the performance of the inverse procedures while firstly solving the problem for all nodes, then for epicardium and endocardium separately. Based on the observations and the logic behind the gradient of sources we define simple rules on how to classify an extrasystole under consideration according to these 3 reconstructions. Furthermore, when the amount of noise is known, we propose a new method with two regularization parameters which assign different weightings to endocardial and epicardial components of the solution.