Reconstruction of transmembrane currents using Support Vector machines and its application to endocardial mapping: A model study

Recent endocardial mapping systems reconstruct an instantaneous image of the endocardial electrical activity performing the inverse problem of electrocardiography (IPE), which consists of estimating the endocardial surface potentials from intracavitary probe potentials. Even though the IPE has been long studied, it still being paid attention due to its ill-posed nature, and many different regularization techniques have been explored in this setting. In this study we analyzed support vector machines (SVM) as an alternative regularization technique regarding their robustness against ill-posed problems. We propose here two new SVM algorithms, specifically adapted to the ill-posing issues of the IPE, and develop the equations for endocardial mapping of transmembrane currents. We show, both in simple simulations and in a previously developed cellular automata, that the ill-posing robustness of the SVM is higher when compared to regularized approaches during the depolarization phase. In conclusion, the properties of the developed SVM algorithms stand for an appropriate framework for addressing the IPE.