Improved Machine Learning Strategies and Algorithms for Transmembrane Potential Estimation in Homogeneous Medium.

Introduction. Research on improved methods for the inverse problem in cardiology and electrophysiology is active today. Recently, the use of machine learning methods has been proposed, allowing us to consider the biophysical equations of the problem. In this work, we propose to explore improvements in using kernel methods for estimating the inverse problem, with kernel given by the Green's function for the infinite homogeneous potential and with recently proposed cross-validation strategies for least squares estimation. Materials and Methods. Three solvers were implemented: least squares with Zero-Order Tikhonov (ZOT) regularization, Support Vector Regression (SVR), and constrained L2 (CL2) optimization. The study evaluates transmembrane action potential estimation in 1D (fiber) and 2D (tissue) simulations using the Luo-Rudy model. Experiments and results. The ZOT method was the most unstable. The SVR method provided biased results, although intermediate and acceptable accuracy, except at the edges of spatial action potentials. The CL2 method provided better performance under certain conditions of the implemented cross-validation procedure. Conclusions. Kernel methods, with refined algorithmic formulations and cross-validation criteria, offer an alternative for cardiac inverse problem estimation.