A Recursive Cellular Automaton that Reconstructs Transmembrane Voltages with a Range-Adjusted Tikhonov-Method

Tikhonov methods usually lead to solutions of low amplitude that are distributed around zero. When reconstructing transmembrane voltages (TMVs) in the myocardium, the signal is therefore often not in the physiological range of between around -80mV and 10mV. In this article, we propose an adjusted Tikhonov method that reconstructs TMVs in the correct range, given an estimate of one polarized node in the heart and an estimated set of nodes that have depolarized in the preceding time step. It is shown that when feeding the reconstructed TMVs into a simple cellular automaton recursively, and when using the computed excitation propagation as a prior for the Tikhonov method, it is possible to reconstruct the excitation propagation throughout the ventricular myocardium. The method requires an estimate of the region of initial activation.