Forcing Transmembrane Voltages to Decrease Slowly: A Temporal Regularization for ECG Imaging

ECG imaging aims to reconstruct the cardiac electrical activity from non-invasive measurements of body surface potentials (BSP) by finding unique and physiologically meaningful solutions to the inverse problem of electrocardiography. This can be accomplished using regularization, which reduces the space of admissible solutions by demanding solution properties that are already known beforehand. Messnarz et. al. proposed a regularization scheme that requires transmembrane voltages (TMV) to not decrease over time. We suggest a generalization of this method that forces TMVs to decrease only slowly and as a result can also be applied to irregular cardiac activity. We first develop the method using a simplified spherical geometry and then show its benefit for imaging fibrillatory activity on a realistic geometry of the atria.