Noninvasive Reconstruction of Transmural Transmembrane Potential with Simultaneous Estimation of Prior Model Error

To reconstruct electrical activity in the heart from body-surface electrocardiograms (ECGs) is an ill-posed inverse problem. Electrophysiological models have been found effective in regularizing these inverse problems by incorporating a priori knowledge about how the electrical potential in the heart propagates over time. However, these models suffer from model errors arising from, for example, parameters associated with tissue properties and the earliest sites of excitation. We present a Bayesian approach to simultaneously estimate transmembrane potential (TMP) signals and prior model errors, exploiting sparsity of the error in the gradient domain in the form of a novel sparse prior based on variational lower bound of the generalized Gaussian distribution. In synthetic and real-data experiments, we demonstrate the improvement of accuracy in TMP reconstruction brought by simultaneous model error estimation. We further provide theoretical and empirical justifications for the change of performances in the presented method at the presence of different model errors.