A novel total variation based noninvasive transmural electrophysiological imaging

Abstract

While tomographic imaging of cardiac structure and kinetics has improved substantially, electrophysiological mapping of the heart is still restricted to the body or heart surface with little or no depth information beneath. The progress in reconstructing transmural action potentials from surface voltage data has been hindered by the challenges of intrinsic ill-posedness and the lack of a unique solution in the absence of prior assumptions. In this work, we propose to exploit the unique spatial property of transmural action potentials that it is often piecewise smooth with a steep boundary (gradient) separating the depolarized and repolarized regions. This steep gradient could reveal normal or disrupted electrical propagation wavefronts, or pinpoint the border between viable and necrotic tissue. In this light, we propose a novel adaption of the total-variation (TV) prior into the reconstruction of transmural action potentials, where a variational TV operator is defined instead of a common discrete operator, and the TV-minimization is solved by a sequence of weighted, first-order L2-norm minimizations. In a large set of phantom experiments performed on image-derived human heart-torso models, the proposed method is shown to outperform existing quadratic methods in preserving the steep gradient of action potentials along the border of infarcts, as well as in capturing the disruption to the normal path of electrical wavefronts. The former is further attested by real-data experiments on two post-infarction human subjects, demonstrating the potential of the proposed method in revealing the location and shape of the underlying infarcts when existing quadratic methods fail to do so. © 2013 Springer-Verlag.