Variational Bayesian electrophysiological imaging of myocardial infarction.

The presence, size, and distribution of ischemic tissue bear significant prognostic and therapeutic implication for ventricular arrhythmias. While many approaches to 3D infarct detection have been developed via electrophysiological (EP) imaging from noninvasive electrocardiographic data, this ill-posed inverse problem remains challenging especially for septal infarcts that are hidden from body-surface data. We propose a variational Bayesian framework for EP imaging of 3D infarct using a total-variation prior. The posterior distribution of intramural action potential and all regularization parameters are estimated from body-surface data by minimizing the Kullback-Leibler divergence. Because of the uncertainty introduced in prior models, we hypothesize that the solution uncertainty plays as important a role as the point estimate in interpreting the reconstruction. This is verified in a set of phantom and real-data experiments, where regions of low confidence help to eliminate false-positives and to accurately identify infarcts of various locations (including septum) and distributions. Owing to the ability of total-variation prior in extracting the boundary between smooth regions, the presented method also has the potential to outline infarct border that is the most critical region responsible for ventricular arrhvthmias.

Noninvasive transmural electrophysiological imaging based on minimization of total-variation functional.

While tomographic imaging of cardiac structure and kinetics has improved substantially, electrophysiological mapping of the heart is still restricted to the surface with little or no depth information beneath. The progress in reconstructing 3-D action potential from surface voltage data has been hindered by the intrinsic ill-posedness of the problem and the lack of a unique solution in the absence of prior assumptions. In this work, we propose a novel adaption of the total-variation (TV) prior to exploit the unique spatial property of transmural action potential of being piecewise smooth with a steep boundary (gradient) separating depolarized and repolarized regions. We present a variational TV-prior instead of a common discrete TV-prior for improved robustness to mesh resolution, and solve the TV-minimization by a sequence of weighted, first-order L2-norm minimization. In a large set of phantom experiments, the proposed method is shown to outperform existing quadratic methods in preserving the steep gradient of action potential along the border of infarcts, as well as in capturing the disruption to the normal path of electrical wavefronts. Real-data experiments also further demonstrate the potential of the proposed method in revealing the location and shape of infarcts when quadratic methods fail to do so.

A novel total variation based noninvasive transmural electrophysiological imaging.

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 piece-wise 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.

Localization of sparse transmural excitation stimuli from surface mapping.

As in-silico 3D electrophysiological (EP) models start to play an essential role in revealing transmural EP characteristics and diseased substrates in individual hearts, there arises a critical challenge to properly initialize these models, i.e., determine the location of excitation stimuli without a trial-and-error process. In this paper, we present a novel method to localize transmural stimuli based on their spatial sparsity using surface mapping data. In order to overcome the mathematical ill-posedness caused by the limited measurement data, a neighborhood-smoothness constraint is used to first obtain a low-resolution estimation of sparse solution. This is then used to initialize an iterative, re-weighted minimum-norm regularization to enforce a sparse solution and thereby overcome the physical ill-posedness of the electromagnetic inverse problem. Phantom experiments are performed on a human heart-torso model to evaluate this method in localizing excitation stimuli at different regions and depths within the ventricles, as well as to test its feasibility in differentiating multiple remotely or close distributed stimuli. Real-data experiments are performed on a healthy and an infarcted porcine heart, where activation isochronous simulated with the reconstructed stimuli are significantly closer to the catheterized mapping data than other stimuli configurations. This method has the potential to benefit the current research in subject-specific EP modeling as well as to facilitate clinical decisions involving device pacing and ectopic foci.