Noninvasive Transmural Electrophysiological Imaging Based on Minimization of Total-Variation Functional

Abstract

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.

Noninvasive electrocardiographic imaging of chronic myocardial infarct scar

“…The third method of the inverse solution, which was designed to complement the second one, is Variational Bayesian Electrophysiological Imaging with a total-variation prior (VB-TV) proposed by Xu et al [23, 24]. The VB-TV method is well suited to extracting cardiac source activity along the MI-scar border in 3D due to the inherent ability of a total-variation prior to extract strongly localized boundaries between homogeneous regions.…”

L_0 Norm Based Sparse Regularization for Non-invasive Infarct Detection Using ECG Signal

“…It has been shown that inverse ECG can be used to detect or quantify myocardial infarcts [1,2]. The main challenge in inverse ECG is the need to solve a severely ill-posed problem.…”

“…To address this problem, various regularization techniques have been used in the literature. For the purpose of infarct detection, sparse regularization in the spatial gradient domain of the action potential has been shown to be effective [2]. It is based on the idea that between depolarization and repolarization (i.e.…”

“…L1 norm penalty was used to enforce sparsity to the gradient of action potential and epicardial potential was obtained as inverse solution in [3,4]. In [1,2], total-variation minimization was used to enforce sparsity and the inverse solution obtained was applied to quantify transmural infarcts at different locations of the heart. However, the performance of sparse regularization based inverse ECG methods in the presence of nontransmural infarcts, especially endocardial infarcts, remains largely unexplored.…”

Examining the Impact of Prior Models in Transmural Electrophysiological Imaging: A Hierarchical Multiple-Model Bayesian Approach

“…In a deterministic setting, spatial and/or temporal smoothness of the source models have been commonly enforced through different numerical techniques such as Tikhonov regularization (zero-order, first-order, and second-order) [25], [22] and truncated SVD [26], [27], [24]. Recently, L 1-norm based sparsity models have also been used to enforce low-dimensional features of the solutions in space [28], [29], [30], [31], [18]. In a probabilistic setting, similarly, Gaussian prior density distributions have been used to enforce the smoothness of the epicardial source distribution [32], [33], [34], [35], [36], [37], [38], while total-variation prior has been recently adopted to preserve the structural sparsity of transmural source distribution [39].…”