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 inference of patient-specific intramural electrical activity from surface electrocardiograms (ECG) lacks a unique solution in the absence of prior assumptions. While 3D cardiac electrophysiological models emerged to be a viable vehicle for constraining this inference with knowledge about the spatiotemporal dynamics of cardiac excitation, it is important for the inference to be robust to errors in these highdimensional model predictions given the limited ECG data. We present an innovative solution to this problem by exploiting the low-dimensional structure of the solution space -a powerful regularizer in overcoming the lack of measurements -within the dynamic inference guided by physiological models. We present the first Bayesian inference framework that allows the exploration of both the spatial sparsity of cardiac excitation and its complex nonlinear spatiotemporal dynamics for an improved inference of patient-specific intramural electrical activity. The benefit of this integration is verified in both synthetic and real-data experiments, where we present one of the first detailed, point-by-point comparison of the reconstructed electrical activity to in-vivo catheter mapping data.
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 neighborhoodsmoothness 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.
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