Jingjia Xu

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.

Lp-Norm Regularization in Volumetric Imaging of Cardiac Current Sources

Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm (1 < p < 2) constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.

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.

Noninvasive electrocardiographic imaging of chronic myocardial infarct scar.

BACKGROUND Myocardial infarction (MI) scar constitutes a substrate for ventricular tachycardia (VT), and an accurate delineation of infarct scar may help to identify reentrant circuits and thus facilitate catheter ablation. One of the recent advancements in characterization of a VT substrate is its volumetric delineation within the ventricular wall by noninvasive electrocardiographic imaging. This paper compares, in four specific cases, epicardial and volumetric inverse solutions, using magnetic resonance imaging (MRI) with late gadolinium enhancement as a gold standard. METHODS For patients with chronic MI, who presented at Glasgow Western Infirmary, delayed-enhancement MRI and 120-lead body surface potential mapping (BSPM) data were acquired and 4 selected cases were later made available to a wider community as part of the 2007 PhysioNet/Computers in Cardiology Challenge. These data were used to perform patient-specific inverse solutions for epicardial electrograms and morphology-based criteria were applied to delineate infarct scar on the epicardial surface. Later, the Rochester group analyzed the same data by means of a novel inverse solution for reconstructing intramural transmembrane potentials, to delineate infarct scar in three dimensions. Comparison of the performance of three specific inverse-solution algorithms is presented here, using scores based on the 17-segment ventricular division scheme recommended by the American Heart Association. RESULTS The noninvasive methods delineating infarct scar as three-dimensional (3D) intramural distribution of transmembrane action potentials outperform estimates providing scar delineation on the epicardial surface in all scores used for comparison. In particular, the extent of infarct scar (its percentage mass relative to the total ventricular mass) is rendered more accurately by the 3D estimate. Moreover, the volumetric rendition of scar border provides better clues to potential targets for catheter ablation. CONCLUSIONS Electrocardiographic inverse solution providing transmural distribution of ventricular action potentials is a promising tool for noninvasively delineating the extent and location of chronic MI scar. Further validation on a larger data set with detailed gold-standard data is needed to confirm observations reported in this study.

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.

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.

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

Noninvasive cardiac electrophysiological (EP) imaging aims to mathematically reconstruct the spatiotemporal dynamics of cardiac sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, a fixed-model approach enforces the source distribution to follow a pre-assumed structure that does not always match the varying spatiotemporal distribution of actual sources. To understand the model-data relation and examine the impact of prior models, we present a multiple-model approach for volumetric cardiac EP imaging where multiple prior models are included and automatically picked by the available ECG data. Multiple models are incorporated as an Lp-norm prior for sources, where p is an unknown hyperparameter with a prior uniform distribution. To examine how different combinations of models may be favored by different measurement data, the posterior distribution of cardiac sources and hyperparameter p is calculated using a Markov Chain Monte Carlo (MCMC) technique. The importance of multiple-model prior was assessed in two sets of synthetic and real-data experiments, compared to fixed-model priors (using Laplace and Gaussian priors). The results showed that the posterior combination of models (the posterior distribution of p) as determined by the ECG data differed substantially when reconstructing sources with different sizes and structures. While the use of fixed models is best suited in situations where the prior assumption fits the actual source structures, the use of an automatically adaptive set of models may have the ability to better address model-data mismatch and to provide consistent performance in reconstructing sources with different properties.

Hierarchical multiple-model Bayesian approach to transmural electrophysiological imaging.

Noninvasive electrophysiological (EP) imaging of the heart aims to mathematically reconstruct the spatiotemporal dynamics of cardiac current sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, this approach enforces the source distribution to follow a preassumed spatial structure that does not always match the varying spatiotemporal distribution of current sources. We propose a hierarchical Bayesian approach to transmural EP imaging that employs a continuous combination of multiple models, each reflecting a specific spatial property for current sources. Multiple models are incorporated as an Lp-norm prior for current sources, where p is an unknown hyperparameter with a prior probabilistic distribution. The current source estimation is obtained as an optimally weighted combination of solutions across all models, the weight being determined from the posterior distribution of p inferred from ECG data. The accuracy of our approach is assessed in a set of synthetic and real-data experiments on human heart-torso models. While the use of fixed models (L1- and L2-norm) only properly recovers sources with specific structures, our method delivers consistent performance in reconstructing sources with various extents and structures.

Evaluation of 2-norm versus sparsity regularization in spline-based joint reconstruction of epicardial and endocardial potentials from body-surface measurements

Cardiac electrical imaging, reconstruction of cardiac electrical activity from body surface potentials, has gained increasing clinical interest as a noninvasive imaging modality for underlying electrophysiological phenomena. We have previously presented an approach using 1) a transmural regularization to improve the joint reconstruction of electrical potentials on both the inner and outer surface of the ventricles; and 2) a nonlinear low-order dynamic spline-based parameterization to provide temporal regularization. This approach was tested for localizing endocardial pacing locations obtained from healthy hearts during catheter-based stimulation, using imprecise thorax geometry derived from limited computed tomographic scans. Results were promising, but the reconstructed solutions were overly smooth in space and time. Recently, L1-norm based spatial sparsity methods such as total-variation regularization have been reported to return more realistically sharp solutions in cardiac electrical imaging. In this paper, we compare and evaluate the performance of L2-norm based Tikhonov and L1-norm based total-variation regularization in conjunction with the spline parameterization and the transmural regularization. Numerical experiments were conducted on three subjects, each with multiple (~ 20) endocardial pacing sites and evaluated against true pacing locations reported by the CARTO catheter mapping system. Variability was observed in the performance of the two methods across both pacing sites and subjects. However, the dependence of the results on subjects and ventricular pacing locations suggests that there is some correlation between the results and the specific geometry in each case. In our future work, we will investigate the approach of automatically inferring an optimal regularization norm from the data rather than fixing it a priori.

Electrophysiological imaging of volumetric infarct border using a spatio-temporal LP-norm constraint

Imaging the bioelectrical source distribution along the infarct border is of important therapeutic potential as infarct border is the common site for reentry circuits leading to life-threatening arrhythmias. Although it can be tackled by computational reconstruction of volumetric cardiac source using body-surface voltage data, the problem is notoriously ill-posed without a unique solution. Progress towards 3D cardiac source reconstruction is further hindered by the complex spatio-temporal property of cardiac current sources, which decides that common L1 and L2-norm constraints are not proper because the underlying assumption is either too focal or too smooth to reflect the property of the source distribution. In this work, we propose a general regularization with Lp-norm (1 <; p <; 2) constraint to bridge the gap between L1 and L2 solutions in cardiac source reconstruction along the infarct border. We further incorporate temporal information into Lp-norm constraint to promote consistency over time as well as robustness to noise. In a set of computer-simulated and real-data experiments, we demonstrate the superiority of the proposed method in reflecting the complex spatial structure of source distribution along 3D infarct border during the ST-segment of an ECG cycle, over L1 or L2 counterparts.