Binary optimization for source localization in the inverse problem of ECG

Abstract

The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance.

Inverse localization of ischemia in a 3D realistic geometry: A level set approach

“…Then, the forward model was solved and BSPMs were corrupted by AWGN with different SNRs. In order to evaluate the inverse solutions, a binary output was considered (healthy/ischemic) as presented in figure 2, and the following metrics were used [6,7]: (1) the correlation coefficient (CC) between the real and the reconstructed configuration;…”

“…Several works have analyzed the the IPE in terms of localizing cardiac ischemic regions [4][5][6][7]. In these studies the ischemic regions are assessed by reconstructing the transmembrane or the epicardial potentials at a single time-instant during the plateau phase of the action poten-tial, thus ignoring the spatiotemporal correlation information contained in the BSPMs.…”

ECG imaging of ventricular tachycardia: evaluation against simultaneous non-contact mapping and CMR-derived grey zone

“…To perform ECG imaging, TMVs were used as a source model [24,34,42,46,56,62] and the related BSPMs for TMV sources in a volumetric finite element grid of the ventricles were computed under quasistatic assumptions using the bidomain model [17]. Calculations on the personalized patient geometry as in [45] yield a linear formulation of the forward problem that relates the TMVs in the heart x 2 R n (n ¼ 2346) to the potentials at m BPSM electrodes b 2 R m (m ¼ 51), where A 2 R mÂn is the lead field matrix:…”

“…3 to demonstrate the effect of this choice. Spatio-temporal regularization with the method by Huiskamp and Greensite is well suited for stable reconstruction across the time points of a VT cycle, compared to methods that identify focal activity or that operate on single time points [46,49,50]. Further, it is better suited for cases with large scars compared to spatio-temporal methods that make rigorous assumptions on action potential shapes and tissue excitability, such as rule-based approaches [47] or the critical times method [26].…”

Comparison of Baseline Wander Removal Techniques considering the Preservation of ST Changes in the Ischemic ECG: A Simulation Study

“…We can adjust the models that govern the action potential (AP) in the cardiac myocyte to represent ischemia-induced change, let the electrical depolarization and subsequent repolarization propagate in the heart, and generate the body surface potential map on the chest. We can then place electrodes on the torso and extract the simulated 12-lead ECG [17, 18]. With this approach, we have the advantage of being able to locate the most relevant fiducial points (e.g., QRS complex or ST segment) in the simulated ECG and are thus capable of performing an analysis that is free of detection errors.…”