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.
Electrocardiographic imaging (ECG imaging) is a method to depict electrophysiological processes in the heart. It is an emerging technology with the potential of making the therapy of cardiac arrhythmia less invasive, less expensive, and more precise. A major challenge for integrating the method into clinical workflow is the seamless and correct identification and localization of electrodes on the thorax and their assignment to recorded channels. This work proposes a camera-based system, which can localize all electrode positions at once and to an accuracy of approximately 1+/-1 mm. A system for automatic identification of individual electrodes is implemented that overcomes the need of manual annotation. For this purpose, a system of markers is suggested, which facilitates a precise localization to subpixel accuracy and robust identification using an error-correcting code. The accuracy of the presented system in identifying and localizing electrodes is validated in a phantom study. Its overall capability is demonstrated in a clinical scenario.
Electrocardiographic imaging (ECGI) is a non-invasive diagnostical tool solving the inverse problem of ECG, which means the reconstruction of electrical potentials in the heart from the ECG data. The ill-posednees of this problem makes necessary addition of a-priori information. A typical approach is the Tikhonov regularization looking for the best balance between minimizing the data misfit and the regularization term which characterizes desired properties of the solution. However, the quality of an obtained solution, and as a result its clinical relevance, could be significantly improved by application of methods for non-smooth regularization. In this work we introduced a possible dictionary definition for the electrical sources in the heart: we subdivided the heart into 100 pieces and considered them to constitute the columns of our dictionary. We also provided a short discussion on differences between synthesis and analysis models, tested the analysis algorithm with a penalty matrix which is not related to the defined dictionary (discrete gradient operator for all heart points) and compared the performance of these three algorithms for two simulated ventricular ectopic foci. The analysis method with the gradient operator showed a slightly superior performance although all methods correctly identified the regions of interest.
D. Potyagaylo, W. H. W. Schulze, and O. Dössel. Local regularization of endocardial and epicardial surfaces for better localization of ectopic beats in the inverse problem of ECG. In Computing in Cardiology Conference, vol. 41, pp. 837-840, 2014
The problem of non-invasively finding cardiac electri- cal sources from body surface potential maps (BSPM) is ill-posed. A standard Tikhonov regularization approach to the problem produces a solution biased toward the elec- trodes and thus to the left ventricular epicardium, which limits its potential to reconstruct endocardial sources. In this work we consider a transmembrane voltages based in- verse problem of ECG for the identification of extrasys- tole origins from simulated BSPM. With use of a pair of heart wall epicardial/endocardial extrasystoles and a pair of septal ectopic foci we demonstrate the performance of the inverse procedures while firstly solving the problem for all nodes, then for epicardium and endocardium sep- arately. Based on the observations and the logic behind the gradient of sources we define simple rules on how to classify an extrasystole under consideration according to these 3 reconstructions. Furthermore, when the amount of noise is known, we propose a new method with two regu- larization parameters which assign different weightings to endocardial and epicardial components of the solution.
Solving the inverse problem of electrocardiography could help to diagnose and to plan the treatment of heart diseases. The conductivity distribution within the body is important to solve the inverse problem. In this work the influence of neglecting an organ as an inhomogeneity on the forward and inverse problem was investigated. For different simplified body models optimal conductivities were determined by minimizing the error between the BSPMs produced by this model and reference BSPMs calculated with a complex model containing eight segmented organs. The BSPMs from simulated catheter stimulations were used for the optimization. With the obtained optimal conductivities lead-field matrices were calculated and compared to the lead-field matrix of the complex model. Besides the heart, the lungs and the intracardial blood, we found that the liver also plays an important role to describe the relationship between the activation in the heart and the body surface potential map correctly.
Electrocardiographic imaging (ECGI) facilitates the non-invasive reconstruction of electrical activity in the entire heart at once. ECGI requires both recordings of multi-channel ECG signals as well as an MRI-based model of the thorax. The model is used to solve the underlying Poissons problem, which relates the gradient of transmembrane voltages in the heart to the ECG and is a spatial differential equation. In ECGI, this relationship has to be established before starting inverse calculations, i.e. the forward problem has to be solved. It solution depends strongly on the spatial discretization of the model, as its resolution affects the representation of the source gradients. To study the convergence of resolution-related effects in the forward problem, we use a simplified thorax model which allows for very high resolutions. An ECG is produced for the excitation origin of a premature ventricular contraction in the apex. The study reveals that the greatest resolution-related effects vanish below a resolution of 5 mm of the cardiac tissue. At below 1 mm, resolution effects stabilize and only marginal effects from the spatial structure of the mesh persist down to a resolution of 0.25 mm.