Impact of the Endocardium in a Parameter Optimization to Solve the Inverse Problem of Electrocardiography

Electrocardiographic imaging aims at reconstructing cardiac electrical events from electrical signals measured on the body surface. The most common approach relies on the inverse solution of the Laplace equation in the torso to reconstruct epicardial potential maps from body surface potential maps. Here we apply a method based on a parameter identification problem to reconstruct both activation and repolarization times. From an ansatz of action potential, based on the Mitchell-Schaeffer ionic model, we compute body surface potential signals. The inverse problem is reduced to the identification of the parameters of the Mitchell-Schaeffer model. We investigate whether solving the inverse problem with the endocardium improves the results or not. We solved the parameter identification problem on two different meshes: one with only the epicardium, and one with both the epicardium and the endocardium. We compared the results on both the heart (activation and repolarization times) and the torso. The comparison was done on validation data of sinus rhythm and ventricular pacing. We found similar results with both meshes in 6 cases out of 7: the presence of the endocardium slightly improved the activation times. This was the most visible on a sinus beat, leading to the conclusion that inclusion of the endocardium would be useful in situations where endo-epicardial gradients in activation or repolarization times play an important role

Doctor of Philosophy

dissertationInverse Electrocardiography (ECG) aims to noninvasively estimate the electrophysiological activity of the heart from the voltages measured at the body surface, with promising clinical applications in diagnosis and therapy. The main challenge of this emerging technique lies in its mathematical foundation: an inverse source problem governed by partial differential equations (PDEs) which is severely ill-conditioned. Essential to the success of inverse ECG are computational methods that reliably achieve accurate inverse solutions while harnessing the ever-growing complexity and realism of the bioelectric simulation. This dissertation focuses on the formulation, optimization, and solution of the inverse ECG problem based on finite element methods, consisting of two research thrusts. The first thrust explores the optimal finite element discretization specifically oriented towards the inverse ECG problem. In contrast, most existing discretization strategies are designed for forward problems and may become inappropriate for the corresponding inverse problems. Based on a Fourier analysis of how discretization relates to ill-conditioning, this work proposes refinement strategies that optimize approximation accuracy o f the inverse ECG problem while mitigating its ill-conditioning. To fulfill these strategies, two refinement techniques are developed: one uses hybrid-shaped finite elements whereas the other adapts high-order finite elements. The second research thrust involves a new methodology for inverse ECG solutions called PDE-constrained optimization, an optimization framework that flexibly allows convex objectives and various physically-based constraints. This work features three contributions: (1) fulfilling optimization in the continuous space, (2) formulating rigorous finite element solutions, and (3) fulfilling subsequent numerical optimization by a primal-dual interiorpoint method tailored to the given optimization problem's specific algebraic structure. The efficacy o f this new method is shown by its application to localization o f cardiac ischemic disease, in which the method, under realistic settings, achieves promising solutions to a previously intractable inverse ECG problem involving the bidomain heart model. In summary, this dissertation advances the computational research of inverse ECG, making it evolve toward an image-based, patient-specific modality for biomedical research

Atrial location optimization by electrical measures for Electrocardiographic Imaging

[EN] Background: The Electrocardiographic Imaging (ECGI) technique, used to non-invasively reconstruct the epicardial electrical activity, requires an accurate model of the atria and torso anatomy. Here we evaluate a new automatic methodology able to locate the atrial anatomy within the torso based on an intrinsic electrical parameter of the ECGI solution. Methods: In 28 realistic simulations of the atrial electrical activity, we randomly displaced the atrial anatomy for +/- 2.5 cm and +/- 30 degrees on each axis. An automatic optimization method based on the L-curve curvature was used to estimate the original position using exclusively non-invasive data. Results: The automatic optimization algorithm located the atrial anatomy with a deviation of 0.5 +/- 0.5 cm in position and 16.0 +/- 10.7 degrees in orientation. With these approximate locations, the obtained electrophysiological maps reduced the average error in atrial rate measures from 1.1 +/- 1.1 Hz to 0.5 +/- 1.0 Hz and in the phase singularity position from 7.2 +/- 4.0 cm to 1.6 +/- 1.7 cm (p < 0.01). Conclusions: This proposed automatic optimization may help to solve spatial inaccuracies provoked by cardiac motion or respiration, as well as to use ECGI on torso and atrial anatomies from different medical image systems.This work was supported in part by: Generalitat Valenciana Grants [APOSTD/2017] and projects [GVA/2018/103]; Nvidia Corporation with GPU QUADRO P6000 donation.Gisbert Soler, V.; Jiménez-Serrano, S.; Roses-Albert, E.; Rodrigo Bort, M. (2020). Atrial location optimization by electrical measures for Electrocardiographic Imaging. Computers in Biology and Medicine. 127:1-8. https://doi.org/10.1016/j.compbiomed.2020.104031S18127Cuculich, P. S., Zhang, J., Wang, Y., Desouza, K. A., Vijayakumar, R., Woodard, P. K., & Rudy, Y. 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3D HEART SIMULATION AND ANALYSIS

This paper presents a new way to solve the inverse problem of electrocardiography in terms of heart model parameters. The developed event estimation and recognition method is based on an optimization system of heart model parameters. An ANN-based preliminary ECG analyzer system has been created to reduce the searching space of the optimization algorithm. The optimal model parameters were determined by minimizing the objective functions, as relations of the observed and model-generated body surface ECGs. The final evaluation results, validated by physicians were about 86\% correct. Starting from the fact that input ECGs contained various malfunction cases, such as Wolff-Parkinson-White (WPW) syndrome, atrial and ventricular fibrillation, these results suggest that this approach provides a robust inverse solution, circumventing most of the difficulties of the ECG inverse problem