Abstract

The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.

Highlights

  • The non-invasive electrocardiographic imaging (ECGI) is an imaging technique that allows one to non-invasively reconstruct the electrical activity of the heart using electrocardiograms and a patient specific heart-torso geometry

  • We detail the formulation of several methods used for choosing the optimal regularization parameter in terms of, both, the singular value decomposition in the case of the zero-order Tikhonov regularization and the generalized singular value decomposition in the case of L1-Norm regularization of the current density treated as a first-order Tikhonov regularization

  • For Method of Fundamental Solutions (MFS), Generalized Cross Validation (GCV) gives the best estimation of the optimal regularization parameter in terms of relative error (0.24 ± 0.15) and correlation coefficient (0.98 ± 0.04). we notice an improvement by 10% comparing to Robust Generalized Cross Validation (RGCV) and Composite REsidual and Smoothing Operator (CRESO) methods

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Summary

Introduction

The non-invasive electrocardiographic imaging (ECGI) is an imaging technique that allows one to non-invasively reconstruct the electrical activity of the heart using electrocardiograms and a patient specific heart-torso geometry This clinical tool is used by electrophysiologists to understand the mechanisms underlying arrhythmias and to localize targets for ablation therapy, such as for atrial fibrillation (Haissaguerre et al, 2013; Rudy, 2013). This technology is based on a mathematical relationship defining the propagation of the electrical activity between the heart and the torso.

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