A Patchwork Method to Improve the Performance of Current Methods for Solving the Inverse Problem of Electrocardiography

Abstract

Objective: Noninvasive electrocardiographic imaging (ECGI) reconstructs cardiac electrical activity from body surface potential measurements. However, current methods have demonstrated inaccuracies in reconstructing sinus rhythm, and in particular breakthrough sites. This study aims to combine existing inverse algorithms, making the most of their advantages while minimizing their limitations. Method: The "patchwork method" (PM) combines two classical numerical methods for ECGI: the method of fundamental solutions (MFS) and the finite-element method (FEM). We assume that the method with the smallest residual in the predicted torso potentials, computed using the boundary element method (BEM), provides the most accurate solution. The PM selects for each heart node and time step the method whose estimated reconstruction error is smallest. The performance of the PM was evaluated using simulated ectopic and normal ventricular beats. Results: Cardiac potentials and activation maps obtained with the PM (CC=0.63±0.01 and 0.61±0.05 respectively) were more accurate than MFS (CC=0.61±0.01 and 0.48±0.05 respectively), FEM (CC=0.58±0.01 and 0.51±0.02 respectively) or BEM (CC=0.57±0.02 and 0.49±0.02 respectively). The PM also located all epicardial breakthrough sites, whereas the traditional numerical methods usually missed one. Furthermore, the PM showed its robustness and stability in the presence of Gaussian noise added to the torso potentials. Conclusion: The PM overcomes some of the limitations of classical numerical methods, improving the accuracy of mapping important features of activation during sinus rhythm and paced beats. Significance: This novel method for optimizing ECGI solutions opens a new avenue for improving not only ECGI but also other inverse problems.

Direct Estimation of Equivalent Bioelectric Sources Based on Huygens’ Principle

“…Nowadays, the main research effort is toward finding a more efficient regularization technique to increase the accuracy of the above algorithms [9,[28][29][30][31][32][33]. For example, in [34], a "patchwork method", which combines two classical numerical methods for inverse ECG-the method of fundamental solutions (MFS) and the finite-element method (FEM)-is studied to increase the accuracy of the reconstructing sinus rhythm, particularly breakthrough sites. Another field of research work is pointing to improving all existing regularization methods with alternative techniques, such as solving the problem in the wavelet domain, obtaining a sparse solution with multitask elastic net, and transforming it back to the time domain [35].…”