Regularization Techniques for ECG Imaging during Atrial Fibrillation: A Computational Study

Abstract

The inverse problem of electrocardiography is usually analyzed during stationary rhythms. However, the performance of the regularization methods under fibrillatory conditions has not been fully studied. In this work, we assessed different regularization techniques during atrial fibrillation (AF) for estimating four target parameters, namely, epicardial potentials, dominant frequency (DF), phase maps, and singularity point (SP) location. We use a realistic mathematical model of atria and torso anatomy with three different electrical activity patterns (i.e., sinus rhythm, simple AF, and complex AF). Body surface potentials (BSP) were simulated using Boundary Element Method and corrupted with white Gaussian noise of different powers. Noisy BSPs were used to obtain the epicardial potentials on the atrial surface, using 14 different regularization techniques. DF, phase maps, and SP location were computed from estimated epicardial potentials. Inverse solutions were evaluated using a set of performance metrics adapted to each clinical target. For the case of SP location, an assessment methodology based on the spatial mass function of the SP location, and four spatial error metrics was proposed. The role of the regularization parameter for Tikhonov-based methods, and the effect of noise level and imperfections in the knowledge of the transfer matrix were also addressed. Results showed that the Bayes maximum-a-posteriori method clearly outperforms the rest of the techniques but requires a priori information about the epicardial potentials. Among the purely non-invasive techniques, Tikhonov-based methods performed as well as more complex techniques in realistic fibrillatory conditions, with a slight gain between 0.02 and 0.2 in terms of the correlation coefficient. Also, the use of a constant regularization parameter may be advisable since the performance was similar to that obtained with a variable parameter (indeed there was no difference for the zero-order Tikhonov method in complex fibrillatory conditions). Regarding the different targets, DF and SP location estimation were more robust with respect to pattern complexity and noise, and most algorithms provided a reasonable estimation of these parameters, even when the epicardial potentials estimation was inaccurate. Finally, the proposed evaluation procedure and metrics represent a suitable framework for techniques benchmarking and provide useful insights for the clinical practice.

Statistical guidance of VT ablation

“…14 The application of this approach is wide, yet its accuracy of reconstruction is still being defined, and in a recent calibration study was ~1–2 cm distant from sites of ventricular pacing. 15 ECGI has had notable successes, 5 but given the large number of ECGI approaches applied to different arrhythmias, 16 it would be useful to compare methods head-to-head to ensure that they are identifying similar mechanisms and locations.…”

Including a Priori Knowledge in the Solution of the Inverse Problem During Atrial Fibrillation

“…Sinus rhythm and AF patterns are both simulated, from which the epicardial distribution of potentials are calculated applying Tikhonov-based regularization methods. Simulated BSP are referenced to the Wilson Terminal Center, corrupted with additive Gaussian noise (SNR= 20 dB) and filtered using a 4 th -order bandpass Butterworth filter (fc 1 =3 Hz and fc 2 =30Hz for AF models, fc 1 =0 Hz and fc 2 =30Hz for SR) [1,11].…”

“…where y t is the vector containing the torso measurements, and λ 1 is the global regularization parameter, which is computed by using the L-Curve method for the totality of time instants [1]. The solution for this problem is:…”

“…To assess the performance of regularization methods, we propose several metrics, similarly to those proposed in [1,13]. Similarity between real and estimatedx epicardial potentials is quantified by the relative difference measurement star (RDMS), Pearson's correlation coefficient (CC), and root mean squared error (RMSE).…”

Three-dimensional Multiscale Modelling and Simulation of Atria and Torso Electrophysiology

“…Both approaches pursue the same answers in regards the mechanisms and origin of atrial arrhythmias. During the present decade, there have been a number of works based on both, the analysis of the P-wave and torso surface potentials (Keller et al 2010;Weber, Luik, et al 2011;Krueger et al 2012;Lenkova et al 2012;Alday et al 2015;Perez Alday et al 2016) and on the electrocardiographic imaging ECGi (Rudy 2010;Wang et al 2012;Shah et al 2014;Figuera et al 2016).…”