Electrocardiographic Imaging in Atrial Fibrillation: Selection of the Optimal Tikhonov-Regularization Parameter

Abstract

Electrocardiographic imaging (ECGI) allows evaluating the complexity of atrial fibrillation (AF) signals using the Boundary Element Method and Tikhonov regularization. An accurate ECGI reconstruction is dependent on a proper selection of the regularization parameter $(\lambda)$. In this work, two ranges of $\lambda$ are explored to evaluate the effect of $\lambda$ on the quality of the ECGI reconstruction. ECGIs of 20 AF patients were computed using zero (TO), first (T1) and second (T2) order Tikhonov regularization (TR) for two ranges ofv: from 10–⁹ to 10² and 10–¹² to 10–⁴. Dominant frequencies (DF) and the number of rotors obtained with the two ranges and methods were compared. Zero-order Tikhonov showed to be more robust in $\lambda$ selection for different $\lambda$ ranges. For lower $\lambda$ ranges, higher DF was found $(T2,\ p < 0.05)$ and more rotors were detected for T1 and $T2(p < 0.01)$. Differences between TR methods compared by $\lambda$ ranges showed more variability in derived metrics for lower $\lambda$ range $(p < 0.01)$. Optimal ranges for $\lambda$ search differ among T0, T1 and T2. Election of lower than optimal $\lambda$ values result in an increased estimated electrical complexity.