Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. II. Modeling.

Guillaume Attuel,Hussein Yahia,Alain Arneodo,Françoise Argoul,Evgeniya Gerasimova-Chechkina

doi:10.3389/fphys.2019.00480

Abstract

In a companion paper (I. Multifractal analysis of clinical data), we used a wavelet-based multiscale analysis to reveal and quantify the multifractal intermittent nature of the cardiac impulse energy in the low frequency range ≲ 2Hz during atrial fibrillation (AF). It demarcated two distinct areas within the coronary sinus (CS) with regionally stable multifractal spectra likely corresponding to different anatomical substrates. The electrical activity also showed no sign of the kind of temporal correlations typical of cascading processes across scales, thereby indicating that the multifractal scaling is carried by variations in the large amplitude oscillations of the recorded bipolar electric potential. In the present study, to account for these observations, we explore the role of the kinetics of gap junction channels (GJCs), in dynamically creating a new kind of imbalance between depolarizing and repolarizing currents. We propose a one-dimensional (1D) spatial model of a denervated myocardium, where the coupling of cardiac cells fails to synchronize the network of cardiac cells because of abnormal transjunctional capacitive charging of GJCs. We show that this non-ohmic nonlinear conduction 1D modeling accounts quantitatively well for the “multifractal random noise” dynamics of the electrical activity experimentally recorded in the left atrial posterior wall area. We further demonstrate that the multifractal properties of the numerical impulse energy are robust to changes in the model parameters.

Highlights

Atrial fibrillation (AF) is the most common sustained tachyarrhythmia encountered in clinical practice (Nattel and Harada, 2014)
As the longitudinal electric field generated by repeatedly passing Action potentials (APs) drives the gap junction channels (GJCs), we propose in this study to consider the spatio-temporal dynamics of the GJC conductances especially at cardiac intercalated discs where most GJCs reside
Multifractal Analysis of the Simulated Impulse Energy Time-Series With the WT modulus maxima (WTMM) Method of Moments When applying the WTMM method to the impulse energy timeseries E(x, t) obtained by numerically integrating Equation 6 with periodically driven boundary condition (Equation 7) at x = 0 (Figure 3A’), we confirmed that the partition function Z(q, a) (Equation 17) obtained from the wavelet transform (WT) computed with the analysing wavelet g(3) (Figure 3B’) and its skeleton (Figure 3C’), displays scaling properties for q = −1 up to 5 over a range of time-scales larger than the typical interbeat ∼ 0.2 s (Figure 2B)

Summary

Introduction

Atrial fibrillation (AF) is the most common sustained tachyarrhythmia encountered in clinical practice (Nattel and Harada, 2014). It is sometimes not diagnosed until the occurrence of a severe complication such as embolic stroke. Current understanding of the onset and perpetuation of most tachyarrhythmias including AF presumes the involvement of circuit reentries. This scenario was established historically from the observation of reciprocating rhythms initiated in the atrio-ventricular node via the fast and slow pathways of impulse conduction. Atrial flutter and regular tachycardias were inferred to be rooted in circling conduction pathways, as going around anatomical obstacles

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Results

Conclusion