Modeling myocardium structural changes during atrial fibrillation using variable-order derivatives

Abstract

Atrial fibrillation (AF) is characterized by rapid and chaotic electrical impulse propagation. While most computational models of cardiac electrophysiology focus on representing the electrical component, other factors, such as myocardial structure, also play a critical role in sustaining AF. Structural heterogeneities in the myocardium are known to modulate cardiac electrophysiology. This paper presents a novel electrophysiological model of atrial electrical dynamics using variable-order fractional derivatives. Previous studies have used fractional calculus operators with constant fractional orders to represent structural heterogeneities. However, structural alterations are progressive and contribute to AF development. To address this, we design two time-dependent functions for the fractional variable-order, inspired by experimental observations of atrial dilation and de-dilation, as well as stretch-relaxation cycles of cardiomyocytes. A phenomenological model of cardiac ionic kinetics is parameterized to reproduce action potentials under sinus rhythm and AF, and it is integrated into the variable-order model. Fibrillatory propagation is simulated by initiating a reentrant wave, establishing a stable rotor. The simulations are analyzed using phase singularity analysis to characterize propagation dynamics and dominant frequency analysis to quantify the local activation rate. Our results demonstrate that the model captures a diverse range of AF propagation patterns consistent with experimental observations, depending on the parameterization of the variable fractional order. Under sinus rhythm conditions, the propagation dynamics are either insensitive to variations in the variable fractional order or unable to sustain fibrillatory propagation, as expected in healthy atrial tissue. These findings highlight the ability of the variable-order model to integrate structural processes into electrophysiological dynamics, reproducing propagation patterns that align with experimental data. This model represents a promising tool for advancing our understanding of the mechanisms underlying AF.