Variable–Order Model of Cardiac Fibrillation

Abstract

Atrial fibrillation is a cardiac disorder marked by rapid and disorganized electrical activity, leading to atrial mechanical dysfunction. The alterations in electrophysiological properties during this arrhythmia are not solely attributed to electrical remodeling, structural changes in atrial tissue are also involved. This work aims to formulate a mathematical model for fibrillatory electrical conduction through the implementation of variable-order fractional derivatives. The adoption of such an operator is intended to represent the process of structural remodeling, which has been related to the course of atrial fibrillation. Simulations are performed using a simplified model of the ionic kinetics of the cardiac cell membrane, which allows for distinct electrophysiological properties through its parameterization. For the variable order, a fluctuating function is adopted that can be interpreted as the progression of structural remodeling when the order decreases, and the reverse process when the order increases. Fibrillatory propagation is initiated by generating reentrant conduction, also known as a rotor. We observed that, on the one hand, electrical conduction becomes chaotic as the fractional order decreases, and persists under such dynamics while the order increases. On the other hand, rotational activity persists during the fluctuation of the fractional order. Such mesoscopic outcomes depend on the sensitivity of the microscopic electrophysiological properties to the variations of the fractional order. Moreover, both propagation patterns can be associated with the known course of clinical AF. These results suggest that the fractional order model of cardiac electrophysiology may provide insight into the AF underlying mechanisms.