Fractional-order modeling of myocardium structure effects on atrial fibrillation electrograms

Atrial fibrillation (AF) is the most common cardiac arrhythmia with mechanisms of initiation and sustaining that are not fully understood. The clinical procedure for AF contemplates the analysis of the atrial electrograms, whose morphology has been correlated with the underlying structure of the atrial myocardium. This study employs a mathematical model incorporating fractional calculus to simulate cardiac electrical conduction, accounting for tissue structural inhomogeneities using complex-valued orders. Simulations of different wavefront propagation patterns were performed, and virtual electrograms were analyzed using an asymmetry factor. Our results evinced that the shapes of the action potential and the propagating wavefront can be modulated through the fractional order under both healthy and AF conditions. Moreover, the asymmetry factor changes with variations in the fractional order. For a given propagation pattern under AF conditions, variation intervals for the asymmetry factor can be generated by forming sets of simulations with different configurations for the fractional order, representing diverse samples of atrial tissue with varying degrees of structural heterogeneity. This approach successfully reproduces the electrogram negative deflection predominance seen in AF patients, which standard integer-order models cannot predict. Our fractional-order conduction model aligns with the effects of atrial structure on the electrical dynamics observed in clinical AF. Therefore, it offers a valuable tool for studying cardiac electrophysiology, encompassing both electrical and structural interactions of the tissue within a unified model.