Modeling Ion Channel Delays with Fractional Calculus Reveals Early Afterdepolarizations Mechanisms

Noemi Zeraick Monteiro1, Rodrigo Weber dos Santos2, Sandro R Mazorche1
1UFJF, 2Federal University of Juiz de Fora


Abstract

Studying the impact of historical factors on ion channel kinetics is essential for understanding complex phenomena in cardiac electrophysiology, such as early afterdepolarizations (EADs), abnormal depolarizations during the action potential plateau associated with life-threatening arrhythmias. Traditional two-variable models without memory mechanisms struggle to accurately replicate EADs. A mathematical framework was developed by incorporating gamma Mittag-Leffler distributed delays and utilizing tools from Fractional Calculus to extend FitzHugh-Nagumo-type models. The approach was applied to a FitzHugh-Nagumo-type model for cardiac cells to generate EADs. The emergence of these oscillations was studied by analyzing characteristics of the memory kernels, such as their mean and variance. The system's stability was also examined. The potential utility of memory kernels in investigating EADs in simplified cardiac models was highlighted.