Ion Channel Memory Drives Cardiac Early Afterdepolarizations in Fractional Models

Noemi Zeraick Monteiro, Rodrigo Weber dos Santos () and Sandro Rodrigues Mazorche
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Noemi Zeraick Monteiro: Graduate Program in Computational Modeling, Federal University of Juiz de Fora, Juiz de Fora 36036-900, Brazil
Rodrigo Weber dos Santos: Graduate Program in Computational Modeling, Federal University of Juiz de Fora, Juiz de Fora 36036-900, Brazil
Sandro Rodrigues Mazorche: Department of Mathematics, Federal University of Juiz de Fora, Juiz de Fora 36036-900, Brazil

Mathematics, 2025, vol. 13, issue 10, 1-29

Abstract: Understanding how past factors influence ion channel kinetics is essential for understanding complex phenomena in cardiac electrophysiology, such as early afterdepolarizations (EADs), which are abnormal depolarizations during the action potential plateau associated with life-threatening arrhythmias. We developed a mathematical framework that extends Hodgkin-Huxley type equations with gamma Mittag-Leffler distributed delays, using tools from Fractional Calculus. Traditional memoryless two-variable models fail to reproduce EADs. Our approach modifies FitzHugh-Nagumo, Mitchell-Schaeffer, and Karma cardiac models, enabling the generation of EADs in each of them. We analyze the emergence of these oscillations by discussing the fractional parameters and the mean and variance of the memory kernels. Stability observations are also presented.

Keywords: fractional cardiac models; gamma Mittag-Leffler probability density function; delay kernels; early afterdepolarizations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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