A mathematical framework using fractional calculus and distributed delays successfully reproduced early afterdepolarizations in cardiac models, unlike traditional memoryless two-variable models.
Incorporating ion channel memory via fractional calculus into traditional cardiac models enables the simulation of early afterdepolarizations, providing a new framework for studying arrhythmogenesis.
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.
Monteiro et al. (Mon,) conducted a other in Early afterdepolarizations (EADs). Mathematical framework with gamma Mittag-Leffler distributed delays vs. Traditional memoryless two-variable models was evaluated on Generation of early afterdepolarizations (EADs). A mathematical framework using fractional calculus and distributed delays successfully reproduced early afterdepolarizations in cardiac models, unlike traditional memoryless two-variable models.