Capacitive Memory Suppresses Alternans and Promotes Spontaneous Activity in a Fractional-Order Minimal Cardiomyocyte Model

Abstract

Electrical activity in cardiomyocytes is typically modeled using an ideal parallel resistor-capacitor circuit. However, studies have suggested that the passive properties of cell membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduces capacitive memory effects, i.e., dynamics are influenced by the prior membrane potential history. We recently showed that fractional-order membrane dynamics alters ionic currents and spiking rates in a neuronal model. Here, we investigate the effects of fractional-order membrane dynamics in a cardiomyocyte model using the minimal 3-variable Fenton-Karma (FK), chosen because the FK model, with first-order derivative membrane dynamics, does not have short-term memory. We performed simulations for fractional-orders between 0.5 and 1 and variable cycle lengths. We found that the action potential duration (APD) was shortened as the fractional-order decreased, for all cycle lengths. As a consequence, the minimum cycle length (MCL) for loss of 1:1 capture decreased as fractional-order decreased. Further, at short cycle lengths at which APD alternans was present in the first-order model, alternans was suppressed, such that the cycle length for alternans onset decreased for decreasing fractional-order. For fractional-order less than ∼0.82, alternans was not present at any cycle length. Finally, for fractional-order less than ∼0.75, we found that the model produced spontaneous action potentials following pacing. Short-term memory effects were represented by a hypothetical memory “current,” which we found was primarily outward for fractional-order closer to 1, shortening APD, while it was primarily inward for fractional-order closer to 0.5, generating spontaneous action potentials. Collectively, our results suggest the capacitive memory, reproduced by a fractional-order model, may play a role in both alternans formation and suppression and pacemaking.