Cardiac Action Potential Model with Spatial Subcellular Calcium Cycling and Physiological Transmembrane Currents

Abstract

Calcium (Ca) is a key player in excitation-contraction (EC) coupling in the cardiac myocyte. When Ca enters through L-type Ca channels, it opens the ryanodine receptor (RyR) channels on the sarcoplasmic reticulum (SR) which stores a large amount of Ca (Ca induced Ca release). There are about 20,000 SR units and each RyR can sense only the local Ca concentration. Most computer cardiac action potential models use a single Ca concentration, which limits accurate modeling of intracellular Ca cycling. This is because the RyRs do not sense the average Ca concentration of the whole cell. Different aspects limit the utility of various models for investigation of intracellular Ca cycling related phenomena such as delayed afterdepolarizations (DADs) and catecholaminergic polymorphic ventricular tachycardia (CPVT) (since Ca concentrations in these phenomena are strongly heterogeneous within the cell). In order to investigate these phenomena, we developed a mathematical action potential model based on the spatial Ca model by Restrepo et al and physiological transmembrane currents by Shannon et al and Mahajan et al. In order to have more natural sparks, we increased the number of grid points for Ca diffusions from the model by Restrepo et al. Then we tuned the model to exhibit physiological action potential duration (APD) and Ca transients for long and short pacing cycle lengths (PCL). At short PCL, this hybrid model shows both voltage driven alternans due to steep APD restitution and Ca driven alternans due to luminal Ca regulation-mediated mechanism. In addition to alternans, this model exhibits Ca waves and DADs. This mathematical model of the cardiac myocyte provides a sort of minimal model to explore the spatio-temporal aspects of wave initiation, propagation and DAD induction related to normal and pathophysiological conditions.