Modeling Calcium Wave Based on Anomalous Subdiffusion of Calcium Sparks in Cardiac Myocytes

Abstract

Ca2+ sparks and Ca2+ waves play important roles in calcium release and calcium propagation during the excitation-contraction (EC) coupling process in cardiac myocytes. Although the classical Fick's law is widely used to model Ca2+ sparks and Ca2+ waves in cardiac myocytes, it fails to reasonably explain the full-width at half maximum(FWHM) paradox. However, the anomalous subdiffusion model successfully reproduces Ca2+ sparks of experimental results. In this paper, in the light of anomalous subdiffusion of Ca2+ sparks, we develop a mathematical model of calcium wave in cardiac myocytes by using stochastic Ca2+ release of Ca2+ release units (CRUs). Our model successfully reproduces calcium waves with physiological parameters. The results reveal how Ca2+ concentration waves propagate from an initial firing of one CRU at a corner or in the middle of considered region, answer how large in magnitude of an anomalous Ca2+ spark can induce a Ca2+ wave. With physiological Ca2+ currents (2pA) through CRUs, it is shown that an initial firing of four adjacent CRUs can form a Ca2+ wave. Furthermore, the phenomenon of calcium waves collision is also investigated. © 2013 Chen et al.