Modeling calcium wave based on anomalous subdiffusion of calcium sparks in cardiac myocytes

Ca(2+) sparks and Ca(2+) 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 Ca(2+) sparks and Ca(2+) waves in cardiac myocytes, it fails to reasonably explain the full-width at half maximum(FWHM) paradox. However, the anomalous subdiffusion model successfully reproduces Ca(2+) sparks of experimental results. In this paper, in the light of anomalous subdiffusion of Ca(2+) sparks, we develop a mathematical model of calcium wave in cardiac myocytes by using stochastic Ca(2+) release of Ca(2+) release units (CRUs). Our model successfully reproduces calcium waves with physiological parameters. The results reveal how Ca(2+) 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 Ca(2+) spark can induce a Ca(2+) wave. With physiological Ca(2+) currents (2pA) through CRUs, it is shown that an initial firing of four adjacent CRUs can form a Ca(2+) wave. Furthermore, the phenomenon of calcium waves collision is also investigated.