Modelling stochastic calcium waves in cardiac myocytes based on the two-pool CICR model

In this paper, stochastic 1D and 2D models based on the two-pool calcium-induced calcium release (CICR) process are presented. An anisotropic diffusion model is presented that approximates the calcium concentration in the cytosol as well as the sarcoplasmic reticulum (SR). The relative source strengths in 1D and 2D are adjusted to simulate the behaviour of a point source array in the real 3D problem. The numerical conversion presented involves the convolution between the Green's and Heaviside functions. The models are solved using the Crank Nicolson (CN) and alternating direction implicit (ADI) for the 1D and 2D cases, respectively. These methods are known to be stable. Results are presented for the comparison between the two models.