Estimation of stochastic behaviour in cardiac myocytes: I. Ca2+ movements inside the cytosol and sarcoplasmic reticulum on curvilinear domains.

Since the discovery of Ca²⁺ sparks and their stochastic behaviour in cardiac myocytes, models have focused on the inclusion of stochasticity in their studies. While most models pay much attention to the stochastic modelling of cytosolic Ca²⁺ concentration the coupling of Ca²⁺ sparks and blinks in a stochastic model has not been explored fully. The cell morphology in in silico studies in the past is assumed to be Cartesian, spherical or cylindrical. The application on curvilinear grids can easily address certain restrictions posed by such grid set up and provide more realistic cell morphology. In this paper, we present a stochastic reaction-diffusion model that couples Ca²⁺ sparks and blinks in realistic shapes of cells in curvilinear domains. Methodology: Transformation of the model was performed to the curvilinear coordinate system. The set of equations is used to produce Ca²⁺ waves initiated from sparks and blinks. A non-buffered and non-dyed version as well as a buffered and dyed version of these equations were studied in light of observing the dynamics on the two different systems. For comparison, results for both the Cartesian and curvilinear grids are provided. Results and conclusions: A successful demonstration of the application of curvilinear grids serving as basis for future developments.