Multiscale simulation and parallel space-time adaptivity of calcium sparks in cardiac myocytes

Calcium serves as the bidirectional link between the heart's electrical excitation and contraction. Electrical excitation induces an influx of Calcium across the sarcolemma and T-tubular membrane, triggering calcium release from the sarcoplasmic reticulum. Calcium sparks, the fundamental events of calcium release from the SR, are initiated in specialized microdomains where Ryanodine Receptors and L-type calcium channels co-locate. The spatial heterogeneity of Calcium release and the random occurrence of strong release fluxes render simulations challenging. Developing mathematical models and efficient simulations of detailed calcium spark models is crucial to understanding heart function. In this paper, we introduce space-time adaptivity within a parallel computing framework into the multiscale simulation of calcium sparks in cardiac myocytes to improve the stability and performance of these simulations.

We model intracellular calcium concentrations in both the cytoplasm and the SR domains using a set of coupled reaction-diffusion equations. Spatial grid adaptivity is implemented through multilevel finite element methods to account for the spatial heterogeneity of intracellular Ca²⁺ release. Rosenbrock-type techniques handle small time steps for simulating stochastic channel opening and closing in the Ca²⁺ release units (CRUs).

Our test cases demonstrate the superior efficiency of the space-time adaptive approach in optimizing computational resources. The parallel space-time adaptive method accelerates simulations of calcium sparks by a factor of 16.07.

The efficiency and speed gains in Calcium spark simulations are significant and enable modeling based research into previously difficult to tackle questions with regard to sub-micrometer scale models, e.g with respect to local interactions between the Sodium Calcium Exchanger and RyR clusters.