Multiscale modeling and numerical simulation of calcium cycling in cardiac myocytes

Simulation of electrophysiology and intracellular Ca(2+) dynamics in cardiomyocytes comprises fast stochastic dynamics in tiny subcompartments, partial differential equations (PDEs) with stochastic source terms for concentration fields, and the globally coupling membrane potential. We use highly unstructured meshes appropriate for the spatial heterogeneity of intracellular Ca(2+) release, and adaptive time-stepping algorithms appropriate for the simulation of stochastic channel opening and closing in subcompartments like the Ca(2+) release units (CRUs). A set of reactiondiffusion equations describes the behavior of the intracellular concentration fields on length scales from tens of nanometers to cell size (tens of micrometers) and milliseconds to tens of seconds. Detailed highly stochastic CRU models drive source functions in the PDE model. These CRU models cover dynamics with time scales below 1 ms and length scales from a few to a few hundred nm. The spatially detailed Ca(2+) dynamics and the cardiomyocyte membrane potential interact. Membrane potential introduces a global spatial coupling across the whole cell due to its large coupling length. Its dynamics are consequently represented by a set of ordinary differential equations (ODEs). We developed an efficient adaptive finite element simulator interface for the numerical simulation of this multiphysics and multiscale problem. The use of stationary Green functions within the CRU models and highly unstructured meshes for the PDE integration allows for bridging of many orders of magnitude of spatial scale, to represent accurately the Ca(2+) concentration dynamics from within a single CRU up to the level of the whole cell. The time scale separation between fast stochastic CRU dynamics and slower PDE dynamics limits efficiency with traditional approaches. We present new methods to circumvent that problem. We demonstrate large-scale numerical results for a 436 CRU cellular subdomain using many-core parallel machines