Gating-enhanced IMEX splitting methods for cardiac monodomain simulation

摘要

The electrical activity in excitable cardiac tissue can be simulated using the so-called monodomain model. The monodomain model is a continuum-based multi-scale model that consists of non-linear ordinary differential equations describing the electrical activity at the cellular scale along with a semi-linear parabolic partial differential equation describing electrical propagation at the tissue scale. The standard scale-based splitting method for simulating the monodomain model is to split the tissue and cell models, applying different integrators to each. Typically, the tissue model is simulated with an implicit time-integration method, and the cell model is simulated with an explicit or explicit-exponential one. We demonstrate that the application of implicit-explicit (IMEX) linear multistep or Runge-Kutta methods to this splitting can have poor stability properties when the cell model is stiff. We propose a novel gating-enhanced IMEX splitting that treats the tissue variable and the (typically stiff) cell model gating variables together implicitly. The performance of 14 different IMEX methods using both splittings is measured in a variety of one- and two-dimensional experiments. The low incremental overhead combined with the substantially improved stability of the gating-enhanced splitting is shown to result in a performance increase of approximately a factor of four for simulations of the monodomain model with the stiff ten Tusscher-Panfilov model of human endocardial cells.