ODE solving for cardiac action potential models

Just a quick post to highlight a new paper by Jon Cooper, Ray Spiteri and me, which describes the use of Chaste and CellML to solve cardiac action potential model equations.

The paper in Frontiers in Physiology is in a special issue covering Interoperability in Scientific Computing and Health Informatics. If you ever work with action potential models, or indeed any stiff* ODEs, then it is probably worth a read.

The paper aims to:

  • Demonstrate Chaste’s capabilities for nice handling of CellML models, and the range of solvers that can be used;
  • Show the tolerances/timesteps that are required for (i) stability and (ii) accuracy for each model and solver (and highlight the fact you might get plausible looking nonsense if you only check stability!);
  • Present some speed benchmarking on the best ODE solver to use for a wide range of action potential models, in two settings: single-cell (the answer is CVODE); and tissue simulation (the answer is – it depends!). We describe some of the tricks and tips we’ve used to get things as fast as possible (analytic jacobians, lookup tables, choice of compiler etc.).

Comments and feedback are welcome.

*loose definition of ‘stiff’ is ODEs with different timescales at different times/in different equations.

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