Spherical topology in cardiac simulations

Computational simulations of the electrodynamics of cardiac fibrillation yield a great deal of useful data and provide a framework for theoretical explanations of heart behavior. Extending the application of these mathematical models to defibrillation studies requires that a simulation should sustain fibrillation without defibrillation intervention. In accordance with the critical mass hypothesis, the simulated tissue should be of a large enough size. The choice of biperiodic boundary conditions sustains fibrillation for a longer duration than no-flux boundary conditions for a given area, and so is commonly invoked. Here, we show how this leads to a boundary condition artifact that may complicate the analysis of defibrillation efficacy; we implement an alternative coordinate scheme that utilizes spherical shell topology and mitigates singularities in the Laplacian found with the usual spherical curvilinear coordinate system.