A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations—discretisation, ODE-solution, linear system solution, and parallelisation—is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme.