Two-dimensional Chebyshev pseudospectral modelling of cardiac propagation

Bidomain or monodomain modelling has been used widely to study various issu es related to action potential propagation in cardiac tissue. In most of th ese previous studies, the finite difference method is used to solve the par tial differential equations associated with the model. Though the finite di fference approach has provided useful insight in many cases, adequate discr etisation of cardiac tissue with realistic dimensions often requires a larg e number of nodes, making the numerical solution process difficult or impos sible with available computer resources. Here, a Chebyshev pseudospectral m ethod is presented that allows a significant reduction in the number of nod es required for a given solution accuracy. The new method is used to solve the governing nonlinear partial differential equation for the monodomain mo del representing a two-dimensional homogeneous sheet of cardiac tissue. The unknown transmembrane potential is expanded in terms of Chebyshev polynomi al trial functions and the equation is enforced at the Gauss-Lobatto grid p oints. Spatial derivatives are obtained using the fast Fourier transform an d the solution is advanced in time using an explicit technique. Numerical r esults indicate that the pseudospectral approach allows the number of nodes to be reduced by a factor of sixteen, while still maintaining the same err or performance. This makes it possible to perform simulations with the same accuracy using about twelve times less CPU time and memory.