Abstract
Bidomain or monodomain model has frequently been used to study electrical activities in the cardiac tissue. The finite difference method with second order accuracy is commonly used to approximate the spatial derivatives of the governing equations numerically. In this work, a higher order finite difference scheme has been implemented to solve the nonlinear monodomain equation. The unknown transmembrane potential is expanded in terms of Lagrangian interpolating polynomials. Differentiation of the polynomial expansion then gives the finite difference approximation, and the order of the approximation is varied by changing the order of the polynomial. First and second order semi-implicit (implicit-explicit) time-stepping techniques have been used to approximate the temporal derivatives. An explicit finite difference scheme with 512×512×512 nodes and 0.1 μs time step is used as the benchmark for error calculation. As the order of the finite difference approximation is increased, the error potential reduces. However, there is less noticeable error improvement after the ninth order approximation. The use of an operator splitting method as well as a protective zone scheme further improves the performance of the semi-implicit scheme. Numerical results demonstrate that the error can be reduced by a factor of 2.6, while the CPU time can be reduced by a factor of 14.1.