Numerical Simulation of Activation in Anisotropic Myocardium

In this work we consider a macroscopic model of activation in a simplified insulated three-dimensional region of anisotropic myocardium involving the transmembrane potential v and the ionic currents. The model is described by a reaction-diffusion (R-D) system where the component v exhibits a front-like behavior reflecting the features of the excitation process. The system we considered consists of a semilinear parabolic equation coupled with two ordinary differential equations and we studied the regularity conditions on data which guarantee the existence of a unique global strong solution. The numerical solution of the R-D system is obtained by means of a linearization of the reaction term and a Galerkin space discretization. This method allows considerable reduction in computation time. Numerical results are presented and discussed.