Simulation of Transmembrane Potential Propagation in Three-Dimensional Bidomain Cardiac Tissue

The transmembrane potential propagation in a slab of three-dimensional cardiac tissue stimulated by an unipolar extracellular shock on epicardium is simulated for a full cycle of action potential duration. A semi-implicit method is implemented for the first time on a single cpu workstation to numerically calculate the transmembrane potential field in a three-dimensional bidomain incorporating rotational anisotropy and active ionic currents. A fast preconditioned Krylov subspace iterative method is found to efficiently solve the huge number of linear equations at each time step. It is suggested that this methodology can be used to simulate transmembrane potential in cardiac tissue for seconds after an electric defibrillation shock, which requires long time three-dimensional bidomain simulation.