A Highly Efficient and Accurate Algorithm for Solving the Partial Differential Equation in Cardiac Tissue Models

We give a highly efficient, accurate and unconditionally stable algorithm to solve the partial differential equation for simulating the action potential propagation through cardiac tissue. In the new algorithm, we discretize the space domain by combining a compact finite difference scheme with an alternating direction implicit (ADI) scheme, which has fourth-order accuracy for interior mesh points, and second-order accuracy for boundary mesh points. In our computer simulation, we test the new method on a two dimensional Luo-Rudy phase I action potential model. For a fixed mesh grid N , the compact finite difference ADI method yields 50% more accuracy than the Crank-Nicolson ADI method. Furthermore, it costs almost the same amount of time as the Crank-Nicolson ADI method. On the other hand, if we want to obtain the same accuracy, it only costs 49% ∼ 65% of computational time if we use our compact finite difference ADI method instead of the Crank-Nicolson ADI method. Key-Words:Compact finite difference method, ADI, Cardiac tissue models, Computer simulation, Spiral wave