Efficient integration of a realistic two-dimensional cardiac tissue model by domain decomposition

The size of realistic cardiac tissue models has been limited by their high computational demands. In particular, the Luo-Rudy phase II membrane model, used to simulate a thin sheet of ventricular tissue with arrays of coupled ventricular myocytes, is usually limited to 100 x 100 arrays. We introduce a new numerical method based on domain decomposition and a priority queue integration scheme which reduces the computational cost by a factor of 3-17. In the standard algorithm all the nodes advance with the same time step delta t, whose size is limited by the time scale of activation. However, at any given time, many regions may be inactive and do not require the same small delta t and consequent extensive computations. Hence, adjusting delta t locally is a key factor in improving computational efficiency, since most of the computing time is spent calculating ionic currents. This paper proposes an efficient adaptive numerical scheme for integrating a two-dimensional (2-D) propagation model, by incorporating local adjustments of delta t. In this method, alternating direction Cooley-Dodge and Rush-Larsen methods were used for numerical integration. Between consecutive integrations over the whole domain using an implicit method, the model was spatially decomposed into many subdomains, and delta t adjusted locally. The Euler method was used for numerical integration in the subdomains. Local boundary values were determined from the boundary mesh elements of the neighboring subdomains using linear interpolation. Because delta t was defined locally, a priority queue was used to store and order next update times for each subdomain. The subdomain with the earliest update time was given the highest priority and advanced first. This new method yielded stable solutions with relative errors less than 1% and reduced computation time by a factor of 3-17 and will allow much larger (e.g., 500 x 500) models based on realistic membrane kinetics and realistic dimensions to simulate reentry, triggered activity, and their interactions.