Spiral waves in a discrete model of excitable media

A quantitatively reliable discrete cellular automaton model of an excitable medium is developed for the purpose of simulating spiral waves in excitable systems such as myocardial tissue. The relations between the traveling wave solutions in the discrete system and those in the more complex continuous partial differential equation (PDE) representation are explored for both solitary waves (with recovery) and trigger waves (without recovery). The model is first used to re-examine recent reports of spontaneous spiral wave breakup into turbulent wave patterns in homogeneous two-dimensional media, a process that may underlie the transition to fibrillation in the heart. The predictive ability of the model is then tested for the case of a steadily rotating spiral wave in a discrete medium tuned to a particular PDE system. The results are compared with the discrete model theory, the numerical solution of the PDEs, and the predictions of the kinematical theory of spiral waves in excitable media.