Kinematic analysis of spiral waves in a discrete element model of neuromuscular tissue

The authors performed a kinematical analysis of a spiral wave in a discrete cellular automata (CA) model approximating poorly excitable neuromuscular tissue. The CA parameter values for the medium were obtained via matching specific features of the CA traveling wave solutions to those of a particular reaction-diffusion (RD) model. In kinematical theory, the spiral wave is treated as a curve obeying certain equations of motion determined by the dependence of wave speed c on wave front curvature κ in the medium. The authors computed C(κ) in their model directly from the CA excitation rules. Treating the core radius as a phenomenological parameter, they then solved for the (kinematic) theoretical value of the spiral period. The good agreement between the predicted value and the measured CA value demonstrates the quantitative reliability of the authors´ CA modeling approach. Their computationally efficient CA model thus provides a powerful tool for the study of arrhythmogenesis in the heart