Mesoscopic modeling of wave propagation in excitable media

Abstract

A new theoretical model is introduced to abstract the significant factors leading to wave propagation in excitable media. Contrary to the previous theoretical models constructed based on the microscopic physical mechanism, our model is formulated based on experimentally measurable “mesoscopic” characteristics of the media: dispersion relation and curvature relation. Analytic investigations lead to the nonlinear curvature relation which is approximated by a linear relation for a small curvature. Numerical simulations incorporated with the experimental data of the above two characteristics in the Belousov-Zhabotinskii reaction reproduce spiral waves in agreement with experiment. Both stationary rotating spiral waves and a meandering motion of spiral tip are obtained in accord with other experimental and numerical studies. Our results suggest that both the dispersion relation and the curvature relation are important factors leading to those universally observed wave phenomena. The model can be used as a convenient numerical tool to understand the nature of wave propagation in excitable media through extensive numerical experiment.