Reaction-diffusion models of threshold and waveblock in heterogeneous excitable media

Nonlinear and linear reaction-diffusion equation models of heterogeneous excitable media are presented. These models include threshold, but no recovery. The linear model behaves in a similar manner to the nonlinear model under certain parameter constraints. It is shown that if a threshold stimulus is applied near the boundary of heterogeneities in excitability, waveblock and unidirectional propagation may occur. In this case, an excitation front propagates in one direction while propagation in the opposite direction is blocked. Waveblock corresponds to specific time-independent, nonhomogeneous steady state solutions of the models. These steady states are numerically and analytically investigated to determine the critical parameter values for which waveblock will occur.