On Propagation of Excitation Waves in Moving Media: The FitzHugh-Nagumo Model

Background: Existence of flows and convection is an essential and integral feature of many excitable media with wave propagation modes, such as blood coagulation or bioreactors. Methods/Results: Here, propagation of two-dimensional waves is studied in parabolic channel flow of excitable medium of the FitzHugh-Nagumo type. Even if the stream velocity is hundreds of times higher that the wave velocity in motionless medium (w), steady propagation of an excitation wave is eventually established. At high stream velocities, the wave does not span the channel from wall to wall, forming isolated excited regions, which we called "restrictons''. They are especially easy to observe when the model parameters are close to critical ones, at which waves disappear in still medium. In the subcritical region of parameters, a sufficiently fast stream can result in the survival of excitation moving, as a rule, in the form of "restrictons''. For downstream excitation waves, the axial portion of the channel is the most important one in determining their behavior. For upstream waves, the most important region of the channel is the near-wall boundary layers. The roles of transversal diffusion, and of approximate similarity with respect to stream velocity are discussed. Conclusions: These findings clarify mechanisms of wave propagation and survival in flow.