Abstract
BackgroundExistence 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/ResultsHere, 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 (), 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.ConclusionsThese findings clarify mechanisms of wave propagation and survival in flow.
Highlights
The number of biological systems with complex modes of excitation propagation is very large: blood coagulation [1,2], excitable muscular systems [3], ecological systems [4,5], neural tissue [6], etc
Propagation of excitation in many such systems can have the form of travelling pulses or trigger waves, which is typical for active media [11,12,13]
The excitation waves in our study are autowaves: their shape and velocity in the steady-state mode do not depend on the excitation type
Summary
The number of biological systems with complex modes of excitation propagation is very large: blood coagulation [1,2], excitable muscular systems [3], ecological systems [4,5], neural tissue [6], etc. Propagation of excitation in many such systems can have the form of travelling pulses or trigger waves, which is typical for active media [11,12,13]. Use of the simplest models of active media played and still plays a vital role in the understanding of the mechanisms of excitation propagation in strongly non-equilibrium media. 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
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