The effects of nonexcitable regions on signal propagation in excitable media: Propagation failure and reflection

Most physical excitable media have regions of depressed excitability and in many of these systems, the interaction of waves of excitation and these regions is of the utmost interest. In the heart, regions of this nature can disrupt the normal wave of electrical excitation and trigger the onset of dangerous arrhythmias. In order to get insight into the effects of regions of reduced excitability, we consider a model in which the regions are idealized as nonexcitable. We show that the arrhythmia-generating phenomena of propagation failure and reflection occur in the model and attempt to elucidate the dynamical mechanisms underlying these behaviors.; We study propagation failure using the one-dimensional scalar bistable equation with a passive "gap" region. By applying ordering principles for this type of equation, the problem of finding conditions for block is reduced to finding conditions for the existence of steady states solutions. We present a geometrical method that allows one to easily compute the critical gap length above which a steady state solution, and thus block, first occurs. The method also helps uncover the general bifurcation structure of the problem including the stability of the steady state solutions. In obtaining these results, we characterize the relationship between the properties of the system and propagation failure.; Again, we consider wavefront propagation in the one-dimensional reaction diffusion equation with a passive gap region, however we now include recovery dynamics. We numerically explore the behavior of the system for various gap lengths and discover exotic reflection behavior. We introduce a new one variable model for excitable systems and by studying coupled cells described by these dynamics, we demonstrate that reflection is associated with transient dynamics around an unstable periodic orbit. This unstable periodic orbit is shown to be a continuation of the anti-phase orbit of coupled oscillators. Also, we suggest two ways that stable echo oscillations can arise in spatially coupled excitable media and conjecture that some AV nodal tachycardias could be explained by these oscillations.; Finally, we show simulations of activity in a two-dimensional excitable medium with a region of passive diffusion and describe a novel mechanism for the generation of spiral waves that involves reflection. This mechanism appears to be the most physiologically viable mechanism for the induction of the potentially fatal arrhythmias associated with spiral wave dynamics that has been proposed to date.