Stationary propagation of a wave segment along an inhomogeneous excitable stripe

Abstract

We report a numerical and theoretical study of an excitation wave propagating along an inhomogeneous stripe of an excitable medium. The stripe inhomogeneity is due to a jump of the propagation velocity in the direction transverse to the wave motion. Stationary propagating wave segments of rather complicated curved shapes are observed. We demonstrate that the stationary segment shape strongly depends on the initial conditions which are used to initiate the excitation wave. In a certain parameter range, the wave propagation is blocked at the inhomogeneity boundary, although the wave propagation is supported everywhere within the stripe. A free-boundary approach is applied to describe these phenomena which are important for a wide variety of applications from cardiology to information processing.

Wave Propagation in Inhomogeneous Excitable Media

“…In this context, at first glance, another situation, for which the front propagation can be blocked, looks rather counterintuitive (27,39). Indeed, the front can be stopped if the parameter A does not vanish, but it abruptly increases, e.g., A = A L for x ≤ 0 and A = A R for x > 0 with D = 1 everywhere, as shown in Figure 2a.…”

A cellular automaton model for the ventricular myocardium considering the layer structure

“…When the excitation spreading along the longside of an infinitely inhomogeneous stripe is cut, the stationary propagation of a wave segment can be observed. [24] But in the ventricle CA model used here, the impulse spreads across the longside of the slice, which makes it impossible to produce a spiral wave under the normal conditions: the electric impulse spreads very fast under the normal conditions, so even the travelling wave is cut, the cut-down point goes out off the system quickly, and then the spiral wave state cannot come into being. Pathological changes will reduce the conduction ability of the conduction system in the ventricle.…”

Spiral wave initiation in excitable media

“…Generally speaking, this mechanism is based on a well-known observation that an excitation wavefront can be stopped due to a phenomenon termed source-sink mismatch in the cardiology literature [30]. It was found that an excitation wave can be broken at a boundary of a region, where the diffusivity D or the parameter A are significantly larger than in the surrounding tissue [29,31]. Increased values of these parameters result in a faster propagation velocity of an excitation wave, which is proportional to √ AD.…”