Propagation of spiral waves pinned to circular and rectangular obstacles

Abstract

We present an investigation of spiral waves pinned to circular and rectangular obstacles with different circumferences in both thin layers of the Belousov-Zhabotinsky reaction and numerical simulations with the Oregonator model. For circular objects, the area always increases with the circumference. In contrast, we varied the circumference of rectangles with equal areas by adjusting their width w and height h. For both obstacle forms, the propagating parameters (i.e., wavelength, wave period, and velocity of pinned spiral waves) increase with the circumference, regardless of the obstacle area. Despite these common features of the parameters, the forms of pinned spiral waves depend on the obstacle shapes. The structures of spiral waves pinned to circles as well as rectangles with the ratio w/h∼1 are similar to Archimedean spirals. When w/h increases, deformations of the spiral shapes are observed. For extremely thin rectangles with w/h≫1, these shapes can be constructed by employing semicircles with different radii which relate to the obstacle width and the core diameter of free spirals.

Mechanism of Spiral Wave Unpinning in the Belousov–Zhabotinsky Reaction with a DC Electric Field

“…All excitation waves, irrespective of the mechanism of formation and the nature of the substrate medium, have very similar dynamics. The spiral waves can get attracted to heterogeneities in the medium and form very stable rotating patterns around the boundary of these heterogeneities. − Such pinning has been observed in chemical systems and also in physiological tissue, both in the experimental settings and in their mathematical models. − The pinned waves are very stable, and they can only be unpinned by careful external intervention. − This problem has attracted attention recently because such pinned waves are believed to play an essential role in cardiac arrhythmia control …”