Spiral formation and degeneration in heterogeneous excitable media

Spiral Wave Propagation in Communities with Spatially Correlated Heterogeneity

Many multicellular communities propagate signals in a directed manner via excitable waves. Cell-to-cell heterogeneity is a ubiquitous feature of multicellular communities, but the effects of heterogeneity on wave propagation are still unclear. Here, we use a minimal FitzHugh-Nagumo-type model to investigate excitable wave propagation in a two-dimensional heterogeneous community. The model shows three dynamic regimes in which waves either propagate directionally, die out, or spiral indefinitely, and we characterize how these regimes depend on the heterogeneity parameters. We find that in some parameter regimes, spatial correlations in the heterogeneity enhance directional propagation and suppress spiraling. However, in other regimes, spatial correlations promote spiraling, a surprising feature that we explain by demonstrating that these spirals form by a second, distinct mechanism. Finally, we characterize the dynamics using techniques from percolation theory. Despite the fact that percolation theory does not completely describe the dynamics quantitatively because it neglects the details of the excitable propagation, we find that it accounts for the transitions between the dynamic regimes and the general dependency of the spiral period on the heterogeneity and thus provides important insights. Our results reveal that the spatial structure of cell-to-cell heterogeneity can have important consequences for signal propagation in cellular communities.

Mechanism of spiral formation in heterogeneous discretized excitable media

Spiral waves on excitable media strongly influence the functions of living systems in both a positive and negative way. The spiral formation mechanism has thus been one of the major themes in the field of reaction-diffusion systems. Although the widely believed origin of spiral waves is the interaction of traveling waves, the heterogeneity of an excitable medium has recently been suggested as a probable cause. We suggest one possible origin of spiral waves using a Belousov-Zhabotinsky reaction and a discretized FitzHugh-Nagumo model. The heterogeneity of the reaction field is shown to stochastically generate unidirectional sites, which can induce spiral waves. Furthermore, we found that the spiral wave vanished with only a small reduction in the excitability of the reaction field. These results reveal a gentle approach for controlling the appearance of a spiral wave on an excitable medium.

Inwardly rotating spirals in nonuniform excitable media

Inwardly rotating spirals (IRSs) have attracted great attention since their observation in an oscillatory reaction-diffusion system. However, IRSs have not yet been reported in planar excitable media. In the present work we investigate rotating waves in a nonuniform excitable medium, consisting of an inner disk part surrounded by an outer ring part with different excitabilities, by numerical simulations of a simple FitzHugh-Nagumo model. Depending on the excitability of the medium as well as the inhomogeneity, we find the occurrence of IRSs, of which the excitation propagates inwardly to the geometrical spiral tip.