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Many multicellular communities propagate signals in a directed manner viaexcitable waves. Cell-to-cell heterogeneity is a ubiquitous feature ofmulticellular communities, but the effects of heterogeneity on wave propagationare still unclear. Here we use a minimal FitHugh-Nagumo-type model toinvestigate excitable wave propagation in a two-dimensional heterogeneouscommunity. The model shows three dynamic regimes in which waves eitherpropagate directionally, die out, or spiral indefinitely, and we characterizehow these regimes depend on the heterogeneity parameters. We find that in someparameter regimes, spatial correlations in the heterogeneity enhancedirectional propagation and suppress spiraling. However, in other regimes,spatial correlations promote spiraling, a surprising feature that we explain bydemonstrating that these spirals form by a second, distinct mechanism. Finally,we characterize the dependence of the spiral period on the degree ofheterogeneity in the system by using techniques from percolation theory. Ourresults reveal that the spatial structure of cell-to-cell heterogeneity canhave important consequences for signal propagation in cellular communities.

Spiral wave propagation in communities with spatially correlated heterogeneity