  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 FitHugh-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 dependence of the spiral period on the degree of
heterogeneity in the system by using techniques from percolation theory. Our
results reveal that the spatial structure of cell-to-cell heterogeneity can
have important consequences for signal propagation in cellular communities.
