# Spiral wave propagation in communities with spatially correlated heterogeneity

## TL;DR

This study investigates how spatially correlated heterogeneity affects wave propagation in multicellular communities, revealing regimes where heterogeneity promotes directional signals or spirals, with implications for understanding cellular communication.

## Contribution

The paper introduces a minimal model analyzing the impact of spatially correlated heterogeneity on wave dynamics, identifying mechanisms for spiral formation and propagation regimes.

## Key findings

- Spatial correlations can enhance directional wave propagation.
- Certain regimes promote spiral wave formation due to heterogeneity.
- The spiral period depends on the degree of heterogeneity, analyzed via percolation theory.

## Abstract

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.