Abstract

Biological tissues typically lack the regular spatial organisation or homogeneity of engineered materials. To understand the impact of the inherent granularity and stochastic heterogeneity of multicellular tissues on their macroscopic mechanical properties, it can be fruitful to resort to discrete models that capture key physical features of individual tissue components. One popular approach in developmental biology is the vertex model, which assigns a mechanical energy to individual cells and predicts distributions of stress across growing tissues, capturing certain features that risk being “washed away” using traditional homogenisation approaches, while exploiting geometric features that are readily measured experimentally. Complementing numerical simulations, discrete calculus methods provide a powerful set of tools with which to analyse the vertex model. I will show how this approach has revealed features such as couple stresses at tricellular junctions in spatially disordered cellular monolayers.