Instabilities and geometry of growing tissues

TL;DR

This paper develops a continuum model for 2D vertex tissue growth, analyzing mechanical and dynamical instabilities influenced by activity, disorder, and residual stresses, with implications for understanding tissue growth behaviors.

Contribution

It introduces a geometric continuum model for 2D vertex tissues that enables analytical study of growth instabilities and distinguishes elasticity from plasticity.

Findings

Growth instability depends on residual stresses and activity.

The model predicts tissue response varies with geometry and disorder.

It provides a framework to analyze tissue mechanics analytically.

Abstract

We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium statistical mechanics, we calculate both mechanical and dynamical instabilities within a tissue, and their dependence on different variables, including activity, and disorder. Most notably, the tissue's response depends on the existence of mechanical residual stresses in the tissue. Thus, even freely growing tissues may exhibit a growth instability depending on food consumption. Using this geometric model we can readily distinct between elasticity and plasticity in a growing, flowing, tissue.