Non-linear visco-elasto-plastic rheology of a viscous vertex model

TL;DR

This paper develops a mean-field rheological model for a viscous vertex model of biological tissues, capturing non-linear elastic, visco-plastic, and active stress effects, validated through large-amplitude oscillatory shear responses.

Contribution

It introduces a novel mean-field rheological framework for vertex models with explicit viscous friction and active stresses, extending previous models to include non-linear regimes and tissue-level predictions.

Findings

Rheology depends on model details.

Model accurately predicts large-amplitude shear response.

Framework applicable to various cell-based tissue models.

Abstract

Morphogenesis involves complex shape changes of biological tissues. Yet, tissue shape changes depend on tissue rheology, which in turn arises from the interplay of large numbers of cells. Here, we link cell- and tissue-scale mechanics by constructing mean-field rheological relations for the vertex model. In contrast to past work in the field, we study a vertex model with an explicit viscous friction. We also include two different cellular mechanisms creating active, anisotropic stresses. Our mean-field model accounts for cell shape and the non-linear elastic and visco-plastic regimes. We validate our results by predicting the response to large-amplitude oscillatory shear. There are several vertex model variants, and comparing to results from the literature, we show that their rheology depends on a number of model details. Our approach should be sufficiently general to construct non-linear mean-field constitutive relations for any cell-based tissue model.