Multiphase Field Model of Cells on a Substrate: From 3D to 2D

TL;DR

This paper derives a 2D multiphase field model from a 3D version for tissue monolayers, incorporating viscous forces, and demonstrates how intercellular friction influences tissue solidification.

Contribution

It provides a theoretical derivation of 2D models from 3D, including viscous forces, and explores their effects on tissue behavior.

Findings

Intercellular friction solidifies tissue

2D model derivation from 3D model

Viscous forces can be incorporated into the model

Abstract

Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living tissue, the theoretical underpinnings have not been fully explored. We show that a two-dimensional version of the model, which is commonly employed to study tissue monolayers, can be derived from a three-dimensional version in the presence of a substrate. We also show how viscous forces, which arise from friction between different cells, can be included in the model. Finally, we numerically simulate a tissue monolayer, and find that intercellular friction tends to solidify the tissue.