Simulating Organogenesis in COMSOL: Tissue Mechanics

TL;DR

This paper demonstrates how to simulate tissue mechanics during organogenesis using COMSOL, modeling tissue as a viscoelastic material to reproduce experimental and analytical results of tissue deformation and stress relaxation.

Contribution

It introduces a macroscale COMSOL modeling approach for tissue viscoelasticity, bridging discrete cell models and continuum mechanics in developmental biology.

Findings

Successfully reproduces analytical results for sea urchin blastula

Simulates tissue compression and relaxation experiments accurately

Validates COMSOL as a tool for tissue mechanics modeling

Abstract

During growth, tissue expands and deforms. Given its elastic properties, stresses emerge in an expanding and deforming tissue. Cell rearrangements can dissipate these stresses and numerous experiments confirm the viscoelastic properties of tissues [1]-[4]. On long time scales, as characteristic for many developmental processes, tissue is therefore typically represented as a liquid, viscous material and is then described by the Stokes equation [5]-[7]. On short time scales, however, tissues have mainly elastic properties. In discrete cell-based tissue models, the elastic tissue properties are realized by springs between cell vertices [8], [9]. In this article, we adopt a macroscale perspective of tissue and consider it as homogeneous material. Therefore, we may use the "Structural Mechanics" module in COMSOL Multiphysics in order to model the viscoelastic behavior of tissue. Concretely, we consider two examples: first, we aim at numerically reproducing published [10] analytical results for the sea urchin blastula. Afterwards, we numerically solve a continuum mechanics model for the compression and relaxation experiments presented in [4].