Simulating Organogenesis in COMSOL: Tissue Mechanics

During growth, tissue expands anddeforms. Given its elastic properties, stresses emergein an expanding and deforming tissue. Cellrearrangements can dissipate these stresses andnumerous experiments confirm the viscoelasticproperties of tissues [1]–[4]. On long time scales, ascharacteristic for many developmental processes,tissue is therefore typically represented as a liquid,viscous material and is then described by the Stokesequation [5]–[7]. On short time scales, however,tissues have mainly elastic properties. In discretecell-based tissue models, the elastic tissue propertiesare realized by springs between cell vertices [8], [9].In this article, we adopt a macroscale perspective oftissue and consider it as homogeneous material.Therefore, we may use the “Structural Mechanics”module in COMSOL Multiphysics in order to modelthe viscoelastic behavior of tissue. Concretely, weconsider two examples: first, we aim at numericallyreproducing published [10] analytical results for thesea urchin blastula. Afterwards, we numerically solvea continuum mechanics model for the compressionand relaxation experiments presented in [4]