Modeling cellular self-organization in strain-stiffening hydrogels

We derive a three-dimensional hydrogel model as a two-phase system of a fibre network and liquid solvent, where the nonlinear elastic network accounts for the strain-stiffening properties typically encountered in biological gels. We use this model to formulate free boundary value problems for a hydrogel layer that allows for swelling or contraction. We derive two-dimensional plain-strain and plain-stress approximations for thick and thin layers respectively, that are subject to external loads and serve as a minimal model for scaffolds for cell attachment and growth. For the collective evolution of the cells as they mechanically interact with the hydrogel layer, we couple it to an agent-based model that also accounts for the traction force exerted by each cell on the hydrogel sheet and other cells during migration. We develop a numerical algorithm for the coupled system and present results on the influence of strain-stiffening, layer geometry, external load and solvent in/outflux on the shape of the layers and on the cell patterns. In particular, we discuss alignment of cells and chain formation under varying conditions.

Subjects

65Z05

74B05

74B20

92C10

92C17

Agent-based modeling

Cell migration

Hydrogels

Hyperelasticity

Nonlinear diffusion and reaction

DDC Class

570: Life Sciences, Biology

Publication version

publishedVersion

Lizenz

https://creativecommons.org/licenses/by/4.0/

Name

s00466-024-02536-7-1.pdf

Type

Main Article

Size

5.39 MB

Format

Adobe PDF

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Modeling cellular self-organization in strain-stiffening hydrogels