Modeling cellular self-organization in strain-stiffening hydrogels

• Published in: Computational mechanics Vol. 75; no. 2; pp. 875 - 896
• Main Authors: Erhardt, A. H., Peschka, D., Dazzi, C., Schmeller, L., Petersen, A., Checa, S., Münch, A., Wagner, B.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2025; Springer Nature B.V
• Subjects: Agent-based models; Algorithms; Binary systems; Biological properties; Boundary value problems; Classical and Continuum Physics; Computational Science and Engineering; Elastic properties; Engineering; Free boundaries; Hydrogels; Numerical analysis; Original Paper; Solvents; Stiffening; Strain; Theoretical and Applied Mechanics; Thin films; Traction force; 65Z05; 92C10; Hydrogels; Nonlinear diffusion and reaction; 74B05; Agent-based modeling; 92C17; 74B20; Cell migration; Hyperelasticity
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-024-02536-7

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.