WIAS Preprint No. 3076, (2023)

Modeling cellular self-organization in strain-stiffening hydrogels


  • Erhardt, André
    ORCID: 0000-0003-4389-8554
  • Peschka, Dirk
    ORCID: 0000-0002-3047-1140
  • Dazzi, Chiara
  • Schmeller, Leonie
    ORCID: 0000-0001-8144-6028
  • Petersen, Ansgar
  • Checa, Sara
  • Münch, Andreas
  • Wagner, Barbara
    ORCID: 0000-0001-8306-3645

2020 Mathematics Subject Classification

  • 65Z05 74B05 74B20 92C10 92C17




We develop a three-dimensional mathematical model framework for the collective evolution of cell populations by an agent-based model (ABM) that mechanically interacts with the surrounding extracellular matrix (ECM) modeled as a hydrogel. We derive effective two-dimensional models for the geometrical set-up of a thin hydrogel sheet to study cell-cell and cell-hydrogel mechanical interactions for a range of external conditions and intrinsic material properties. We show that without any stretching of the hydrogel sheets, cells show the well-known tendency to form long chains with varying orientations. Our results further show that external stretching of the sheet produces the expected nonlinear strain-softening or stiffening response, with, however, little qualitative variation of the overall cell dynamics for all the materials considered. The behavior is remarkably different when solvent is entering or leaving from strain softening or stiffening hydrogels, respectively.

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