Finite Elements Methods on viscoelastic models for biology

Morphogenesis studies how cells or tissues change shape (embryo, wounds, cancer cells etc.). Research on this topic lead biophysicists to work on the mecanical properties of living tissues. Performing in vitro rheology experiments on drugged cells to cancel activity is a possible approach. The work to be presented focuses on mathematical modeling of biological tissues, relying on experiments on cells in a contraction geometry. The Finite Extension Non-linear Elastic Peterlin (FENE-P) model will be used to seek steady-state solutions for comparison with experiments. Because of its non-linear but highly constrained nature, cumulated with the non smoothness of the geometry, some issues need to be tackled. Some of the remedy to those challenges will be presented. This viscoelastic fluid model managed to provide good fits with experiments. Nevertheless, it appears a future coupling with plastic models may improve comparisons.