Modelling the compression and reorganization of cell aggregates

In this paper, we study the mechanical behaviour of multicellular aggregates using the notion of multiple natural configurations. In particular, we extend the elasto-visco-plastic model proposed in Preziosi et al. (2010, An elasto-visco-plastic model of cell aggregates. J. Theor. Biol., 262, 35–47) taking into account the liquid constituent present in cellular spheroids. Aggregates are treated as porous materials, composed of cells and filled with water. The cellular constituent is responsible for the elastic and the plastic behaviour of the material. The plastic component is due to the rearrangement of adhesion bonds between cells and it is translated into the existence of a yield stress in the macroscopic constitutive equation. On the other hand, the liquid constituent is responsible for the viscous-like response during deformation. The general framework is then applied to describe uniaxial homogeneous compression both when a constant load is applied and when a fixed deformation is imposed and subsequently released. We compare the results of the model with the dynamics observed during the experiments in Forgacs et al. (1998, Viscoelastic properties of living embryonic tissues: a quantitative study. Biophys. J., 74, 2227–2234).