Computational mechanics modelling of cell-substrate contact during cyclic substrate deformation

Experimental testing carried out on various adherent cell types cultured on deformable substrates reveals specific patterns of cell reorientation in response to cyclic stretching of the substrate. In Wang et al. (2001. Specificity of endothelial cell reorientation in response to cyclic mechanical stretching. J. Biomech. 34, 1563), a number of substrate deformation modes were considered: in cases where lateral deformation of the substrate was prohibited (uniaxial case) cells were found to elongate perpendicular to the stretch direction, whereas in cases where the substrate was laterally unrestrained (biaxial case) cells were found to elongate at an angle to the stretch direction. The alignment directions in both cases corresponded to directions of minimum substrate strain. However, the mechanisms underlying such behaviour are not apparent from such in-vitro testing and consequently are not well understood. In this study finite element models are developed in order to investigate the role of cell viscoelasticity in cell debonding and cell realignment under conditions of cyclic substrate stretching using cohesive zone formulations to simulate cell-substrate interfacial behaviour. The characteristic length scale used in such models is based on the length of the receptor-ligand bonds at the cell-substrate interface. Two-dimensional simulations reveal that permanent debonding at the cell-substrate interface occurs due to the accumulation of strain concentrations in the cell. Inclusion of a nucleus in two-dimensional models is shown to have little effect on debonding while discrete cell-substrate contact at focal adhesion sites results in a completion of debonding in fewer cycles. Three-dimensional cohesive zone models are developed in order to compute changes in cell-substrate contact under the aforementioned uniaxial and biaxial modes of substrate deformation. Results reveal that, due to the accumulation of tensile and compressive strains in the cell under cyclic deformation, definite patterns of cell-substrate contact area evolution are computed. With continued cycling, equilibrium contact area profiles with definite orientations are established. These orientations are found to be coincidental with the preferential cell orientation directions seen in the experiments. As no changes in cell morphology are predicted by the models it is concluded that permanent breaking of cell-substrate bonds constitutes the first stage in the process of cell alignment under such mechanical loading.