Modelling of hydrogel extracellular matrix deformation caused by embedded cells

Abstract

Understanding cell behaviour in-vitro presents an important challenge because it is a product of several complex, integrated processes that can explain it in different in-vivo tissues. Adherent cells exert contractile forces which play a significant role in the spatial organization of the extra-cellular matrix (ECM). As a result of those forces, the substrate experiments a deformation process, that is demonstrated in the reduction of its dimensions and consequently in the final shape that acquires. Previously presented models have missed the effect of biological processes such as migration and proliferation. In line with our previous experiences, we present an improved model including these phenomena. To achieve this aim, equilibrium conditions were applied to a reaction-diffusion model for biological growth. The resulting continuum formulation has been implemented in a finite element framework. In absence of experimental data in the literature, a new experimental test was designed. This basically consists in culturing of human fibroblasts within a collagen synthetic hydrogel that is freely suspended in liquid medium. Necessary parameters for the computational model were measured and hydrogel's morphological changes were monitored during 21 days. This is the time required for the hydrogel to reach its minimum diameter. The presented model not only has the capability of simulating the contraction process of a hydrogel due to mechanical interaction cell-substrate and associates cell-generated mechanical forces, substrate deformation, cellular concentration and ECM density but also, the migration and proliferation of cells embedded in the hydrogel. Besides, the model predicts the spatial distribution of cells necessary to reproduce the contraction process observed experimentally. The presented model is a helpful tool to understand the cell-substrate mechano-biological interaction during several phenomena such as morphogenesis, embryogenesis, wound healing or metastasis of tumours.