Cells are often grown within collagen gels in vitro for applications in tissue engineering. The behaviour of these cells is regulated by their mechanical environment; however, the forces exerted by cells in turn affect the mechanical behaviour of the gel. We aim to better understand the interactions between the cells and the gel using mathematical modelling.
We have developed a multiphase model for this system, incorporating cells and their traction forces alongside chemical effects such as osmosis. To date, we have modelled this problem in one-dimensional Cartesian and spherical coordinates, mimicking experiments performed with spheres of collagen gel. However, these gels are often produced in Petri dishes, resulting in a thin disc. We have therefore transformed our model to examine this type of geometry. In this presentation, we will demonstrate how we can exploit thin-film approximations to reduce the two-dimensional system to a leading-order, one-dimensional model. We will also discuss the equilibrium behaviour of this reduced thin-film system.