Pattern formation in multiphase, moving boundary models of tissue growth #

Jacob Jepson, John Billingham, Reuben O’Dea, Nabil Fadai

12:30 Monday in 2Q49.

Part of the Dynamics of reaction-transport systems session.

Abstract #

We analyse a multiphase, moving boundary model that describes tissue growth. We consider the evolution of a motile, viscous cell phase and an inviscid extracellular liquid phase. The model comprises two partial differential equations that govern the cell volume fraction and the cell velocity, together with a moving boundary condition for the tissue edge. Numerical simulations of the model indicate that patterned solutions can be obtained, which correspond to multiple regions of high cell density separated by regions of low cell density. In other parameter regimes, solutions of the model can develop into a forward- or backward-moving travelling wave, corresponding to tissue growth or extinction, respectively. A stability analysis of these travelling-wave solutions provides us with criteria for the occurrence of patterned solutions.