Analysis and modelling of cell motion in an in vitro experiment of wound healing

Collaboration with: Hitesh Mistry, Sandrine Etienne-Manneville, John Billingham

A time-lapse record of cell motion is examined after a cut is made in a monolayer of astrocytes. Cell-flux and cell-density are extracted over periods of time in sections of the record. The data suggests that flux depends more on cell-density than on cell-density gradient, with the average speed of cell motion being approximately constant up to a maximum density. Numerical solutions of a simple model, with flux a function of density and a small amount of diffusion, are qualitatively consistent with the experiment. Curiously, depending on the initial data, the model is inadequate without some mechanism for initiating motion. Diffusion serves such a purpose but the results then depend quite significantly on the amount of diffusion.