Mathematical modeling of corneal epithelial wound healing.

We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically the role of epidermal growth factor. Analysis of the model equations elucidates the interaction and roles of the model parameters in determining the speed of healing and the shape of the traveling wave solutions which correspond to the migration of cells into the wound during the initial phase of healing. We determine an analytic approximation for the speed of traveling wave solutions of the model in terms of the parameters and verify the results numerically. By comparing the predicted speed with experimentally measured healing rates, we conclude that serum-derived factors can alone account for the overall features of the healing process, but that the supply of growth factors by the tear film in the absence of serum-derived factors is not sufficient to give the observed healing rate. Numerical solutions of the model equations also confirm the importance of both migration and mitosis for effective would healing. By modifying the model we obtain an analytic prediction for the healing rate of corneal surface wounds when epidermal growth factor is applied topically to the wound.