A Stochastic Model for Wound Healing

Abstract

We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, p , that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for p ≈ 1. In both one and two dimensions for small p , front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly.