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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 near 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.
We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the transitions b
The mechanisms underlying collective migration, or the coordinated movement of a population of cells, are not well understood despite its ubiquitous nature. As a means to investigate collective migration, we consider a wound healing scenario in which
We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al., IMA J. Math. App. Med., 17, 2000. In this work, the authors showed that for certain parameter values, a hetero
The phenotypic plasticity of cancer cells has received special attention in recent years. Even though related models have been widely studied in terms of mathematical properties, a thorough statistical analysis on parameter estimation and model selec
Next generation wound care technology capable of diagnosing wound parameters, promoting healthy cell growth and reducing pathogenic infections noninvasively will provide patients with an improved standard of care and an accelerated wound repair. Temp