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Bifurcation analysis of critical values for wound closure outcomes in wound healing experiments

机译：Bifurcation analysis of critical values for wound closure outcomes in wound healing experiments

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摘要

A nonlinear partial differential equation containing a nonlocal advection term and a diffusion term is analyzed to study wound closure outcomes in wound healing experiments. There is an extensive literature of similar models for wound healing experiments. In this paper we study the character of wound closure in these experiments in terms of the sensing radius of cells and the force of cell-cell adhesion. We prove a bifurcation result which differentiates uniform closure of the wound from nonuniform closure of the wound, based on a critical value lambda. of the force of cell-cell adhesion parameter lambda. For lambda < lambda(*) the steady state solution u equivalent to 1 of the model is stable and the wound closes uniformly. For lambda < lambda(*) the steady state solution u equivalent to 1 of the model is unstable and the wound closes nonuniformly. We provide numerical simulations of the model to illustrate our results.

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