Threshold Dynamics and Delayed Closure in a Moving-Boundary Model of Epidermal Wound Healing
We analyze how growth-factor production, diffusion, decay, activation thresholds, and wound geometry interact to determine whether epidermal wound closure begins, proceeds continuously, experiences repeated delays, or stops before completion.
Overview
In this talk, I will present a mathematical model for epidermal wound healing based on a reaction–diffusion equation coupled with a moving-boundary law. The model incorporates a threshold mechanism in which wound closure begins only after the concentration of a growth factor reaches a critical level at the wound edge. I will discuss the analytical characterization of waiting times, delayed healing, and complete versus incomplete wound closure. In particular, I will show how diffusion, growth-factor production, and wound geometry determine different healing regimes through explicit mathematical criteria. Finally, I will present numerical simulations that illustrate the theoretical results for both planar and radially symmetric wounds.
Presenters
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Zhang Zhiwen
- Postdoctoral Research Fellow, Applied Mathematics and Computational Science