# American Institute of Mathematical Sciences

February  2004, 4(1): 267-273. doi: 10.3934/dcdsb.2004.4.267

## Modeling the role of angiogenesis in epidermal wound healing

 1 Department of Mathematics and Statistics, Rochester Institute of Technology, Rochester, New York 14623, United States

Received  October 2002 Revised  April 2003 Published  November 2003

The effects of angiogenesis on oxygenation of an epidermal wound are described using a mathematical model. Diffusion equations are used to characterize the dependence of the wounded tissue regeneration on oxygen availability, which in turn affects the production of the Macrophage Derived Growth Factors (MDGFs) and as a result the growth of capillary density. When the capillaries grow beyond a certain point, they contribute to their own growth retardation, and as a result, a negative feedback mechanism is build into the system. The results of this model suggest that in order for an epidermal wound to be healed successfully the levels of oxygen concentration within the wounded area must be low. This process parallels an earlier mathematical model developed to describe the capillary growth in the retina, and demonstrates the generality and application of such a modeling approach to various biological phenomena involving growth factors.
Citation: Sophia A. Maggelakis. Modeling the role of angiogenesis in epidermal wound healing. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 267-273. doi: 10.3934/dcdsb.2004.4.267
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