Numerical Analysis

Fred Vermolen
Delft Institute of Applied Mathematics
Delft University of Technology
Mekelweg 4
2628 CD Delft
the Netherlands

Presenter at Delft Symposium on Mathematical Modeling of Wound Healing

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Date: October 15, 2009. Location Pegasuszaal (Pegasus Lecture Room), Kluyverweg 6, Delft University of Technology, Delft, the Netherlands.

Abstract

Some mathematical issues for wound contraction, angiogenesis and closure

Wound healing is a crucial, but complicated, biological process. Present mathematical models capture the most important features, such as co-agulation, wound contraction, angiogenesis and wound closure. For wound closure, one distinguishes mathematical models incorporating epidermal proliferation and mobility, associated with the regeneration and transport of growth factors as systems of diffusion-reaction equations (such as the models due to Sherratt and Murray) or as a single diffusion-reaction equation with a sharp moving boundary (such as the model due to Adam). The latter model consists of a discontinuous switch mechanism. In this presentation, questions concerning existence and uniqueness of solutions will be evaluated.

Furthermore, a model incorporating wound contraction, angiogenesis and wound closure will be presented. The model consists of a connection of three simplified formalisms for the aforementioned partial processes. Another innovation is the splitting in the model of the subdomains, in which the partial processes take place.

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Last modified: August 9, 2009, by Fred Vermolen