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A simple model of wound healing angiogenesis is presented, and investigated using numerical and asymptotic techniques. The model captures many key qualitative features of the wound healing angiogenic response, such as the propagation of a structural unit into the wound centre. A detailed perturbative study is pursued, and is shown to capture all features of the model. This enables one to show that the level of the angiogenic response predicted by the model is governed to a good approximation by a small number of parameter groupings. Further investigation leads to predictions concerning how one should select between potential optimal means of stimulating cell proliferation in order to increase the level of the angiogenic response.

Original publication

DOI

10.1007/s002850200161

Type

Journal article

Journal

J Math Biol

Publication Date

10/2002

Volume

45

Pages

337 - 374

Keywords

Capillaries, Computer Simulation, Endothelium, Humans, Models, Biological, Neovascularization, Physiologic, Wound Healing