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Angiogenesis, the formation of blood vessels, may be described as a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then develop and organize themselves into a dendritic structure. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this paper we present a mathematical model which describes the rŏle of angiogenesis as observed during (soft-tissue) wound healing. We focus attention on certain principal players involved in this complex process, namely capillary tips, capillary sprouts, fibroblasts, macrophage-derived chemical attractants, oxygen and extracellular matrix. The model consists of a system of nonlinear partial differential equations describing the interactions in space and time of the above substances. Numerical simulations are presented which are in very good qualitative agreement with experimental observations.

Original publication

DOI

10.1098/rspb.1996.0217

Type

Journal article

Journal

Proc Biol Sci

Publication Date

22/11/1996

Volume

263

Pages

1487 - 1493

Keywords

Animals, Capillaries, Chemotaxis, Extracellular Matrix, Fibroblasts, Growth Substances, Macrophages, Models, Biological, Neovascularization, Physiologic, Rabbits, Wound Healing