Mathematical modelling of angiogenesis.

摘要: Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The then grow and develop, driven initially by endothelial cell migration, organize themselves into branched, connected network. Subsequent proliferation near sprout-tips permits further extension capillaries ultimately completes process. Angiogenesis occurs during embryogenesis, wound healing, arthritis growth solid tumours. In this article we first all present review variety mathematical models which have been used describe networks focus on specific recent model uses novel modelling techniques generate both two- three-dimensional vascular structures. focusses key events angiogenesis such as migratory cells exogenous cytokines (tumour angiogenic factors, TAF) secreted tumour; proliferation; interactions with extracellular matrix macromolecules fibronectin; sprout branching anastomosis. Numerical simulations model, using parameter values based experimental data, presented theoretical structures generated compared morphology actual observed vivo experiments. A final conclusions section discusses use possible assay.