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A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. (English) Zbl 0783.92019
Summary: In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Endothelial cells which form the lining of neighbouring blood vessels respond to this chemotactic stimulus in a well-ordered sequence of events consisting, at minimum, of a degradation of their basement membrane, migration, and proliferation.
A model mechanism is presented which includes the diffusion of the TAF into the surrounding host tissue and the response of the endothelial cells to the chemotactic stimulus. The model accounts for the main observed events associated with the endothelial cells during the process of angiogenesis (i.e. cell migration and proliferation); the numerical results compare very well with experimental observations. The situation where the tumour (i.e. the source of TAF) is removed and the vessels recede is also considered.

MSC:
92C50 Medical applications (general)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C35 Physiological flow
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