publication . Article . 1999

A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation

Sleeman, B. D.; Alexander Anderson; Chaplain, M. A. J.;
  • Published: 01 Nov 1999
Abstract An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail.
free text keywords: Angiogenesis, Endothelial cells, Chemotaxis, Haptotaxis, Sturm-Liouville problem, Applied Mathematics, Cell migration, Endothelial stem cell, Mathematical analysis, Fibronectin, biology.protein, biology, Cell, medicine.anatomical_structure, medicine, Mathematical optimization, Motility, Mathematics
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