title: A mathematical model for capillary formation and development in tumor angiogenesis: a review.
abstract: BACKGROUND
  Angiogenesis is a morphogenic process whereby new blood vessels are induced to grow out of a preexisting vasculature. Endothelial cells (EC) form the lining of all blood vessels. Following tumor angiogenic growth factors, EC in neighboring normal capillaries are activated to secrete proteases. These then degrade the basal lamina and permit the EC to migrate into the extracellular matrix.
  
  
  METHODS
  We use mechanisms to produce protease, inhibitors, and fibronectin.
  
  
  RESULTS
  This article reviews a mathematical model originally presented by Levine et al. [Bull Math Biol 2001;63:801-863] and some results of Pamuk [Math Models Methods Appl Sci 2003;13/1:19-33; Math Biosci 2004;189/1:21-38].
  
  
  CONCLUSIONS
  We obtained a very good computational agreement with the rabbit cornea experiments of Folkman [Sci Am 1976;234:58-64]. We also introduce angiostatin to the model for therapeutic case as studied by Ulukaya et al. [Chemotherapy 2004;50/1:43-50].
authors.affiliation: Department of Mathematics, University of Kocaeli, Umuttepe Kampusu, Turkey. spamuk@kou.edu.tr
authors.forename: Serdal
authors.initials: S
authors.lastname: Pamuk
mesh_terms: D043168:Angiostatins; D000818:Animals; D002196:Capillaries / Q000254:growth & development*; D003315:Cornea; D042783:Endothelial Cells / Q000378:metabolism / Q000473:pathology; D005353:Fibronectins / Q000096:biosynthesis; D008954:Models, Biological; D009369:Neoplasms / Q000098:blood supply* / Q000378:metabolism / Q000473:pathology*; D009389:Neovascularization, Pathologic / Q000378:metabolism / Q000473:pathology*; D010447:Peptide Hydrolases / Q000378:metabolism; D011817:Rabbits
chemical_list: D005353:Fibronectins; D043168:Angiostatins; D010447:Peptide Hydrolases