A mathematical model of tumour-induced capillary growth

J Theor Biol. 1985 May 7;114(1):53-73. doi: 10.1016/s0022-5193(85)80255-1.


The corneal limbal vessels of an animal host respond to the presence of a source of Tumour Angiogenesis Factor (TAF) implanted in the cornea by the formation of new capillaries which grow towards the source. This neovasculature can be easily seen and studied and this paper describes a mathematical model of some of the important features of the growth. The model includes the diffusion of TAF, the formation of sprouts from pre-existing vessels and models the movement of these sprouts to form new capillaries as a chemotactic response to the presence of TAF. Numerical results are produced for various values of the parameters which characterize the model and it is suggested that the model might form the framework for further theoretical work on related phenomena such as wound healing or to develop strategies for the investigation of anti-angiogenesis.

MeSH terms

  • Angiogenesis Inducing Agents / metabolism*
  • Animals
  • Capillaries / physiopathology
  • Chemotaxis
  • Cornea / blood supply*
  • Growth Substances / metabolism*
  • Mice
  • Models, Biological*
  • Neoplasm Transplantation
  • Neoplasms, Experimental / physiopathology*
  • Neovascularization, Pathologic / physiopathology*
  • Rabbits


  • Angiogenesis Inducing Agents
  • Growth Substances