Study on the tumor-induced angiogenesis using mathematical models

Cancer Sci. 2018 Jan;109(1):15-23. doi: 10.1111/cas.13395. Epub 2017 Dec 4.


We studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables.

Keywords: angiogenesis; extracellular matrix degradation; hybrid simulation; mathematical model; tumor microenvironment.

Publication types

  • Review

MeSH terms

  • Computer Simulation
  • Extracellular Matrix / metabolism
  • Extracellular Matrix / pathology*
  • Humans
  • Models, Biological
  • Models, Theoretical
  • Neovascularization, Pathologic / metabolism
  • Neovascularization, Pathologic / pathology*
  • Tumor Microenvironment
  • Vascular Endothelial Growth Factors / metabolism*


  • Vascular Endothelial Growth Factors