Vascular phenotype identification and anti-angiogenic treatment recommendation: A pseudo-multiscale mathematical model of angiogenesis

J Theor Biol. 2016 Jun 7:398:162-80. doi: 10.1016/j.jtbi.2016.03.002. Epub 2016 Mar 14.


The development of anti-angiogenic drugs for cancer therapy has yielded some promising candidates, but novel approaches for interventions to angiogenesis have led to disappointing results. In addition, there is a shortage of biomarkers that are predictive of response to anti-angiogenic treatments. Consequently, the complex biochemical and physiological basis for tumour angiogenesis remains incompletely understood. We have adopted a mathematical approach to address these issues, formulating a spatially averaged multiscale model that couples the dynamics of VEGF, Ang1, Ang2 and PDGF, with those of mature and immature endothelial cells and pericyte cells. The model reproduces qualitative experimental results regarding pericyte coverage of vessels after treatment by anti-Ang2, anti-VEGF and combination anti-VEGF/anti-Ang2 antibodies. We used the steady state behaviours of the model to characterise angiogenic and non-angiogenic vascular phenotypes, and used mechanistic perturbations representing hypothetical anti-angiogenic treatments to generate testable hypotheses regarding transitions to non-angiogenic phenotypes that depend on the pre-treatment vascular phenotype. Additionally, we predicted a synergistic effect between anti-VEGF and anti-Ang2 treatments when applied to an immature pre-treatment vascular phenotype, but not when applied to a normalised angiogenic pre-treatment phenotype. Based on these findings, we conclude that changes in vascular phenotype are predicted to be useful as an experimental biomarker of response to treatment. Further, our analysis illustrates the potential value of non-spatial mathematical models for generating tractable predictions regarding the action of anti-angiogenic therapies.

Keywords: Linear stability; Ordinary differential equation; Vessel normalisation.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Angiogenesis Inhibitors / pharmacology
  • Angiogenesis Inhibitors / therapeutic use*
  • Angiopoietin-2 / metabolism
  • Blood Vessels / drug effects
  • Blood Vessels / pathology*
  • Computer Simulation
  • Endothelial Cells / drug effects
  • Endothelial Cells / metabolism
  • Humans
  • Models, Biological*
  • Neovascularization, Pathologic / drug therapy*
  • Neovascularization, Pathologic / pathology
  • Numerical Analysis, Computer-Assisted
  • Phenotype
  • Platelet-Derived Growth Factor / metabolism
  • Vascular Endothelial Growth Factor A / metabolism


  • Angiogenesis Inhibitors
  • Angiopoietin-2
  • Platelet-Derived Growth Factor
  • Vascular Endothelial Growth Factor A