Stochastic model of tumor-induced angiogenesis: Ensemble averages and deterministic equations Articles uri icon

publication date

  • February 2016


  • 2


  • 93

International Standard Serial Number (ISSN)

  • 2470-0045

Electronic International Standard Serial Number (EISSN)

  • 2470-0053


  • A recent conceptual model of tumor-driven angiogenesis including branching, elongation, and anastomosis of blood vessels captures some of the intrinsic multiscale structures of this complex system, yet allowing one to extract a deterministic integro-partial-differential description of the vessel tip density [Phys. Rev. E 90, 062716 (2014)]. Here we solve the stochastic model, show that ensemble averages over many realizations correspond to the deterministic equations, and fit the anastomosis rate coefficient so that the total number of vessel tips evolves similarly in the deterministic and ensemble-averaged stochastic descriptions.


  • Mathematics


  • cell processes & properties; developmental pattern formation; emergence of patterns; stochastic dynamical systems; biological physics