Solitonlike attractor for blood vessel tip density in angiogenesis Articles uri icon

publication date

  • December 2016


  • 6 (062415)


  • 94

International Standard Serial Number (ISSN)

  • 2470-0045

Electronic International Standard Serial Number (EISSN)

  • 2470-0053


  • Recently, numerical simulations of a stochastic model have shown that the density of vessel tips in tumorinduced angiogenesis adopts a solitonlike profile [Sci. Rep. 6, 31296 (2016)]. In this work, we derive and solve the equations for the soliton collective coordinates that indicate how the soliton adapts its shape and velocity to varying chemotaxis and diffusion. The vessel tip density can be reconstructed from the soliton formulas. While the stochastic model exhibits large fluctuations, we show that the location of the maximum vessel tip density for different replicas follows closely the soliton peak position calculated either by ensemble averages or by solving an alternative deterministic description of the density. The simple soliton collective coordinate equations may also be used to ascertain the response of the vessel network to changes in the parameters and thus to control it.


  • Mathematics


  • tumor-induced angiogenesis; mathematical-models; growth-factor; mechanisms; disease