title: Solitonlike attractor for blood vessel tip density in angiogenesis.
abstract: Recently, numerical simulations of a stochastic model have shown that the density of vessel tips in tumor-induced angiogenesis adopts a solitonlike profile [Sci. Rep. 6, 31296 (2016)2045-232210.1038/srep31296]. 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.
authors.affiliation: G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
authors.forename: L L
authors.initials: LL
authors.lastname: Bonilla
authors.affiliation: G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Carretero
authors.affiliation: G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
authors.forename: F
authors.initials: F
authors.lastname: Terragni
mesh_terms: D001808:Blood Vessels / Q000254:growth & development*; D002633:Chemotaxis; D004058:Diffusion; D008954:Models, Biological; D009389:Neovascularization, Pathologic / Q000503:physiopathology*