Randomness in self-organized phenomena. A case study: retinal angiogenesis.
This note presents a review of recent work by the authors on angiogenesis, as a case study for analyzing the role of randomness in the formation of biological patterns. The mathematical description of the formation of new vessels is presented, based on a system of stochastic differential equations, coupled with a branching process, both of them driven by a set of relevant chemotactic underlying fields. A discussion follows about the possible reduction of complexity of the above approach, by mean field approximations of the underlying fields. The crucial role of randomness at the microscale is observed in order to obtain nontrivial realistic vessel networks.
Department of Mathematics, University of Milan, 20133 Milan, Italy. vincenzo.capasso@unimi.it
Vincenzo
V
Capasso
Daniela
D
Morale
Giuseppe
G
Facchetti
D000818:Animals; D049109:Cell Proliferation; D002642:Chick Embryo; D008954:Models, Biological; D018919:Neovascularization, Physiologic / Q000502:physiology*; D012160:Retina / Q000502:physiology*; D013269:Stochastic Processes