RT Journal Article
T1 Integrodifference master equation describing actively growing blood vessels in angiogenesis
A1 López Bonilla, Luis Francisco
A1 Carretero Cerrajero, Manuel
A1 Terragni, Filippo
AB We study a system of particles in a two-dimensional geometry that move according to a reinforced random walk with transition probabilities dependent on the solutions of reaction-diffusion equations (RDEs) for the underlying fields. A birth process and a history-dependent killing process are also considered. This system models tumor-induced angiogenesis, the process of formation of blood vessels induced by a growth factor (GF) released by a tumor. Particles represent vessel tip cells, whose trajectories constitute the growing vessel network. New vessels appear and may fuse with existing ones during their evolution. Thus, the system is described by tracking the density of active tips, calculated as an ensemble average over many realizations of the stochastic process. Such density satisfies a novel discrete master equation with source and sink terms. The sink term is proportional to a space-dependent and suitably fitted killing coefficient. Results are illustrated studying two influential angiogenesis models.
PB Walter de Gruyter
SN 1565-1339
YR 2020
FD 2020-11-18
LK https://hdl.handle.net/10016/31633
UL https://hdl.handle.net/10016/31633
LA eng
NO This work has been supported by the FEDER/Ministerio de Ciencia, Innovación y Universidades – Agencia Estatal de Investigación grant MTM2017-84446-C2-2-R.
DS e-Archivo
RD 27 jul. 2024