  During angiogenesis, new blood vessels headed by a migrating endothelial tip
cell sprout from pre-existing ones. This process is known to be regulated by
two signaling pathways concurrently, vascular endothelial growth factor A
(VEGFA) and Notch-Delta. Extracellular VEGFA activates the intracellular
Notch-Delta pathway in nearby endothelial cells which results in endothelial
(stalk, tip) differentiation. Retinal astrocytes appear to play a crucial role
in polarizing new sprouts by secreting VEGFA. \emph{In vivo} retinal
angiogenesis experiments in neonatal mouse generated quantitative data on daily
cell counts and morphological data of vascular network expanding over
fibronectin-rich matrix. Based on this set of data and other existing ones, we
developed a cell-based, multiscale mathematical model using the cellular Potts
model framework to investigate the sprout evolution by integrating the VEGFA
and Notch-Delta signaling pathways. The model incorporates three levels of
description: intracellular, intercellular, and extracellular. Starting with a
single astrocyte embedded in a fibronectin-rich matrix, we use the model to
assess different scenarios regarding VEGFA levels and its interaction with
matrix proteins. Simulation results suggest that astrocyte-derived VEGFA
gradients along with heterogeneous ECM reproduces sprouting morphology, and the
extension speed is in agreement with experimental data in 7 days postnatal
mouse retina. Results also reproduce empirical observations in sprouting
angiogenesis, including anastomosis, dynamic tip cell competition, and sprout
regression as a result of Notch blockade.
