… three-dimensional mathematical model for the dynamics of vascular endothelial cells during
sprouting angiogenesis… model for simulating three-dimensional angiogenic morphogenesis. …

… in this three dimensional model is simulated in a box of size 250 × 250 × 125 μm 3 , it starts
from a central capillary 72 , and the new sprouts grow along the gradient of angiogenic factor…

… we develop a three-dimensional (3D), off-lattice, hybrid model of … and capillary sprout
formation, our hybrid model allows us to … the model to account for the action of anti-angiogenic …

… that models endothelial cells (EC) as physical agents on a discrete three-dimensional
grid. The coordinates of the agents and events such as proliferation and migration occur in …

… The model shows how stochastic generation of vascular sprouts combined with a set of …
of a specialized three-dimensional vascular structure with a high degree of organization. …

… tumor angiogenic factors (TAFs). We perform simulations of the siting of capillary sprouts on
an … approximation of the dynamic equations of some angiogenesis activators and inhibitors. …

… vessel accumulate to form capillary sprouts, which move towards … model into a three-dimensional
space. Wu et al.[12] presented a three-dimensional model of solid tumor angiogenesis …

… ), whereas highly stiff or dense matrices significantly limit sprout elongation in three-dimensional
environments (Shamloo & Heilshorn, 2010). At the same time, EC migration remodels …

… the sprouting angiogenesis. The model is a hybrid, which a lattice-based cellular Potts model
reproduces … Shirinifard et al. presented a three dimensional cell-based model to study on …

… on these results, we are currently developing an assay for studying the migration,
proliferation, and differentiation of human endothelial and pericyte-like cells in three-dimensional …