Novel approach to vascular network modeling in 3D

Abstract

A simulation of a hybrid multi-scale phase-field model which describes the dynamics of the interface that divides the new capillaries and the stroma was performed. Four equations model the behaviour of proliferating endothelial cells (ECs) in response to a gradient of a pro-angiogenic factor (T), leading to the growth and time evolution of a tree of vascular vessels from sprouts emerging from the original capillar. New sprouts are pulled by activated tip cells and move with a velocity proportional to the gradient of angiogenic factors. The sources of pro-angiogenic factor are hypoxic cells. This factor diffuses throughout a three-dimensional system and is consumed by the ECs whose proliferation is governed by an order parameter (φ). Higher values of chemotactic response led to an increase of the number of ramifications in the vessels, which were thinner; higher values of proliferation rate to thicker vessels and a more ramified network and an increase in the number of hypoxic cells led to a higher number of branches, higher angiogenic factor consumption, longer and internally more proliferative vessels.