Dynamics of vascular branching morphogenesis: the effect of blood and tissue flow

Vascularization of embryonic organs or tumors starts from a primitive lattice of capillaries. Upon perfusion, this lattice is remodeled into branched arteries and veins. Adaptation to mechanical forces is implied to play a major role in arterial patterning. However, numerical simulations of vessel adaptation to haemodynamics has so far failed to predict any realistic vascular pattern. We present in this article a theoretical modeling of vascular development in the yolk sac based on three features of vascular morphogenesis: the disconnection of side branches from main branches, the reconnection of dangling sprouts ("dead ends"), and the plastic extension of interstitial tissue, which we have observed in vascular morphogenesis. We show that the effect of Poiseuille flow in the vessels can be modeled by aggregation of random walkers. Solid tissue expansion can be modeled by a Poiseuille (parabolic) deformation, hence by deformation under hits of random walkers. Incorporation of these features, which are of a mechanical nature, leads to realistic modeling of vessels, with important biological consequences. The model also predicts the outcome of simple mechanical actions, such as clamping of vessels or deformation of tissue by the presence of obstacles. This study offers an explanation for flow-driven control of vascular branching morphogenesis.