On the preservation of vessel bifurcations during flow-mediated angiogenic remodelling
Fig 1
Flow-migration coupling within the A branch model.
An idealised model of a vessel bifurcation with shear stress differences present. (A) The network consists of a feeding vessel connected to a draining vessel by a short proximal path and a longer distal path. Blue arrows indicate the direction of flow throughout the network. Flow at the bifurcation near the inlet diverges, while flow near the outlet converges. The difference in path lengths results in different levels of flow/shear stress within each branch. (B) The network was discretised and seeded with an initial number of ECs (agents). Pressure boundary conditions (black) and values of flow (blue) and shear stress (red) are given in the initial configuration of the network. Periodic boundary conditions were prescribed at the inlet and outlet in order to keep the total number of cells within the simulation constant. In this model we are concerned with EC behaviour at flow-convergent bifurcations where two options to migrate against the flow exist: which path to the migrating ECs choose, and what determines this choice? (C) Vessel lumens are approximated in 3D by wrapping the number of cells in the vessel, n, each with width w, into the circumference of a circle. Flow and shear stress are then calculated using the Hagen-Poiseuille equation.