Mathematical models of developmental vascular remodelling: A review
Fig 9
The Chen (A), PolNet (B), and Ghaffari (C) approaches are the 3 flow-focused models of vascular remodelling currently available in the literature.
(A) Chen and colleagues [15] coupled long-time series confocal imaging of the developing zebrafish midbrain vasculature (in vivo) with a fluid-structure interaction model to predict which vessels would undergo pruning during vascular development. (B) The PolNet group [7,8,13,18] compared live in vivo images of the retinal vasculature in neonatal mice with a 3D lattice-Boltzmann reconstruction of the blood flow to show that endothelial cell polarity (bi) aligns against the direction of flow, with polarisation strength inversely proportional to the wall shear stress (Bii). (C) Ghaffari [80,81] coupled time-lapse microscopy images of flow dynamics in ex ovo quail embryos with a finite element model of the 2D Navier–Stokes equations to understand how the flow evolves during development. Subfigures A, B, and C are adapted with permission from Chen and colleagues [15], Franco and colleagues [13], and Ghaffari and colleagues [80], respectively.