Figure 5.

(A–C) Typical vascular networks formed by 4 initial sprouts located along x = 0.22 at positions y = 0.1, 0.2, 0.3, 0.4; x being plotted along the abscissa and y along the ordinate – migrating across a 2-dimensional domain under the influence of VEGF for various values of C₀, the maximum VEGF concentration per lattice site. (A) Optimal VEGF concentration, C₀ = 0.015 pg/lattice volume. The bias of movement is overwhelmingly in the forward direction. Branching and anastomoses are observed to occur as the vasculature penetrates deeper into the stroma. The resulting networks are qualitatively similar to those observed experimentally in Sholley et al. (1984). (B) C₀ = 0.005 pg/lattice volume. The amount of VEGF is too low to induce proliferation or polarization of the tip cell, leading to a poorly developed and stunted vasculature that does not reach the VEGF source within the time frame of simulations (3 days). (C) C₀ = 0.030 pg/lattice volume. Due to a high VEGF concentration, over-stimulation of endothelial cells occurs, and extensive branching, anastomoses and lateral movement of the tip cell is observed. Due to excessive lateral movement, the vasculature that does not reach the VEGF source within the time frame of simulations (3 days). (D) Assumed branching probability P_b of the migrating tip cell (black curve), and assumed extension probability P_m of the capillary (blue curve), expressed as functions of total fraction of activated VEGFR2 per cell.