On the preservation of vessel bifurcations during flow-mediated angiogenic remodelling
Fig 2
Simple bifurcation rules (BRs 1 through 4).
The mean diameter was calculated over all segments composing the proximal branch (blue) and the distal branch (red). Snapshots of the network at various time points are presented on the far right of every panel. (A) Simulations using BR 1 always resulted in the regression of the distal branch and bifurcation loss, as all cells chose to enter the high-flow proximal branch. (B) In BR 2, cells always chose the path that requires the smallest change in migration direction, resulting in the loss of the proximal branch and the bifurcation. This simulation experiences numerous oscillations in diameter as the distal path is twice the length of the proximal path, and it takes several trips around before the smoothing algorithm settles down the diameter fluctuations (these oscillations have a period of roughly 30 time steps while the length of the distal path round-trip is 30 segments and agents move 1 segment at a time). (C) Mean diameter and standard deviation for the 10 runs using BR3. Using a random number generator to determine which branch each cell entered with equal probability resulted in stabilisation of both branches and no discernible difference in diameter between the two branches. (D) Mean diameter and results of each run using BR 4. Using unequal probability between the two branches, while favouring the high-flow branch, resulted in a form of diameter control, as the high-flow proximal branch stabilised at a larger diameter than the low-flow distal branch.