On the preservation of vessel bifurcations during flow-mediated angiogenic remodelling
Fig 4
Competitive oscillations between the flow-based mechanism (shear stress) and collective-based mechanism (junction forces) achieves bifurcation stability.
(A) The probability of each branch of pulling in new cells at the bifurcation, Pi, is given by the weighted average of the shear stress probability Pτi and the cell number probability Pni. (B) The branch probability over time for an example stable simulation with a value of α = 0.45. The branch probability at the bifurcation oscillated slightly over time, with the probability of the high-flow proximal branch averaging to a higher value (dark blue, mean 0.6456) than the low-flow distal branch (dark red, mean 0.3544). (C) The individual components of these probabilities also oscillate over time in both the proximal branch (left) and the distal branch (right), with alternating peaks in shear stress (dark blue/red, solid line) and cell number probability (light blue/red, dashed-dot line). Additionally, a peak in either component in one branch was accompanied by a trough the that same probability component in the other branch. These data suggest that the shear stress and cell number components interact competitively at stable bifurcations, each compensating for increases in the other to prevent either of the two components from dominating the bifurcation (which would result in a loss of one of the two branches).