Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?
Fig 7
Comparison of approximate solutions with numerical solutions for the PC-1 (power-cost (PC) optimization beyond single branching).
Approximate solutions define linear boundaries on the c1c2-plane between different categories of the solution space: collapse to daughter endpoint, collapse to parent endpoint, and no-collapse. The different categories calculated from numerical simulation are marked by different colors as indicated in the figure. (a) An example of symmetric branching in vessel radius with parameter values: |V0V1| = |V0V2| = |V1V2| = 1, r0 = 1.20, r1 = 1, and r2 = 1, where c1 and c2 take values in the range [0,20]. (b) Zoomed version of (a) into the plane [0,2] × [0,2] with the same resolution as in (a). (c) An example of asymmetric branching in vessel radius with parameter values: |V0V1| = 0.8, |V0V2| = |V1V2| = 1, r0 = 1.1, r1 = 0.85, and r2 = 1, where c1 and c2 take values in the range [0,20]. (d) Zoomed version of (c) into the plane [0,2] × [0,2] with the same resolution as in (c).