Finite-size corrections for networks with both area-preserving and area-increasing branching.
(A) As in Figure 3B, we numerically determine the scaling exponent α by OLS regression within a group of artificial networks spanning roughly 8 orders of magnitude in body mass (blood volume). The exponent obtained from a group is plotted against the size of the smallest network in that group (as measured by the number of capillaries, Ncap,S). Many groups are built by systematically increasing the size of the smallest network, resulting in the depicted graph. In all cases the branching ratio was n = 2. Black circles: numerical values. Red curve: analytical approximation, Equation 23. Green curve: Best fit to the shape of Equation 23, . (B) As in (A), except that each exponent is plotted against the number of levels NS of the smallest network in the group from which it was determined. We display results obtained for a branching ratio n = 2 (black circles) and n = 3 (green circles). The red circles mark the predictions of the WBE model, since NS = 25 for the smallest network (a shrew, meaning N̅ = 24 plus 1 level for pulsatile flow) in the case of n = 2, and NS = 16 for n = 3.