Why does some biological networks deviate from Hess-Murray law and why is this question of importance?

Abstract

Complex flow systems such as the vascular and respiratory trees are made of large and small vessels in series. This compromise between large and small vessels is due to the fact that systems involve both translational and transmural flows. The optimal arrangement of vessels in these tree-networks seems to obey to Hess-Murray law, which pointed out a relationship that links the radius of a parent vessel to the radii of the daughter (immediately downstream after a vessel bifurcation): the reduction of vessel size by a constant factor (2−1/3). However, there are some experimental evidences that there are tree networks that present larger sizes than predicted by the Hess-Murray law.