  Flow networks efficiently transport nutrients and other solutes in many
physical systems, such as plant and animal vasculature. In the case of the
animal circulatory system, an adequate oxygen and nutrient supply is not
guaranteed everywhere: as nutrients travel through the microcirculation and get
absorbed, they become less available at the venous side of the vascular
network. Ensuring that the nutrient distribution is homogeneous provides a
fitness advantage, as all tissue gets enough supply to survive while waste is
minimized. How do animals build such a uniform perfusing flow system? We
propose a local adaptation rule for the vessel radii that is able to equalize
perfusion, while minimizing energy dissipation to circulate the flow and the
material cost. The rule is a combination of different objective cost functions
that compete to produce complex network morphologies ranging from hierarchical
architectures to uniform mesh grids, depending on how each cost is weighted. We
find that our local adaptation rules are consistent with experimental data of
the rat mesentery vasculature.
