  Transport networks are typically optimized, either by evolutionary pressures
in biological systems, or by human design, in engineered structures. In the
case of systems such as the animal vasculature, the transport of fluids is not
only hindered by the inherent resistance to flow but also kept in a dynamic
state by the pulsatile nature of the heart and elastic properties of the vessel
walls. While this imparted pulsatility necessarily increases the dissipation of
energy caused by the resistance, the vessel elasticity helps to reduce overall
dissipation by attenuating the amplitude of the pulsatile components of the
flow. However, we find that this reduction in energy loss comes at the price of
increasing the time required to respond to changes in the flow boundary
conditions for vessels longer than a critical size. In this regime, dissipation
and response time are found to follow a simple power law scaling relation in
single vessels as well as hierarchically structured networks. Applying
biologically relevant parameters to the model suggests that animal vascular
networks may have evolved to maintain a minimal response time over lesser
dissipation.
