  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 hindered
by the inherent viscous resistance to flow while being 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 both
in single vessels as well as hierarchically structured networks. We validate
the model in human vasculature and apply biologically relevant parameters to
show that response time has to be considered alongside dissipation as an
important fitness cost function in the evolutionary optimization of animal
vascular networks.
