  Existing models of adaptation in biological flow networks consider their
constituent vessels (e.g. veins and arteries) to be rigid, thus predicting a
non physiological response when the drive (e.g. the heart) is dynamic. Here we
show that incorporating pulsatile driving and properties such as fluid inertia
and vessel compliance into a general adaptation framework fundamentally changes
the expected structure at steady state of a minimal one-loop network. In
particular, pulsatility is observed to give rise to resonances which can
stabilize loops for a much broader class of metabolic cost functions than
predicted by existing theories. Our work points to the need for a more
realistic treatment of adaptation in biological flow networks, especially those
driven by a pulsatile source, and provides insights into pathologies that
emerge when such pulsatility is disrupted in human beings.
