Pulsatile Driving Stabilizes Loops in Elastic Flow Networks*

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.