Adaptation and Loop Stabilization in Periodically Driven Elastic Flow Networks

Existing theories of long-term structural adaptation in biological flow networks consider their constituent vessels (eg. arteries and veins) to be rigid. In other words, they ignore wave propagation at short time-scales due to vessel-wall compliance and fluid inertia, which is particularly important when the driving source (e.g. the heart) is pulsatile. Here we present an improved theory for adaptation with a remodeling signal that incorporates a comprehensive model of short-term pulsatile dynamics in elastic vessels, and hence more closely resembles actual biological remodeling at long time-scales. Importantly, we show that pulsatility stabilizes loops and prevents vascular shunting for a much broader range of metabolic cost parameters than predicted by existing theories. We also show under what conditions primary loops, closer to the driving source, are prioritized over secondary and tertiary ones, in a hierarchical network architecture. Our work emphasizes the interplay of short and long timescales in biological adaptation and its important effect on long-term structure. It also provides possible insights into the role played by pulsatile driving in mammalian vasculature, and into pathologies that emerge when such pulsatility is disrupted.