Hierarchical Loop Stabilization in Periodically Driven Elastic Networks

Network remodeling, or adaptation, in the presence of periodically driven forcings has hereto remained largely unexplored, despite the fact that a broad class of biological transport networks, e.g., animal vasculature, depends on periodic driving (pulsatility of the heart) to maintain flow. Here we propose a new adaptation model that incorporates the effect of short-term flow pulsatility into the long-term remodeling signal for periodically driven elastic networks and is consistent with optimality principles of dissipation and metabolic cost minimization. Using this model to adapt hierarchical elastic networks with multiple levels of looping, we show that very different network architectures are possible at steady state depending on the driving frequency of the pulsatile source and the geometric asymmetry of the paths between the externally driven nodes of the network. Specifically resonant frequencies are shown to prioritize the stabilization of fully looped structures or higher level loops proximal to the source, whereas antiresonant frequencies predominantly stabilize loop-less structures or lower-level loops distal to the source. Thus, this model offers a mechanism that can explain the stabilization of phenotypically diverse loopy network architectures in response to source pulsatility under physiologically relevant conditions and in the absence of other known loop stabilization mechanisms, such as random fluctuations in the load or perfusion homogenization.