Fluid flow dynamics in networks of compliant vessels

Flow networks appear in a wide variety of natural and artificial contexts, and as such, a significant number of works have aimed to study their properties. However, most of these previous efforts have focused on continuous and dynamically invariant flow through networks of rigid vessels. Here, we develop a theoretical model of pulsatile flow using compliant vessels that interact with the flow and are capable of storing material and elastic energy. Pressure pulses can propagate, dissipate and scatter in such a fluidic network, and the system can support complex and rich dynamics. We solve for the flow and pressure profiles at any point within the network as a function of the properties of the input and output pressure or current waveforms, and we study the sensitivity of the dynamic flow profile to alterations or complete removal of single vessels. We use this to calculate not only the necessary power needed to maintain such a flow profile but also the power required to alter the profile, and show how a network can be optimized with respect to both. Finally, we explore possible applications of this work to biological systems such as the human vasculature network.