Mechanical response in elastic fluid flow networks

TL;DR

This paper investigates how elastic fluid flow networks respond dynamically to changes in their power source, revealing two distinct response regimes influenced by wavefront decay and fluid diffusion, with implications for biological vascular systems.

Contribution

It introduces a model analyzing the response times of elastic fluid networks, identifying two regimes and suggesting biological vascular networks operate near an optimal response regime.

Findings

Two response regimes: wavefront decay dominated and diffusion dominated.

Response time regimes depend on system size, with a critical size separating behaviors.

Biological vascular networks likely evolved near the minimal response time regime.

Abstract

The dynamics of flow within a material transport network is dependent upon the dynamics of its power source. Responding to a change of these dynamics is critical for the fitness of living flow networks, e.g. the animal vasculature, which are subject to frequent and sudden shifts when the pump (the heart) transitions between different steady states. The combination of flow resistance, fluid inertia, and elasticity of the vessel walls causes the flow and pressure of the fluid throughout the network to respond to these transitions and adapt to the new power source operating profiles over a nonzero time scale. We find that this response time can exist in one of two possible regimes; one dominated by the decay rate of travelling wavefronts and independent of system size, and one dominated by the diffusive nature of the fluid mechanical energy over large length scales. These regimes are shown to exist for both single vessels and hierarchically structured networks with systems smaller than a critical size in the former and larger systems in the later. Applying biologically relevant parameters to the model suggests that animal vascular networks may have evolved to occupy a state within the minimal response time regime but close to this critical system size.