Resilience in Hierarchical Fluid Flow Networks

TL;DR

This paper explores how hierarchical structures in fluid flow networks, like brain vasculature, influence their ability to reroute flow after damage, revealing that highly conductive veins can shield parts of the network and enhance overall resilience.

Contribution

It introduces a model of flow rerouting in hierarchical networks and demonstrates how vein conductivity and topology affect network resilience and damage containment.

Findings

Highly conductive veins act as flow barriers and shields.

Increasing vein conductivity beyond a threshold does not improve shielding.

Grid arrangements of veins modestly enhance network resilience.

Abstract

The structure of flow networks determines their function under normal conditions as well as their response to perturbative damage. Brain vasculature often experiences transient or permanent occlusions in the finest vessels, but it is not clear how these micro-clots affect the large scale blood flow or to what extent they decrease functionality. Motivated by this, we investigate how flow is rerouted after the occlusion of a single edge in networks with a hierarchy in edge conductivities. We find that in 2D networks, vessels formed by highly conductive edges serve as barriers to contain the displacement of flow due to a localized perturbation. In this way, the vein provides shielding from damage to surrounding edges. We show that once the conductivity of the vein surpasses an initial minimal value, further increasing the conductivity can no longer extend the shielding provided by the vein. Rather, the length scale of the shielding is set by the network topology. Upon understanding the effects of a single vein, we investigate the global resilience of networks with complex hierarchical order. We find that a system of veins arranged in a grid is able to modestly increase the overall network resilience, outperforming a parallel vein pattern.