Network community structure and resilience to localized damage: application to brain microcirculation

TL;DR

This study models cerebrovascular networks to analyze how community structure affects their resilience to damage, revealing that stronger community structures increase the risk of significant flow reductions upon occlusion.

Contribution

The paper introduces a novel network model reproducing cerebrovascular community structure and analytically links community strength to flow reduction risk after damage.

Findings

Stronger community structure increases probability of large flow reductions.

Flow reduction distribution follows Cauchy laws with heavy tails.

Network resilience decreases with increasing community strength.

Abstract

In cerebrovascular networks, some vertices are more connected to each other than with the rest of the vasculature, defining a community structure. Here, we introduce a class of model networks built by rewiring Random Regular Graphs, which enables to reproduce this community structure and other topological properties of cerebrovascular networks. We use these model networks to study the global flow reduction induced by the removal of a single edge. We analytically show that this global flow reduction can be expressed as a function of the initial flow rate in the removed edge and of a topological quantity, both of which display probability distributions following Cauchy laws, i.e. with large tails. As a result, we show that the distribution of blood flow reductions is strongly influenced by the community structure. In particular, the probability of large flow reductions increases substantially when the community structure is stronger, weakening the network resilience to single capillary occlusions. We discuss the implications of these findings in the context of Alzheimer's Disease, in which the importance of vascular mechanisms, including capillary occlusions, is beginning to be uncovered.