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 reproduction of 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 Alzheimers Disease, in which the importance of vascular mechanisms, including capillary occlusions, is beginning to be uncovered. Statement of significance“Occlusions of capillary vessels, the smallest blood vessels in the brain, are involved in major diseases, including Alzheimers Disease and ischemic stroke. To better understand their impact on cerebral blood flow, we theoretically study the vessel network response to a single occlusion. We show that the reduction of blood flow at network scale is a function of the initial blood flow in the occluded vessel and of a topological quantity, both of which have broad distributions, that is, with significant probabilities of extreme values. Using model networks built from Random Regular Graphs, we show that the presence of communities in the network (subparts more connected to each other than with the rest of the vasculature) yield a broader distribution of the topological quantity. This weakens the resilience of brain vessel networks to single capillary occlusions, which may contribute to the pathogenicity of capillary occlusions in the brain”.
Highlights
Cerebral hypoperfusion, i.e. the decrease of cerebral blood flow, is a common feature of many brain diseases, including neurodegenerative diseases, such as Alzheimer’s Disease (AD) [1, 2], and cerebrovascular diseases, such as hypoperfusion dementia [3]
This contributes to a positive feedback loop, where decreased cerebral blood flow triggers biological pathways leading to increased amyloid β production in the brain, and directly impairs its elimination by the flowing blood
In the same way that the Rks, despite being specific realizations of graphs which belong to the Regular Graphs (RRGs) ensemble, display on average higher modularities than more probable realizations directly drawn from the RRG ensemble, we may expect that other topological peculiarities of the community structure in the Voronoi and mouse networks might systematically bias the width of the Cauchy distribution
Summary
I.e. the decrease of cerebral blood flow, is a common feature of many brain diseases, including neurodegenerative diseases, such as Alzheimer’s Disease (AD) [1, 2], and cerebrovascular diseases, such as hypoperfusion dementia [3]. Many realizations of RRGs of arbitrary size can be constructed, and they locally behave like trees, enabling analytical derivations that provide insight on their asymptotic behavior in the limit of large sizes We modify this ideal RRG model to provide a simple generation scheme that enables the strength of the communities to be controlled by rewiring together a finite number of elementary RRGs. As a third model, we use random networks constructed from Voronoi diagrams of sets of points homogeneously distributed in 3D space, following [19]. We will denote by Rk a subfamily of rewired RRGs built from a set of RRGs whose size is distributed to reproduce the communities of cerebrovascular networks, as further introduced in Section III B, and with k rewirings Both RRG and rewired RRG models are ideal graphs of infinite dimension [17, 23, 24, 29], which are not embedded in the physical space (i.e. vertices have no a priori physical spatial coordinates). We recover the 3-connectivity of the graph by removing recursively all dangling vertices (vertices of connectivity one), and we keep only the largest connected component
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