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Review
. 2017 Oct 15;160:73-83.
doi: 10.1016/j.neuroimage.2016.11.006. Epub 2016 Nov 11.

Multi-scale Brain Networks

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Free PMC article
Review

Multi-scale Brain Networks

Richard F Betzel et al. Neuroimage. .
Free PMC article

Abstract

The network architecture of the human brain has become a feature of increasing interest to the neuroscientific community, largely because of its potential to illuminate human cognition, its variation over development and aging, and its alteration in disease or injury. Traditional tools and approaches to study this architecture have largely focused on single scales-of topology, time, and space. Expanding beyond this narrow view, we focus this review on pertinent questions and novel methodological advances for the multi-scale brain. We separate our exposition into content related to multi-scale topological structure, multi-scale temporal structure, and multi-scale spatial structure. In each case, we recount empirical evidence for such structures, survey network-based methodological approaches to reveal these structures, and outline current frontiers and open questions. Although predominantly peppered with examples from human neuroimaging, we hope that this account will offer an accessible guide to any neuroscientist aiming to measure, characterize, and understand the full richness of the brain's multiscale network structure-irrespective of species, imaging modality, or spatial resolution.

Keywords: Brain networks; Complex networks; Graph theory; Multi-layer; Multi-resolution; Multi-scale; Network neuroscience.

Figures

Fig. 1
Fig. 1
The multi-scale brain. Brain networks are organized across multiple spatiotemporal scales and also can be analyzed at topological (network) scales ranging from individual nodes to the network as a whole. Images of neuronal ensemble recordings, segmented axons, brain evolution, and gray-matter development adapted with permission from Buzsáki (2004), Beyer et al. (2013), Krubitzer (2009) and Gogtay et al. (2004).
Fig. 2
Fig. 2
Schematic figure illustrating multi-scale community detection. Networks exhibit community structure over a range of different topological scales. In panels (A) and (B) we show communities detected in a structural connectivity network at two different topological scales (the colors in the surface plots indicate the community to which each region is assigned). We investigate these scales by tuning the resolution parameter in modularity maximization (a common community detection approach) to γ = 1 and γ = 2.5. In panel (C) we illustrate the multi-resolution approach for “sweeping” through a range of resolution parameters to detect communities at different scales, this time using a synthetic network constructed to have hierarchical community structure (hierarchical levels that divide the network into 2, 4, and 8 communities). To identify topological scales of interest (ranges of γ), we calculated the mean pairwise variation of information (VI) of all partitions detected at each value of γ. Low values of VI indicate that on average the detected partitions were similar to one another. The metric VI achieves local minima at scales that uncover the planted hierarchical communities; at values of γ where none of the planted hierarchical communities are detected, VI takes on non-zero values, indicating lack of consensus across detected partitions and highlighting values of γ at which community structure is not present.
Fig. 3
Fig. 3
Multi-scale rich club and core-periphery analysis. (A) The rich club coefficient, ϕbin, for the observed network (black) and the mean over an ensemble of random networks (gray) as a function of node degree, k. The ratio of these two measures defines the normalized rich club coefficient, ϕnorm. Values of k for which the observed rich club coefficient is statistically greater than that of a random network define the rich club regime. (B) Most studies focus on a rich club defined at a single k value and use it to classify edges as “rich club” (rich node to rich node), “feeder” (rich node to non-rich node), or “non-rich club” (non-rich node to non-rich node). The number of edges assigned to each class is highly dependent upon the k at which the rich club is defined. (C) We show edge classifications at three different values of k, in order to highlight that classifications (and the subsequent interpretation) can vary dramatically, even across statistically significant rich clubs. (D) Core–periphery classification can be performed using a parameterized model (Rombach et al., 2014). The parameters (α, β) determine the size of the core relative to the periphery and how sharply the two are divided from one another (Bassett et al., 2013b). At different parameter values the model identifies different cores and different peripheries, and assigns each node a “coreness” score. (E) As an example, we show two sets of coreness scores ordered from smallest to largest. The two sets vary in terms of the core size and constitution. (F) For the same two sets, we show the topographic distribution of coreness scores. Note: In both the rich club and core–periphery examples, the network studied was a structural network used in a previous study (Betzel et al., 2016c).
Fig. 4
Fig. 4
Schematic figure illustrating multi-layer network construction and community detection. Individual networks can be combined in a meaningful way to form a multi-layer network. In panel (A) we show four example networks, each of which contains the same 25 nodes but arranged in different configurations. The links in these networks could represent fluctuating functional connections over time (e.g., within a single scan or over development), connections estimated during different tasks, different frequency bands, or different connection modalities (e.g., structural connections weighted by streamline count or fractional anisotropy or functional connections measured as correlations or coherence). (B) To combine individual layers, links are added from node i to itself across layers. These links can be added ordinally, linking a node to itself in adjacent layers, or categorically, linking a node to itself across all layers. The result is a multi-layer network. (C) Multi-layer networks can be analyzed using many now-standard measures in network science, including—but not limited to—community detection algorithms. The resulting estimate of communities allows us to track the formation and dissolution of communities across layers and report properties of individual nodes—e.g., their flexiblity, which measures how frequently a node changes its community assignment.

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