Modular Brain Networks

Graph coarse-graining reveals differences in the module-level structure of functional brain networks

Networks have become a standard tool for analyzing functional magnetic resonance imaging (fMRI) data. In this approach, brain areas and their functional connections are mapped to the nodes and links of a network. Even though this mapping reduces the complexity of the underlying data, it remains challenging to understand the structure of the resulting networks due to the large number of nodes and links. One solution is to partition networks into modules and then investigate the modules' composition and relationship with brain functioning. While this approach works well for single networks, understanding differences between two networks by comparing their partitions is difficult and alternative approaches are thus necessary. To this end, we present a coarse-graining framework that uses a single set of data-driven modules as a frame of reference, enabling one to zoom out from the node- and link-level details. As a result, differences in the module-level connectivity can be understood in a transparent, statistically verifiable manner. We demonstrate the feasibility of the method by applying it to networks constructed from fMRI data recorded from 13 healthy subjects during rest and movie viewing. While independently partitioning the rest and movie networks is shown to yield little insight, the coarse-graining framework enables one to pinpoint differences in the module-level structure, such as the increased number of intra-module links within the visual cortex during movie viewing. In addition to quantifying differences due to external stimuli, the approach could also be applied in clinical settings, such as comparing patients with healthy controls.

Evolution of network architecture in a granular material under compression

As a granular material is compressed, the particles and forces within the system arrange to form complex and heterogeneous collective structures. Force chains are a prime example of such structures, and are thought to constrain bulk properties such as mechanical stability and acoustic transmission. However, capturing and characterizing the evolving nature of the intrinsic inhomogeneity and mesoscale architecture of granular systems can be challenging. A growing body of work has shown that graph theoretic approaches may provide a useful foundation for tackling these problems. Here, we extend the current approaches by utilizing multilayer networks as a framework for directly quantifying the progression of mesoscale architecture in a compressed granular system. We examine a quasi-two-dimensional aggregate of photoelastic disks, subject to biaxial compressions through a series of small, quasistatic steps. Treating particles as network nodes and interparticle forces as network edges, we construct a multilayer network for the system by linking together the series of static force networks that exist at each strain step. We then extract the inherent mesoscale structure from the system by using a generalization of community detection methods to multilayer networks, and we define quantitative measures to characterize the changes in this structure throughout the compression process. We separately consider the network of normal and tangential forces, and find that they display a different progression throughout compression. To test the sensitivity of the network model to particle properties, we examine whether the method can distinguish a subsystem of low-friction particles within a bath of higher-friction particles. We find that this can be achieved by considering the network of tangential forces, and that the community structure is better able to separate the subsystem than a purely local measure of interparticle forces alone. The results discussed throughout this study suggest that these network science techniques may provide a direct way to compare and classify data from systems under different external conditions or with different physical makeup.

Heterogeneous Aging Effects on Functional Connectivity in Different Cortical Regions: A Resting-State Functional MRI Study Using Functional Data Analysis

Brain aging is a complex and heterogeneous process characterized by the selective loss and preservation of brain functions. This study examines the normal aging effects on the cerebral cortex by characterizing changes in functional connectivity using resting-state fMRI data. Previous resting-state fMRI studies on normal aging have examined specific networks of the brain, whereas few studies have examined cortical-cortical connectivities across the entire brain. To characterize the effects of normal aging on the cerebral cortex, we proposed the Pearson functional product-moment correlation coefficient for measuring functional connectivity, which has advantages over the traditional correlation coefficient. The distinct patterns of changes in functional connectivity within and among the four cerebral lobes clarified the effects of normal aging on cortical function. Besides, the advantages of the proposed approach over other methods considered were demonstrated through simulation comparisons. The results showed heterogeneous changes in functional connectivity in normal aging. Specifically, the elderly group exhibited enhanced inter-lobe connectivity between the frontal lobe and the other lobes. Inter-lobe connectivity decreased between the temporal and parietal lobes. The results support the frontal aging hypothesis proposed in behavioral and structural MRI studies. In conclusion, functional correlation analysis enables differentiation of changes in functional connectivities and characterizes the heterogeneous aging effects in different cortical regions.

Small-World Brain Networks Revisited

It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be widely applied to analysis of neuroimaging and other neuroscience data as part of the rapid growth of the new field of connectomics. Here, we review briefly the foundational concepts of graph theoretical estimation and generation of small-world networks. We take stock of some of the key developments in the field in the past decade and we consider in some detail the implications of recent studies using high-resolution tract-tracing methods to map the anatomical networks of the macaque and the mouse. In doing so, we draw attention to the important methodological distinction between topological analysis of binary or unweighted graphs, which have provided a popular but simple approach to brain network analysis in the past, and the topology of weighted graphs, which retain more biologically relevant information and are more appropriate to the increasingly sophisticated data on brain connectivity emerging from contemporary tract-tracing and other imaging studies. We conclude by highlighting some possible future trends in the further development of weighted small-worldness as part of a deeper and broader understanding of the topology and the functional value of the strong and weak links between areas of mammalian cortex.

Stability of Network Communities as a Function of Task Complexity

The analysis of the community architecture in functional brain networks has revealed important relations between specific behavioral patterns and characteristic features of the associated functional organization. Numerous studies have assessed changes in functional communities during different states of awareness, learning, information processing, and various behavioral patterns. The robustness of detected communities within a network has been an often-discussed topic in complex systems research. However, our knowledge regarding the intersubject stability of functional communities in the human brain while performing different tasks is still lacking. In this study, we examined the variability of functional communities in weighted undirected graphs based on fMRI recordings of healthy participants across three conditions: the resting state, syllable production as a simple vocal motor task, and meaningful speech production representing a complex behavioral pattern with cognitive involvement. On the basis of the constructed empirical networks, we simulated a large cohort of artificial graphs and performed a leave-one-out stability analysis to assess the sensitivity of communities in the group-averaged networks with respect to perturbations in the averaging cohort. We found that the stability of partitions derived from group-averaged networks depended on task complexity. The determined community architecture in mean networks reflected within-behavior network stability and between-behavior flexibility of the human functional connectome. The sensitivity of functional communities increased from rest to syllable production to speaking, which suggests that the approximation quality of the community structure in the average network to reflect individual per-participant partitions depends on task complexity.

Hierarchical organization of functional connectivity in the mouse brain: a complex network approach

This paper represents a contribution to the study of the brain functional connectivity from the perspective of complex networks theory. More specifically, we apply graph theoretical analyses to provide evidence of the modular structure of the mouse brain and to shed light on its hierarchical organization. We propose a novel percolation analysis and we apply our approach to the analysis of a resting-state functional MRI data set from 41 mice. This approach reveals a robust hierarchical structure of modules persistent across different subjects. Importantly, we test this approach against a statistical benchmark (or null model) which constrains only the distributions of empirical correlations. Our results unambiguously show that the hierarchical character of the mouse brain modular structure is not trivially encoded into this lower-order constraint. Finally, we investigate the modular structure of the mouse brain by computing the Minimal Spanning Forest, a technique that identifies subnetworks characterized by the strongest internal correlations. This approach represents a faster alternative to other community detection methods and provides a means to rank modules on the basis of the strength of their internal edges.

ASD Validity

ASD research is at an important crossroads. The ASD diagnosis is important for assigning a child to early behavioral intervention and explaining a child’s condition. But ASD research has not provided a diagnosis-specific medical treatment, or a consistent early predictor, or a unified life course. If the ASD diagnosis also lacks biological and construct validity, a shift away from studying ASD-defined samples would be warranted. Consequently, this paper reviews recent findings for the neurobiological validity of ASD, the construct validity of ASD diagnostic criteria, and the construct validity of ASD spectrum features. The findings reviewed indicate that the ASD diagnosis lacks biological and construct validity. The paper concludes with proposals for research going forward.

Flow-Based Network Analysis of the Caenorhabditis elegans Connectome

We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios.

One of the goals of systems neuroscience is to elucidate the relationship between the structure of neuronal networks and the functional dynamics that they implement. An ideal model organism to study such interactions is the roundworm C. elegans, which not only has a fully mapped connectome, but has also been the object of extensive behavioural, genetic and neurophysiological experiments. Here we present an analysis of the neuronal network of C. elegans from a dynamical flow perspective. Our analysis reveals a multi-scale organisation of the signal flow in the network linked to anatomical and functional features of neurons, as well as identifying different neuronal roles in relation to signal propagation. We use our computational framework to explore biological input-response scenarios as well as exhaustive in silico ablations, which we relate to experimental findings reported in the literature.

Disrupted Network Topology in Patients with Stable and Progressive Mild Cognitive Impairment and Alzheimer's Disease

Recent findings suggest that Alzheimer's disease (AD) is a disconnection syndrome characterized by abnormalities in large-scale networks. However, the alterations that occur in network topology during the prodromal stages of AD, particularly in patients with stable mild cognitive impairment (MCI) and those that show a slow or faster progression to dementia, are still poorly understood. In this study, we used graph theory to assess the organization of structural MRI networks in stable MCI (sMCI) subjects, late MCI converters (lMCIc), early MCI converters (eMCIc), and AD patients from 2 large multicenter cohorts: ADNI and AddNeuroMed. Our findings showed an abnormal global network organization in all patient groups, as reflected by an increased path length, reduced transitivity, and increased modularity compared with controls. In addition, lMCIc, eMCIc, and AD patients showed a decreased path length and mean clustering compared with the sMCI group. At the local level, there were nodal clustering decreases mostly in AD patients, while the nodal closeness centrality detected abnormalities across all patient groups, showing overlapping changes in the hippocampi and amygdala and nonoverlapping changes in parietal, entorhinal, and orbitofrontal regions. These findings suggest that the prodromal and clinical stages of AD are associated with an abnormal network topology.

Optimally controlling the human connectome: the role of network topology

To meet ongoing cognitive demands, the human brain must seamlessly transition from one brain state to another, in the process drawing on different cognitive systems. How does the brain's network of anatomical connections help facilitate such transitions? Which features of this network contribute to making one transition easy and another transition difficult? Here, we address these questions using network control theory. We calculate the optimal input signals to drive the brain to and from states dominated by different cognitive systems. The input signals allow us to assess the contributions made by different brain regions. We show that such contributions, which we measure as energy, are correlated with regions' weighted degrees. We also show that the network communicability, a measure of direct and indirect connectedness between brain regions, predicts the extent to which brain regions compensate when input to another region is suppressed. Finally, we identify optimal states in which the brain should start (and finish) in order to minimize transition energy. We show that the optimal target states display high activity in hub regions, implicating the brain's rich club. Furthermore, when rich club organization is destroyed, the energy cost associated with state transitions increases significantly, demonstrating that it is the richness of brain regions that makes them ideal targets.

Functional Brain Networks: Does the Choice of Dependency Estimator and Binarization Method Matter?

The human brain can be modelled as a complex networked structure with brain regions as individual nodes and their anatomical/functional links as edges. Functional brain networks are constructed by first extracting weighted connectivity matrices, and then binarizing them to minimize the noise level. Different methods have been used to estimate the dependency values between the nodes and to obtain a binary network from a weighted connectivity matrix. In this work we study topological properties of EEG-based functional networks in Alzheimer’s Disease (AD). To estimate the connectivity strength between two time series, we use Pearson correlation, coherence, phase order parameter and synchronization likelihood. In order to binarize the weighted connectivity matrices, we use Minimum Spanning Tree (MST), Minimum Connected Component (MCC), uniform threshold and density-preserving methods. We find that the detected AD-related abnormalities highly depend on the methods used for dependency estimation and binarization. Topological properties of networks constructed using coherence method and MCC binarization show more significant differences between AD and healthy subjects than the other methods. These results might explain contradictory results reported in the literature for network properties specific to AD symptoms. The analysis method should be seriously taken into account in the interpretation of network-based analysis of brain signals.

Local Patterns to Global Architectures: Influences of Network Topology on Human Learning

A core question in cognitive science concerns how humans acquire and represent knowledge about their environments. To this end, quantitative theories of learning processes have been formalized in an attempt to explain and predict changes in brain and behavior. We connect here statistical learning approaches in cognitive science, which are rooted in the sensitivity of learners to local distributional regularities, and network science approaches to characterizing global patterns and their emergent properties. We focus on innovative work that describes how learning is influenced by the topological properties underlying sensory input. The confluence of these theoretical approaches and this recent empirical evidence motivate the importance of scaling-up quantitative approaches to learning at both the behavioral and neural levels.

Connectome sensitivity or specificity: which is more important?

Connectomes with high sensitivity and high specificity are unattainable with current axonal fiber reconstruction methods, particularly at the macro-scale afforded by magnetic resonance imaging. Tensor-guided deterministic tractography yields sparse connectomes that are incomplete and contain false negatives (FNs), whereas probabilistic methods steered by crossing-fiber models yield dense connectomes, often with low specificity due to false positives (FPs). Densely reconstructed probabilistic connectomes are typically thresholded to improve specificity at the cost of a reduction in sensitivity. What is the optimal tradeoff between connectome sensitivity and specificity? We show empirically and theoretically that specificity is paramount. Our evaluations of the impact of FPs and FNs on empirical connectomes indicate that specificity is at least twice as important as sensitivity when estimating key properties of brain networks, including topological measures of network clustering, network efficiency and network modularity. Our asymptotic analysis of small-world networks with idealized modular structure reveals that as the number of nodes grows, specificity becomes exactly twice as important as sensitivity to the estimation of the clustering coefficient. For the estimation of network efficiency, the relative importance of specificity grows linearly with the number of nodes. The greater importance of specificity is due to FPs occurring more prevalently between network modules rather than within them. These spurious inter-modular connections have a dramatic impact on network topology. We argue that efforts to maximize the sensitivity of connectome reconstruction should be realigned with the need to map brain networks with high specificity.

Dependency Network Analysis (DEPNA) Reveals Context Related Influence of Brain Network Nodes

Communication between and within brain regions is essential for information processing within functional networks. The current methods to determine the influence of one region on another are either based on temporal resolution, or require a predefined model for the connectivity direction. However these requirements are not always achieved, especially in fMRI studies, which have poor temporal resolution. We thus propose a new graph theory approach that focuses on the correlation influence between selected brain regions, entitled Dependency Network Analysis (D_EPNA). Partial correlations are used to quantify the level of influence of each node during task performance. As a proof of concept, we conducted the D_EPNA on simulated datasets and on two empirical motor and working memory fMRI tasks. The simulations revealed that the D_EPNA correctly captures the network’s hierarchy of influence. Applying D_EPNA to the functional tasks reveals the dynamics between specific nodes as would be expected from prior knowledge. To conclude, we demonstrate that D_EPNA can capture the most influencing nodes in the network, as they emerge during specific cognitive processes. This ability opens a new horizon for example in delineating critical nodes for specific clinical interventions.

From regions to connections and networks: new bridges between brain and behavior

Connections and interactions among distributed brain areas are increasingly recognized as the basis for cognitive operations and a diverse repertoire of behaviors. Analytic advances have allowed for brain connectivity to be represented and quantified at multiple levels: from single connections to communities and networks. This review traces the trajectory of network neuroscience, focusing on how connectivity patterns can be related to cognition and behavior. As recent initiatives for open science provide access to imaging and phenotypic data with great detail and depth, we argue that approaches capable of directly modeling multivariate relationships between brain and behavior will become increasingly important in the field.

Atypical Structural Connectome Organization and Cognitive Impairment in Young Survivors of Acute Lymphoblastic Leukemia

Survivors of pediatric acute lymphoblastic leukemia (ALL) are at increased risk for cognitive impairments that disrupt everyday functioning and decrease quality of life. The specific biological mechanisms underlying cognitive impairment following ALL remain largely unclear, but previous studies consistently demonstrate significant white matter pathology. We aimed to extend this literature by examining the organization of the white matter connectome in young patients with a history of ALL treated with chemotherapy only. We applied graph theoretical analysis to diffusion tensor imaging obtained from 31 survivors of ALL age 5-19 years and 39 matched healthy controls. Results indicated significantly lower small-worldness (p = 0.007) and network clustering coefficient (p = 0.019), as well as greater cognitive impairment (p = 0.027) in the ALL group. Regional analysis indicated that clustered connectivity in parietal, frontal, hippocampal, amygdalar, thalamic, and occipital regions was altered in the ALL group. Random forest analysis revealed a model of connectome and demographic variables that could automatically classify survivors of ALL as having cognitive impairment or not (accuracy = 0.89, p < 0.0001). These findings provide further evidence of brain injury in young survivors of ALL, even those without a history of central nervous system (CNS) disease or cranial radiation. Efficiency of local information processing, reorganization of hub connectivity, and cognitive reserve may contribute to cognitive outcome in these children. Certain connectome properties showed U-shaped relationships with cognitive impairment suggesting an optimal range of regional connectivity.

Functional connectivity and structural covariance between regions of interest can be measured more accurately using multivariate distance correlation

Studies of brain-wide functional connectivity or structural covariance typically use measures like the Pearson correlation coefficient, applied to data that have been averaged across voxels within regions of interest (ROIs). However, averaging across voxels may result in biased connectivity estimates when there is inhomogeneity within those ROIs, e.g., sub-regions that exhibit different patterns of functional connectivity or structural covariance. Here, we propose a new measure based on “distance correlation”; a test of multivariate dependence of high dimensional vectors, which allows for both linear and non-linear dependencies. We used simulations to show how distance correlation out-performs Pearson correlation in the face of inhomogeneous ROIs. To evaluate this new measure on real data, we use resting-state fMRI scans and T1 structural scans from 2 sessions on each of 214 participants from the Cambridge Centre for Ageing & Neuroscience (Cam-CAN) project. Pearson correlation and distance correlation showed similar average connectivity patterns, for both functional connectivity and structural covariance. Nevertheless, distance correlation was shown to be 1) more reliable across sessions, 2) more similar across participants, and 3) more robust to different sets of ROIs. Moreover, we found that the similarity between functional connectivity and structural covariance estimates was higher for distance correlation compared to Pearson correlation. We also explored the relative effects of different preprocessing options and motion artefacts on functional connectivity. Because distance correlation is easy to implement and fast to compute, it is a promising alternative to Pearson correlations for investigating ROI-based brain-wide connectivity patterns, for functional as well as structural data.

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We introduce distance correlation as a new measure of ROI-based connectivity.

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It can be used for functional connectivity and structural covariance analyses.

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Simulations show that distance correlation copes with inhomogeneous ROIs.

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In real data, distance correlation is more reliable and robust than Pearson correlation.

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Distance correlation improves correspondence between different ROI definitions.

Network-Level Structure-Function Relationships in Human Neocortex

The dynamics of spontaneous fluctuations in neural activity are shaped by underlying patterns of anatomical connectivity. While numerous studies have demonstrated edge-wise correspondence between structural and functional connections, much less is known about how large-scale coherent functional network patterns emerge from the topology of structural networks. In the present study, we deploy a multivariate statistical technique, partial least squares, to investigate the association between spatially extended structural networks and functional networks. We find multiple statistically robust patterns, reflecting reliable combinations of structural and functional subnetworks that are optimally associated with one another. Importantly, these patterns generally do not show a one-to-one correspondence between structural and functional edges, but are instead distributed and heterogeneous, with many functional relationships arising from nonoverlapping sets of anatomical connections. We also find that structural connections between high-degree hubs are disproportionately represented, suggesting that these connections are particularly important in establishing coherent functional networks. Altogether, these results demonstrate that the network organization of the cerebral cortex supports the emergence of diverse functional network configurations that often diverge from the underlying anatomical substrate.

Comparative Connectomics

We introduce comparative connectomics, the quantitative study of cross-species commonalities and variations in brain network topology that aims to discover general principles of network architecture of nervous systems and the identification of species-specific features of brain connectivity. By comparing connectomes derived from simple to more advanced species, we identify two conserved themes of wiring: the tendency to organize network topology into communities that serve specialized functionality and the general drive to enable high topological integration by means of investment of neural resources in short communication paths, hubs, and rich clubs. Within the space of wiring possibilities that conform to these common principles, we argue that differences in connectome organization between closely related species support adaptations in cognition and behavior.

Generative models of the human connectome

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of the human connectome remain incompletely understood. Earlier work in model organisms has suggested that wiring rules based on geometric relationships (distance) can account for many but likely not all topological features. Here we systematically explore a family of generative models of the human connectome that yield synthetic networks designed according to different wiring rules combining geometric and a broad range of topological factors. We find that a combination of geometric constraints with a homophilic attachment mechanism can create synthetic networks that closely match many topological characteristics of individual human connectomes, including features that were not included in the optimization of the generative model itself. We use these models to investigate a lifespan dataset and show that, with age, the model parameters undergo progressive changes, suggesting a rebalancing of the generative factors underlying the connectome across the lifespan.

Dynamic fluctuations coincide with periods of high and low modularity in resting-state functional brain networks

We investigate the relationship of resting-state fMRI functional connectivity estimated over long periods of time with time-varying functional connectivity estimated over shorter time intervals. We show that using Pearson's correlation to estimate functional connectivity implies that the range of fluctuations of functional connections over short time-scales is subject to statistical constraints imposed by their connectivity strength over longer scales. We present a method for estimating time-varying functional connectivity that is designed to mitigate this issue and allows us to identify episodes where functional connections are unexpectedly strong or weak. We apply this method to data recorded from N=80 participants, and show that the number of unexpectedly strong/weak connections fluctuates over time, and that these variations coincide with intermittent periods of high and low modularity in time-varying functional connectivity. We also find that during periods of relative quiescence regions associated with default mode network tend to join communities with attentional, control, and primary sensory systems. In contrast, during periods where many connections are unexpectedly strong/weak, default mode regions dissociate and form distinct modules. Finally, we go on to show that, while all functional connections can at times manifest stronger (more positively correlated) or weaker (more negatively correlated) than expected, a small number of connections, mostly within the visual and somatomotor networks, do so a disproportional number of times. Our statistical approach allows the detection of functional connections that fluctuate more or less than expected based on their long-time averages and may be of use in future studies characterizing the spatio-temporal patterns of time-varying functional connectivity.