Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity

Functional Connectivity Prediction With Deep Learning for Graph Transformation

Inferring resting-state functional connectivity (FC) from anatomical brain wiring, known as structural connectivity (SC), is of enormous significance in neuroscience for understanding biological neuronal networks and treating mental diseases. Both SC and FC are networks where the nodes are brain regions, and in SC, the edges are the physical fiber nerves among the nodes, while in FC, the edges are the nodes' coactivation relations. Despite the importance of SC and FC, until very recently, the rapidly growing research body on this topic has generally focused on either linear models or computational models that rely heavily on heuristics and simple assumptions regarding the mapping between FC and SC. However, the relationship between FC and SC is actually highly nonlinear and complex and contains considerable randomness; additional factors, such as the subject's age and health, can also significantly impact the SC-FC relationship and hence cannot be ignored. To address these challenges, here, we develop a novel SC-to-FC generative adversarial network (SF-GAN) framework for mapping SC to FC, along with additional metafeatures based on a newly proposed graph neural network-based generative model that is capable of learning the stochasticity. Specifically, a new graph-based conditional generative adversarial nets model is proposed, where edge convolution layers are leveraged to encode the graph patterns in the SC in the form of a graph representation. New edge deconvolution layers are then utilized to decode the representation back to FC. Additional metafeatures of subjects' profile information are integrated into the graph representation with newly designed sparse-regularized layers that can automatically select features that impact FC. Finally, we have also proposed new post hoc explainer of our SF-GAN, which can identify which subgraphs in SC strongly influence which subgraphs in FC by a new multilevel edge-correlation-guided graph clustering problem. The results of experiments conducted to test the new model confirm that it significantly outperforms existing state-of-the-art methods, with additional interpretability for identifying important metafeatures and subgraphs.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Open datasets and code for multi-scale relations on structure, function and neuro-genetics in the human brain

The human brain is an extremely complex network of structural and functional connections that operate at multiple spatial and temporal scales. Investigating the relationship between these multi-scale connections is critical to advancing our comprehension of brain function and disorders. However, accurately predicting structural connectivity from its functional counterpart remains a challenging pursuit. One of the major impediments is the lack of public repositories that integrate structural and functional networks at diverse resolutions, in conjunction with modular transcriptomic profiles, which are essential for comprehensive biological interpretation. To mitigate this limitation, our contribution encompasses the provision of an open-access dataset consisting of derivative matrices of functional and structural connectivity across multiple scales, accompanied by code that facilitates the investigation of their interrelations. We also provide additional resources focused on neuro-genetic associations of module-level network metrics, which present promising opportunities to further advance research in the field of network neuroscience, particularly concerning brain disorders.

Relation of connectome topology to brain volume across 103 mammalian species

The brain connectome is an embedded network of anatomically interconnected brain regions, and the study of its topological organization in mammals has become of paramount importance due to its role in scaffolding brain function and behavior. Unlike many other observable networks, brain connections incur material and energetic cost, and their length and density are volumetrically constrained by the skull. Thus, an open question is how differences in brain volume impact connectome topology. We address this issue using the MaMI database, a diverse set of mammalian connectomes reconstructed from 201 animals, covering 103 species and 12 taxonomy orders, whose brain size varies over more than 4 orders of magnitude. Our analyses focus on relationships between volume and modular organization. After having identified modules through a multiresolution approach, we observed how connectivity features relate to the modular structure and how these relations vary across brain volume. We found that as the brain volume increases, modules become more spatially compact and dense, comprising more costly connections. Furthermore, we investigated how spatial embedding shapes network communication, finding that as brain volume increases, nodes' distance progressively impacts communication efficiency. We identified modes of variation in network communication policies, as smaller and bigger brains show higher efficiency in routing- and diffusion-based signaling, respectively. Finally, bridging network modularity and communication, we found that in larger brains, modular structure imposes stronger constraints on network signaling. Altogether, our results show that brain volume is systematically related to mammalian connectome topology and that spatial embedding imposes tighter restrictions on larger brains.

Substructure of the brain's Cingulo-Opercular network

The Cingulo-Opercular network (CON) is an executive network of the human brain that regulates actions. CON is composed of many widely distributed cortical regions that are involved in top-down control over both lower-level (i.e., motor) and higher-level (i.e., cognitive) functions, as well as in processing of painful stimuli. Given the topographical and functional heterogeneity of the CON, we investigated whether subnetworks within the CON support separable aspects of action control. Using precision functional mapping (PFM) in 15 participants with > 5 hours of resting state functional connectivity (RSFC) and task data, we identified three anatomically and functionally distinct CON subnetworks within each individual. These three distinct subnetworks were linked to Decisions, Actions, and Feedback (including pain processing), respectively, in convergence with a meta-analytic task database. These Decision, Action and Feedback subnetworks represent pathways by which the brain establishes top-down goals, transforms those goals into actions, implemented as movements, and processes critical action feedback such as pain.

Stimulus-dependent functional network topology in mouse visual cortex

Information is processed by networks of neurons in the brain. On the timescale of sensory processing, those neuronal networks have relatively fixed anatomical connectivity, while functional connectivity, which defines the interactions between neurons, can vary depending on the ongoing activity of the neurons within the network. We thus hypothesized that different types of stimuli, which drive different neuronal activities in the network, could lead those networks to display stimulus-dependent functional connectivity patterns. To test this hypothesis, we analyzed electrophysiological data from the Allen Brain Observatory, which utilized Neuropixels probes to simultaneously record stimulus-evoked activity from hundreds of neurons across 6 different regions of mouse visual cortex. The recordings had single-cell resolution and high temporal fidelity, enabling us to determine fine-scale functional connectivity. Comparing the functional connectivity patterns observed when different stimuli were presented to the mice, we made several nontrivial observations. First, while the frequencies of different connectivity motifs (i.e., the patterns of connectivity between triplets of neurons) were preserved across stimuli, the identities of the neurons within those motifs changed. This means that functional connectivity dynamically changes along with the input stimulus, but does so in a way that preserves the motif frequencies. Secondly, we found that the degree to which functional modules are contained within a single brain region (as opposed to being distributed between regions) increases with increasing stimulus complexity. This suggests a mechanism for how the brain could dynamically alter its computations based on its inputs. Altogether, our work reveals unexpected stimulus-dependence to the way groups of neurons interact to process incoming sensory information.

Multi-modal and multi-subject modular organization of human brain networks

The human brain is a complex network of anatomically interconnected brain areas. Spontaneous neural activity is constrained by this architecture, giving rise to patterns of statistical dependencies between the activity of remote neural elements. The non-trivial relationship between structural and functional connectivity poses many unsolved challenges about cognition, disease, development, learning and aging. While numerous studies have focused on statistical relationships between edge weights in anatomical and functional networks, less is known about dependencies between their modules and communities. In this work, we investigate and characterize the relationship between anatomical and functional modular organization of the human brain, developing a novel multi-layer framework that expands the classical concept of multi-layer modularity. By simultaneously mapping anatomical and functional networks estimated from different subjects into communities, this approach allows us to carry out a multi-subject and multi-modal analysis of the brain's modular organization. Here, we investigate the relationship between anatomical and functional modules during resting state, finding unique and shared structures. The proposed framework constitutes a methodological advance in the context of multi-layer network analysis and paves the way to further investigate the relationship between structural and functional network organization in clinical cohorts, during cognitively demanding tasks, and in developmental or lifespan studies.

Detecting hierarchical organization of pervasive communities by modular decomposition of Markov chain

Connecting nodes that contingently co-appear, which is a common process of networking in social and biological systems, normally leads to modular structure characterized by the absence of definite boundaries. This study seeks to find and evaluate methods to detect such modules, which will be called 'pervasive' communities. We propose a mathematical formulation to decompose a random walk spreading over the entire network into localized random walks as a proxy for pervasive communities. We applied this formulation to biological and social as well as synthetic networks to demonstrate that it can properly detect communities as pervasively structured objects. We further addressed a question that is fundamental but has been little discussed so far: What is the hierarchical organization of pervasive communities and how can it be extracted? Here we show that hierarchical organization of pervasive communities is unveiled from finer to coarser layers through discrete phase transitions that intermittently occur as the value for a resolution-controlling parameter is quasi-statically increased. To our knowledge, this is the first elucidation of how the pervasiveness and hierarchy, both hallmarks of community structure of real-world networks, are unified.

Reaction-diffusion models in weighted and directed connectomes

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional epiphenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our high-precision connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances.

Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway.

In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation were performed in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

Unusual Mathematical Approaches Untangle Nervous Dynamics

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry, topology, group theory and category theory can assess neuronal issues and provide experimentally testable hypotheses. The Monge’s theorem might contribute to our visual ability of depth perception and the brain connectome can be tackled in terms of tunnelling nanotubes. The multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of knot theory/braid groups. Presheaves from category theory permit the tackling of nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. Further, the physical concepts of soft-matter polymers and nematic colloids might shed new light on neurulation in mammalian embryos. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. For instance, our framework leads to the conjecture that the development of the nervous system might be correlated with the occurrence of local thermal changes in embryo–fetal tissues.

Harmonizing functional connectivity reduces scanner effects in community detection

Community detection on graphs constructed from functional magnetic resonance imaging (fMRI) data has led to important insights into brain functional organization. Large studies of brain community structure often include images acquired on multiple scanners across different studies. Differences in scanner can introduce variability into the downstream results, and these differences are often referred to as scanner effects. Such effects have been previously shown to significantly impact common network metrics. In this study, we identify scanner effects in data-driven community detection results and related network metrics. We assess a commonly employed harmonization method and propose new methodology for harmonizing functional connectivity that leverage existing knowledge about network structure as well as patterns of covariance in the data. Finally, we demonstrate that our new methods reduce scanner effects in community structure and network metrics. Our results highlight scanner effects in studies of brain functional organization and provide additional tools to address these unwanted effects. These findings and methods can be incorporated into future functional connectivity studies, potentially preventing spurious findings and improving reliability of results.

The broad edge of synchronization: Griffiths effects and collective phenomena in brain networks

Many of the amazing functional capabilities of the brain are collective properties stemming from the interactions of large sets of individual neurons. In particular, the most salient collective phenomena in brain activity are oscillations, which require the synchronous activation of many neurons. Here, we analyse parsimonious dynamical models of neural synchronization running on top of synthetic networks that capture essential aspects of the actual brain anatomical connectivity such as a hierarchical-modular and core-periphery structure. These models reveal the emergence of complex collective states with intermediate and flexible levels of synchronization, halfway in the synchronous-asynchronous spectrum. These states are best described as broad Griffiths-like phases, i.e. an extension of standard critical points that emerge in structurally heterogeneous systems. We analyse different routes (bifurcations) to synchronization and stress the relevance of 'hybrid-type transitions' to generate rich dynamical patterns. Overall, our results illustrate the complex interplay between structure and dynamics, underlining key aspects leading to rich collective states needed to sustain brain functionality. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Brain Mapping of Behavioral Domains Using Multi-Scale Networks and Canonical Correlation Analysis

Simultaneous mapping of multiple behavioral domains into brain networks remains a major challenge. Here, we shed some light on this problem by employing a combination of machine learning, structural and functional brain networks at different spatial resolutions (also known as scales), together with performance scores across multiple neurobehavioral domains, including sensation, motor skills, and cognition. Provided by the Human Connectome Project, we make use of three cohorts: 640 participants for model training, 160 subjects for validation, and 200 subjects for model performance testing thus enhancing prediction generalization. Our modeling consists of two main stages, namely dimensionality reduction in brain network features at multiple scales, followed by canonical correlation analysis, which determines an optimal linear combination of connectivity features to predict multiple behavioral performance scores. To assess the differences in the predictive power of each modality, we separately applied three different strategies: structural unimodal, functional unimodal, and multimodal, that is, structural in combination with functional features of the brain network. Our results show that the multimodal association outperforms any of the unimodal analyses. Then, to answer which human brain structures were most involved in predicting multiple behavioral scores, we simulated different synthetic scenarios in which in each case we completely deleted a brain structure or a complete resting state network, and recalculated performance in its absence. In deletions, we found critical structures to affect performance when predicting single behavioral domains, but this occurred in a lesser manner for prediction of multi-domain behavior. Overall, our results confirm that although there are synergistic contributions between brain structure and function that enhance behavioral prediction, brain networks may also be mutually redundant in predicting multidomain behavior, such that even after deletion of a structure, the connectivity of the others can compensate for its lack in predicting behavior.

Strengthened and posterior-shifted structural rich-club organization in people who use cocaine

BACKGROUND

People with cocaine use disorder (CUD) often have abnormal cognitive function and brain structure. Cognition is supported by brain networks that typically have characteristics like rich-club organization, which is a group of regions that are highly connected across the brain and to each other, and small worldness, which is a balance between local and long-distance connections. However, it is unknown whether there are abnormalities in structural brain network connectivity of CUD.

METHODS

Using diffusion-weighted imaging, we measured structural connectivity in 37 people with CUD and 38 age-matched controls. We identified differences in rich-club organization and whether such differences related to small worldness and behavior. We also tested whether rich-club reorganization was associated with caudate and putamen structural connectivity due to the relevance of the dopamine system to cocaine use.

RESULTS

People with CUD had a higher normalized rich-club coefficient than controls, more edges connecting rich-club nodes to each other and to non-rich-club nodes, and fewer edges connecting non-rich-club nodes. Rich-club nodes were shifted posterior and lateral. Rich-club reorganization was related to lower clustered connectivity around individual nodes found in CUD, to increased impulsivity, and to a decrease in caudate connectivity.

CONCLUSIONS

These findings are consistent with previous work showing increased rich-club connectivity in conditions associated with a hypofunctional dopamine system. The posterior shift in rich-club nodes in CUD suggests that the structural connectivity of posterior regions may be more impacted than previously recognized in models based on brain function and morphology.

Network communication models narrow the gap between the modular organization of structural and functional brain networks

Structural and functional brain networks are modular. Canonical functional systems, such as the default mode network, are well-known modules of the human brain and have been implicated in a large number of cognitive, behavioral and clinical processes. However, modules delineated in structural brain networks inferred from tractography generally do not recapitulate canonical functional systems. Neuroimaging evidence suggests that functional connectivity between regions in the same systems is not always underpinned by anatomical connections. As such, direct structural connectivity alone would be insufficient to characterize the functional modular organization of the brain. Here, we demonstrate that augmenting structural brain networks with models of indirect (polysynaptic) communication unveils a modular network architecture that more closely resembles the brain's established functional systems. We find that diffusion models of polysynaptic connectivity, particularly communicability, narrow the gap between the modular organization of structural and functional brain networks by 20-60%, whereas routing models based on single efficient paths do not improve mesoscopic structure-function correspondence. This suggests that functional modules emerge from the constraints imposed by local network structure that facilitates diffusive neural communication. Our work establishes the importance of modeling polysynaptic communication to understand the structural basis of functional systems.

Local structure-function relationships in human brain networks across the lifespan

A growing number of studies have used stylized network models of communication to predict brain function from structure. Most have focused on a small set of models applied globally. Here, we compare a large number of models at both global and regional levels. We find that globally most predictors perform poorly. At the regional level, performance improves but heterogeneously, both in terms of variance explained and the optimal model. Next, we expose synergies among predictors by using pairs to jointly predict FC. Finally, we assess age-related differences in global and regional coupling across the human lifespan. We find global decreases in the magnitude of structure-function coupling with age. We find that these decreases are driven by reduced coupling in sensorimotor regions, while higher-order cognitive systems preserve local coupling with age. Our results describe patterns of structure-function coupling across the cortex and how this may change with age.

Quantitative mapping of the brain's structural connectivity using diffusion MRI tractography: A review

Diffusion magnetic resonance imaging (dMRI) tractography is an advanced imaging technique that enables in vivo reconstruction of the brain's white matter connections at macro scale. It provides an important tool for quantitative mapping of the brain's structural connectivity using measures of connectivity or tissue microstructure. Over the last two decades, the study of brain connectivity using dMRI tractography has played a prominent role in the neuroimaging research landscape. In this paper, we provide a high-level overview of how tractography is used to enable quantitative analysis of the brain's structural connectivity in health and disease. We focus on two types of quantitative analyses of tractography, including: 1) tract-specific analysis that refers to research that is typically hypothesis-driven and studies particular anatomical fiber tracts, and 2) connectome-based analysis that refers to research that is more data-driven and generally studies the structural connectivity of the entire brain. We first provide a review of methodology involved in three main processing steps that are common across most approaches for quantitative analysis of tractography, including methods for tractography correction, segmentation and quantification. For each step, we aim to describe methodological choices, their popularity, and potential pros and cons. We then review studies that have used quantitative tractography approaches to study the brain's white matter, focusing on applications in neurodevelopment, aging, neurological disorders, mental disorders, and neurosurgery. We conclude that, while there have been considerable advancements in methodological technologies and breadth of applications, there nevertheless remains no consensus about the "best" methodology in quantitative analysis of tractography, and researchers should remain cautious when interpreting results in research and clinical applications.

Attention networks and the intrinsic network structure of the human brain

Attention network theory distinguishes three independent systems, each supported by its own distributed network: an alerting network to deploy attentional resources in anticipation, an orienting network to direct attention to a cued location, and a control network to select relevant information at the expense of concurrently available information. Ample behavioral and neuroimaging evidence supports the dissociation of the three attention domains. The strong assumption that each attentional system is realized through a separable network, however, raises the question how these networks relate to the intrinsic network structure of the brain. Our understanding of brain networks has advanced majorly in the past years due to the increasing focus on brain connectivity. The brain is intrinsically organized into several large‐scale networks whose modular structure persists across task states. Existing proposals on how the presumed attention networks relate to intrinsic networks rely mostly on anecdotal and partly contradictory arguments. We addressed this issue by mapping different attention networks at the level of cifti‐grayordinates. Resulting group maps were compared to the group‐level topology of 23 intrinsic networks, which we reconstructed from the same participants' resting state fMRI data. We found that all attention domains recruited multiple and partly overlapping intrinsic networks and converged in the dorsal fronto‐parietal and midcingulo‐insular network. While we observed a preference of each attentional domain for its own set of intrinsic networks, implicated networks did not match well to those proposed in the literature. Our results indicate a necessary refinement of the attention network theory.

Prenatal stress dysregulates resting-state functional connectivity and sensory motifs

Prenatal stress (PS) can impact fetal brain structure and function and contribute to higher vulnerability to neurodevelopmental and neuropsychiatric disorders. To understand how PS alters evoked and spontaneous neocortical activity and intrinsic brain functional connectivity, mesoscale voltage imaging was performed in adult C57BL/6NJ mice that had been exposed to auditory stress on gestational days 12-16, the age at which neocortex is developing. PS mice had a four-fold higher basal corticosterone level and reduced amplitude of cortical sensory-evoked responses to visual, auditory, whisker, forelimb, and hindlimb stimuli. Relative to control animals, PS led to a general reduction of resting-state functional connectivity, as well as reduced inter-modular connectivity, enhanced intra-modular connectivity, and altered frequency of auditory and forelimb spontaneous sensory motifs. These resting-state changes resulted in a cortical connectivity pattern featuring disjoint but tight modules and a decline in network efficiency. The findings demonstrate that cortical connectivity is sensitive to PS and exposed offspring may be at risk for adult stress-related neuropsychiatric disorders.

Multiscale communication in cortico-cortical networks

Signaling in brain networks unfolds over multiple topological scales. Areas may exchange information over local circuits, encompassing direct neighbours and areas with similar functions, or over global circuits, encompassing distant neighbours with dissimilar functions. Here we study how the organization of cortico-cortical networks mediate localized and global communication by parametrically tuning the range at which signals are transmitted on the white matter connectome. We show that brain regions vary in their preferred communication scale. By investigating the propensity for brain areas to communicate with their neighbors across multiple scales, we naturally reveal their functional diversity: unimodal regions show preference for local communication and multimodal regions show preferences for global communication. We show that these preferences manifest as region- and scale-specific structure-function coupling. Namely, the functional connectivity of unimodal regions emerges from monosynaptic communication in small-scale circuits, while the functional connectivity of transmodal regions emerges from polysynaptic communication in large-scale circuits. Altogether, the present findings reveal that communication preferences are highly heterogeneous across the cortex, shaping regional differences in structure-function coupling.

The R1-weighted connectome: complementing brain networks with a myelin-sensitive measure

Myelin plays a crucial role in how well information travels between brain regions. Complementing the structural connectome, obtained with diffusion MRI tractography, with a myelin-sensitive measure could result in a more complete model of structural brain connectivity and give better insight into white-matter myeloarchitecture. In this work we weight the connectome by the longitudinal relaxation rate (R1), a measure sensitive to myelin, and then we assess its added value by comparing it with connectomes weighted by the number of streamlines (NOS). Our analysis reveals differences between the two connectomes both in the distribution of their weights and the modular organization. Additionally, the rank-based analysis shows that R1 can be used to separate transmodal regions (responsible for higher-order functions) from unimodal regions (responsible for low-order functions). Overall, the R1-weighted connectome provides a different perspective on structural connectivity taking into account white matter myeloarchitecture.

In the present work, we show that by using a myelin-sensitive measure we can complement the diffusion MRI-based connectivity and provide a different picture of the brain organization. We show that the R1-weighted average distribution does not follow the same trend as the number of streamlines strength distribution, and the two connectomes exhibit different modular organization. We also show that unimodal cortical regions tend to be connected by more streamlines, but the connections exhibit a lower R1-weighted average, while the transmodal regions have higher R1-weighted average but fewer streamlines. This could imply that the unimodal regions require more connections with lower myelination, whereas the transmodal regions rely on connections with higher myelination.

A Comprehensive Analysis of Multilayer Community Detection Algorithms for Application to EEG-Based Brain Networks

Modular organization is an emergent property of brain networks, responsible for shaping communication processes and underpinning brain functioning. Moreover, brain networks are intrinsically multilayer since their attributes can vary across time, subjects, frequency, or other domains. Identifying the modular structure in multilayer brain networks represents a gateway toward a deeper understanding of neural processes underlying cognition. Electroencephalographic (EEG) signals, thanks to their high temporal resolution, can give rise to multilayer networks able to follow the dynamics of brain activity. Despite this potential, the community organization has not yet been thoroughly investigated in brain networks estimated from EEG. Furthermore, at the state of the art, there is still no agreement about which algorithm is the most suitable to detect communities in multilayer brain networks, and a way to test and compare them all under a variety of conditions is lacking. In this work, we perform a comprehensive analysis of three algorithms at the state of the art for multilayer community detection (namely, genLouvain, DynMoga, and FacetNet) as compared with an approach based on the application of a single-layer clustering algorithm to each slice of the multilayer network. We test their ability to identify both steady and dynamic modular structures. We statistically evaluate their performances by means of ad hoc benchmark graphs characterized by properties covering a broad range of conditions in terms of graph density, number of clusters, noise level, and number of layers. The results of this simulation study aim to provide guidelines about the choice of the more appropriate algorithm according to the different properties of the brain network under examination. Finally, as a proof of concept, we show an application of the algorithms to real functional brain networks derived from EEG signals collected at rest with closed and open eyes. The test on real data provided results in agreement with the conclusions of the simulation study and confirmed the feasibility of multilayer analysis of EEG-based brain networks in both steady and dynamic conditions.

Network topology of the marmoset connectome

The brain is a complex network of interconnected and interacting neuronal populations. Global efforts to understand the emergence of behavior and the effect of perturbations depend on accurate reconstruction of white matter pathways, both in humans and in model organisms. An emerging animal model for next-generation applied neuroscience is the common marmoset (Callithrix jacchus). A recent open respository of retrograde and anterograde tract tracing presents an opportunity to systematically study the network architecture of the marmoset brain (Marmoset Brain Architecture Project; http://www.marmosetbrain.org). Here we comprehensively chart the topological organization of the mesoscale marmoset cortico-cortical connectome. The network possesses multiple nonrandom attributes that promote a balance between segregation and integration, including near-minimal path length, multiscale community structure, a connective core, a unique motif composition, and multiple cavities. Altogether, these structural attributes suggest a link between network architecture and function. Our findings are consistent with previous reports across a range of species, scales, and reconstruction technologies, suggesting a small set of organizational principles universal across phylogeny. Collectively, these results provide a foundation for future anatomical, functional, and behavioral studies in this model organism.

The thalamus integrates the macrosystems of the brain to facilitate complex, adaptive brain network dynamics

The human brain is a complex, adaptive system comprised of billions of cells with trillions of connections. The interactions between the elements of the system oppose this seemingly limitless capacity by constraining the system's dynamic repertoire, enforcing distributed neural states that balance integration and differentiation. How this trade-off is mediated by the brain, and how the emergent, distributed neural patterns give rise to cognition and awareness, remains poorly understood. Here, I argue that the thalamus is well-placed to arbitrate the interactions between distributed neural assemblies in the cerebral cortex. Different classes of thalamocortical connections are hypothesized to promote either feed-forward or feedback processing modes in the cerebral cortex. This activity can be conceptualized as emerging dynamically from an evolving attractor landscape, with the relative engagement of distinct distributed circuits providing differing constraints over the manner in which brain state trajectories change over time. In addition, inputs to the distinct thalamic populations from the cerebellum and basal ganglia, respectively, are proposed to differentially shape the attractor landscape, and hence, the temporal evolution of cortical assemblies. The coordinated engagement of these neural macrosystems is then shown to share key characteristics with prominent models of cognition, attention and conscious awareness. In this way, the crucial role of the thalamus in mediating the distributed, multi-scale network organization of the central nervous system can be related to higher brain function.

Altered network architecture of functional brain communities in chronic nociplastic pain

Neuroimaging has enhanced our understanding of the neural correlates of pain. Yet, how neural circuits interact and contribute to persistent pain remain largely unknown. Here, we investigate the mesoscale organization of the brain through intrinsic functional communities generated from resting state functional MRI data from two independent datasets, a discovery cohort of 43 Fibromyalgia (FM) patients and 20 healthy controls (HC) as well as a replication sample of 34 FM patients and 21 HC. Using normalized mutual information, we found that the global network architecture in chronic pain patients is less stable (more variable). Subsequent analyses of node community assignment revealed the composition of the communities differed between FM and HC. Furthermore, differences in network organization were associated with the changes in the composition of communities between patients with varying levels of clinical pain. Together, this work demonstrates that intrinsic network communities differ substantially between patients with FM and controls. These differences may represent a novel aspect of the pathophysiology of chronic nociplastic pain.

Geometric renormalization unravels self-similarity of the multiscale human connectome

Structural connectivity in the brain is typically studied by reducing its observation to a single spatial resolution. However, the brain possesses a rich architecture organized over multiple scales linked to one another. We explored the multiscale organization of human connectomes using datasets of healthy subjects reconstructed at five different resolutions. We found that the structure of the human brain remains self-similar when the resolution of observation is progressively decreased by hierarchical coarse-graining of the anatomical regions. Strikingly, a geometric network model, where distances are not Euclidean, predicts the multiscale properties of connectomes, including self-similarity. The model relies on the application of a geometric renormalization protocol which decreases the resolution by coarse-graining and averaging over short similarity distances. Our results suggest that simple organizing principles underlie the multiscale architecture of human structural brain networks, where the same connectivity law dictates short- and long-range connections between different brain regions over many resolutions. The implications are varied and can be substantial for fundamental debates, such as whether the brain is working near a critical point, as well as for applications including advanced tools to simplify the digital reconstruction and simulation of the brain.

Aerobic Exercise Induces Functional and Structural Reorganization of CNS Networks in Multiple Sclerosis: A Randomized Controlled Trial

Objectives: Evidence from animal studies suggests that aerobic exercise may promote neuroplasticity and could, therefore, provide therapeutic benefits for neurological diseases such as multiple sclerosis (MS). However, the effects of exercise in human CNS disorders on the topology of brain networks, which might serve as an outcome at the interface between biology and clinical performance, remain poorly understood.

Methods: We investigated functional and structural networks in patients with relapsing-remitting MS in a clinical trial of standardized aerobic exercise. Fifty-seven patients were randomly assigned to moderate-intensity exercise for 3 months or a non-exercise control group. We reconstructed functional networks based on resting-state functional magnetic resonance imaging (MRI) and used probabilistic tractography on diffusion-weighted imaging data for structural networks.

Results: At baseline, compared to 30 healthy controls, patients exhibited decreased structural connectivity that was most pronounced in hub regions of the brain. Vice versa, functional connectivity was increased in hubs. After 3 months, we observed hub independent increased functional connectivity in the exercise group while the control group presented a loss of functional hub connectivity. On a structural level, the control group remained unchanged, while the exercise group had also increased connectivity. Increased clustering of hubs indicates a better structural integration and internal connectivity at the top of the network hierarchy.

Conclusion: Increased functional connectivity of hubs contrasts a loss of structural connectivity in relapsing-remitting MS. Under an exercise condition, a further hub independent increase of functional connectivity seems to translate in higher structural connectivity of the whole brain.

Default-mode network streams for coupling to language and control systems

The human brain is organized into large-scale networks identifiable using resting-state functional connectivity (RSFC). These functional networks correspond with broad cognitive domains; for example, the Default-mode network (DMN) is engaged during internally oriented cognition. However, functional networks may contain hierarchical substructures corresponding with more specific cognitive functions. Here, we used individual-specific precision RSFC to test whether network substructures could be identified in 10 healthy human brains. Across all subjects and networks, individualized network subdivisions were more valid-more internally homogeneous and better matching spatial patterns of task activation-than canonical networks. These measures of validity were maximized at a hierarchical scale that contained ∼83 subnetworks across the brain. At this scale, nine DMN subnetworks exhibited topographical similarity across subjects, suggesting that this approach identifies homologous neurobiological circuits across individuals. Some DMN subnetworks matched known features of brain organization corresponding with cognitive functions. Other subnetworks represented separate streams by which DMN couples with other canonical large-scale networks, including language and control networks. Together, this work provides a detailed organizational framework for studying the DMN in individual humans.

Organizing principles of whole-brain functional connectivity in zebrafish larvae

Network science has begun to reveal the fundamental principles by which large-scale brain networks are organized, including geometric constraints, a balance between segregative and integrative features, and functionally flexible brain areas. However, it remains unknown whether whole-brain networks imaged at the cellular level are organized according to similar principles. Here, we analyze whole-brain functional networks reconstructed from calcium imaging data recorded in larval zebrafish. Our analyses reveal that functional connections are distance-dependent and that networks exhibit hierarchical modular structure and hubs that span module boundaries. We go on to show that spontaneous network structure places constraints on stimulus-evoked reconfigurations of connections and that networks are highly consistent across individuals. Our analyses reveal basic organizing principles of whole-brain functional brain networks at the mesoscale. Our overarching methodological framework provides a blueprint for studying correlated activity at the cellular level using a low-dimensional network representation. Our work forms a conceptual bridge between macro- and mesoscale network neuroscience and opens myriad paths for future studies to investigate network structure of nervous systems at the cellular level.

Human hippocampal CA3 damage disrupts both recent and remote episodic memories

Neocortical-hippocampal interactions support new episodic (event) memories, but there is conflicting evidence about the dependence of remote episodic memories on the hippocampus. In line with systems consolidation and computational theories of episodic memory, evidence from model organisms suggests that the cornu ammonis 3 (CA3) hippocampal subfield supports recent, but not remote, episodic retrieval. In this study, we demonstrated that recent and remote memories were susceptible to a loss of episodic detail in human participants with focal bilateral damage to CA3. Graph theoretic analyses of 7.0-Tesla resting-state fMRI data revealed that CA3 damage disrupted functional integration across the medial temporal lobe (MTL) subsystem of the default network. The loss of functional integration in MTL subsystem regions was predictive of autobiographical episodic retrieval performance. We conclude that human CA3 is necessary for the retrieval of episodic memories long after their initial acquisition and functional integration of the default network is important for autobiographical episodic memory performance.

Determining the Hierarchical Architecture of the Human Brain Using Subject-Level Clustering of Functional Networks

Optimal integration and segregation of neuronal connections are necessary for efficient large-scale network communication between distributed cortical regions while allowing for modular specialization. This dynamic in the cortex is enabled at the network mesoscale by the organization of nodes into communities. Previous in vivo efforts to map the mesoscale architecture in humans had several limitations. Here we characterize a consensus multiscale community organization of the functional cortical network. We derive this consensus from the clustering of subject-level networks. We applied this analysis to magnetic resonance imaging data from 1003 healthy individuals part of the Human Connectome Project. The hierarchical atlas and code will be made publicly available for future investigators.

Delineating the Regional Economic Geography of China by the Approach of Community Detection

With the obvious regionalization trend in the new period of urbanization in China, the scientific delineation of functional regions (FRs) at different scales has become a heated topic recently. Since the 20th century, western academia has formed a basic idea of metropolitan areas’ (MAs) delineation based on population density and commuting rate, for which the subjectivity of threshold setting is difficult to overcome. In this study, community detection algorithms from the field of network science are employed, namely the Louvain algorithm with adjustable resolutions and Combo with high-precision output, respectively. We take the nationwide car-hailing data set as an example to explore a bottom-up method for delineating regional economic geography at different scales based on the interconnection strength between nodes. It was found that most of the prefecture-level cities in China have a dominant commuting region and two or three secondary commuting sub-regions, while regional central cities have extended their commuting hinterlands over jurisdictional boundaries, which is not common due to the larger initial administrative divisions and the comprehensive development niveau of cities. The feasibility and limitation of community detection partitioning algorithms in the application of regional science are verified. It is supposed to be widely used in regional delimitation supported by big data. Both of the two algorithms show a shortage of ignorance of spatial proximity. It is necessary to explore new algorithms that can adjust both accuracy and spatial distance as parameters.

Reconfiguration of Cortical Networks in MDD Uncovered by Multiscale Community Detection with fMRI

Major depressive disorder (MDD) is known to be associated with altered interactions between distributed brain regions. How these regional changes relate to the reorganization of cortical functional systems, and their modulation by antidepressant medication, is relatively unexplored. To identify changes in the community structure of cortical functional networks in MDD, we performed a multiscale community detection algorithm on resting-state functional connectivity networks of unmedicated MDD (uMDD) patients (n = 46), medicated MDD (mMDD) patients (n = 38), and healthy controls (n = 50), which yielded a spectrum of multiscale community partitions. we selected an optimal resolution level by identifying the most stable community partition for each group. uMDD and mMDD groups exhibited a similar reconfiguration of the community structure of the visual association and the default mode systems but showed different reconfiguration profiles in the frontoparietal control (FPC) subsystems. Furthermore, the central system (somatomotor/salience) and 3 frontoparietal subsystems showed strengthened connectivity with other communities in uMDD but, with the exception of 1 frontoparietal subsystem, returned to control levels in mMDD. These findings provide evidence for reconfiguration of specific cortical functional systems associated with MDD, as well as potential effects of medication in restoring disease-related network alterations, especially those of the FPC system.

Multi-scale detection of hierarchical community architecture in structural and functional brain networks

Community detection algorithms have been widely used to study the organization of complex networks like the brain. These techniques provide a partition of brain regions (or nodes) into clusters (or communities), where nodes within a community are densely interconnected with one another. In their simplest application, community detection algorithms are agnostic to the presence of community hierarchies: clusters embedded within clusters of other clusters. To address this limitation, we exercise a multi-scale extension of a common community detection technique, and we apply the tool to synthetic graphs and to graphs derived from human neuroimaging data, including structural and functional imaging data. Our multi-scale community detection algorithm links a graph to copies of itself across neighboring topological scales, thereby becoming sensitive to conserved community organization across levels of the hierarchy. We demonstrate that this method is sensitive to topological inhomogeneities of the graph’s hierarchy by providing a local measure of community stability and inter-scale reliability across topological scales. We compare the brain’s structural and functional network architectures, and we demonstrate that structural graphs display a more prominent hierarchical community organization than functional graphs. Finally, we build an explicitly multimodal multiplex graph that combines both structural and functional connectivity in a single model, and we identify the topological scales where resting state functional connectivity and underlying structural connectivity show similar versus unique hierarchical community architecture. Together, our results demonstrate the advantages of the multi-scale community detection algorithm in studying hierarchical community structure in brain graphs, and they illustrate its utility in modeling multimodal neuroimaging data.

Spectral Clustering via sparse graph structure learning with application to Proteomic Signaling Networks in Cancer

Clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables are presented. As opposed to standard approaches for graph clustering that assume known graph structures, the edge structure of the unknown graph is first estimated using sparse regression based approaches for sparse graph structure learning. Subsequently, graph clustering on the lower dimensional projections of the graph is performed based on Laplacian embeddings using a penalized k-means approach, motivated by Dirichlet process mixture models in Bayesian nonparametrics. In contrast to standard algorithmic approaches for known graphs, the proposed method allows estimation and inference for both graph structure learning and clustering. More importantly, the arguments for Laplacian embeddings as suitable projections for graph clustering are formalized by providing theoretical support for the consistency of the eigenspace of the estimated graph Laplacians. Fast computational algorithms are proposed to scale the method to large number of nodes. Extensive simulations are presented to compare the clustering performance with standard methods. The methods are applied to a novel pan-cancer proteomic data set, and protein networks and clusters are evaluated across multiple different cancer types.

Nonparametric weighted stochastic block models

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e., continuous or discrete, signed or unsigned, bounded or unbounded), as well as arbitrary weight transformations, and describe an unsupervised model selection approach to choose the best network description. We illustrate the application of our method to a variety of empirical weighted networks, such as global migrations, voting patterns in congress, and neural connections in the human brain.

Subgenual anterior cingulate cortex controls sadness-induced modulations of cognitive and emotional network hubs

The regulation of cognitive and emotional processes is critical for proper executive functions and social behavior, but its specific mechanisms remain unknown. Here, we addressed this issue by studying with functional magnetic resonance imaging the changes in network topology that underlie competitive interactions between emotional and cognitive networks in healthy participants. Our behavioral paradigm contrasted periods with high emotional and cognitive demands by including a sadness provocation task followed by a spatial working memory task. The sharp contrast between successive tasks was designed to enhance the separability of emotional and cognitive networks and reveal areas that regulate the flow of information between them (hubs). By applying graph analysis methods on functional connectivity between 20 regions of interest in 22 participants we identified two main brain network modules, one dorsal and one ventral, and their hub areas: the left dorsolateral prefrontal cortex (dlPFC) and the left medial frontal pole (mFP). These hub areas did not modulate their mutual functional connectivity following sadness but they did so through an interposed area, the subgenual anterior cingulate cortex (sACC). Our results identify dlPFC and mFP as areas regulating interactions between emotional and cognitive networks, and suggest that their modulation by sadness experience is mediated by sACC.

Navigation of brain networks

We show that the combination of topology and geometry in mammalian cortical networks allows for near-optimal decentralized communication under navigation routing. Following a simple propagation rule based on local knowledge of the distance between cortical regions, we demonstrate that brain networks can be successfully navigated with efficiency that is comparable to shortest paths routing. This finding helps to conciliate the major progress achieved over more than a decade of connectomics research, under the assumption of communication via shortest paths, with recent questions raised by the biologically unrealistic requirements involved in the computation of optimal routes. Our results reiterate the importance of the brain’s spatial embedding, suggesting a three-way relationship between connectome geometry, topology, and communication.

Understanding the mechanisms of neural communication in large-scale brain networks remains a major goal in neuroscience. We investigated whether navigation is a parsimonious routing model for connectomics. Navigating a network involves progressing to the next node that is closest in distance to a desired destination. We developed a measure to quantify navigation efficiency and found that connectomes in a range of mammalian species (human, mouse, and macaque) can be successfully navigated with near-optimal efficiency (>80% of optimal efficiency for typical connection densities). Rewiring network topology or repositioning network nodes resulted in 45–60% reductions in navigation performance. We found that the human connectome cannot be progressively randomized or clusterized to result in topologies with substantially improved navigation performance (>5%), suggesting a topological balance between regularity and randomness that is conducive to efficient navigation. Navigation was also found to (i) promote a resource-efficient distribution of the information traffic load, potentially relieving communication bottlenecks, and (ii) explain significant variation in functional connectivity. Unlike commonly studied communication strategies in connectomics, navigation does not mandate assumptions about global knowledge of network topology. We conclude that the topology and geometry of brain networks are conducive to efficient decentralized communication.

Default mode network abnormalities in posttraumatic stress disorder: A novel network-restricted topology approach

Disruption in the default mode network (DMN) has been implicated in numerous neuropsychiatric disorders, including posttraumatic stress disorder (PTSD). However, studies have largely been limited to seed-based methods and involved inconsistent definitions of the DMN. Recent advances in neuroimaging and graph theory now permit the systematic exploration of intrinsic brain networks. In this study, we used resting-state functional magnetic resonance imaging (fMRI), diffusion MRI, and graph theoretical analyses to systematically examine the DMN connectivity and its relationship with PTSD symptom severity in a cohort of 65 combat-exposed US Veterans. We employed metrics that index overall connectivity strength, network integration (global efficiency), and network segregation (clustering coefficient). Then, we conducted a modularity and network-based statistical analysis to identify DMN regions of particular importance in PTSD. Finally, structural connectivity analyses were used to probe whether white matter abnormalities are associated with the identified functional DMN changes. We found decreased DMN functional connectivity strength to be associated with increased PTSD symptom severity. Further topological characterization suggests decreased functional integration and increased segregation in subjects with severe PTSD. Modularity analyses suggest a spared connectivity in the posterior DMN community (posterior cingulate, precuneus, angular gyrus) despite overall DMN weakened connections with increasing PTSD severity. Edge-wise network-based statistical analyses revealed a prefrontal dysconnectivity. Analysis of the diffusion networks revealed no alterations in overall strength or prefrontal structural connectivity. DMN abnormalities in patients with severe PTSD symptoms are characterized by decreased overall interconnections. On a finer scale, we found a pattern of prefrontal dysconnectivity, but increased cohesiveness in the posterior DMN community and relative sparing of connectivity in this region. The DMN measures established in this study may serve as a biomarker of disease severity and could have potential utility in developing circuit-based therapeutics.

Optimized connectome architecture for sensory-motor integration

The intricate connectivity patterns of neural circuits support a wide repertoire of communication processes and functional interactions. Here we systematically investigate how neural signaling is constrained by anatomical connectivity in the mesoscale Drosophila (fruit fly) brain network. We use a spreading model that describes how local perturbations, such as external stimuli, trigger global signaling cascades that spread through the network. Through a series of simple biological scenarios we demonstrate that anatomical embedding potentiates sensory-motor integration. We find that signal spreading is faster from nodes associated with sensory transduction (sensors) to nodes associated with motor output (effectors). Signal propagation was accelerated if sensor nodes were activated simultaneously, suggesting a topologically mediated synergy among sensors. In addition, the organization of the network increases the likelihood of convergence of multiple cascades towards effector nodes, thereby facilitating integration prior to motor output. Moreover, effector nodes tend to coactivate more frequently than other pairs of nodes, suggesting an anatomically enhanced coordination of motor output. Altogether, our results show that the organization of the mesoscale Drosophila connectome imparts privileged, behaviorally relevant communication patterns among sensors and effectors, shaping their capacity to collectively integrate information.

The complex network spanned by neurons and their axonal projections promotes a diverse set of functions. In the present report, we study how the topological organization of the fruit fly brain supports sensory-motor integration. Using a simple communication model, we demonstrate that the topology of this network allows efficient coordination among sensory and motor neurons. Our results suggest that brain network organization may profoundly shape the functional repertoire of this simple organism.

Phase-synchronization-based parcellation of resting state fMRI signals reveals topographically organized clusters in early visual cortex

Resting-state fMRI is widely used to study brain function and connectivity. However, interpreting patterns of resting state (RS) fMRI activity remains challenging as they may arise from different neuronal mechanisms than those triggered by exogenous events. Currently, this limits the use of RS-fMRI for understanding cortical function in health and disease. Here, we examine the phase synchronization (PS) properties of blood-oxygen level dependent (BOLD) signals obtained during visual field mapping (VFM) and RS with 7T fMRI. This data-driven approach exploits spatiotemporal covariations in the phase of BOLD recordings to establish the presence of clusters of synchronized activity. We find that, in both VFM and RS data, selecting the most synchronized neighboring recording sites identifies spatially localized PS clusters that follow the topographic organization of the visual cortex. However, in activity obtained during VFM, PS is spatially more extensive than in RS activity, likely reflecting stimulus-driven interactions between local responses. Nevertheless, the similarity of the PS clusters obtained for RS and stimulus-driven fMRI suggest that they share a common neuroanatomical origin. Our finding justifies and facilitates direct comparison of RS and stimulus-evoked activity.

Fluctuations between high- and low-modularity topology in time-resolved functional connectivity

Modularity is an important topological attribute for functional brain networks. Recent human fMRI studies have reported that modularity of functional networks varies not only across individuals being related to demographics and cognitive performance, but also within individuals co-occurring with fluctuations in network properties of functional connectivity, estimated over short time intervals. However, characteristics of these time-resolved functional networks during periods of high and low modularity have remained largely unexplored. In this study we investigate basic spatiotemporal properties of time-resolved networks in the high and low modularity periods during rest, with a particular focus on their spatial connectivity patterns, temporal homogeneity and test-retest reliability. We show that spatial connectivity patterns of time-resolved networks in the high and low modularity periods are represented by increased and decreased dissociation of the default mode network module from task-positive network modules, respectively. We also find that the instances of time-resolved functional connectivity sampled from within the high (respectively, low) modularity period are relatively homogeneous (respectively, heterogeneous) over time, indicating that during the low modularity period the default mode network interacts with other networks in a variable manner. We confirmed that the occurrence of the high and low modularity periods varies across individuals with moderate inter-session test-retest reliability and that it is correlated with previously-reported individual differences in the modularity of functional connectivity estimated over longer timescales. Our findings illustrate how time-resolved functional networks are spatiotemporally organized during periods of high and low modularity, allowing one to trace individual differences in long-timescale modularity to the variable occurrence of network configurations at shorter timescales.

Spontaneous brain network activity: Analysis of its temporal complexity

The brain operates in a complex way. The temporal complexity underlying macroscopic and spontaneous brain network activity is still to be understood. In this study, we explored the brain's complexity by combining functional connectivity, graph theory, and entropy analyses in 25 healthy people using task-free functional magnetic resonance imaging. We calculated the pairwise instantaneous phase synchrony between 8,192 brain nodes for a total of 200 time points. This resulted in graphs for which time series of clustering coefficients (the "cliquiness" of a node) and participation coefficients (the between-module connectivity of a node) were estimated. For these two network metrics, sample entropy was calculated. The procedure produced a number of results: (1) Entropy is higher for the participation coefficient than for the clustering coefficient. (2) The average clustering coefficient is negatively related to its associated entropy, whereas the average participation coefficient is positively related to its associated entropy. (3) The level of entropy is network-specific to the participation coefficient, but not to the clustering coefficient. High entropy for the participation coefficient was observed in the default-mode, visual, and motor networks. These results were further validated using an independent replication dataset. Our work confirms that brain networks are temporally complex. Entropy is a good candidate metric to explore temporal network alterations in diseases with paroxysmal brain disruptions, including schizophrenia and epilepsy.

Network component analysis reveals developmental trajectories of structural connectivity and specific alterations in autism spectrum disorder

The structural organization of the brain can be characterized as a hierarchical ensemble of segregated modules linked by densely interconnected hub regions that facilitate distributed functional interactions. Disturbances to this network may be an important marker of abnormal development. Recently, several neurodevelopmental disorders, including autism spectrum disorder (ASD), have been framed as disorders of connectivity but the full nature and timing of these disturbances remain unclear. In this study, we use non-negative matrix factorization, a data-driven, multivariate approach, to model the structural network architecture of the brain as a set of superposed subnetworks, or network components. In an openly available dataset of 196 subjects scanned between 5 and 85 years we identify a set of robust and reliable subnetworks that develop in tandem with age and reflect both anatomically local and long-range, network hub connections. In a second experiment, we compare network components in a cohort of 51 high-functioning ASD adolescents to a group of age-matched controls. We identify a specific subnetwork representing an increase in local connection strength in the cingulate cortex in ASD (t = 3.44, P < 0.001). This work highlights possible long-term implications of alterations to the developmental trajectories of specific cortical subnetworks. Hum Brain Mapp 38:4169-4184, 2017. © 2017 Wiley Periodicals, Inc.

The epidemic spreading model and the direction of information flow in brain networks

The interplay between structural connections and emerging information flow in the human brain remains an open research problem. A recent study observed global patterns of directional information flow in empirical data using the measure of transfer entropy. For higher frequency bands, the overall direction of information flow was from posterior to anterior regions whereas an anterior-to-posterior pattern was observed in lower frequency bands. In this study, we applied a simple Susceptible-Infected-Susceptible (SIS) epidemic spreading model on the human connectome with the aim to reveal the topological properties of the structural network that give rise to these global patterns. We found that direct structural connections induced higher transfer entropy between two brain regions and that transfer entropy decreased with increasing distance between nodes (in terms of hops in the structural network). Applying the SIS model, we were able to confirm the empirically observed opposite information flow patterns and posterior hubs in the structural network seem to play a dominant role in the network dynamics. For small time scales, when these hubs acted as strong receivers of information, the global pattern of information flow was in the posterior-to-anterior direction and in the opposite direction when they were strong senders. Our analysis suggests that these global patterns of directional information flow are the result of an unequal spatial distribution of the structural degree between posterior and anterior regions and their directions seem to be linked to different time scales of the spreading process.

The modular organization of human anatomical brain networks: Accounting for the cost of wiring

Brain networks are expected to be modular. However, existing techniques for estimating a network's modules make it difficult to assess the influence of organizational principles such as wiring cost reduction on the detected modules. Here we present a modification of an existing module detection algorithm that allowed us to focus on connections that are unexpected under a cost-reduction wiring rule and to identify modules from among these connections. We applied this technique to anatomical brain networks and showed that the modules we detected differ from those detected using the standard technique. We demonstrated that these novel modules are spatially distributed, exhibit unique functional fingerprints, and overlap considerably with rich clubs, giving rise to an alternative and complementary interpretation of the functional roles of specific brain regions. Finally, we demonstrated that, using the modified module detection approach, we can detect modules in a developmental dataset that track normative patterns of maturation. Collectively, these findings support the hypothesis that brain networks are composed of modules and provide additional insight into the function of those modules.