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

Response inhibition in premotor cortex corresponds to a complex reshuffle of the mesoscopic information network

Recent studies have explored functional and effective neural networks in animal models; however, the dynamics of information propagation among functional modules under cognitive control remain largely unknown. Here, we addressed the issue using transfer entropy and graph theory methods on mesoscopic neural activities recorded in the dorsal premotor cortex of rhesus monkeys. We focused our study on the decision time of a Stop-signal task, looking for patterns in the network configuration that could influence motor plan maturation when the Stop signal is provided. When comparing trials with successful inhibition to those with generated movement, the nodes of the network resulted organized into four clusters, hierarchically arranged, and distinctly involved in information transfer. Interestingly, the hierarchies and the strength of information transmission between clusters varied throughout the task, distinguishing between generated movements and canceled ones and corresponding to measurable levels of network complexity. Our results suggest a putative mechanism for motor inhibition in premotor cortex: a topological reshuffle of the information exchanged among ensembles of neurons.

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.

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'.

Hyperbolic disc embedding of functional human brain connectomes using resting-state fMRI

The brain presents a real complex network of modular, small-world, and hierarchical nature, which are features of non-Euclidean geometry. Using resting-state functional magnetic resonance imaging, we constructed a scale-free binary graph for each subject, using internodal time series correlation of regions of interest as a proximity measure. The resulting network could be embedded onto manifolds of various curvatures and dimensions. While maintaining the fidelity of embedding (low distortion, high mean average precision), functional brain networks were found to be best represented in the hyperbolic disc. Using the 𝕊¹/ℍ² model, we reduced the dimension of the network into two-dimensional hyperbolic space and were able to efficiently visualize the internodal connections of the brain, preserving proximity as distances and angles on the hyperbolic discs. Each individual disc revealed relevance with its anatomic counterpart and absence of center-spaced node. Using the hyperbolic distance on the 𝕊¹/ℍ² model, we could detect the anomaly of network in autism spectrum disorder subjects. This procedure of embedding grants us a reliable new framework for studying functional brain networks and the possibility of detecting anomalies of the network in the hyperbolic disc on an individual scale.

Increased network centrality of the anterior insula in early abstinence from alcohol

Abnormal resting‐state functional connectivity, as measured by functional magnetic resonance imaging (MRI), has been reported in alcohol use disorders (AUD), but findings are so far inconsistent. Here, we exploited recent developments in graph‐theoretical analyses, enabling improved resolution and fine‐grained representation of brain networks, to investigate functional connectivity in 35 recently detoxified alcohol dependent patients versus 34 healthy controls. Specifically, we focused on the modular organization, that is, the presence of tightly connected substructures within a network, and on the identification of brain regions responsible for network integration using an unbiased approach based on a large‐scale network composed of more than 600 a priori defined nodes. We found significant reductions in global connectivity and region‐specific disruption in the network topology in patients compared with controls. Specifically, the basal brain and the insular–supramarginal cortices, which form tightly coupled modules in healthy subjects, were fragmented in patients. Further, patients showed a strong increase in the centrality of the anterior insula, which exhibited stronger connectivity to distal cortical regions and weaker connectivity to the posterior insula. Anterior insula centrality, a measure of the integrative role of a region, was significantly associated with increased risk of relapse. Exploratory analysis suggests partial recovery of modular structure and insular connectivity in patients after 2 weeks. These findings support the hypothesis that, at least during the early stages of abstinence, the anterior insula may drive exaggerated integration of interoceptive states in AUD patients with possible consequences for decision making and emotional states and that functional connectivity is dynamically changing during treatment.

Deep sr-DDL: Deep structurally regularized dynamic dictionary learning to integrate multimodal and dynamic functional connectomics data for multidimensional clinical characterizations

We propose a novel integrated framework that jointly models complementary information from resting-state functional MRI (rs-fMRI) connectivity and diffusion tensor imaging (DTI) tractography to extract biomarkers of brain connectivity predictive of behavior. Our framework couples a generative model of the connectomics data with a deep network that predicts behavioral scores. The generative component is a structurally-regularized Dynamic Dictionary Learning (sr-DDL) model that decomposes the dynamic rs-fMRI correlation matrices into a collection of shared basis networks and time varying subject-specific loadings. We use the DTI tractography to regularize this matrix factorization and learn anatomically informed functional connectivity profiles. The deep component of our framework is an LSTM-ANN block, which uses the temporal evolution of the subject-specific sr-DDL loadings to predict multidimensional clinical characterizations. Our joint optimization strategy collectively estimates the basis networks, the subject-specific time-varying loadings, and the neural network weights. We validate our framework on a dataset of neurotypical individuals from the Human Connectome Project (HCP) database to map to cognition and on a separate multi-score prediction task on individuals diagnosed with Autism Spectrum Disorder (ASD) in a five-fold cross validation setting. Our hybrid model outperforms several state-of-the-art approaches at clinical outcome prediction and learns interpretable multimodal neural signatures of brain organization.

Compensatory functional connectome changes in a rat model of traumatic brain injury

Penetrating cortical impact injuries alter neuronal communication beyond the injury epicentre, across regions involved in affective, sensorimotor and cognitive processing. Understanding how traumatic brain injury reorganizes local and brain wide nodal interactions may provide valuable quantitative parameters for monitoring pathological progression and recovery. To this end, we investigated spontaneous fluctuations in the functional MRI signal obtained at 11.1 T in rats sustaining controlled cortical impact and imaged at 2- and 30-days post-injury. Graph theory-based calculations were applied to weighted undirected matrices constructed from 12 879 pairwise correlations between functional MRI signals from 162 regions. Our data indicate that on Days 2 and 30 post-controlled cortical impact there is a significant increase in connectivity strength in nodes located in contralesional cortical, thalamic and basal forebrain areas. Rats imaged on Day 2 post-injury had significantly greater network modularity than controls, with influential nodes (with high eigenvector centrality) contained within the contralesional module and participating less in cross-modular interactions. By Day 30, modularity and cross-modular interactions recover, although a cluster of nodes with low strength and low eigenvector centrality remain in the ipsilateral cortex. Our results suggest that changes in node strength, modularity, eigenvector centrality and participation coefficient track early and late traumatic brain injury effects on brain functional connectivity. We propose that the observed compensatory functional connectivity reorganization in response to controlled cortical impact may be unfavourable to brain wide communication in the early post-injury period.

The unbalanced reorganization of weaker functional connections induces the altered brain network topology in schizophrenia

Network neuroscience shed some light on the functional and structural modifications occurring to the brain associated with the phenomenology of schizophrenia. In particular, resting-state functional networks have helped our understanding of the illness by highlighting the global and local alterations within the cerebral organization. We investigated the robustness of the brain functional architecture in 44 medicated schizophrenic patients and 40 healthy comparators through an advanced network analysis of resting-state functional magnetic resonance imaging data. The networks in patients showed more resistance to disconnection than in healthy controls, with an evident discrepancy between the two groups in the node degree distribution computed along a percolation process. Despite a substantial similarity of the basal functional organization between the two groups, the expected hierarchy of healthy brains' modular organization is crumbled in schizophrenia, showing a peculiar arrangement of the functional connections, characterized by several topologically equivalent backbones. Thus, the manifold nature of the functional organization's basal scheme, together with its altered hierarchical modularity, may be crucial in the pathogenesis of schizophrenia. This result fits the disconnection hypothesis that describes schizophrenia as a brain disorder characterized by an abnormal functional integration among brain regions.

Mapping the living mouse brain neural architecture: strain-specific patterns of brain structural and functional connectivity

Mapping brain structural and functional connectivity (FC) became an essential approach in neuroscience as network properties can underlie behavioral phenotypes. In mouse models, revealing strain-related patterns of brain wiring is crucial, since these animals are used to answer questions related to neurological or neuropsychiatric disorders. C57BL/6 and BALB/cJ strains are two of the primary "genetic backgrounds" for modeling brain disease and testing therapeutic approaches. However, extensive literature describes basal differences in the behavioral, neuroanatomical and neurochemical profiles of the two strains, which raises questions on whether the observed effects are pathology specific or depend on the genetic background of each strain. Here, we performed a systematic comparative exploration of brain structure and function of C57BL/6 and BALB/cJ mice using Magnetic Resonance Imaging (MRI). We combined deformation-based morphometry (DBM), diffusion MRI and high-resolution fiber mapping (hrFM) along with resting-state functional MRI (rs-fMRI) and demonstrated brain-wide differences in the morphology and "connectome" features of the two strains. Essential inter-strain differences were depicted regarding the size and the fiber density (FD) within frontal cortices, along cortico-striatal, thalamic and midbrain pathways as well as genu and splenium of corpus callosum. Structural dissimilarities were accompanied by specific FC patterns, emphasizing strain differences in frontal and basal forebrain functional networks as well as hubness characteristics. Rs-fMRI data further indicated differences of reward-aversion circuitry and default mode network (DMN) patterns. The inter-hemispherical FC showed flexibility and strain-specific adjustment of their patterns in agreement with the structural characteristics.

A joint network optimization framework to predict clinical severity from resting state functional MRI data

We propose a novel optimization framework to predict clinical severity from resting state fMRI (rs-fMRI) data. Our model consists of two coupled terms. The first term decomposes the correlation matrices into a sparse set of representative subnetworks that define a network manifold. These subnetworks are modeled as rank-one outer-products which correspond to the elemental patterns of co-activation across the brain; the subnetworks are combined via patient-specific non-negative coefficients. The second term is a linear regression model that uses the patient-specific coefficients to predict a measure of clinical severity. We validate our framework on two separate datasets in a ten fold cross validation setting. The first is a cohort of fifty-eight patients diagnosed with Autism Spectrum Disorder (ASD). The second dataset consists of sixty three patients from a publicly available ASD database. Our method outperforms standard semi-supervised frameworks, which employ conventional graph theoretic and statistical representation learning techniques to relate the rs-fMRI correlations to behavior. In contrast, our joint network optimization framework exploits the structure of the rs-fMRI correlation matrices to simultaneously capture group level effects and patient heterogeneity. Finally, we demonstrate that our proposed framework robustly identifies clinically relevant networks characteristic of ASD.

How the Brain Transitions from Conscious to Subliminal Perception

We study the transition in the functional networks that characterize the human brains' conscious-state to an unconscious subliminal state of perception by using k-core percolation. We find that the most inner core (i.e., the most connected kernel) of the conscious-state functional network corresponds to areas which remain functionally active when the brain transitions from the conscious-state to the subliminal-state. That is, the inner core of the conscious network coincides with the subliminal-state. Mathematical modeling allows to interpret the conscious to subliminal transition as driven by k-core percolation, through which the conscious state is lost by the inactivation of the peripheral k-shells of the conscious functional network. Thus, the inner core and most robust component of the conscious brain corresponds to the unconscious subliminal state. This finding imposes constraints to theoretical models of consciousness, in that the location of the core of the functional brain network is in the unconscious part of the brain rather than in the conscious state as previously thought.

Altered Forebrain Functional Connectivity and Neurotransmission in a Kinase-Inactive Met Mouse Model of Autism

MET, the gene encoding the tyrosine kinase receptor for hepatocyte growth factor, is a susceptibility gene for autism spectrum disorder (ASD). Genetically altered mice with a kinase-inactive Met offer a potential model for understanding neural circuit organization changes in autism. Here, we focus on the somatosensory thalamocortical circuitry because distinct somatosensory sensitivity phenotypes accompany ASD, and this system plays a major role in sensorimotor and social behaviors in mice. We employed resting-state functional magnetic resonance imaging and in vivo high-resolution proton MR spectroscopy to examine neuronal connectivity and neurotransmission of wild-type, heterozygous Met-Emx1, and fully inactive homozygous Met-Emx1 mice. Met-Emx1 brains showed impaired maturation of large-scale somatosensory network connectivity when compared with wild-type controls. Significant sex × genotype interaction in both network features and glutamate/gamma-aminobutyric acid (GABA) balance was observed. Female Met-Emx1 brains showed significant connectivity and glutamate/GABA balance changes in the somatosensory thalamocortical system when compared with wild-type brains. The glutamate/GABA ratio in the thalamus was correlated with the connectivity between the somatosensory cortex and the thalamus in heterozygous Met-Emx1 female brains. The findings support the hypothesis that aberrant functioning of the somatosensory thalamocortical system is at the core of the conspicuous somatosensory behavioral phenotypes observed in Met-Emx1 mice.

Ketamine and selective activation of parvalbumin interneurons inhibit stress-induced dendritic spine elimination

Stress is a major risk factor for the onset of many psychiatric diseases. In rodent models, chronic stress induces depression and impairs excitatory neurotransmission. However, little is known about the effect of stress on synaptic circuitry during the development of behavioral symptoms. Using two-photon transcranial imaging, we studied the effect of repeated restraint stress on dendritic spine plasticity in the frontal cortex in vivo. We found that restraint stress induced dendritic spine loss by decreasing the rate of spine formation and increasing the rate of spine elimination. The N-methyl-D-aspartate receptor antagonist ketamine inhibited stress-induced spine loss mainly by protecting mushroom spines from elimination. Ketamine also induced re-formation of spines in close proximity to previously stress-eliminated spines. Electrophysiological and in vivo imaging experiments showed that ketamine enhanced activity of parvalbumin (PV) interneurons under stress and counterbalanced the stress-induced net loss of PV axonal boutons. In addition, selective chemogenetic excitation of PV interneurons mimicked the protective effects of ketamine on dendritic spines against stress. Collectively, our data provide new insights on the effects of ketamine on synaptic circuitry under stress and a possible mechanism to counteract stress-induced synaptic impairments through PV interneuron activation.

Disrupted modular organization of primary sensory brain areas in schizophrenia

Abnormal brain resting-state functional connectivity has been consistently observed in patients affected by schizophrenia (SCZ) using functional MRI and other neuroimaging techniques. Graph theoretical methods provide a framework to investigate these defective functional interactions and their effects on the organization of brain connectivity networks. A few studies have shown altered distribution of connectivity within and between functional modules in SCZ patients, an indication of imbalanced functional segregation ad integration. However, no major alterations of modular organization have been reported in patients, and unambiguous identification of the neural substrates affected remains elusive. Recently, it has been demonstrated that current modularity analysis methods suffer from a fundamental and severe resolution limit, as they fail to detect features that are smaller than a scale determined by the size of the entire connectivity network. This resolution limit is likely to have hampered the ability to resolve differences between patients and controls in previous studies. Here, we apply Surprise, a novel resolution limit-free approach, to study the modular organization of resting state functional connectivity networks in a large cohort of SCZ patients and in matched healthy controls. Leveraging these important methodological advances we find new evidence of substantial fragmentation and reorganization involving primary sensory, auditory and visual areas in SCZ patients. Conversely, frontal and prefrontal areas, typically associated with higher cognitive functions, appear to be largely unaffected, with changes selectively involving language and speech processing areas. Our findings support the hypothesis that cognitive dysfunction in SCZ may involve deficits occurring already at early stages of sensory processing.

Statistics of the network of organic chemistry

A comprehensive analysis of statistical properties of a network of organic reactions reveals several generic traits. This knowledge can be used in the development of optimal reaction sequences.

Hub-driven remote synchronization in brain networks

The phenomenon of “remote synchronization” (RS), first observed in a star network of oscillators, involves synchronization of unconnected peripheral nodes through a hub that maintains independent dynamics. In the RS regime the central hub was thought to serve as a passive gate for information transfer between nodes. Here, we investigate the physical origin of this phenomenon. Surprisingly, we find that a hub node can drive remote synchronization of peripheral oscillators even in the presence of a repulsive mean field, thus actively governing network dynamics while remaining asynchronous. We study this novel phenomenon in complex networks endowed with multiple hub-nodes, a ubiquitous feature of many real-world systems, including brain connectivity networks. We show that a change in the natural frequency of a single hub can alone reshape synchronization patterns across the entire network, and switch from direct to remote synchronization, or to hub-driven desynchronization. Hub-driven RS may provide a mechanism to account for the role of structural hubs in the organization of brain functional connectivity networks.

Organization and hierarchy of the human functional brain network lead to a chain-like core

The brain is a paradigmatic example of a complex system: its functionality emerges as a global property of local mesoscopic and microscopic interactions. Complex network theory allows to elicit the functional architecture of the brain in terms of links (correlations) between nodes (grey matter regions) and to extract information out of the noise. Here we present the analysis of functional magnetic resonance imaging data from forty healthy humans at rest for the investigation of the basal scaffold of the functional brain network organization. We show how brain regions tend to coordinate by forming a highly hierarchical chain-like structure of homogeneously clustered anatomical areas. A maximum spanning tree approach revealed the centrality of the occipital cortex and the peculiar aggregation of cerebellar regions to form a closed core. We also report the hierarchy of network segregation and the level of clusters integration as a function of the connectivity strength between brain regions.

The exact Laplacian spectrum for the Dyson hierarchical network

We consider the Dyson hierarchical graph , that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter σ ∈ (1/2, 1]. Exploiting the deterministic recursivity through which is built, we are able to derive explicitly the whole set of the eigenvalues and the eigenvectors for its Laplacian matrix. Given that the Laplacian operator is intrinsically implied in the analysis of dynamic processes (e.g., random walks) occurring on the graph, as well as in the investigation of the dynamical properties of connected structures themselves (e.g., vibrational structures and relaxation modes), this result allows addressing analytically a large class of problems. In particular, as examples of applications, we study the random walk and the continuous-time quantum walk embedded in , the relaxation times of a polymer whose structure is described by , and the community structure of in terms of modularity measures.

Community detection in weighted brain connectivity networks beyond the resolution limit

Graph theory provides a powerful framework to investigate brain functional connectivity networks and their modular organization. However, most graph-based methods suffer from a fundamental resolution limit that may have affected previous studies and prevented detection of modules, or "communities", that are smaller than a specific scale. Surprise, a resolution-limit-free function rooted in discrete probability theory, has been recently introduced and applied to brain networks, revealing a wide size-distribution of functional modules (Nicolini and Bifone, 2016), in contrast with many previous reports. However, the use of Surprise is limited to binary networks, while brain networks are intrinsically weighted, reflecting a continuous distribution of connectivity strengths between different brain regions. Here, we propose Asymptotical Surprise, a continuous version of Surprise, for the study of weighted brain connectivity networks, and validate this approach in synthetic networks endowed with a ground-truth modular structure. We compare Asymptotical Surprise with leading community detection methods currently in use and show its superior sensitivity in the detection of small modules even in the presence of noise and intersubject variability such as those observed in fMRI data. We apply our novel approach to functional connectivity networks from resting state fMRI experiments, and demonstrate a heterogeneous modular organization, with a wide distribution of clusters spanning multiple scales. Finally, we discuss the implications of these findings for the identification of connector hubs, the brain regions responsible for the integration of the different network elements, showing that the improved resolution afforded by Asymptotical Surprise leads to a different classification compared to current methods.

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Methods to study modularity of brain connectivity networks have a resolution limit.

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Asymptotical Surprise, a nearly resolution-limit-free method for weighted graphs, is proposed.

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Improved sensitivity and specificity are demonstrated in model networks.

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Resting state functional connectivity networks consist of heterogeneous modules.

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Classification of hubs in function connectivity networks should be revised.