Adaptive reconfiguration of fractal small-world human brain functional networks

Rich club organization and intermodule communication in the cat connectome

Macroscopic brain networks have been shown to display several properties of an efficient communication architecture. In light of global communication, the formation of a densely connected neural "rich club" of hubs is of particular interest, because brain hubs have been suggested to play a key role in enabling short communication pathways within neural networks. Here, analyzing the cat connectome as reconstructed from tract tracing data (Scannell et al., 1995), we provide several lines of evidence of an important role of the structural rich club to interlink functional domains. First, rich club hub nodes were found to be mostly present at the boundaries between functional communities and well represented among intermodule hubs, displaying a diverse connectivity profile. Second, rich club connections, linking nodes of the rich club, and feeder connections, linking non-rich club nodes to rich club nodes, were found to comprise 86% of the intermodule connections, whereas local connections between peripheral nodes mostly spanned between nodes of the same functional community. Third, almost 90% of all intermodule communication paths were found to follow a sequence or "path motif" that involved rich club or feeder edges and thus traversed a rich club node. Together, our findings provide evidence of the structural rich club to form a central infrastructure for intermodule communication in the brain.

Multi-task connectivity reveals flexible hubs for adaptive task control

Extensive evidence suggests the human ability to adaptively implement a wide variety of tasks is preferentially due to the operation of a fronto-parietal brain network. We hypothesized that this network’s adaptability is made possible by ‘flexible hubs’ – brain regions that rapidly update their pattern of global functional connectivity according to task demands. We utilized recent advances in characterizing brain network organization and dynamics to identify mechanisms consistent with the flexible hub theory. We found that the fronto-parietal network’s brain-wide functional connectivity pattern shifted more than other networks’ across a variety of task states, and that these connectivity patterns could be used to identify the current task. Further, these patterns were consistent across practiced and novel tasks, suggesting reuse of flexible hub connectivity patterns facilitates adaptive (novel) task performance. Together, these findings support a central role for fronto-parietal flexible hubs in cognitive control and adaptive implementation of task demands generally.

Graph theoretical analysis of resting magnetoencephalographic functional connectivity networks

Complex networks have been observed to comprise small-world properties, believed to represent an optimal organization of local specialization and global integration of information processing at reduced wiring cost. Here, we applied magnitude squared coherence to resting magnetoencephalographic time series in reconstructed source space, acquired from controls and patients with schizophrenia, and generated frequency-dependent adjacency matrices modeling functional connectivity between virtual channels. After configuring undirected binary and weighted graphs, we found that all human networks demonstrated highly localized clustering and short characteristic path lengths. The most conservatively thresholded networks showed efficient wiring, with topographical distance between connected vertices amounting to one-third as observed in surrogate randomized topologies. Nodal degrees of the human networks conformed to a heavy-tailed exponentially truncated power-law, compatible with the existence of hubs, which included theta and alpha bilateral cerebellar tonsil, beta and gamma bilateral posterior cingulate, and bilateral thalamus across all frequencies. We conclude that all networks showed small-worldness, minimal physical connection distance, and skewed degree distributions characteristic of physically-embedded networks, and that these calculations derived from graph theoretical mathematics did not quantifiably distinguish between subject populations, independent of bandwidth. However, post-hoc measurements of edge computations at the scale of the individual vertex revealed trends of reduced gamma connectivity across the posterior medial parietal cortex in patients, an observation consistent with our prior resting activation study that found significant reduction of synthetic aperture magnetometry gamma power across similar regions. The basis of these small differences remains unclear.

Functional cortical hubs in the eyes-closed resting human brain from an electrophysiological perspective using magnetoencephalography

It is not clear whether specific brain areas act as hubs in the eyes-closed (EC) resting state, which is an unconstrained state free from any passive or active tasks. Here, we used electrophysiological magnetoencephalography (MEG) signals to study functional cortical hubs in 88 participants. We identified several multispectral cortical hubs. Although cortical hubs vary slightly with different applied measures and frequency bands, the most consistent hubs were observed in the medial and posterior cingulate cortex, the left dorsolateral superior frontal cortex, and the left pole of the middle temporal cortex. Hubs were characterized as connector nodes integrating EC resting state functional networks. Hubs in the gamma band were more likely to include midline structures. Our results confirm the existence of multispectral cortical cores in EC resting state functional networks based on MEG and imply the existence of optimized functional networks in the resting brain.

Functional brain networks for sensory maintenance in top-down selective attention to audiovisual inputs

Sensory maintenance in top-down selective attention to audiovisual inputs involves distributed cortical activations, while the connectivity between the widespread cortical regions has not been well understood. Graph theory has been demonstrated to be a useful tool in the analysis of brain networks. In this study, we used graph theoretical analysis to investigate the functional brain networks for sensory maintenance in top-down selective attention to audiovisual inputs. Electroencephalograms (EEGs) of 30 channels were recorded from 13 young healthy subjects during a passive view task and a top-down intersensory selective attention task. Phase synchronization indices of EEG signals in pair were computed to construct weighted brain networks. We found small-world properties of the brain networks during both passive view state and top-down selective attentional state in α, β, and γ bands. In addition, the significantly increased clustering coefficient and decreased characteristic path length were observed for brain networks during attentional state compared with passive view state in both β band and γ band. Our results suggest that functional brain networks in higher frequency bands, i.e., β band and γ band, are integrated in different ways during attentional state compared with passive view state.

The effects of music on brain functional networks: a network analysis

The human brain can dynamically adapt to the changing surroundings. To explore this issue, we adopted graph theoretical tools to examine changes in electroencephalography (EEG) functional networks while listening to music. Three different excerpts of Chinese Guqin music were played to 16 non-musician subjects. For the main frequency intervals, synchronizations between all pair-wise combinations of EEG electrodes were evaluated with phase lag index (PLI). Then, weighted connectivity networks were created and their organizations were characterized in terms of an average clustering coefficient and characteristic path length. We found an enhanced synchronization level in the alpha2 band during music listening. Music perception showed a decrease of both normalized clustering coefficient and path length in the alpha2 band. Moreover, differences in network measures were not observed between musical excerpts. These experimental results demonstrate an increase of functional connectivity as well as a more random network structure in the alpha2 band during music perception. The present study offers support for the effects of music on human brain functional networks with a trend toward a more efficient but less economical architecture.

Neuronal functional connection graphs among multiple areas of the rat somatosensory system during spontaneous and evoked activities

Small-World Networks (SWNs) represent a fundamental model for the comprehension of many complex man-made and biological networks. In the central nervous system, SWN models have been shown to fit well both anatomical and functional maps at the macroscopic level. However, the functional microscopic level, where the nodes of a network are represented by single neurons, is still poorly understood. At this level, although recent evidences suggest that functional connection graphs exhibit small-world organization, it is not known whether and how these maps, potentially distributed in multiple brain regions, change across different conditions, such as spontaneous and stimulus-evoked activities. We addressed these questions by analyzing the data from simultaneous multi-array extracellular recordings in three brain regions of rats, diversely involved in somatosensory information processing: the ventropostero-lateral thalamic nuclei, the primary somatosensory cortex and the centro-median thalamic nuclei. From both spike and Local Field Potential (LFP) recordings, we estimated the functional connection graphs by using the Normalized Compression Similarity for spikes and the Phase Synchrony for LFPs. Then, by using graph-theoretical statistics, we characterized the functional topology both during spontaneous activity and sensory stimulation. Our main results show that: (i) spikes and LFPs show SWN organization during spontaneous activity; (ii) after stimulation onset, while substantial functional graph reconfigurations occur both in spike and LFPs, small-worldness is nonetheless preserved; (iii) the stimulus triggers a significant increase of inter-area LFP connections without modifying the topology of intra-area functional connections. Finally, investigating computationally the functional substrate that supports the observed phenomena, we found that (iv) the fundamental concept of cell assemblies, transient groups of activating neurons, can be described by small-world networks. Our results suggest that activity of neurons from multiple areas of the rat somatosensory system contributes to the integration of local computations arisen in distributed functional cell assemblies according to the principles of SWNs.

Cell assemblies (sequences of neuronal activations), seem to represent a functional unit of information processing. However, it remains unclear how groups of neurons may organize their activity during information processing, working as a sole functional unit. One prominent principle in complex network theory is covered by small-world networks, in which each node is easily reachable by each other and organized in highly dense clusters. Small-world networks have been already observed on large scales in human and primate brain areas while their presence at the neuronal level remains unclear. The aim of this work was to investigate the possibility that functional, related neural populations, encompassing multiple brain regions, could be organized in small-world networks. We investigated the coherent neuronal activity among multiple rat brain regions involved in somatosensory information processing. We found that the recorded neuronal populations represented small-world networks and that these topologies were maintained during stimulations. Furthermore, by using simulations to explore the hidden substrates supporting the observed topological features, we inferred that small-world networks represent a plausible topology for cell assemblies. This work suggests that the coherent activity of neurons from multiple brain areas promotes the integration of local computations, the functional principle of small-world networks.

Imaging human connectomes at the macroscale

At macroscopic scales, the human connectome comprises anatomically distinct brain areas, the structural pathways connecting them and their functional interactions. Annotation of phenotypic associations with variation in the connectome and cataloging of neurophenotypes promise to transform our understanding of the human brain. In this Review, we provide a survey of magnetic resonance imaging–based measurements of functional and structural connectivity. We highlight emerging areas of development and inquiry and emphasize the importance of integrating structural and functional perspectives on brain architecture.

Acoustic-Friction Networks and the Evolution of Precursor Rupture Fronts in Laboratory Earthquakes

The evolution of shear rupture fronts in laboratory earthquakes is analysed with the corresponding functional networks, constructed over acoustic emission friction-patterns. We show that the mesoscopic characteristics of functional networks carry the characteristic time for each phase of the rupture evolution. The classified rupture fronts in network states–obtained from a saw-cut fault and natural faulted Westerly granite - show a clear separation into three main groups, indicating different states of rupture fronts. With respect to the scaling of local ruptures' durations with the networks' parameters, we show that the gap in the classified fronts could be related to the possibility of a separation between slow and regular fronts.

Moment-to-moment brain signal variability: a next frontier in human brain mapping?

Neuroscientists have long observed that brain activity is naturally variable from moment-to-moment, but neuroimaging research has largely ignored the potential importance of this phenomenon. An emerging research focus on within-person brain signal variability is providing novel insights, and offering highly predictive, complementary, and even orthogonal views of brain function in relation to human lifespan development, cognitive performance, and various clinical conditions. As a result, brain signal variability is evolving as a bona fide signal of interest, and should no longer be dismissed as meaningless noise when mapping the human brain.

Graph analysis of the human connectome: promise, progress, and pitfalls

The human brain is a complex, interconnected network par excellence. Accurate and informative mapping of this human connectome has become a central goal of neuroscience. At the heart of this endeavor is the notion that brain connectivity can be abstracted to a graph of nodes, representing neural elements (e.g., neurons, brain regions), linked by edges, representing some measure of structural, functional or causal interaction between nodes. Such a representation brings connectomic data into the realm of graph theory, affording a rich repertoire of mathematical tools and concepts that can be used to characterize diverse anatomical and dynamical properties of brain networks. Although this approach has tremendous potential - and has seen rapid uptake in the neuroimaging community - it also has a number of pitfalls and unresolved challenges which can, if not approached with due caution, undermine the explanatory potential of the endeavor. We review these pitfalls, the prevailing solutions to overcome them, and the challenges at the forefront of the field.

Structural foundations of resting-state and task-based functional connectivity in the human brain

Magnetic resonance imaging enables the noninvasive mapping of both anatomical white matter connectivity and dynamic patterns of neural activity in the human brain. We examine the relationship between the structural properties of white matter streamlines (structural connectivity) and the functional properties of correlations in neural activity (functional connectivity) within 84 healthy human subjects both at rest and during the performance of attention- and memory-demanding tasks. We show that structural properties, including the length, number, and spatial location of white matter streamlines, are indicative of and can be inferred from the strength of resting-state and task-based functional correlations between brain regions. These results, which are both representative of the entire set of subjects and consistently observed within individual subjects, uncover robust links between structural and functional connectivity in the human brain.

The thalamus and brainstem act as key hubs in alterations of human brain network connectivity induced by mild propofol sedation

Despite their routine use during surgical procedures, no consensus has yet been reached on the precise mechanisms by which hypnotic anesthetic agents produce their effects. Molecular, animal and human studies have suggested disruption of thalamocortical communication as a key component of anesthetic action at the brain systems level. Here, we used the anesthetic agent, propofol, to modulate consciousness and to evaluate differences in the interactions of remote neural networks during altered consciousness. We investigated the effects of propofol, at a dose that produced mild sedation without loss of consciousness, on spontaneous cerebral activity of 15 healthy volunteers using functional magnetic resonance imaging (fMRI), exploiting oscillations (<0.1 Hz) in blood oxygenation level-dependent signal across functionally connected brain regions. We considered the data as a graph, or complex network of nodes and links, and used eigenvector centrality (EC) to characterize brain network properties. The EC mapping of fMRI data in healthy humans under propofol mild sedation demonstrated a decrease of centrality of the thalamus versus an increase of centrality within the pons of the brainstem, highlighting the important role of these two structures in regulating consciousness. Specifically, the decrease of thalamus centrality results from its disconnection from a widespread set of cortical and subcortical regions, while the increase of brainstem centrality may be a consequence of its increased influence, in the mildly sedated state, over a few highly central cortical regions key to the default mode network such as the posterior and anterior cingulate cortices.

A signal-processing pipeline for magnetoencephalography resting-state networks

To study functional connectivity using magnetoencephalographic (MEG) data, the high-quality source-level reconstruction of brain activity constitutes a critical element. MEG resting-state networks (RSNs) have been documented by means of a dedicated processing pipeline: MEG recordings are decomposed by independent component analysis (ICA) into artifact and brain components (ICs); next, the channel maps associated with the latter ones are projected into the source space and the resulting voxel-wise weights are used to linearly combine the IC time courses. An extensive description of the proposed pipeline is provided here, along with an assessment of its performances with respect to alternative approaches. The following investigations were carried out: (1) ICA decomposition algorithm. Synthetic data are used to assess the sensitivity of the ICA results to the decomposition algorithm, by testing FastICA, INFOMAX, and SOBI. FastICA with deflation approach, a standard solution, provides the best decomposition. (2) Recombination of brain ICs versus subtraction of artifactual ICs (at the channel level). Both the recombination of the brain ICs in the sensor space and the classical procedure of subtracting the artifactual ICs from the recordings provide a suitable reconstruction, with a lower distortion using the latter approach. (3) Recombination of brain ICs after localization versus localization of artifact-corrected recordings. The brain IC recombination after source localization, as implemented in the proposed pipeline, provides a lower source-level signal distortion. (4) Detection of RSNs. The accuracy in source-level reconstruction by the proposed pipeline is confirmed by an improved specificity in the retrieval of RSNs from experimental data.

Functional and effective connectivity: a review

Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain's functional architecture and operational principles. The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead.

A new statistical approach for the extraction of adjacency matrix from effective connectivity networks

Graph theory is a powerful mathematical tool recently introduced in neuroscience field for quantitatively describing the main properties of investigated connectivity networks. Despite the technical advancements provided in the last few years, further investigations are needed for overcoming actual limitations in the field. In fact, the absence of a common procedure currently applied for the extraction of the adjacency matrix from a connectivity pattern has been leading to low consistency and reliability of ghaph indexes among the investigated population. In this paper we proposed a new approach for adjacency matrix extraction based on a statistical threshold as valid alternative to empirical approaches, extensively used in Neuroscience field (i.e. fixing the edge density). In particular we performed a simulation study for investigating the effects of the two different extraction approaches on the topological properties of the investigated networks. In particular, the comparison was performed on two different datasets, one composed by uncorrelated random signals (null-model) and the other one by signals acquired on a mannequin head used as a phantom (EEG null-model). The results highlighted the importance to use a statistical threshold for the adjacency matrix extraction in order to describe the real existing topological properties of the investigated networks. The use of an empirical threshold led to an erroneous definition of small-world properties for the considered connectivity patterns.

Structure out of chaos: functional brain network analysis with EEG, MEG, and functional MRI

The brain is the characteristic of a complex structure. By representing brain function, measured with EEG, MEG, and fMRI, as an abstract network, methods for the study of complex systems can be applied. These network studies have revealed insights in the complex, yet organized, architecture that is evidently present in brain function. We will discuss some technical aspects of formation and assessment of the functional brain networks. Moreover, the results that have been reported in this respect in the last years, in healthy brains as well as in functional brain networks of subjects with a neurological or psychiatrical disease, will be reviewed.

Posteromedial cortex glutamate and GABA predict intrinsic functional connectivity of the default mode network

The balance between excitatory glutamatergic projection neurons and inhibitory GABAergic interneurons determines the function of cortical microcircuits. How these neurotransmitters relate to the functional status of an entire macro-scale network remains unknown. The posteromedial cortex (PMC) is the default mode network (DMN) node with the greatest functional connectivity; therefore, we hypothesized that PMC glutamate and GABA predict intrinsic functional connectivity (iFC) across the entire DMN. In 20 healthy men, we combined J-resolved magnetic resonance spectroscopy to measure glutamate and GABA in the PMC and resting fMRI followed by group Independent Components Analysis to extract the entire DMN. We showed that, controlling for age and partial GM volume in the MRS voxel, PMC glutamate and GABA explained about half of the variance of DMN iFC (represented by the network's beta coefficient for rest). Glutamate correlated positively and GABA correlated negatively with DMN iFC; in an alternative statistical model which included the glutamate/GABA ratio, the ratio correlated positively with DMN iFC. Age had no independent association with DMN iFC. No other network was associated with PMC glutamate or GABA. We conclude that regional neurotransmitter concentrations in a network node strongly predict network but not global brain iFC.

Small-world networks in individuals at ultra-high risk for psychosis and first-episode schizophrenia during a working memory task

Disturbances of functional interaction between different brain regions have been hypothesized to be the major pathophysiological mechanism underlying the cognitive deficits of schizophrenia. We investigated the small-world functional networks in individuals at ultra-high risk (UHR) for psychosis, first-episode schizophrenia (FESPR) patients, and healthy controls. All participants underwent the electroencephalogram during a control task and a working memory (WM) task. Small-world properties of the theta band were reduced in FESPR relative to controls during the WM task. Small-worldness of the UHR during the WM task exhibited intermediate value between that of controls and FESPR. These results imply that the suboptimal organization of the brain network may play a pivotal role in the schizophrenia pathophysiology.

The connectivity of functional cores reveals different degrees of segregation and integration in the brain at rest

The principles of functional specialization and integration in the resting brain are implemented in a complex system of specialized networks that share some degree of interaction. Recent studies have identified wider functional modules compared to previously defined networks and reported a small-world architecture of brain activity in which central nodes balance the pressure to evolve segregated pathways with the integration of local systems. The accurate identification of such central nodes is crucial but might be challenging for several reasons, e.g. inter-subject variability and physiological/pathological network plasticity, and recent works reported partially inconsistent results concerning the properties of these cortical hubs. Here, we applied a whole-brain data-driven approach to extract cortical functional cores and examined their connectivity from a resting state fMRI experiment on healthy subjects. Two main statistically significant cores, centered on the posterior cingulate cortex and the supplementary motor area, were extracted and their functional connectivity maps, thresholded at three statistical levels, revealed the presence of two complex systems. One system is consistent with the default mode network (DMN) and gradually connects to visual regions, the other centered on motor regions and gradually connects to more sensory-specific portions of cortex. These two large scale networks eventually converged to regions belonging to the medial aspect of the DMN, potentially allowing inter-network interactions.

Persistent brain network homology from the perspective of dendrogram

The brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level. The problem with this standard method is that we do not have any generally accepted criteria for determining a proper threshold. Thus, we propose a novel multiscale framework that models all brain networks generated over every possible threshold. Our approach is based on persistent homology and its various representations such as the Rips filtration, barcodes, and dendrograms. This new persistent homological framework enables us to quantify various persistent topological features at different scales in a coherent manner. The barcode is used to quantify and visualize the evolutionary changes of topological features such as the Betti numbers over different scales. By incorporating additional geometric information to the barcode, we obtain a single linkage dendrogram that shows the overall evolution of the network. The difference between the two networks is then measured by the Gromov-Hausdorff distance over the dendrograms. As an illustration, we modeled and differentiated the FDG-PET based functional brain networks of 24 attention-deficit hyperactivity disorder children, 26 autism spectrum disorder children, and 11 pediatric control subjects.

Spatiotemporal reconfiguration of large-scale brain functional networks during propofol-induced loss of consciousness

Applying graph theoretical analysis of spontaneous BOLD fluctuations in functional magnetic resonance imaging (fMRI), we investigated whole-brain functional connectivity of 11 healthy volunteers during wakefulness and propofol-induced loss of consciousness (PI-LOC). After extraction of regional fMRI time series from 110 cortical and subcortical regions, we applied a maximum overlap discrete wavelet transformation and investigated changes in the brain's intrinsic spatiotemporal organization. During PI-LOC, we observed a breakdown of subcortico-cortical and corticocortical connectivity. Decrease of connectivity was pronounced in thalamocortical connections, whereas no changes were found for connectivity within primary sensory cortices. Graph theoretical analyses revealed significant changes in the degree distribution and local organization metrics of brain functional networks during PI-LOC: compared with a random network, normalized clustering was significantly increased, as was small-worldness. Furthermore we observed a profound decline in long-range connections and a reduction in whole-brain spatiotemporal integration, supporting a topological reconfiguration during PI-LOC. Our findings shed light on the functional significance of intrinsic brain activity as measured by spontaneous BOLD signal fluctuations and help to understand propofol-induced loss of consciousness.

Redundancy as a graph-based index of frequency specific MEG functional connectivity

We used a recently proposed graph index to investigate connectivity redundancy in resting state MEG recordings. Usually, brain network analyses consider indexes linked to the shortest paths between cerebral regions. However, important information might be lost about alternative trails by neglecting longer pathways. We measured the redundancy of the connectivity by considering the multiple paths at the global level (i.e., scalar redundancy), across different path lengths (i.e., vector redundancy), and between node pairs (i.e., matrix redundancy). We applied this approach to a robust frequency domain functional connectivity measure, the corrected imaginary part of coherence. The redundancy in the MEG networks, for each frequency band, was significantly (P < 0.05) higher than in the random graphs, thus, confirming a natural tendency of the brain to present multiple interaction pathways between different specialized areas. Notably, this difference was more evident and localized among the channels covering the parietooccipital areas in the alpha range of MEG oscillations (7.5–13 Hz), as expected in the resting state conditions. Interestingly enough, the results obtained with the redundancy indexes were poorly correlated with those obtained using shortest paths only, and more sensitive with respect to those obtained by considering walk-based indexes.

Analyzing self-similar and fractal properties of the C. elegans neural network

The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron "giant component" of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been "rewired" to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.

High-resolution EEG analysis of power spectral density maps and coherence networks in a proportional reasoning task

Proportional reasoning is very important logical skill required in mathematics and science problem solving as well as in everyday life decisions. However, there is a lack of studies on neurophysiological correlates of proportional reasoning. To explore the brain activity of healthy adults while performing a balance scale task, we used high-resolution EEG techniques and graph-theory based connectivity analysis. After unskilled subjects learned how to properly solve the task, their cortical power spectral density (PSD) maps revealed an increased parietal activity in the beta band. This indicated that subjects started to perform calculations. In addition, the number of inter-hemispheric connections decreased after learning, implying a rearrangement of the brain activity. Repeated performance of the task led to the PSD decrease in the beta and gamma bands among parietal and frontal regions along with a synchronization of lower frequencies. These findings suggest that repetition led to a more automatic task performance. Subjects were also divided in two groups according to their scores on the test of logical thinking (TOLT). Although no group differences in the accuracy and reaction times were found, EEG data showed higher activity in the beta and gamma bands for the group that scored better on TOLT. Learning and repetition induced changes in the pattern of functional connectivity were evident for all frequency bands. Overall, the results indicated that higher frequency oscillations in frontal and parietal regions are particularly important for proportional reasoning.

Synchronization dynamics and evidence for a repertoire of network states in resting EEG

Intrinsically driven neural activity generated at rest exhibits complex spatiotemporal dynamics characterized by patterns of synchronization across distant brain regions. Mounting evidence suggests that these patterns exhibit fluctuations and nonstationarity at multiple time scales. Resting-state electroencephalographic (EEG) recordings were examined in 12 young adults for changes in synchronization patterns on a fast time scale in the range of tens to hundreds of milliseconds. Results revealed that EEG dynamics continuously underwent rapid transitions between intermittently stable states. Numerous approximate recurrences of states were observed within single recording epochs, across different epochs separated by longer times, and between participants. For broadband (4-30 Hz) data, a majority of states could be grouped into three families, suggesting the existence of a limited repertoire of core states that is continually revisited and shared across participants. Our results document the existence of fast synchronization dynamics iterating amongst a small set of core networks in the resting brain, complementing earlier findings of nonstationary dynamics in electromagnetic recordings and transient EEG microstates.

Predicting errors from reconfiguration patterns in human brain networks

Task preparation is a complex cognitive process that implements anticipatory adjustments to facilitate future task performance. Little is known about quantitative network parameters governing this process in humans. Using functional magnetic resonance imaging (fMRI) and functional connectivity measurements, we show that the large-scale topology of the brain network involved in task preparation shows a pattern of dynamic reconfigurations that guides optimal behavior. This network could be decomposed into two distinct topological structures, an error-resilient core acting as a major hub that integrates most of the network's communication and a predominantly sensory periphery showing more flexible network adaptations. During task preparation, core-periphery interactions were dynamically adjusted. Task-relevant visual areas showed a higher topological proximity to the network core and an enhancement in their local centrality and interconnectivity. Failure to reconfigure the network topology was predictive for errors, indicating that anticipatory network reconfigurations are crucial for successful task performance. On the basis of a unique network decoding approach, we also develop a general framework for the identification of characteristic patterns in complex networks, which is applicable to other fields in neuroscience that relate dynamic network properties to behavior.

Relations between BOLD fMRI-derived resting brain activity and cerebral blood flow

Consistent resting brain activity patterns have been repeatedly demonstrated using measures derived from resting BOLD fMRI data. While those metrics are presumed to reflect underlying spontaneous brain activity (SBA), it is challenging to prove that association because resting BOLD fMRI metrics are purely model-free and scale-free variables. Cerebral blood flow (CBF) is typically closely coupled to brain metabolism and is used as a surrogate marker for quantifying regional brain function, including resting function. Assessing the correlations between resting BOLD fMRI measures and CBF correlation should provide a means of linking of those measures to the underlying SBA, and a means to quantify those scale-free measures. The purpose of this paper was to examine the CBF correlations of 3 widely used neuroimaging-based SBA measures, including seed-region based functional connectivity (FC), regional homogeneity (ReHo), and amplitude of low frequency fluctuation (ALFF). Test-retest data were acquired to check the stability of potential correlations across time. Reproducible posterior cingulate cortex (PCC) FC vs regional CBF correlations were found in much of the default mode network and visual cortex. Dorsal anterior cingulate cortex (ACC) FC vs CBF correlations were consistently found in bilateral prefrontal cortex. Both ReHo and ALFF were found to be reliably correlated with CBF in most of brain cortex. None of the assessed SBA measures was correlated with whole brain mean CBF. These findings suggest that resting BOLD fMRI-derived measures are coupled with regional CBF and are therefore linked to regional SBA.

Messages from the brain connectivity regarding neural correlates of consciousness

Consciousness has become a legitimate theme of neuroscientific discourse over the last two decades. Neuroscientific investigation seeking neural correlates of consciousness (NCC) has ranged from the neuronal level to the system level. Regarding system level studies, there is a large body of evidence supporting the idea that functional connectivity studies can help in examining NCC. Functional connectivity studies have suggested the involvement of the thalamo-cortical, frontoparietal, and other cortico-cortical connectivity under anesthetic-induced unconsciousness and in disorders of consciousness. Likewise, effective connectivity has been used to investigate the causal interactions among elements of functional connectivity in various consciousness states, and provided a deeper understanding of NCC. Moreover, as an extended version of connectivity studies, complex network methods have also been used for studies on NCC. In this review, we focused on the aspect of the brain system level of NCC including functional and effective connectivity networks from methodological perspectives. In addition, as for states of consciousness, anesthetic-induced unconsciousness and disorders of consciousness are the main subjects. This review discusses what we have learned from recent studies about the exploration of human brain connectivity on consciousness and its neural correlates.

Large-scale cortical correlation structure of spontaneous oscillatory activity

Little is known about the brain-wide correlation of electrophysiological signals. We found that spontaneous oscillatory neuronal activity exhibited frequency-specific spatial correlation structure in the human brain. We developed an analysis approach that discounts spurious correlation of signal power caused by the limited spatial resolution of electrophysiological measures. We applied this approach to source estimates of spontaneous neuronal activity reconstructed from magnetoencephalography. Overall, correlation of power across cortical regions was strongest in the alpha to beta frequency range (8–32 Hz) and correlation patterns depended on the underlying oscillation frequency. Global hubs resided in the medial temporal lobe in the theta frequency range (4–6 Hz), in lateral parietal areas in the alpha to beta frequency range (8–23 Hz) and in sensorimotor areas for higher frequencies (32–45 Hz). Our data suggest that interactions in various large-scale cortical networks may be reflected in frequency-specific power envelope correlations.

Brain network of semantic integration in sentence reading: insights from independent component analysis and graph theoretical analysis

A set of cortical and sub-cortical brain structures has been linked with sentence-level semantic processes. However, it remains unclear how these brain regions are organized to support the semantic integration of a word into sentential context. To look into this issue, we conducted a functional magnetic resonance imaging (fMRI) study that required participants to silently read sentences with semantically congruent or incongruent endings and analyzed the network properties of the brain with two approaches, independent component analysis (ICA) and graph theoretical analysis (GTA). The GTA suggested that the whole-brain network is topologically stable across conditions. The ICA revealed a network comprising the supplementary motor area (SMA), left inferior frontal gyrus, left middle temporal gyrus, left caudate nucleus, and left angular gyrus, which was modulated by the incongruity of sentence ending. Furthermore, the GTA specified that the connections between the left SMA and left caudate nucleus as well as that between the left caudate nucleus and right thalamus were stronger in response to incongruent vs. congruent endings.

Psychopathology and the human connectome: toward a transdiagnostic model of risk for mental illness

The panoply of cognitive, affective, motivational, and social functions that underpin everyday human experience requires precisely choreographed patterns of interaction between networked brain regions. Perhaps not surprisingly, diverse forms of psychopathology are characterized by breakdowns in these interregional relationships. Here, we discuss how functional brain imaging has provided insights into the nature of brain dysconnectivity in mental illness. Synthesizing work to date, we propose that genetic and environmental risk factors impinge upon systems-level circuits for several core dimensions of cognition, producing transdiagnostic symptoms. We argue that risk-associated disruption of these circuits mediates susceptibility to broad domains of psychopathology rather than discrete disorders.

The Integration of the Glutamatergic and the White Matter Hypotheses of Schizophrenia's Etiology

BACKGROUND

schizophrenia's endophenotipic profile is not only generally complex, but often varies from case to case. The perspective of trying to define specific anatomic correlates of the syndrome has led to disappointing results. In that context, neurophysiologic hypotheses (e.g. glutamatergic hypothesis) and connectivity hypotheses became prominent. Nevertheless, despite their commitment to the principle of denying 'localist' views and approaching the syndrome's endophenotype from a whole brain perspective, efforts to integrate both have not flourished at this moment in time.

OBJECTIVES

This paper aims to introduce a new etiological model that integrates the glutamatergic and the WM (WM) hypotheses of schizophrenia's etiology. This model proposes to serve as a framework in order to relate to patterns of brain abnormalities from the onset of the syndrome to stages of advanced chronification.

HIGHLIGHTS

Neurotransmitter abnormalities forego noticeable WM abnormalities. The former, chiefly represented by NMDAR hypo-function and associated molecular cascades, is related to the first signs of cell loss. This process is both directly and indirectly integrated to the underpinning of WM structural abnormalities; not only is the excess of glutamate toxic to the WM, but its disruption is associated to the expression of known genetic risk factors (e.g., NRG-1). A second level of the model develops the idea that abnormal neurotransmission within specific neural populations ('motifs') impair particular cognitive abilities, while subsequent WM structural abnormalities impair the integration of brain functions and multimodality. As a result of this two-stage dynamic, the affected individual progresses from experiencing specific cognitive and psychological deficits, to a condition of cognitive and existential fragmentation, linked to hardly reversible decreases in psychosocial functioning.

Studying the topological organization of the cerebral blood flow fluctuations in resting state

In this paper the cerebral blood flow (CBF) in resting state obtained from SPECT imaging is employed as a hemodynamics descriptor to study the concurrent changes between brain structures and to build binarized connectivity graphs. The statistical similarity in CBF between pairs of regions was measured by computing the Pearson correlation coefficient across 31 normal subjects. We demonstrated the CBF connectivity matrices follow 'small-world' attributes similar to previous studies using different modalities of neuroimaging data (MRI, fMRI, EEG, MEG). The highest concurrent fluctuations in CBF were detected between homologous cortical regions (homologous callosal connections). It was found that the existence of structural core regions or hubs positioned on a high proportion of shortest paths within the CBF network. These were anatomically distributed in frontal, limbic, occipital and parietal regions that suggest its important role in functional integration. Our findings point to a new possibility of using CBF variable to investigate the brain networks based on graph theory in normal and pathological states. Likewise, it opens a window to future studies to link covariation between morphometric descriptors, axonal connectivity and CBF processes with a potential diagnosis applications.

The development of hub architecture in the human functional brain network

Functional hubs are brain regions that play a crucial role in facilitating communication among parallel, distributed brain networks. The developmental emergence and stability of hubs, however, is not well understood. The current study used measures of network topology drawn from graph theory to investigate the development of functional hubs in 99 participants, 10-20 years of age. We found that hub architecture was evident in late childhood and was stable from adolescence to early adulthood. Connectivity between hub and non-hub ("spoke") regions, however, changed with development. From childhood to adolescence, the strength of connections between frontal hubs and cortical and subcortical spoke regions increased. From adolescence to adulthood, hub-spoke connections with frontal hubs were stable, whereas connectivity between cerebellar hubs and cortical spoke regions increased. Our findings suggest that a developmentally stable functional hub architecture provides the foundation of information flow in the brain, whereas connections between hubs and spokes continue to develop, possibly supporting mature cognitive function.

A signal-processing-based approach to time-varying graph analysis for dynamic brain network identification

In recent years, there has been a growing need to analyze the functional connectivity of the human brain. Previous studies have focused on extracting static or time-independent functional networks to describe the long-term behavior of brain activity. However, a static network is generally not sufficient to represent the long term communication patterns of the brain and is considered as an unreliable snapshot of functional connectivity. In this paper, we propose a dynamic network summarization approach to describe the time-varying evolution of connectivity patterns in functional brain activity. The proposed approach is based on first identifying key event intervals by quantifying the change in the connectivity patterns across time and then summarizing the activity in each event interval by extracting the most informative network using principal component decomposition. The proposed method is evaluated for characterizing time-varying network dynamics from event-related potential (ERP) data indexing the error-related negativity (ERN) component related to cognitive control. The statistically significant connectivity patterns for each interval are presented to illustrate the dynamic nature of functional connectivity.

How the statistical validation of functional connectivity patterns can prevent erroneous definition of small-world properties of a brain connectivity network

The application of Graph Theory to the brain connectivity patterns obtained from the analysis of neuroelectrical signals has provided an important step to the interpretation and statistical analysis of such functional networks. The properties of a network are derived from the adjacency matrix describing a connectivity pattern obtained by one of the available functional connectivity methods. However, no common procedure is currently applied for extracting the adjacency matrix from a connectivity pattern. To understand how the topographical properties of a network inferred by means of graph indices can be affected by this procedure, we compared one of the methods extensively used in Neuroscience applications (i.e. fixing the edge density) with an approach based on the statistical validation of achieved connectivity patterns. The comparison was performed on the basis of simulated data and of signals acquired on a polystyrene head used as a phantom. The results showed (i) the importance of the assessing process in discarding the occurrence of spurious links and in the definition of the real topographical properties of the network, and (ii) a dependence of the small world properties obtained for the phantom networks from the spatial correlation of the neighboring electrodes.

Individual classification of ADHD patients by integrating multiscale neuroimaging markers and advanced pattern recognition techniques

Accurate classification or prediction of the brain state across individual subject, i.e., healthy, or with brain disorders, is generally a more difficult task than merely finding group differences. The former must be approached with highly informative and sensitive biomarkers as well as effective pattern classification/feature selection approaches. In this paper, we propose a systematic methodology to discriminate attention deficit hyperactivity disorder (ADHD) patients from healthy controls on the individual level. Multiple neuroimaging markers that are proved to be sensitive features are identified, which include multiscale characteristics extracted from blood oxygenation level dependent (BOLD) signals, such as regional homogeneity (ReHo) and amplitude of low-frequency fluctuations. Functional connectivity derived from Pearson, partial, and spatial correlation is also utilized to reflect the abnormal patterns of functional integration, or, dysconnectivity syndromes in the brain. These neuroimaging markers are calculated on either voxel or regional level. Advanced feature selection approach is then designed, including a brain-wise association study (BWAS). Using identified features and proper feature integration, a support vector machine (SVM) classifier can achieve a cross-validated classification accuracy of 76.15% across individuals from a large dataset consisting of 141 healthy controls and 98 ADHD patients, with the sensitivity being 63.27% and the specificity being 85.11%. Our results show that the most discriminative features for classification are primarily associated with the frontal and cerebellar regions. The proposed methodology is expected to improve clinical diagnosis and evaluation of treatment for ADHD patient, and to have wider applications in diagnosis of general neuropsychiatric disorders.

Voxel scale complex networks of functional connectivity in the rat brain: neurochemical state dependence of global and local topological properties

Network analysis of functional imaging data reveals emergent features of the brain as a function of its topological properties. However, the brain is not a homogeneous network, and the dependence of functional connectivity parameters on neuroanatomical substrate and parcellation scale is a key issue. Moreover, the extent to which these topological properties depend on underlying neurochemical changes remains unclear. In the present study, we investigated both global statistical properties and the local, voxel-scale distribution of connectivity parameters of the rat brain. Different neurotransmitter systems were stimulated by pharmacological challenge (d-amphetamine, fluoxetine, and nicotine) to discriminate between stimulus-specific functional connectivity and more general features of the rat brain architecture. Although global connectivity parameters were similar, mapping of local connectivity parameters at high spatial resolution revealed strong neuroanatomical dependence of functional connectivity in the rat brain, with clear differentiation between the neocortex and older brain regions. Localized foci of high functional connectivity independent of drug challenge were found in the sensorimotor cortices, consistent with the high neuronal connectivity in these regions. Conversely, the topological properties and node roles in subcortical regions varied with neurochemical state and were dependent on the specific dynamics of the different functional processes elicited.

Cognitive dysfunction in early multiple sclerosis: altered centrality derived from resting-state functional connectivity using magneto-encephalography

BACKGROUND

Cognitive dysfunction in multiple sclerosis (MS) is frequent. Insight into underlying mechanisms would help to develop therapeutic strategies.

OBJECTIVE

To explore the relationship of cognitive performance to patterns of nodal centrality derived from magneto-encephalography (MEG).

METHODS

34 early relapsing-remitting MS patients (median EDSS 2.0) and 28 age- and gender-matched healthy controls (HC) had a MEG, a neuropsychological assessment and structural MRI. Resting-state functional connectivity was determined by the synchronization likelihood. Eigenvector Centrality (EC) was used to quantify for each sensor its connectivity and importance within the network. A cognition-score was calculated, and normalized grey and white matter volumes were determined. EC was compared per sensor and frequency band between groups using permutation testing, and related to cognition.

RESULTS

Patients had lower grey and white matter volumes than HC, male patients lower cognitive performance than female patients. In HC, EC distribution showed highest nodal centrality over bi-parietal sensors ("hubs"). In patients, nodal centrality was even higher bi-parietally (theta-band) but markedly lower left temporally (upper alpha- and beta-band). Lower cognitive performance correlated to decreased nodal centrality over left temporal (lower alpha-band) and right temporal (beta-band) sensors, and to increased nodal centrality over right parieto-temporal sensors (beta-band). Network changes were most pronounced in male patients.

CONCLUSIONS

Partial functional disconnection of the temporal regions was associated with cognitive dysfunction in MS; increased centrality in parietal hubs may reflect a shift from temporal to possibly less efficient parietal processing. To better understand patterns and dynamics of these network changes, longitudinal studies are warranted, also addressing the influence of gender.

Non-stationarity in the "resting brain's" modular architecture

Task-free functional magnetic resonance imaging (TF-fMRI) has great potential for advancing the understanding and treatment of neurologic illness. However, as with all measures of neural activity, variability is a hallmark of intrinsic connectivity networks (ICNs) identified by TF-fMRI. This variability has hampered efforts to define a robust metric of connectivity suitable as a biomarker for neurologic illness. We hypothesized that some of this variability rather than representing noise in the measurement process, is related to a fundamental feature of connectivity within ICNs, which is their non-stationary nature. To test this hypothesis, we used a large (n = 892) population-based sample of older subjects to construct a well characterized atlas of 68 functional regions, which were categorized based on independent component analysis network of origin, anatomical locations, and a functional meta-analysis. These regions were then used to construct dynamic graphical representations of brain connectivity within a sliding time window for each subject. This allowed us to demonstrate the non-stationary nature of the brain’s modular organization and assign each region to a “meta-modular” group. Using this grouping, we then compared dwell time in strong sub-network configurations of the default mode network (DMN) between 28 subjects with Alzheimer’s dementia and 56 cognitively normal elderly subjects matched 1∶2 on age, gender, and education. We found that differences in connectivity we and others have previously observed in Alzheimer’s disease can be explained by differences in dwell time in DMN sub-network configurations, rather than steady state connectivity magnitude. DMN dwell time in specific modular configurations may also underlie the TF-fMRI findings that have been described in mild cognitive impairment and cognitively normal subjects who are at risk for Alzheimer’s dementia.

The remarkable, yet not extraordinary, human brain as a scaled-up primate brain and its associated cost

Neuroscientists have become used to a number of "facts" about the human brain: It has 100 billion neurons and 10- to 50-fold more glial cells; it is the largest-than-expected for its body among primates and mammals in general, and therefore the most cognitively able; it consumes an outstanding 20% of the total body energy budget despite representing only 2% of body mass because of an increased metabolic need of its neurons; and it is endowed with an overdeveloped cerebral cortex, the largest compared with brain size. These facts led to the widespread notion that the human brain is literally extraordinary: an outlier among mammalian brains, defying evolutionary rules that apply to other species, with a uniqueness seemingly necessary to justify the superior cognitive abilities of humans over mammals with even larger brains. These facts, with deep implications for neurophysiology and evolutionary biology, are not grounded on solid evidence or sound assumptions, however. Our recent development of a method that allows rapid and reliable quantification of the numbers of cells that compose the whole brain has provided a means to verify these facts. Here, I review this recent evidence and argue that, with 86 billion neurons and just as many nonneuronal cells, the human brain is a scaled-up primate brain in its cellular composition and metabolic cost, with a relatively enlarged cerebral cortex that does not have a relatively larger number of brain neurons yet is remarkable in its cognitive abilities and metabolism simply because of its extremely large number of neurons.

Altered small-world brain networks in schizophrenia patients during working memory performance

Impairment of working memory (WM) performance in schizophrenia patients (SZ) is well-established. Compared to healthy controls (HC), SZ patients show aberrant blood oxygen level dependent (BOLD) activations and disrupted functional connectivity during WM performance. In this study, we examined the small-world network metrics computed from functional magnetic resonance imaging (fMRI) data collected as 35 HC and 35 SZ performed a Sternberg Item Recognition Paradigm (SIRP) at three WM load levels. Functional connectivity networks were built by calculating the partial correlation on preprocessed time courses of BOLD signal between task-related brain regions of interest (ROIs) defined by group independent component analysis (ICA). The networks were then thresholded within the small-world regime, resulting in undirected binarized small-world networks at different working memory loads. Our results showed: 1) at the medium WM load level, the networks in SZ showed a lower clustering coefficient and less local efficiency compared with HC; 2) in SZ, most network measures altered significantly as the WM load level increased from low to medium and from medium to high, while the network metrics were relatively stable in HC at different WM loads; and 3) the altered structure at medium WM load in SZ was related to their performance during the task, with longer reaction time related to lower clustering coefficient and lower local efficiency. These findings suggest brain connectivity in patients with SZ was more diffuse and less strongly linked locally in functional network at intermediate level of WM when compared to HC. SZ show distinctly inefficient and variable network structures in response to WM load increase, comparing to stable highly clustered network topologies in HC.

Altered small-world brain networks in schizophrenia patients during working memory performance

Impairment of working memory (WM) performance in schizophrenia patients (SZ) is well-established. Compared to healthy controls (HC), SZ patients show aberrant blood oxygen level dependent (BOLD) activations and disrupted functional connectivity during WM performance. In this study, we examined the small-world network metrics computed from functional magnetic resonance imaging (fMRI) data collected as 35 HC and 35 SZ performed a Sternberg Item Recognition Paradigm (SIRP) at three WM load levels. Functional connectivity networks were built by calculating the partial correlation on preprocessed time courses of BOLD signal between task-related brain regions of interest (ROIs) defined by group independent component analysis (ICA). The networks were then thresholded within the small-world regime, resulting in undirected binarized small-world networks at different working memory loads. Our results showed: 1) at the medium WM load level, the networks in SZ showed a lower clustering coefficient and less local efficiency compared with HC; 2) in SZ, most network measures altered significantly as the WM load level increased from low to medium and from medium to high, while the network metrics were relatively stable in HC at different WM loads; and 3) the altered structure at medium WM load in SZ was related to their performance during the task, with longer reaction time related to lower clustering coefficient and lower local efficiency. These findings suggest brain connectivity in patients with SZ was more diffuse and less strongly linked locally in functional network at intermediate level of WM when compared to HC. SZ show distinctly inefficient and variable network structures in response to WM load increase, comparing to stable highly clustered network topologies in HC.

Emergence of a small-world functional network in cultured neurons

The functional networks of cultured neurons exhibit complex network properties similar to those found in vivo. Starting from random seeding, cultures undergo significant reorganization during the initial period in vitro, yet despite providing an ideal platform for observing developmental changes in neuronal connectivity, little is known about how a complex functional network evolves from isolated neurons. In the present study, evolution of functional connectivity was estimated from correlations of spontaneous activity. Network properties were quantified using complex measures from graph theory and used to compare cultures at different stages of development during the first 5 weeks in vitro. Networks obtained from young cultures (14 days in vitro) exhibited a random topology, which evolved to a small-world topology during maturation. The topology change was accompanied by an increased presence of highly connected areas (hubs) and network efficiency increased with age. The small-world topology balances integration of network areas with segregation of specialized processing units. The emergence of such network structure in cultured neurons, despite a lack of external input, points to complex intrinsic biological mechanisms. Moreover, the functional network of cultures at mature ages is efficient and highly suited to complex processing tasks.