Small-world properties of nonlinear brain activity in schizophrenia

Intra- and inter-brain synchronization during musical improvisation on the guitar

Humans interact with the environment through sensory and motor acts. Some of these interactions require synchronization among two or more individuals. Multiple-trial designs, which we have used in past work to study interbrain synchronization in the course of joint action, constrain the range of observable interactions. To overcome the limitations of multiple-trial designs, we conducted single-trial analyses of electroencephalography (EEG) signals recorded from eight pairs of guitarists engaged in musical improvisation. We identified hyper-brain networks based on a complex interplay of different frequencies. The intra-brain connections primarily involved higher frequencies (e.g., beta), whereas inter-brain connections primarily operated at lower frequencies (e.g., delta and theta). The topology of hyper-brain networks was frequency-dependent, with a tendency to become more regular at higher frequencies. We also found hyper-brain modules that included nodes (i.e., EEG electrodes) from both brains. Some of the observed network properties were related to musical roles during improvisation. Our findings replicate and extend earlier work and point to mechanisms that enable individuals to engage in temporally coordinated joint action.

Cerebral energy metabolism and the brain's functional network architecture: an integrative review

Recent functional magnetic resonance imaging (fMRI) studies have emphasized the contributions of synchronized activity in distributed brain networks to cognitive processes in both health and disease. The brain's 'functional connectivity' is typically estimated from correlations in the activity time series of anatomically remote areas, and postulated to reflect information flow between neuronal populations. Although the topological properties of functional brain networks have been studied extensively, considerably less is known regarding the neurophysiological and biochemical factors underlying the temporal coordination of large neuronal ensembles. In this review, we highlight the critical contributions of high-frequency electrical oscillations in the γ-band (30 to 100 Hz) to the emergence of functional brain networks. After describing the neurobiological substrates of γ-band dynamics, we specifically discuss the elevated energy requirements of high-frequency neural oscillations, which represent a mechanistic link between the functional connectivity of brain regions and their respective metabolic demands. Experimental evidence is presented for the high oxygen and glucose consumption, and strong mitochondrial performance required to support rhythmic cortical activity in the γ-band. Finally, the implications of mitochondrial impairments and deficits in glucose metabolism for cognition and behavior are discussed in the context of neuropsychiatric and neurodegenerative syndromes characterized by large-scale changes in the organization of functional brain networks.

Modulatory interactions of resting-state brain functional connectivity

The functional brain connectivity studies are generally based on the synchronization of the resting-state functional magnetic resonance imaging (fMRI) signals. Functional connectivity measures usually assume a stable relationship over time; however, accumulating studies have reported time-varying properties of strength and spatial distribution of functional connectivity. The present study explored the modulation of functional connectivity between two regions by a third region using the physiophysiological interaction (PPI) technique. We first identified eight brain networks and two regions of interest (ROIs) representing each of the networks using a spatial independent component analysis. A voxel-wise analysis was conducted to identify regions that showed modulatory interactions (PPI) with the two ROIs of each network. Mostly, positive modulatory interactions were observed within regions involved in the same system. For example, the two regions of the dorsal attention network revealed modulatory interactions with the regions related to attention, while the two regions of the extrastriate network revealed modulatory interactions with the regions in the visual cortex. In contrast, the two regions of the default mode network (DMN) revealed negative modulatory interactions with the regions in the executive network, and vice versa, suggesting that the activities of one network may be associated with smaller within network connectivity of the competing network. These results validate the use of PPI analysis to study modulation of resting-state functional connectivity by a third region. The modulatory effects may provide a better understanding of complex brain functions.

Intra- and inter-frequency brain network structure in health and schizophrenia

Empirical studies over the past two decades have provided support for the hypothesis that schizophrenia is characterized by altered connectivity patterns in functional brain networks. These alterations have been proposed as genetically mediated diagnostic biomarkers and are thought to underlie altered cognitive functions such as working memory. However, the nature of this dysconnectivity remains far from understood. In this study, we perform an extensive analysis of functional connectivity patterns extracted from MEG data in 14 subjects with schizophrenia and 14 healthy controls during a 2-back working memory task. We investigate uni-, bi- and multivariate properties of sensor time series by computing wavelet entropy of and correlation between time series, and by constructing binary networks of functional connectivity both within and between classical frequency bands ([Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]). Networks are based on the mutual information between wavelet time series, and estimated for each trial window separately, enabling us to consider both network topology and network dynamics. We observed significant decreases in time series entropy and significant increases in functional connectivity in the schizophrenia group in comparison to the healthy controls and identified an inverse relationship between these measures across both subjects and sensors that varied over frequency bands and was more pronounced in controls than in patients. The topological organization of connectivity was altered in schizophrenia specifically in high frequency [Formula: see text] and [Formula: see text] band networks as well as in the [Formula: see text]-[Formula: see text] cross-frequency networks. Network topology varied over trials to a greater extent in patients than in controls, suggesting disease-associated alterations in dynamic network properties of brain function. Our results identify signatures of aberrant neurophysiological behavior in schizophrenia across uni-, bi- and multivariate scales and lay the groundwork for further clinical studies that might lead to the discovery of new intermediate phenotypes.

Altered topological patterns of large-scale brain functional networks during passive hyperthermia

In this study, we simulated environmental heat exposure to 18 participants, and obtained functional magnetic resonance image (fMRI) data during resting state. Brain functional networks were constructed over a wide range of sparsity threshold according to a prior atlas dividing the whole cerebrum into 90 regions. Results of graph theoretical approaches showed that although brain networks in both normal and hyperthermia conditions exhibited economical small-world property, significant alterations in both global and nodal network metrics were demonstrated during hyperthermia. Specifically, a lower clustering coefficient, maintained shortest path length, a lower small-worldness, a lower mean local efficiency were found, indicating a tendency shift to a randomized network. Additionally, significant alterations in nodal efficiency were found in bilateral gyrus rectus, bilateral parahippocampal gyrus, bilateral insula, right caudate nucleus, bilateral putamen, left temporal pole of middle temporal gyrus, right inferior temporal gyrus. In consideration of physiological system changes, we found that the alterations of normalized clustering coefficient, small-worldness, mean normalized local efficiency were significantly correlated with the rectal temperature alteration, but failed to obtain significant correlations with the weight loss. More importantly, behavioral attention network test (ANT) after MRI scanning showed that the ANT effects were altered and correlated with the alterations of some global metrics (normalized shortest path length and normalized global efficiency) and prefrontal nodal efficiency (right dorsolateral superior frontal gyrus, right middle frontal gyrus and left orbital inferior frontal gyrus), implying behavioral deficits in executive control effects and maintained alerting and orienting effects during passive hyperthermia. The present study provided the first evidence for human brain functional disorder during passive hyperthermia according to graph theoretical analysis using resting-state fMRI.

Heritability of resting state EEG functional connectivity patterns

We examined the genetic architecture of functional brain connectivity measures in resting state electroencephalographic (EEG) recordings. Previous studies in Dutch twins have suggested that genetic factors are a main source of variance in functional brain connectivity derived from EEG recordings. In addition, qualitative descriptors of the brain network derived from graph analysis - network clustering and average path length - are also heritable traits. Here we replicated previous findings for connectivity, quantified by the synchronization likelihood, and the graph theoretical parameters cluster coefficient and path length in an Australian sample of 16-year-old twins (879) and their siblings (93). Modeling of monozygotic and dizygotic twins and sibling resemblance indicated heritability estimates of the synchronization likelihood (27-74%) and cluster coefficient and path length in the alpha and theta band (40-44% and 23-40% respectively) and path length in the beta band frequency (41%). This corroborates synchronization likelihood and its graph theoretical derivatives cluster coefficient and path length as potential endophenotypes for behavioral traits and neurological disorders.

Reorganization of functional brain networks during the recovery of stroke: a functional MRI study

Studies have demonstrated that reorganization of the cortex after stroke contributed to the recovery of motor function. However, these studies paid much more attention to the reorganization of motor-related brain regions and motor executive network which only contained tens of brain regions, ignoring the change in brain-wide network during the restoration of motor function. Based on this consideration, this paper investigated the functional reorganization of brain-wide network during the recovery after stroke from the perspective of graph theory. At four time points (less than 10 days, around 2 weeks, 1 month and 3 months) after stroke onset, we obtained the functional MRI (fMRI) data of stroke patients when they were doing finger tapping task. Based on the fMRI data, we constructed the brain-wide functional network which consisted of 264 putative functional areas for each subject at each time point. Then the topological parameters (e.g., characteristic path length and cluster coefficient) of these brain networks were examined. Results showed that the brain networks shifted towards a non-optimal topological configuration with low small-worldness during the process of recovery. And this finding may broaden our knowledge about the reorganization of brain function during recovery after stroke.

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 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.

Nicotinic modulation of intrinsic brain networks in schizophrenia

The nicotinic receptor is a promising drug target currently being investigated for the treatment of cognitive symptoms in schizophrenia. A key step in this process is the development of noninvasive functional neuroimaging biomarkers that can be used to determine if nicotinic agents are eliciting their targeted biological effect, ideally through modulation of a fundamental aspect of neuronal function. To that end, neuroimaging researchers are beginning to understand how nicotinic modulation affects "intrinsic" brain networks to elicit potentially therapeutic effects. An intrinsic network is a functionally and (often) structurally connected network of brain areas whose activity reflects a fundamental neurobiological organizational principle of the brain. This review summarizes findings of the effects of nicotinic drugs on three topics related to intrinsic brain network activity: (1) the default mode network, a group of brain areas for which activity is maximal at rest and reduced during cognitive tasks, (2) the salience network, which integrates incoming sensory data with prior internal representations to guide future actions and change predictive values, and (3) multi-scale complex network dynamics, which describe these brain's ability to efficiency integrate information while preserving local functional specialization. These early findings can be used to inform future neuroimaging studies that examine the network effects of nicotinic agents.

Directionality in hyperbrain networks discriminates between leaders and followers in guitar duets

To investigate whether directionality in hyperbrain networks reflects different roles during interpersonal action coordination (IAC), we recorded EEG data from pairs of guitarists playing together as musical leaders versus followers. We used an asymmetric index of in-phase synchronization to analyze hyperbrain networks of directed functional connectivity in the alpha and beta frequency ranges for time segments around coordinated play onsets. After exploring the small-world characteristics of the networks at different thresholds, we examined the directed connection strengths within and between brains. As predicted, we found evidence suggesting that the musical roles of leader and follower are associated with different patterns of directed between-brain couplings. The functional significance of these differences for IAC requires further study.

Functional connectivity abnormalities during contextual processing in schizophrenia and in Parkinson's disease

Functional connectivity was evaluated in patients with schizophrenia (SC) and in patients with Parkinson's disease (PD) during the performance of a local contextual processing paradigm, to investigate the proposition that functional disconnection is involved with contextual processing deficits in these populations. To this end, we utilized event-related EEG signals, synchronization likelihood and graph theoretical analysis. Local context was defined as the occurrence of a predictive sequence of stimuli before the presentation of a target event. In the SC patients, we observed a decrease in path length (L) in the beta band, for the predictive sequence and for predicted and random targets, compared with controls. These abnormalities were associated with weaker frontal-temporal-parietal connections. In the PD patients we found longer L (theta band) for predicted targets, and higher cluster coefficients for both the predictive sequence (theta band) and predicted targets (alpha and theta bands), compared with controls. Detection of predicted targets was associated with weaker frontal-parietal connections in PD. No group differences were found for randomized standard stimuli in both SC and PD patients. These findings provide evidence of task-specific functional connectivity abnormalities within frontal networks during local contextual processing.

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.

Apparent motion perception in patients with paranoid schizophrenia

Impaired perceptual inference has been suggested to be at the core of positive symptoms in schizophrenia. Apparent motion (AM) is a visual illusion in which perceptual inference gives rise to the experience of a single object moving back and forth when two spatially separated objects are flashed in alternation. Here, we investigated the strength of AM perception in patients with paranoid schizophrenia. Patients were less susceptible to the illusion as indicated by a lower probability of motion perception at the individual's optimal presentation frequency for AM. In addition, the probability of AM perception was inversely related to delusional conviction in the patient group. These results suggest that schizophrenia may be associated with a reduced susceptibility to visual phenomena that commonly rely on perceptual inference.

Modulation of EEG functional connectivity networks in subjects undergoing repetitive transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a noninvasive brain stimulation technique that utilizes magnetic fluxes to alter cortical activity. Continuous theta-burst repetitive TMS (cTBS) results in long-lasting decreases in indices of cortical excitability, and alterations in performance of behavioral tasks. We investigated the effects of cTBS on cortical function via functional connectivity and graph theoretical analysis of EEG data. Thirty-one channel resting-state EEG recordings were obtained before and after 40 s of cTBS stimulation to the left primary motor cortex. Functional connectivity between nodes was assessed in multiple frequency bands using lagged max-covariance, and subsequently thresholded to construct undirected graphs. After cTBS, we find widespread decreases in functional connectivity in the alpha band. There are also simultaneous increases in functional connectivity in the high-beta bands, especially amongst anterior and interhemispheric connections. The analysis of the undirected graphs reveals that interhemispheric and interregional connections are more likely to be modulated after cTBS than local connections. There is also a shift in the topology of network connectivity, with an increase in the clustering coefficient after cTBS in the beta bands, and a decrease in clustering and increase in path length in the alpha band, with the alpha-band connectivity primarily decreased near the site of stimulation. cTBS produces widespread alterations in cortical functional connectivity, with resulting shifts in cortical network topology.

Network analysis of auditory hallucinations in nonpsychotic individuals

BACKGROUND

Auditory verbal hallucinations (AVH) are a cardinal feature of schizophrenia and can severely disrupt behavior and decrease quality of life. Identification of areas with high functional connectivity (so-called hub regions) that are associated with the predisposition to hallucinate may provide potential targets for neuromodulation in the treatment of AVH.

METHODS

Resting-state fMRI scans during which no hallucinations had occurred were acquired from 29 nonpsychotic individuals with AVH and 29 matched controls. These nonpsychotic individuals with AVH provide the opportunity to study AVH without several confounds associated with schizophrenia, such as antipsychotic medication use and other symptoms related to the illness. Hub regions were identified by assessing weighted connectivity strength and betweenness centrality across groups using a permutation analysis.

RESULTS

Nonpsychotic individuals with AVH exhibited increased functioning as hub regions in the temporal cortices and the posterior cingulate/precuneus, which is an important area in the default mode network (DMN), compared to the nonhallucinating controls. In addition, the right inferior temporal gyrus, left paracentral lobule and right amygdala were less important as a hub region in the AVH group.

CONCLUSIONS

These results suggest that the predisposition to hallucinate may be related to aberrant functioning of the DMN and the auditory cortices.

Connectivity and phase coherence in neural network models of interconnected Z(4)-bi-stable units

A phenomenological neural network model with bi-stable oscillatory units is used to model up- and down-states. These states have been observed in vivo in biological neuronal systems and feature oscillatory, limit cycle type of behavior in the up-states. A network is formed by a set of interconnected units. Two different types of network layouts are considered in this work: networks with hierarchical connections and hubs and networks with random connections. The phase coherence between the different units is analyzed and compared to the connectivity distance between nodes. In addition the connectivity degree of a node is associated to the average phase coherence with all other units. The results show that we may be able to identify the set of hubs in a network based on the phase coherence estimates between the different nodes. If the network is very dense or randomly connected, the underlying network structure, however, can not be derived uniquely from the phase coherence.

Magnetic resonance imaging and graph theoretical analysis of complex brain networks in neuropsychiatric disorders

Neurological and psychiatric disorders disturb higher cognitive functions and are accompanied by aberrant cortico-cortical axonal pathways or synchronizations of neural activity. A large proportion of neuroimaging studies have focused on examining the focal morphological abnormalities of various gray and white matter structures or the functional activities of brain areas during goal-directed tasks or the resting state, which provides vast quantities of information on both the structural and functional alterations in the patients' brain. However, these studies often ignore the interactions among multiple brain regions that constitute complex brain networks underlying higher cognitive function. Information derived from recent advances of noninvasive magnetic resonance imaging (MRI) techniques and computational methodologies such as graph theory have allowed researchers to explore the patterns of structural and functional connectivity of healthy and diseased brains in vivo. In this article, we summarize the recent advances made in the studies of both structural (gray matter morphology and white matter fibers) and functional (synchronized neural activity) brain networks based on human MRI data pertaining to neuropsychiatric disorders. These studies bring a systems-level perspective to the alterations of the topological organization of complex brain networks and the underlying pathophysiological mechanisms. Specifically, noninvasive imaging of structural and functional brain networks and follow-up graph-theoretical analyses demonstrate the potential to establish systems-level biomarkers for clinical diagnosis, progression monitoring, and treatment effects evaluation for neuropsychiatric disorders.

The problem of thresholding in small-world network analysis

Graph theory deterministically models networks as sets of vertices, which are linked by connections. Such mathematical representation of networks, called graphs are increasingly used in neuroscience to model functional brain networks. It was shown that many forms of structural and functional brain networks have small-world characteristics, thus, constitute networks of dense local and highly effective distal information processing. Motivated by a previous small-world connectivity analysis of resting EEG-data we explored implications of a commonly used analysis approach. This common course of analysis is to compare small-world characteristics between two groups using classical inferential statistics. This however, becomes problematic when using measures of inter-subject correlations, as it is the case in commonly used brain imaging methods such as structural and diffusion tensor imaging with the exception of fibre tracking. Since for each voxel, or region there is only one data point, a measure of connectivity can only be computed for a group. To empirically determine an adequate small-world network threshold and to generate the necessary distribution of measures for classical inferential statistics, samples are generated by thresholding the networks on the group level over a range of thresholds. We believe that there are mainly two problems with this approach. First, the number of thresholded networks is arbitrary. Second, the obtained thresholded networks are not independent samples. Both issues become problematic when using commonly applied parametric statistical tests. Here, we demonstrate potential consequences of the number of thresholds and non-independency of samples in two examples (using artificial data and EEG data). Consequently alternative approaches are presented, which overcome these methodological issues.

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.

The anatomical distance of functional connections predicts brain network topology in health and schizophrenia

The human brain is a topologically complex network embedded in anatomical space. Here, we systematically explored relationships between functional connectivity, complex network topology, and anatomical (Euclidean) distance between connected brain regions, in the resting-state functional magnetic resonance imaging brain networks of 20 healthy volunteers and 19 patients with childhood-onset schizophrenia (COS). Normal between-subject differences in average distance of connected edges in brain graphs were strongly associated with variation in topological properties of functional networks. In addition, a club or subset of connector hubs was identified, in lateral temporal, parietal, dorsal prefrontal, and medial prefrontal/cingulate cortical regions. In COS, there was reduced strength of functional connectivity over short distances especially, and therefore, global mean connection distance of thresholded graphs was significantly greater than normal. As predicted from relationships between spatial and topological properties of normal networks, this disorder-related proportional increase in connection distance was associated with reduced clustering and modularity and increased global efficiency of COS networks. Between-group differences in connection distance were localized specifically to connector hubs of multimodal association cortex. In relation to the neurodevelopmental pathogenesis of schizophrenia, we argue that the data are consistent with the interpretation that spatial and topological disturbances of functional network organization could arise from excessive "pruning" of short-distance functional connections in schizophrenia.

On the discovery of group-consistent graph substructure patterns from brain networks

Complex networks constitute a recurring issue in the analysis of neuroimaging data. Recently, network motifs have been identified as patterns of interconnections since they appear in a significantly higher number than in randomized networks, in a given ensemble of anatomical or functional connectivity graphs. The current approach for detecting and enumerating motifs in brain networks requires a predetermined motif repertoire and can operate only with motifs of small size (consisting of few nodes). There is a growing interest in methodologies for frequent graph-based pattern mining in large graph datasets that can facilitate adaptive design of motifs. The results presented in this paper are based on the graph-based Substructure pattern mining (gSpan) algorithm and introduce a manifold of ways to exploit it for data-driven motif extraction in connectomics research. Functional connectivity graphs from electroencephalographic (EEG) recordings during resting state and mental calculations are used to demonstrate our approach. Relying on either time-invariant or time-evolving graphs, characteristic motifs associated with various frequency bands were derived and compared. With a suitable manipulation, the gSpan discovers motifs which are specific to performing mental arithmetics. Finally, the subject-dependent temporal signatures of motifs' appearance revealed the transient nature of the evolving functional connectivity (math-related motifs "come and go").

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.

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.

Using computational models to relate structural and functional brain connectivity

Modern imaging methods allow a non-invasive assessment of both structural and functional brain connectivity. This has lead to the identification of disease-related alterations affecting functional connectivity. The mechanism of how such alterations in functional connectivity arise in a structured network of interacting neural populations is as yet poorly understood. Here we use a modeling approach to explore the way in which this can arise and to highlight the important role that local population dynamics can have in shaping emergent spatial functional connectivity patterns. The local dynamics for a neural population is taken to be of the Wilson–Cowan type, whilst the structural connectivity patterns used, describing long-range anatomical connections, cover both realistic scenarios (from the CoComac database) and idealized ones that allow for more detailed theoretical study. We have calculated graph–theoretic measures of functional network topology from numerical simulations of model networks. The effect of the form of local dynamics on the observed network state is quantified by examining the correlation between structural and functional connectivity. We document a profound and systematic dependence of the simulated functional connectivity patterns on the parameters controlling the dynamics. Importantly, we show that a weakly coupled oscillator theory explaining these correlations and their variation across parameter space can be developed. This theoretical development provides a novel way to characterize the mechanisms for the breakdown of functional connectivity in diseases through changes in local dynamics.

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.

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.

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.

Changes in community structure of resting state functional connectivity in unipolar depression

Major depression is a prevalent disorder that imposes a significant burden on society, yet objective laboratory-style tests to assist in diagnosis are lacking. We employed network-based analyses of “resting state” functional neuroimaging data to ascertain group differences in the endogenous cortical activity between healthy and depressed subjects.

We additionally sought to use machine learning techniques to explore the ability of these network-based measures of resting state activity to provide diagnostic information for depression. Resting state fMRI data were acquired from twenty two depressed outpatients and twenty two healthy subjects matched for age and gender. These data were anatomically parcellated and functional connectivity matrices were then derived using the linear correlations between the BOLD signal fluctuations of all pairs of cortical and subcortical regions.

We characterised the hierarchical organization of these matrices using network-based matrics, with an emphasis on their mid-scale “modularity” arrangement. Whilst whole brain measures of organization did not differ between groups, a significant rearrangement of their community structure was observed. Furthermore we were able to classify individuals with a high level of accuracy using a support vector machine, primarily through the use of a modularity-based metric known as the participation index.

In conclusion, the application of machine learning techniques to features of resting state fMRI network activity shows promising potential to assist in the diagnosis of major depression, now suggesting the need for validation in independent data sets.

Nicotine increases brain functional network efficiency

Despite the use of cholinergic therapies in Alzheimer's disease and the development of cholinergic strategies for schizophrenia, relatively little is known about how the system modulates the connectivity and structure of large-scale brain networks. To better understand how nicotinic cholinergic systems alter these networks, this study examined the effects of nicotine on measures of whole-brain network communication efficiency. Resting state fMRI was acquired from fifteen healthy subjects before and after the application of nicotine or placebo transdermal patches in a single blind, crossover design. Data, which were previously examined for default network activity, were analyzed with network topology techniques to measure changes in the communication efficiency of whole-brain networks. Nicotine significantly increased local efficiency, a parameter that estimates the network's tolerance to local errors in communication. Nicotine also significantly enhanced the regional efficiency of limbic and paralimbic areas of the brain, areas which are especially altered in diseases such as Alzheimer's disease and schizophrenia. These changes in network topology may be one mechanism by which cholinergic therapies improve brain function.

Brain excitability and connectivity of neuronal assemblies in Alzheimer's disease: from animal models to human findings

The human brain contains about 100 billion neurons forming an intricate network of innumerable connections, which continuously adapt and rewire themselves following inputs from external and internal environments as well as the physiological synaptic, dendritic and axonal sculpture during brain maturation and throughout the life span. Growing evidence supports the idea that Alzheimer's disease (AD) targets selected and functionally connected neuronal networks and, specifically, their synaptic terminals, affecting brain connectivity well before producing neuronal loss and compartmental atrophy. The understanding of the molecular mechanisms underlying the dismantling of neuronal circuits and the implementation of 'clinically oriented' methods to map-out the dynamic interactions amongst neuronal assemblies will enhance early/pre-symptomatic diagnosis and monitoring of disease progression. More important, this will open the avenues to innovative treatments, bridging the gap between molecular mechanisms and the variety of symptoms forming disease phenotype. In the present review a set of evidence supports the idea that altered brain connectivity, exhausted neural plasticity and aberrant neuronal activity are facets of the same coin linked to age-related neurodegenerative dementia of Alzheimer type. Investigating their respective roles in AD pathophysiology will help in translating findings from basic research to clinical applications.

Nonlinear analysis of electroencephalogram at rest and during cognitive tasks in patients with schizophrenia

BACKGROUND

In spite of the large number of studies on schizophrenia, a full understanding of its core pathology still eludes us. The application of the nonlinear theory of electroencephalography (EEG) analysis provides an interesting tool to differentiate between physiologic conditions (e.g., resting state and mathematical task) and normal and pathologic brain activities. The aim of the present study was to investigate nonlinear EEG activity in patients with schizophrenia.

METHODS

We recorded 19-lead EEGs in patients with stable schizophrenia and healthy controls under 4 different conditions: eyes closed, eyes open, forward counting and backward counting. A nonlinear measure of complexity was calculated by means of correlation dimension (D2).

RESULTS

We included 17 patients and 17 controls in our analysis. Comparing the 2 populations, we observed greater D2 values in the patient group. In controls, increased D2 values were observed during active states (eyes open and the 2 cognitive tasks) compared with baseline conditions. This increase of brain complexity, which can be interpreted as an increase of information processing and integration, was not preserved in the patient population.

LIMITATIONS

Patients with schizophrenia were taking antipsychotic medications, so the presence of medication effects cannot be excluded.

CONCLUSION

Our results suggest that patients with schizophrenia present changes in brain activity compared with healthy controls, and this pathologic alteration can be successfully studied with nonlinear EEG analysis.

Modeling the outcome of structural disconnection on resting-state functional connectivity

A growing body of experimental evidence suggests that functional connectivity at rest is shaped by the underlying anatomical structure. Furthermore, the organizational properties of resting-state functional networks are thought to serve as the basis for an optimal cognitive integration. A disconnection at the structural level, as occurring in some brain diseases, would then lead to functional and presumably cognitive impairments. In this work, we propose a computational model to investigate the role of a structural disconnection (encompassing putative local/global and axonal/synaptic mechanisms) on the organizational properties of emergent functional networks. The brain's spontaneous neural activity and the corresponding hemodynamic response were simulated using a large-scale network model, consisting of local neural populations coupled through white matter fibers. For a certain coupling strength, simulations reproduced healthy resting-state functional connectivity with graph properties in the range of the ones reported experimentally. When the structural connectivity is decreased, either globally or locally, the resultant simulated functional connectivity exhibited a network reorganization characterized by an increase in hierarchy, efficiency and robustness, a decrease in small-worldness and clustering and a narrower degree distribution, in the same way as recently reported for schizophrenia patients. Theoretical results indicate that most disconnection-related neuropathologies should induce the same qualitative changes in resting-state brain activity.

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.

Identifying important nodes in weighted functional brain networks: a comparison of different centrality approaches

We compare different centrality metrics which aim at an identification of important nodes in complex networks. We investigate weighted functional brain networks derived from multichannel electroencephalograms recorded from 23 healthy subject under resting-state eyes-open or eyes-closed conditions. Although we observe the metrics strength, closeness, and betweenness centrality to be related to each other, they capture different spatial and temporal aspects of important nodes in these networks associated with behavioral changes. Identifying and characterizing of these nodes thus benefits from the application of several centrality metrics.

Modulations of functional connectivity in the healthy and schizophrenia groups during task and rest

Connectivity analysis using functional magnetic resonance imaging (fMRI) data is an important area, useful for the identification of biomarkers for various mental disorders, including schizophrenia. Most studies to date have focused on resting data, while the study of functional connectivity during task and the differences between task and rest are of great interest as well. In this work, we examine the graph-theoretical properties of the connectivity maps constructed using spatial components derived from independent component analysis (ICA) for healthy controls and patients with schizophrenia during an auditory oddball task (AOD) and at extended rest. We estimate functional connectivity using the higher-order statistical dependence, i.e., mutual information among the ICA spatial components, instead of the typically used temporal correlation. We also define three novel topological metrics based on the modules of brain networks obtained using a clustering approach. Our experimental results show that although the schizophrenia patients preserve the small-world property, they present a significantly lower small-worldness during both AOD task and rest when compared to the healthy controls, indicating a consistent tendency towards a more random organization of brain networks. In addition, the task-induced modulations to topological measures of several components involving motor, cerebellum and parietal regions are altered in patients relative to controls, providing further evidence for the aberrant connectivity in schizophrenia.

Anatomical connectivity influences both intra- and inter-brain synchronizations

Recent development in diffusion spectrum brain imaging combined to functional simulation has the potential to further our understanding of how structure and dynamics are intertwined in the human brain. At the intra-individual scale, neurocomputational models have already started to uncover how the human connectome constrains the coordination of brain activity across distributed brain regions. In parallel, at the inter-individual scale, nascent social neuroscience provides a new dynamical vista of the coupling between two embodied cognitive agents. Using EEG hyperscanning to record simultaneously the brain activities of subjects during their ongoing interaction, we have previously demonstrated that behavioral synchrony correlates with the emergence of inter-brain synchronization. However, the functional meaning of such synchronization remains to be specified. Here, we use a biophysical model to quantify to what extent inter-brain synchronizations are related to the anatomical and functional similarity of the two brains in interaction. Pairs of interacting brains were numerically simulated and compared to real data. Results show a potential dynamical property of the human connectome to facilitate inter-individual synchronizations and thus may partly account for our propensity to generate dynamical couplings with others.

Simple models of human brain functional networks

Human brain functional networks are embedded in anatomical space and have topological properties--small-worldness, modularity, fat-tailed degree distributions--that are comparable to many other complex networks. Although a sophisticated set of measures is available to describe the topology of brain networks, the selection pressures that drive their formation remain largely unknown. Here we consider generative models for the probability of a functional connection (an edge) between two cortical regions (nodes) separated by some Euclidean distance in anatomical space. In particular, we propose a model in which the embedded topology of brain networks emerges from two competing factors: a distance penalty based on the cost of maintaining long-range connections; and a topological term that favors links between regions sharing similar input. We show that, together, these two biologically plausible factors are sufficient to capture an impressive range of topological properties of functional brain networks. Model parameters estimated in one set of functional MRI (fMRI) data on normal volunteers provided a good fit to networks estimated in a second independent sample of fMRI data. Furthermore, slightly detuned model parameters also generated a reasonable simulation of the abnormal properties of brain functional networks in people with schizophrenia. We therefore anticipate that many aspects of brain network organization, in health and disease, may be parsimoniously explained by an economical clustering rule for the probability of functional connectivity between different brain areas.

Fragmentation: loss of global coherence or breakdown of modularity in functional brain architecture?

Psychiatric illnesses characterized by disorganized cognition, such as schizophrenia, have been described in terms of fragmentation and hence understood as reduction in functional brain connectivity, particularly in prefrontal and parietal areas. However, as graph theory shows, relatively small numbers of nonlocal connections are sufficient to ensure global coherence in the modular small-world network structure of the brain. We reconsider fragmentation in this perspective. Computational studies have shown that for a given level of connectivity in a model of coupled nonlinear oscillators, modular small-world networks evolve from an initially random organization. Here we demonstrate that with decreasing connectivity, the probability of evolving into a modular small-world network breaks down at a critical point, which scales to the percolation function of random networks with a universal exponent of α = 1.17. Thus, according to the model, local modularity systematically breaks down before there is loss of global coherence in network connectivity. We, therefore, propose that fragmentation may involve, at least in its initial stages, the inability of a dynamically evolving network to sustain a modular small-world structure. The result is in a shift in the balance in schizophrenia from local to global functional connectivity.

Activity-dependent neuronal model on complex networks

Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behavior: these avalanches are characterized by a power law distribution for the size and duration, features found in other problems in the context of the physics of complex systems. We present a recent model inspired in self-organized criticality, which consists of an electrical network with threshold firing, refractory period, and activity-dependent synaptic plasticity. The model reproduces the critical behavior of the distribution of avalanche sizes and durations measured experimentally. Moreover, the power spectra of the electrical signal reproduce very robustly the power law behavior found in human electroencephalogram (EEG) spectra. We implement this model on a variety of complex networks, i.e., regular, small-world, and scale-free and verify the robustness of the critical behavior.

Exploration and modulation of brain network interactions with noninvasive brain stimulation in combination with neuroimaging

Much recent work in systems neuroscience has focused on how dynamic interactions between different cortical regions underlie complex brain functions such as motor coordination, language and emotional regulation. Various studies using neuroimaging and neurophysiologic techniques have suggested that in many neuropsychiatric disorders, these dynamic brain networks are dysregulated. Here we review the utility of combined noninvasive brain stimulation and neuroimaging approaches towards greater understanding of dynamic brain networks in health and disease. Brain stimulation techniques, such as transcranial magnetic stimulation and transcranial direct current stimulation, use electromagnetic principles to alter brain activity noninvasively, and induce focal but also network effects beyond the stimulation site. When combined with brain imaging techniques such as functional magnetic resonance imaging, positron emission tomography and electroencephalography, these brain stimulation techniques enable a causal assessment of the interaction between different network components, and their respective functional roles. The same techniques can also be applied to explore hypotheses regarding the changes in functional connectivity that occur during task performance and in various disease states such as stroke, depression and schizophrenia. Finally, in diseases characterized by pathologic alterations in either the excitability within a single region or in the activity of distributed networks, such techniques provide a potential mechanism to alter cortical network function and architectures in a beneficial manner.

Schizophrenia, neuroimaging and connectomics

Schizophrenia is frequently characterized as a disorder of brain connectivity. Neuroimaging has played a central role in supporting this view, with nearly two decades of research providing abundant evidence of structural and functional connectivity abnormalities in the disorder. In recent years, our understanding of how schizophrenia affects brain networks has been greatly advanced by attempts to map the complete set of inter-regional interactions comprising the brain's intricate web of connectivity; i.e., the human connectome. Imaging connectomics refers to the use of neuroimaging techniques to generate these maps which, combined with the application of graph theoretic methods, has enabled relatively comprehensive mapping of brain network connectivity and topology in unprecedented detail. Here, we review the application of these techniques to the study of schizophrenia, focusing principally on magnetic resonance imaging (MRI) research, while drawing attention to key methodological issues in the field. The published findings suggest that schizophrenia is associated with a widespread and possibly context-independent functional connectivity deficit, upon which are superimposed more circumscribed, context-dependent alterations associated with transient states of hyper- and/or hypo-connectivity. In some cases, these changes in inter-regional functional coupling dynamics can be related to measures of intra-regional dysfunction. Topological disturbances of functional brain networks in schizophrenia point to reduced local network connectivity and modular structure, as well as increased global integration and network robustness. Some, but not all, of these functional abnormalities appear to have an anatomical basis, though the relationship between the two is complex. By comprehensively mapping connectomic disturbances in patients with schizophrenia across the entire brain, this work has provided important insights into the highly distributed character of neural abnormalities in the disorder, and the potential functional consequences that these disturbances entail.