Functional connectivity patterns of human magnetoencephalographic recordings: a 'small-world' network?

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.

Small-World Properties in Mild Cognitive Impairment and Early Alzheimer's Disease: A Cortical Thickness MRI Study

BACKGROUND

Small-world network consists of networks with local specialization and global integration. Our objective is to detect small-world properties alteration based on cortical thickness in mild cognitive impairment (MCI) including stables and converters, and early Alzheimer's disease (AD) compared to controls.

METHODS

MRI scans of 13 controls, 10 MCI, and 10 with early AD were retrospectively analyzed; 11 MCI converters, 11 MCI stables, and 10 controls from the ADNI website were also included.

RESULTS

There were significantly decreased local efficiencies in patients with MCI and AD compared to controls; and MCI patients showed increased global efficiency compared to AD and controls. The MCI converters experience the worst local efficiency during the converting period to AD; the stables, however, have highest local and global efficiency.

CONCLUSIONS

The abnormal cortical thickness-based small-world properties in MCI and AD as well as the distinct patterns between two MCI subtypes suggest that small-world network analysis has the potential to better differentiate different stages of early dementia.

Analyzing complex functional brain networks: Fusing statistics and network science to understand the brain*†

Complex functional brain network analyses have exploded over the last decade, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has facilitated these analyses and enabled examining the brain as an integrated system that produces complex behaviors. While the field of statistics has been integral in advancing activation analyses and some connectivity analyses in functional neuroimaging research, it has yet to play a commensurate role in complex network analyses. Fusing novel statistical methods with network-based functional neuroimage analysis will engender powerful analytical tools that will aid in our understanding of normal brain function as well as alterations due to various brain disorders. Here we survey widely used statistical and network science tools for analyzing fMRI network data and discuss the challenges faced in filling some of the remaining methodological gaps. When applied and interpreted correctly, the fusion of network scientific and statistical methods has a chance to revolutionize the understanding of brain function.

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.

A review of functional magnetic resonance imaging for Brainnetome

The functional brain network using blood-oxygen-level-dependent (BOLD) functional magnetic resonance imaging (fMRI) has revealed the potentials for probing brain architecture, as well as for identifying clinical biomarkers for brain diseases. In the general context of Brainnetome, this review focuses on the development of approaches for modeling and analyzing functional brain networks with BOLD fMRI. The prospects for these approaches are also discussed.

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.

Intra- and interbrain synchronization and network properties when playing guitar in duets

To further test and explore the hypothesis that synchronous oscillatory brain activity supports interpersonally coordinated behavior during dyadic music performance, we simultaneously recorded the electroencephalogram (EEG) from the brains of each of 12 guitar duets repeatedly playing a modified Rondo in two voices by C.G. Scheidler. Indicators of phase locking and of within-brain and between-brain phase coherence were obtained from complex time-frequency signals based on the Gabor transform. Analyses were restricted to the delta (1-4 Hz) and theta (4-8 Hz) frequency bands. We found that phase locking as well as within-brain and between-brain phase-coherence connection strengths were enhanced at frontal and central electrodes during periods that put particularly high demands on musical coordination. Phase locking was modulated in relation to the experimentally assigned musical roles of leader and follower, corroborating the functional significance of synchronous oscillations in dyadic music performance. Graph theory analyses revealed within-brain and hyperbrain networks with small-worldness properties that were enhanced during musical coordination periods, and community structures encompassing electrodes from both brains (hyperbrain modules). We conclude that brain mechanisms indexed by phase locking, phase coherence, and structural properties of within-brain and hyperbrain networks support interpersonal action coordination (IAC).

Capturing dynamic patterns of task-based functional connectivity with EEG

A new approach to trace the dynamic patterns of task-based functional connectivity, by combining signal segmentation, dynamic time warping (DTW), and Quality Threshold (QT) clustering techniques, is presented. Electroencephalography (EEG) signals of 5 healthy subjects were recorded as they performed an auditory oddball and a visual modified oddball tasks. To capture the dynamic patterns of functional connectivity during the execution of each task, EEG signals are segmented into durations that correspond to the temporal windows of previously well-studied event-related potentials (ERPs). For each temporal window, DTW is employed to measure the functional similarities among channels. Unlike commonly used temporal similarity measures, such as cross correlation, DTW compares time series by taking into consideration that their alignment properties may vary in time. QT clustering analysis is then used to automatically identify the functionally connected regions in each temporal window. For each task, the proposed approach was able to establish a unique sequence of dynamic pattern (observed in all 5 subjects) for brain functional connectivity.

Neuroimaging in amyotrophic lateral sclerosis

The catastrophic system failure in amyotrophic lateral sclerosis is characterized by progressive neurodegeneration within the corticospinal tracts, brainstem nuclei and spinal cord anterior horns, with an extra-motor pathology that has overlap with frontotemporal dementia. The development of computed tomography and, even more so, MRI has brought insights into neurological disease, previously only available through post-mortem study. Although largely research-based, radionuclide imaging has continued to provide mechanistic insights into neurodegenerative disorders. The evolution of MRI to use advanced sequences highly sensitive to cortical and white matter structure, parenchymal metabolites and blood flow, many of which are now applicable to the spinal cord as well as the brain, make it a uniquely valuable tool for the study of a multisystem disorder such as amyotrophic lateral sclerosis. This comprehensive review considers the full range of neuroimaging techniques applied to amyotrophic lateral sclerosis over the last 25 years, the biomarkers they have revealed and future developments.

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.

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.

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.

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.

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 brain matures with stronger functional connectivity and decreased randomness of its network

We investigated the development of the brain's functional connectivity throughout the life span (ages 5 through 71 years) by measuring EEG activity in a large population-based sample. Connectivity was established with Synchronization Likelihood. Relative randomness of the connectivity patterns was established with Watts and Strogatz' (1998) graph parameters C (local clustering) and L (global path length) for alpha (~10 Hz), beta (~20 Hz), and theta (~4 Hz) oscillation networks. From childhood to adolescence large increases in connectivity in alpha, theta and beta frequency bands were found that continued at a slower pace into adulthood (peaking at ~50 yrs). Connectivity changes were accompanied by increases in L and C reflecting decreases in network randomness or increased order (peak levels reached at ~18 yrs). Older age (55+) was associated with weakened connectivity. Semi-automatically segmented T1 weighted MRI images of 104 young adults revealed that connectivity was significantly correlated to cerebral white matter volume (alpha oscillations: r = 33, p<01; theta: r = 22, p<05), while path length was related to both white matter (alpha: max. r = 38, p<001) and gray matter (alpha: max. r = 36, p<001; theta: max. r = 36, p<001) volumes. In conclusion, EEG connectivity and graph theoretical network analysis may be used to trace structural and functional development of the brain.

Large-scale cortical network properties predict future sound-to-word learning success

The human brain possesses a remarkable capacity to interpret and recall novel sounds as spoken language. These linguistic abilities arise from complex processing spanning a widely distributed cortical network and are characterized by marked individual variation. Recently, graph theoretical analysis has facilitated the exploration of how such aspects of large-scale brain functional organization may underlie cognitive performance. Brain functional networks are known to possess small-world topologies characterized by efficient global and local information transfer, but whether these properties relate to language learning abilities remains unknown. Here we applied graph theory to construct large-scale cortical functional networks from cerebral hemodynamic (fMRI) responses acquired during an auditory pitch discrimination task and found that such network properties were associated with participants' future success in learning words of an artificial spoken language. Successful learners possessed networks with reduced local efficiency but increased global efficiency relative to less successful learners and had a more cost-efficient network organization. Regionally, successful and less successful learners exhibited differences in these network properties spanning bilateral prefrontal, parietal, and right temporal cortex, overlapping a core network of auditory language areas. These results suggest that efficient cortical network organization is associated with sound-to-word learning abilities among healthy, younger adults.

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.

Discovering oscillatory interaction networks with M/EEG: challenges and breakthroughs

The systems-level neuronal mechanisms that coordinate temporally, anatomically and functionally distributed neuronal activity into coherent cognitive operations in the human brain have remained poorly understood. Synchronization of neuronal oscillations may regulate network communication and could thus serve as such a mechanism. Evidence for this hypothesis, however, was until recently sparse, as methodological challenges limit the investigation of interareal interactions with non-invasive magneto- and electroencephalography (M/EEG) recordings. Nevertheless, recent advances in M/EEG source reconstruction and clustering methods support complete phase-interaction mappings that are essential for uncovering the large-scale neuronal assemblies and their functional roles. These data show that synchronization is a robust and behaviorally significant phenomenon in task-relevant cortical networks and could hence bind distributed neuronal processing to coherent cognitive states.

Graph-based network analysis in schizophrenia

Over the last few years, many studies have been published using modern network analysis of the brain. Researchers and practical doctors alike should understand this method and its results on the brain evaluation at rest, during activation and in brain disease. The studies are noninvasive and usually performed with elecroencephalographic, magnetoencephalographic, magnetic resonance imaging and diffusion tensor imaging brain recordings. Different tools for analysis have been developed, although the methods are in their early stages. The results of these analyses are of special value. Studies of these tools in schizophrenia are important because widespread and local network disturbances can be evaluated by assessing integration, segregation and several structural and functional properties. With the help of network analyses, the main findings in schizophrenia are lower optimum network organization, less efficiently wired networks, less local clustering, less hierarchical organization and signs of disconnection. There are only about twenty five relevant papers on the subject today. Only a few years of study of these methods have produced interesting results and it appears promising that the development of these methods will present important knowledge for both the preclinical signs of schizophrenia and the methods’ therapeutic effects.

Markov models for fMRI correlation structure: Is brain functional connectivity small world, or decomposable into networks?

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems.

Tinnitus: network pathophysiology-network pharmacology

Tinnitus, the phantom perception of sound, is a prevalent disorder. One in 10 adults has clinically significant subjective tinnitus, and for one in 100, tinnitus severely affects their quality of life. Despite the significant unmet clinical need for a safe and effective drug targeting tinnitus relief, there is currently not a single Food and Drug Administration (FDA)-approved drug on the market. The search for drugs that target tinnitus is hampered by the lack of a deep knowledge of the underlying neural substrates of this pathology. Recent studies are increasingly demonstrating that, as described for other central nervous system (CNS) disorders, tinnitus is a pathology of brain networks. The application of graph theoretical analysis to brain networks has recently provided new information concerning their topology, their robustness and their vulnerability to attacks. Moreover, the philosophy behind drug design and pharmacotherapy in CNS pathologies is changing from that of "magic bullets" that target individual chemoreceptors or "disease-causing genes" into that of "magic shotguns," "promiscuous" or "dirty drugs" that target "disease-causing networks," also known as network pharmacology. In the present work we provide some insight into how this knowledge could be applied to tinnitus pathophysiology and pharmacotherapy.

A strong parietal hub in the small-world network of coloured-hearing synaesthetes during resting state EEG

We investigated whether functional brain networks are different in coloured-hearing synaesthetes compared with non-synaesthetes. Based on resting state electroencephalographic (EEG) activity, graph-theoretical analysis was applied to functional connectivity data obtained from different frequency bands (theta, alpha1, alpha2, and beta) of 12 coloured-hearing synaesthetes and 13 non-synaesthetes. The analysis of functional connectivity was based on estimated intra-cerebral sources of brain activation using standardized low-resolution electrical tomography. These intra-cerebral sources of brain activity were subjected to graph-theoretical analysis yielding measures representing small-world network characteristics (cluster coefficients and path length). In addition, brain regions with strong interconnections were identified (so-called hubs), and the interconnectedness of these hubs were quantified using degree as a measure of connectedness. Our analysis was guided by the two-stage model proposed by Hubbard and Ramachandran (2005). In this model, the parietal lobe is thought to play a pivotal role in binding together the synaesthetic perceptions (hyperbinding). In addition, we hypothesized that the auditory cortex and the fusiform gyrus would qualify as strong hubs in synaesthetes. Although synaesthetes and non-synaesthetes demonstrated a similar small-world network topology, the parietal lobe turned out to be a stronger hub in synaesthetes than in non-synaesthetes supporting the two-stage model. The auditory cortex was also identified as a strong hub in these coloured-hearing synaesthetes (for the alpha2 band). Thus, our a priori hypotheses receive strong support. Several additional hubs (for which no a priori hypothesis has been formulated) were found to be different in terms of the degree measure in synaesthetes, with synaesthetes demonstrating stronger degree measures indicating stronger interconnectedness. These hubs were found in brain areas known to be involved in controlling memory processes (alpha1: hippocampus and retrosplenial area), executive functions (alpha1 and alpha2: ventrolateral prefrontal cortex; theta: inferior frontal cortex), and the generation of perceptions (theta: extrastriate cortex; beta: subcentral area). Taken together this graph-theoretical analysis of the resting state EEG supports the two-stage model in demonstrating that the left-sided parietal lobe is a strong hub region, which is stronger functionally interconnected in synaesthetes than in non-synaesthetes. The right-sided auditory cortex is also a strong hub supporting the idea that coloured-hearing synaesthetes demonstrate a specific auditory cortex. A further important point is that these hub regions are even differently operating at rest supporting the idea that these hub characteristics are predetermining factors of coloured-hearing synaesthesia.

Interindividual reaction time variability is related to resting-state network topology: an electroencephalogram study

Both anatomical and functional brain network studies have drawn great attention recently. Previous studies have suggested the significant impacts of brain network topology on cognitive function. However, the relationship between non-task-related resting-state functional brain network topology and overall efficiency of sensorimotor processing has not been well identified. In the present study, we investigated the relationship between non-task-related resting-state functional brain network topology and reaction time (RT) in a Go/Nogo task using an electroencephalogram (EEG). After estimating the functional connectivity between each pair of electrodes, graph analysis was applied to characterize the network topology. Two fundamental measures, clustering coefficient (functional segregation) and characteristic path length (functional integration), as well as "small-world-ness" (the ratio between the clustering coefficient and characteristic path length) were calculated in five frequency bands. Then, the correlations between the network measures and RT were evaluated in each band separately. The present results showed that increased overall functional connectivity in alpha and gamma frequency bands was correlated with a longer RT. Furthermore, shorter RT was correlated with a shorter characteristic path length in the gamma band. This result suggested that human RTs were likely to be related to the efficiency of the brain integrating information across distributed brain regions. The results also showed that a longer RT was related to an increased gamma clustering coefficient and decreased small-world-ness. These results provided further evidence of the association between the resting-state functional brain network and cognitive function.

Functional embedding predicts the variability of neural activity

Neural activity is irregular and unpredictable, yet little is known about why this is the case and how this property relates to the functional architecture of the brain. Here we show that the variability of a region’s activity systematically varies according to its topological role in functional networks. We recorded the resting-state electroencephalogram (EEG) and constructed undirected graphs of functional networks. We measured the centrality of each node in terms of the number of connections it makes (degree), the ease with which the node can be reached from other nodes in the network (efficiency) and the tendency of the node to occupy a position on the shortest paths between other pairs of nodes in the network (betweenness). As a proxy for variability, we estimated the information content of neural activity using multiscale entropy analysis. We found that the rate at which information was generated was largely predicted by centrality. Namely, nodes with greater degree, betweenness, and efficiency were more likely to have high information content, while peripheral nodes had relatively low information content. These results suggest that the variability of regional activity reflects functional embedding.

Population rate coding in recurrent neuronal networks with unreliable synapses

Neuron transmits spikes to postsynaptic neurons through synapses. Experimental observations indicated that the communication between neurons is unreliable. However most modelling and computational studies considered deterministic synaptic interaction model. In this paper, we investigate the population rate coding in an all-to-all coupled recurrent neuronal network consisting of both excitatory and inhibitory neurons connected with unreliable synapses. We use a stochastic on-off process to model the unreliable synaptic transmission. We find that synapses with suitable successful transmission probability can enhance the encoding performance in the case of weak noise; while in the case of strong noise, the synaptic interactions reduce the encoding performance. We also show that several important synaptic parameters, such as the excitatory synaptic strength, the relative strength of inhibitory and excitatory synapses, as well as the synaptic time constant, have significant effects on the performance of the population rate coding. Further simulations indicate that the encoding dynamics of our considered network cannot be simply determined by the average amount of received neurotransmitter for each neuron in a time instant. Moreover, we compare our results with those obtained in the corresponding random neuronal networks. Our numerical results demonstrate that the network randomness has the similar qualitative effect as the synaptic unreliability but not completely equivalent in quantity.

Does sleep restore the topology of functional brain networks?

Previous studies have shown that healthy anatomical as well as functional brain networks have small-world properties and become less optimal with brain disease. During sleep, the functional brain network becomes more small-world-like. Here we test the hypothesis that the functional brain network during wakefulness becomes less optimal after sleep deprivation (SD). Electroencephalography (EEG) was recorded five times a day after a night of SD and after a night of normal sleep in eight young healthy subjects, both during eyes-closed and eyes-open resting state. Overall synchronization was determined with the synchronization likelihood (SL) and the phase lag index (PLI). From these coupling strength matrices the normalized clustering coefficient C (a measurement of local clustering) and path length L (a measurement of global integration) were computed. Both measures were normalized by dividing them by their corresponding C-s and L-s values of random control networks. SD reduced alpha band C/C-s and L/L-s and theta band C/C-s during eyes-closed resting state. In contrast, SD increased gamma-band C/C-s and L/L-s during eyes-open resting state. Functional relevance of these changes in network properties was suggested by their association with sleep deprivation-induced performance deficits on a sustained attention simple reaction time task. The findings indicate that SD results in a more random network of alpha-coupling and a more ordered network of gamma-coupling. The present study shows that SD induces frequency-specific changes in the functional network topology of the brain, supporting the idea that sleep plays a role in the maintenance of an optimal functional network.

Hierarchical organization of brain functional networks during visual tasks

The functional network of the brain is known to demonstrate modular structure over different hierarchical scales. In this paper, we systematically investigated the hierarchical modular organizations of the brain functional networks that are derived from the extent of phase synchronization among high-resolution EEG time series during a visual task. In particular, we compare the modular structure of the functional network from EEG channels with that of the anatomical parcellation of the brain cortex. Our results show that the modular architectures of brain functional networks correspond well to those from the anatomical structures over different levels of hierarchy. Most importantly, we find that the consistency between the modular structures of the functional network and the anatomical network becomes more pronounced in terms of vision, sensory, vision-temporal, motor cortices during the visual task, which implies that the strong modularity in these areas forms the functional basis for the visual task. The structure-function relationship further reveals that the phase synchronization of EEG time series in the same anatomical group is much stronger than that of EEG time series from different anatomical groups during the task and that the hierarchical organization of functional brain network may be a consequence of functional segmentation of the brain cortex.

Disrupted brain connectivity networks in drug-naive, first-episode major depressive disorder

BACKGROUND

Neuroimaging studies have shown that major depressive disorder (MDD) is accompanied by structural and functional abnormalities in specific brain regions and connections; yet, little is known about alterations of the topological organization of whole-brain networks in MDD patients.

METHODS

Thirty drug-naive, first-episode MDD patients and 63 healthy control subjects underwent a resting-state functional magnetic resonance imaging scan. The whole-brain functional networks were constructed by thresholding partial correlation matrices of 90 brain regions, and their topological properties (e.g., small-world, efficiency, and nodal centrality) were analyzed using graph theory-based approaches. Nonparametric permutation tests were further used for group comparisons of topological metrics.

RESULTS

Both the MDD and control groups showed small-world architecture in brain functional networks, suggesting a balance between functional segregation and integration. However, compared with control subjects, the MDD patients showed altered quantitative values in the global properties, characterized by lower path length and higher global efficiency, implying a shift toward randomization in their brain networks. The MDD patients exhibited increased nodal centralities, predominately in the caudate nucleus and default-mode regions, including the hippocampus, inferior parietal, medial frontal, and parietal regions, and reduced nodal centralities in the occipital, frontal (orbital part), and temporal regions. The altered nodal centralities in the left hippocampus and the left caudate nucleus were correlated with disease duration and severity.

CONCLUSIONS

These results suggest that depressive disorder is associated with disruptions in the topological organization of functional brain networks and that this disruption may contribute to disturbances in mood and cognition in MDD patients.

Brain graphs: graphical models of the human brain connectome

Brain graphs provide a relatively simple and increasingly popular way of modeling the human brain connectome, using graph theory to abstractly define a nervous system as a set of nodes (denoting anatomical regions or recording electrodes) and interconnecting edges (denoting structural or functional connections). Topological and geometrical properties of these graphs can be measured and compared to random graphs and to graphs derived from other neuroscience data or other (nonneural) complex systems. Both structural and functional human brain graphs have consistently demonstrated key topological properties such as small-worldness, modularity, and heterogeneous degree distributions. Brain graphs are also physically embedded so as to nearly minimize wiring cost, a key geometric property. Here we offer a conceptual review and methodological guide to graphical analysis of human neuroimaging data, with an emphasis on some of the key assumptions, issues, and trade-offs facing the investigator.

On the Influence of Amplitude on the Connectivity between Phases

In recent studies, functional connectivities have been reported to display characteristics of complex networks that have been suggested to concur with those of the underlying structural, i.e., anatomical, networks. Do functional networks always agree with structural ones? In all generality, this question can be answered with "no": for instance, a fully synchronized state would imply isotropic homogeneous functional connections irrespective of the "real" underlying structure. A proper inference of structure from function and vice versa requires more than a sole focus on phase synchronization. We show that functional connectivity critically depends on amplitude variations, which implies that, in general, phase patterns should be analyzed in conjunction with the corresponding amplitude. We discuss this issue by comparing the phase synchronization patterns of interconnected Wilson-Cowan models vis-à-vis Kuramoto networks of phase oscillators. For the interconnected Wilson-Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators' amplitudes. In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics. Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large.

Robust emergence of small-world structure in networks of spiking neurons

Spontaneous activity in biological neural networks shows patterns of dynamic synchronization. We propose that these patterns support the formation of a small-world structure-network connectivity optimal for distributed information processing. We present numerical simulations with connected Hindmarsh-Rose neurons in which, starting from random connection distributions, small-world networks evolve as a result of applying an adaptive rewiring rule. The rule connects pairs of neurons that tend fire in synchrony, and disconnects ones that fail to synchronize. Repeated application of the rule leads to small-world structures. This mechanism is robustly observed for bursting and irregular firing regimes.

Fast and robust image segmentation by small-world neural oscillator networks

Inspired by the temporal correlation theory of brain functions, researchers have presented a number of neural oscillator networks to implement visual scene segmentation problems. Recently, it is shown that many biological neural networks are typical small-world networks. In this paper, we propose and investigate two small-world models derived from the well-known LEGION (locally excitatory and globally inhibitory oscillator network) model. To form a small-world network, we add a proper proportion of unidirectional shortcuts (random long-range connections) to the original LEGION model. With local connections and shortcuts, the neural oscillators can not only communicate with neighbors but also exchange phase information with remote partners. Model 1 introduces excitatory shortcuts to enhance the synchronization within an oscillator group representing the same object. Model 2 goes further to replace the global inhibitor with a sparse set of inhibitory shortcuts. Simulation results indicate that the proposed small-world models could achieve synchronization faster than the original LEGION model and are more likely to bind disconnected image regions belonging together. In addition, we argue that these two models are more biologically plausible.

Brain Hodotopy: From Esoteric Concept to Practical Surgical Applications

BACKGROUND:

The traditional neurosurgical approach to cerebral lesions is based on the classic view of a rigid brain organization in fixed “eloquent” areas. However, this method is brought into discussion by the conceptual and methodological advances in neurosciences that provide a more dynamic representation of the anatomo-functional distribution of the human central nervous system (CNS).

OBJECTIVE AND METHODS:

We review the relevant literature concerning the main features of the modern CNS representation and their implications in neurosurgical practice.

RESULTS:

The CNS is an integrated, wide, plastic network made up of cortical functional epicenters, “topic organization,” connected by both short-local and large-scale white matter fibers, ie, “hodological organization.” According to this model, called hodotopic, brain function results from parallel streams of information dynamically modulated within an interactive, multimodal, and widely distributed circuit. The application of this framework, which can be studied by combining preoperative, intraoperative, and postoperative mapping techniques, enables the neurosurgeon exploration of the individual anatomo-functional architecture, including neurocognitive and emotional aspects. Thus, it is possible to adapt the surgical approach specifically to each patient and to each lesion according to the individual organization. Several experiences demonstrate the possibility of removing regions traditionally considered inoperable without inducing permanent deficits and the potential use of these areas as a safe passage to deeper territories.

CONCLUSION:

We advocate the more systematic integration of a hodotopical view of the CNS to improve the surgical indications and planning for brain lesions, with the goal of optimizing both the extent of resection and functional outcome.

Functional connectivity hubs in the human brain

Brain networks appear to have few and well localized regions with high functional connectivity density (hubs) for fast integration of neural processing, and their dysfunction could contribute to neuropsychiatric diseases. However the variability in the distribution of these brain hubs is unknown due in part to the overwhelming computational demands associated to their localization. Recently we developed a fast algorithm to map the local functional connectivity density (lFCD). Here we extend our method to map the global density (gFDC) taking advantage of parallel computing. We mapped the gFCD in the brain of 1031 subjects from the 1000 Functional Connectomes project and show that the strongest hubs are located in regions of the default mode network (DMN) and in sensory cortices, whereas subcortical regions exhibited the weakest hubs. The strongest hubs were consistently located in ventral precuneus/cingulate gyrus (previously identified by other analytical methods including lFCD) and in primary visual cortex (BA 17/18), which highlights their centrality to resting connectivity networks. In contrast and after rescaling, hubs in prefrontal regions had lower gFCD than lFCD, which suggests that their local functional connectivity (as opposed to long-range connectivity) prevails in the resting state. The power scaling of the probability distribution of gFCD hubs (as for lFCD) was consistent across research centers further corroborating the "scale-free" topology of brain networks. Within and between-subject variability for gFCD were twice than that for lFCD (20% vs. 12% and 84% vs. 34%, respectively) suggesting that gFCD is more sensitive to individual differences in functional connectivity.

Functional connectivity hubs in the human brain

Brain networks appear to have few and well localized regions with high functional connectivity density (hubs) for fast integration of neural processing, and their dysfunction could contribute to neuropsychiatric diseases. However the variability in the distribution of these brain hubs is unknown due in part to the overwhelming computational demands associated to their localization. Recently we developed a fast algorithm to map the local functional connectivity density (lFCD). Here we extend our method to map the global density (gFDC) taking advantage of parallel computing. We mapped the gFCD in the brain of 1031 subjects from the 1000 Functional Connectomes project and show that the strongest hubs are located in regions of the default mode network (DMN) and in sensory cortices, whereas subcortical regions exhibited the weakest hubs. The strongest hubs were consistently located in ventral precuneus/cingulate gyrus (previously identified by other analytical methods including lFCD) and in primary visual cortex (BA 17/18), which highlights their centrality to resting connectivity networks. In contrast and after rescaling, hubs in prefrontal regions had lower gFCD than lFCD, which suggests that their local functional connectivity (as opposed to long-range connectivity) prevails in the resting state. The power scaling of the probability distribution of gFCD hubs (as for lFCD) was consistent across research centers further corroborating the "scale-free" topology of brain networks. Within and between-subject variability for gFCD were twice than that for lFCD (20% vs. 12% and 84% vs. 34%, respectively) suggesting that gFCD is more sensitive to individual differences in functional connectivity.

Functional brain network efficiency predicts intelligence

The neuronal causes of individual differences in mental abilities such as intelligence are complex and profoundly important. Understanding these abilities has the potential to facilitate their enhancement. The purpose of this study was to identify the functional brain network characteristics and their relation to psychometric intelligence. In particular, we examined whether the functional network exhibits efficient small-world network attributes (high clustering and short path length) and whether these small-world network parameters are associated with intellectual performance. High-density resting state electroencephalography (EEG) was recorded in 74 healthy subjects to analyze graph-theoretical functional network characteristics at an intracortical level. Ravens advanced progressive matrices were used to assess intelligence. We found that the clustering coefficient and path length of the functional network are strongly related to intelligence. Thus, the more intelligent the subjects are the more the functional brain network resembles a small-world network. We further identified the parietal cortex as a main hub of this resting state network as indicated by increased degree centrality that is associated with higher intelligence. Taken together, this is the first study that substantiates the neural efficiency hypothesis as well as the Parieto-Frontal Integration Theory (P-FIT) of intelligence in the context of functional brain network characteristics. These theories are currently the most established intelligence theories in neuroscience. Our findings revealed robust evidence of an efficiently organized resting state functional brain network for highly productive cognitions.

Sparse brain network recovery under compressed sensing

Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the small- n large- p situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l(1)-norm penalty, also known as the least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity. LASSO is a well-known decoding algorithm in the compressed sensing (CS). The CS theory states that LASSO can reconstruct the exact sparse signal even from a small set of noisy measurements. We briefly show that the penalized linear regression for partial correlation estimation is related to CS. It opens a new possibility that the proposed framework can be used for a sparse brain network recovery. As an illustration, we construct sparse brain networks of 97 regions of interest (ROIs) obtained from FDG-PET imaging data for the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. As validation, we check the network reproducibilities by leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.