Adaptive reconfiguration of fractal small-world human brain functional networks

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.

Age-related changes in topological organization of structural brain networks in healthy individuals

The aim of this study was to examine structural brain networks using regional gray matter volume, as well as to investigate changes in small-world and modular organization with normal aging. We constructed structural brain networks composed of 90 regions in young, middle, and old age groups. We randomly selected 350 healthy subjects for each group from a Japanese magnetic resonance image database. Structural brain networks in three age groups showed economical small-world properties, providing high global and local efficiency for parallel information processing at low connection cost. The small-world efficiency and node betweenness varied significantly and revealed a U- or inverted U-curve model tendency among three age groups. Results also demonstrated that structural brain networks exhibited a modular organization in which the connections between regions are much denser within modules than between them. The modular organization of structural brain networks was similar between the young and middle age groups, but quite different from the old group. In particular, the old group showed a notable decrease in the connector ratio and the intermodule connections. Combining the results of small-world efficiency, node betweenness and modular organization, we concluded that the brain network changed slightly, developing into a more distributed organization from young to middle age. The organization eventually altered greatly, shifting to a more localized organization in old age. Our findings provided quantitative insights into topological principles of structural brain networks and changes related to normal aging.

Structural connectivity allows for multi-threading during rest: the structure of the cortex leads to efficient alternation between resting state exploratory behavior and default mode processing

Despite the absence of stimulation or task conditions the cortex exhibits highly structured spatio-temporal activity patterns. These patterns are known as resting state networks (RSNs) and emerge as low-frequency fluctuations (<0.1 Hz) observed in the fMRI signal of human subjects during rest. We are interested in the relationship between structural connectivity of the cortex and the fluctuations exhibited during resting conditions. We are especially interested in the effect of degree of connectivity on resting state dynamics as the default mode network (DMN) is highly connected. We find in experimental resting fMRI data that the DMN is the functional network that is most frequently active and for the longest time. In large-scale computational simulations of the cortex based on the corresponding underlying DTI/DSI based neuroanatomical connectivity matrix, we additionally find a strong correlation between the mean degree of functional networks and the proportion of time they are active. By artificially modifying different types of neuroanatomical connectivity matrices in the model, we were able to demonstrate that only models based on structural connectivity containing hubs give rise to this relationship. We conclude that, during rest, the cortex alternates efficiently between explorations of its externally oriented functional repertoire and internally oriented processing as a consequence of the DMN's high degree of connectivity.

Structure-function relationship of working memory activity with hippocampal and prefrontal cortex volumes

A rapidly increasing number of studies are quantifying the system-level network architecture of the human brain based on structural-to-structural and functional-to-functional relationships. However, a largely unexplored area is the nature and existence of "cross-modal" structural-functional relationships, in which, for example, the volume (or other morphological property) of one brain region is related to the functional response to a given task either in that same brain region, or another brain region. The present study investigated whether the gray matter volume of a selected group of structures (superior, middle, and inferior frontal gyri, thalamus, and hippocampus) was correlated with the fMRI response to a working memory task, within a mask of regions previously identified as involved with working memory. The subjects included individuals with schizophrenia, their siblings, and healthy controls (n = 154 total). Using rigorous permutation testing to define the null distribution, we found that the volume of the superior and middle frontal gyri was correlated with working memory activity within clusters in the intraparietal sulcus (i.e., dorsal parietal cortex) and that the volume of the hippocampus was correlated with working memory activity within clusters in the dorsal anterior cingulate cortex and left inferior frontal gyrus. However, we did not find evidence that the identified structure-function relationships differed between subject groups. These results show that long-distance structural-functional relationships exist within the human brain. The study of such cross-modal relationships represents an additional approach for studying systems-level interregional brain networks.

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.

Emergent criticality in complex turing B-type atomic switch networks

Recent advances in the neuromorphic operation of atomic switches as individual synapse-like devices demonstrate the ability to process information with both short-term and long-term memorization in a single two terminal junction. Here it is shown that atomic switches can be self-assembled within a highly interconnected network of silver nanowires similar in structure to Turing’s “B-Type unorganized machine”, originally proposed as a randomly connected network of NAND logic gates. In these experimental embodiments,complex networks of coupled atomic switches exhibit emergent criticality similar in nature to previously reported electrical activity of biological brains and neuron assemblies. Rapid fluctuations in electrical conductance display metastability and power law scaling of temporal correlation lengths that are attributed to dynamic reorganization of the interconnected electro-ionic network resulting from induced non-equilibrium thermodynamic instabilities. These collective properties indicate a potential utility for realtime,multi-input processing of distributed sensory data through reservoir computation. We propose these highly coupled, nonlinear electronic networks as an implementable hardware-based platform toward the creation of physically intelligent machines.

Using large-scale neural models to interpret connectivity measures of cortico-cortical dynamics at millisecond temporal resolution

Over the last two decades numerous functional imaging studies have shown that higher order cognitive functions are crucially dependent on the formation of distributed, large-scale neuronal assemblies (neurocognitive networks), often for very short durations. This has fueled the development of a vast number of functional connectivity measures that attempt to capture the spatiotemporal evolution of neurocognitive networks. Unfortunately, interpreting the neural basis of goal directed behavior using connectivity measures on neuroimaging data are highly dependent on the assumptions underlying the development of the measure, the nature of the task, and the modality of the neuroimaging technique that was used. This paper has two main purposes. The first is to provide an overview of some of the different measures of functional/effective connectivity that deal with high temporal resolution neuroimaging data. We will include some results that come from a recent approach that we have developed to identify the formation and extinction of task-specific, large-scale neuronal assemblies from electrophysiological recordings at a ms-by-ms temporal resolution. The second purpose of this paper is to indicate how to partially validate the interpretations drawn from this (or any other) connectivity technique by using simulated data from large-scale, neurobiologically realistic models. Specifically, we applied our recently developed method to realistic simulations of MEG data during a delayed match-to-sample (DMS) task condition and a passive viewing of stimuli condition using a large-scale neural model of the ventral visual processing pathway. Simulated MEG data using simple head models were generated from sources placed in V1, V4, IT, and prefrontal cortex (PFC) for the passive viewing condition. The results show how closely the conclusions obtained from the functional connectivity method match with what actually occurred at the neuronal network level.

Distributed processing; distributed functions?

After more than twenty years busily mapping the human brain, what have we learned from neuroimaging? This review (coda) considers this question from the point of view of structure-function relationships and the two cornerstones of functional neuroimaging; functional segregation and integration. Despite remarkable advances and insights into the brain's functional architecture, the earliest and simplest challenge in human brain mapping remains unresolved: We do not have a principled way to map brain function onto its structure in a way that speaks directly to cognitive neuroscience. Having said this, there are distinct clues about how this might be done: First, there is a growing appreciation of the role of functional integration in the distributed nature of neuronal processing. Second, there is an emerging interest in data-driven cognitive ontologies, i.e., that are internally consistent with functional anatomy. We will focus this review on the growing momentum in the fields of functional connectivity and distributed brain responses and consider this in the light of meta-analyses that use very large data sets to disclose large-scale structure-function mappings in the human brain.

The organization of strong links in complex networks

Many complex systems reveal a small-world topology, which allows simultaneously local and global efficiency in the interaction between system constituents. Here, we report the results of a comprehensive study that investigates the relation between the clustering properties in such small-world systems and the strength of interactions between its constituents, quantified by the link weight. For brain, gene, social and language networks, we find a local integrative weight organization in which strong links preferentially occur between nodes with overlapping neighbourhoods; we relate this to global robustness of the clustering to removal of the weakest links. Furthermore, we identify local learning rules that establish integrative networks and improve network traffic in response to past traffic failures. Our findings identify a general organization for complex systems that strikes a balance between efficient local and global communication in their strong interactions, while allowing for robust, exploratory development of weak interactions.

Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory

It is shown how to compute effective and functional connection matrices (eCMs and fCMs) from anatomical CMs (aCMs) and corresponding strength-of-connection matrices (sCMs) using propagator methods in which neural interactions play the role of scatterings. This analysis demonstrates how network effects dress the bare propagators (the sCMs) to yield effective propagators (the eCMs) that can be used to compute the covariances customarily used to define fCMs. The results incorporate excitatory and inhibitory connections, multiple structures and populations, asymmetries, time delays, and measurement effects. They can also be postprocessed in the same manner as experimental measurements for direct comparison with data and thereby give insights into the role of coarse-graining, thresholding, and other effects in determining the structure of CMs. The spatiotemporal results show how to generalize CMs to include time delays and how natural network modes give rise to long-range coherence at resonant frequencies. The results are demonstrated using tractable analytic cases via neural field theory of cortical and corticothalamic systems. These also demonstrate close connections between the structure of CMs and proximity to critical points of the system, highlight the importance of indirect links between brain regions and raise the possibility of imaging specific levels of indirect connectivity. Aside from the results presented explicitly here, the expression of the connections among aCMs, sCMs, eCMs, and fCMs in terms of propagators opens the way for propagator theory to be further applied to analysis of connectivity.

Fast reconfiguration of high-frequency brain networks in response to surprising changes in auditory input

How do human brain networks react to dynamic changes in the sensory environment? We measured rapid changes in brain network organization in response to brief, discrete, salient auditory stimuli. We estimated network topology and distance parameters in the immediate central response period, <1 s following auditory presentation of standard tones interspersed with occasional deviant tones in a mismatch-negativity (MMN) paradigm, using magnetoencephalography (MEG) to measure synchronization of high-frequency (gamma band; 33-64 Hz) oscillations in healthy volunteers. We found that global small-world parameters of the networks were conserved between the standard and deviant stimuli. However, surprising or unexpected auditory changes were associated with local changes in clustering of connections between temporal and frontal cortical areas and with increased interlobar, long-distance synchronization during the 120- to 250-ms epoch (coinciding with the MMN-evoked response). Network analysis of human MEG data can resolve fast local topological reconfiguration and more long-range synchronization of high-frequency networks as a systems-level representation of the brain's immediate response to salient stimuli in the dynamically changing sensory environment.

How reliable are the functional connectivity networks of MEG in resting states?

We investigated the reliability of nodal network metrics of functional connectivity (FC) networks of magnetoencephalography (MEG) covering the whole brain at the sensor level in the eyes-closed (EC) and eyes-open (EO) resting states. Mutual information (MI) was employed as a measure of FC between sensors in theta, alpha, beta, and gamma frequency bands of MEG signals. MI matrices were assessed with three nodal network metrics, i.e., nodal degree (Dnodal), nodal efficiency (Enodal), and betweenness centrality (normBC). Intraclass correlation (ICC) values were calculated as a measure of reliability. We observed that the test-retest reliabilities of the resting states ranged from a poor to good level depending on the bands and metrics used for defining the nodal centrality. The dominant alpha-band FC network changes were the salient features of the state-related FC changes. The FC networks in the EO resting state showed greater reliability when assessed by Dnodal (maximum mean ICC = 0.655) and Enodal (maximum mean ICC = 0.604) metrics. The gamma-band FC network was less reliable than the theta, alpha, and beta networks across the nodal network metrics. However, the sensor-wise ICC values for the nodal centrality metrics were not uniformly distributed, that is, some sensors had high reliability. This study provides a sense of how the nodal centralities of the human resting state MEG are distributed at the sensor level and how reliable they are. It also provides a fundamental scientific background for continued examination of the resting state of human MEG.

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.

COHERENT STATES, FRACTALS AND BRAIN WAVES

I show that a functional representation of self-similarity (as the one occurring in fractals) is provided by squeezed coherent states. In this way, the dissipative model of brain is shown to account for the self-similarity in brain background activity suggested by power-law distributions of power spectral densities of electrocorticograms. I also briefly discuss the action-perception cycle in the dissipative model with reference to intentionality in terms of trajectories in the memory state space.

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.

Frequency-dependent functional connectivity within resting-state networks: an atlas-based MEG beamformer solution

The brain consists of functional units with more-or-less specific information processing capabilities, yet cognitive functions require the co-ordinated activity of these spatially separated units. Magnetoencephalography (MEG) has the temporal resolution to capture these frequency-dependent interactions, although, due to volume conduction and field spread, spurious estimates may be obtained when functional connectivity is estimated on the basis of the extra-cranial recordings directly. Connectivity estimates on the basis of reconstructed sources may similarly be affected by biases introduced by the source reconstruction approach.

Here we propose an analysis framework to reliably determine functional connectivity that is based around two main ideas: (i) functional connectivity is computed for a set of atlas-based ROIs in anatomical space that covers almost the entire brain, aiding the interpretation of MEG functional connectivity/network studies, as well as the comparison with other modalities; (ii) volume conduction and similar bias effects are removed by using a functional connectivity estimator that is insensitive to these effects, namely the Phase Lag Index (PLI).

Our analysis approach was applied to eyes-closed resting-state MEG data for thirteen healthy participants. We first demonstrate that functional connectivity estimates based on phase coherence, even at the source-level, are biased due to the effects of volume conduction and field spread. In contrast, functional connectivity estimates based on PLI are not affected by these biases. We then looked at mean PLI, or weighted degree, over areas and subjects and found significant mean connectivity in three (alpha, beta, gamma) of the five (including theta and delta) classical frequency bands tested. These frequency-band dependent patterns of resting-state functional connectivity were distinctive; with the alpha and beta band connectivity confined to posterior and sensorimotor areas respectively, and with a generally more dispersed pattern for the gamma band. Generally, these patterns corresponded closely to patterns of relative source power, suggesting that the most active brain regions are also the ones that are most-densely connected.

Our results reveal for the first time, using an analysis framework that enables the reliable characterisation of resting-state dynamics in the human brain, how resting-state networks of functionally connected regions vary in a frequency-dependent manner across the cortex.

Altered resting state complexity in schizophrenia

The complexity of the human brain's activity and connectivity varies over temporal scales and is altered in disease states such as schizophrenia. Using a multi-level analysis of spontaneous low-frequency fMRI data stretching from the activity of individual brain regions to the coordinated connectivity pattern of the whole brain, we investigate the role of brain signal complexity in schizophrenia. Specifically, we quantitatively characterize the univariate wavelet entropy of regional activity, the bivariate pairwise functional connectivity between regions, and the multivariate network organization of connectivity patterns. Our results indicate that univariate measures of complexity are less sensitive to disease state than higher level bivariate and multivariate measures. While wavelet entropy is unaffected by disease state, the magnitude of pairwise functional connectivity is significantly decreased in schizophrenia and the variance is increased. Furthermore, by considering the network structure as a function of correlation strength, we find that network organization specifically of weak connections is strongly correlated with attention, memory, and negative symptom scores and displays potential as a clinical biomarker, providing up to 75% classification accuracy and 85% sensitivity. We also develop a general statistical framework for the testing of group differences in network properties, which is broadly applicable to studies where changes in network organization are crucial to the understanding of brain function.

Inferring network connectivity by delayed feedback control

We suggest a control based approach to topology estimation of networks with N elements. This method first drives the network to steady states by a delayed feedback control; then performs structural perturbations for shifting the steady states M times; and finally infers the connection topology from the steady states' shifts by matrix inverse algorithm (M = N) or l(1)-norm convex optimization strategy applicable to estimate the topology of sparse networks from M << N perturbations. We discuss as well some aspects important for applications, such as the topology reconstruction quality and error sources, advantages and disadvantages of the suggested method, and the influence of (control) perturbations, inhomegenity, sparsity, coupling functions, and measurement noise. Some examples of networks with Chua's oscillators are presented to illustrate the reliability of the suggested technique.

Input-rate modulation of γ oscillations is sensitive to network topology, delays and short-term plasticity

Simulated networks of excitatory and inhibitory neurons have previously been shown to reproduce critical features of experimental data regarding neural coding in V1, such as a positive relationship between thalamic input spike rate and the power of gamma frequency oscillations. This effect, referred to as modulated gamma power, could represent a neural code in V1 for stimulus characteristics that affect thalamic spike rate such as contrast or intensity. The simulated network's assumptions included homogeneous random connectivity, equal synaptic delays after spike arrival, and constant synaptic efficacies. Plausible alternative assumptions include small world connectivity, a wide distribution of axonal propagation delays, and short term synaptic plasticity, and here we assess the individual impact of each of these on the model's success in reproducing modulated gamma power. First, we developed several alternative algorithms for simulating directed networks with clustered connectivity and balanced excitation and inhibition. We found that modulated gamma power was absent in all small-world networks that had a relatively low abundance of reciprocal connectivity, which suggests that such motifs are present in V1 cortical networks at levels at least equal to those found in random networks. We also found in a different network type that the balance of excitation and inhibition could be destroyed when the network was in the small-world regime. Given all neurons had identical in-degrees, this result suggests that balance relies on motif distributions as well as mean connectivity. Second, altering the distribution of axonal delays had little effect, but increasing the mean delay led to a secondary gamma modulation at harmonics of the main peak, and since this is not observed experimentally, it suggests a mean delay in V1 networks less than 2 ms. Finally, we compared two types of excitatory synaptic plasticity, and found that modulated beta power emerged in addition to gamma power for one type, in the presence of short term depression in interneurons. This article is part of a Special Issue entitled "Neural Coding".

Functional Brain Network Characterization and Adaptivity during Task Practice in Healthy Volunteers and People with Schizophrenia

Cognitive remediation involves task practice and may improve deficits in people suffering from schizophrenia, but little is known about underlying neurophysiological mechanisms. In people with schizophrenia and controls, we used magnetoencephalography (MEG) to examine accuracy and practice-related changes in parameters indexing neural network structure and activity, to determine whether these might be useful assays of the efficacy of cognitive remediation. Two MEG recordings were acquired during performance of a tone discrimination task used to improve the acuity of auditory processing, before and after ∼2.5 h of task practice. Accuracy before practice was negatively correlated with beta-band cost efficiency, a graph theoretical measure of network organization. Synthetic aperture magnetometry was used to localize brain oscillations with high spatial accuracy; results demonstrated sound and sensorimotor modulations of the beta band in temporo-parietal regions and the sensorimotor cortex respectively. High-gamma activity also correlated with sensorimotor processing during the task, with activation of auditory regions following sound stimulation, and activation of the left sensorimotor cortex preceding the button press. High-gamma power in the left frontal cortex was also found to correlate with accuracy. Following practice, sound-induced broad-band power in the left angular gyri increased. Accuracy improved and was found to correlate with increased mutual information (MI) between sensors in temporal-parietal regions in the beta band but not global cost efficiency. Based on these results, we conclude that hours of task practice can induce meso-scale changes such as increased power in relevant brain regions as well as changes in MI that correlate with improved accuracy.

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.

Brain network analysis: separating cost from topology using cost-integration

A statistically principled way of conducting brain network analysis is still lacking. Comparison of different populations of brain networks is hard because topology is inherently dependent on wiring cost, where cost is defined as the number of edges in an unweighted graph. In this paper, we evaluate the benefits and limitations associated with using cost-integrated topological metrics. Our focus is on comparing populations of weighted undirected graphs that differ in mean association weight, using global efficiency. Our key result shows that integrating over cost is equivalent to controlling for any monotonic transformation of the weight set of a weighted graph. That is, when integrating over cost, we eliminate the differences in topology that may be due to a monotonic transformation of the weight set. Our result holds for any unweighted topological measure, and for any choice of distribution over cost levels. Cost-integration is therefore helpful in disentangling differences in cost from differences in topology. By contrast, we show that the use of the weighted version of a topological metric is generally not a valid approach to this problem. Indeed, we prove that, under weak conditions, the use of the weighted version of global efficiency is equivalent to simply comparing weighted costs. Thus, we recommend the reporting of (i) differences in weighted costs and (ii) differences in cost-integrated topological measures with respect to different distributions over the cost domain. We demonstrate the application of these techniques in a re-analysis of an fMRI working memory task. We also provide a Monte Carlo method for approximating cost-integrated topological measures. Finally, we discuss the limitations of integrating topology over cost, which may pose problems when some weights are zero, when multiplicities exist in the ranks of the weights, and when one expects subtle cost-dependent topological differences, which could be masked by cost-integration.

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.

General and specific functional connectivity disturbances in first-episode schizophrenia during cognitive control performance

BACKGROUND

Cognitive control impairments in schizophrenia are thought to arise from dysfunction of interconnected networks of brain regions, but interrogating the functional dynamics of large-scale brain networks during cognitive task performance has proved difficult. We used functional magnetic resonance imaging to generate event-related whole-brain functional connectivity networks in participants with first-episode schizophrenia and healthy control subjects performing a cognitive control task.

METHODS

Functional connectivity during cognitive control performance was assessed between each pair of 78 brain regions in 23 patients and 25 control subjects. Network properties examined were region-wise connectivity, edge-wise connectivity, global path length, clustering, small-worldness, global efficiency, and local efficiency.

RESULTS

Patients showed widespread functional connectivity deficits in a large-scale network of brain regions, which primarily affected connectivity between frontal cortex and posterior regions and occurred irrespective of task context. A more circumscribed and task-specific connectivity impairment in frontoparietal systems related to cognitive control was also apparent. Global properties of network topology in patients were relatively intact.

CONCLUSIONS

The first episode of schizophrenia is associated with a generalized connectivity impairment affecting most brain regions but that is particularly pronounced for frontal cortex. Superimposed on this generalized deficit, patients show more specific cognitive-control-related functional connectivity reductions in frontoparietal regions. These connectivity deficits occur in the context of relatively preserved global network organization.

Extracting message inter-departure time distributions from the human electroencephalogram

The complex connectivity of the cerebral cortex is a topic of much study, yet the link between structure and function is still unclear. The processing capacity and throughput of information at individual brain regions remains an open question and one that could potentially bridge these two aspects of neural organization. The rate at which information is emitted from different nodes in the network and how this output process changes under different external conditions are general questions that are not unique to neuroscience, but are of interest in multiple classes of telecommunication networks. In the present study we show how some of these questions may be addressed using tools from telecommunications research. An important system statistic for modeling and performance evaluation of distributed communication systems is the time between successive departures of units of information at each node in the network. We describe a method to extract and fully characterize the distribution of such inter-departure times from the resting-state electroencephalogram (EEG). We show that inter-departure times are well fitted by the two-parameter Gamma distribution. Moreover, they are not spatially or neurophysiologically trivial and instead are regionally specific and sensitive to the presence of sensory input. In both the eyes-closed and eyes-open conditions, inter-departure time distributions were more dispersed over posterior parietal channels, close to regions which are known to have the most dense structural connectivity. The biggest differences between the two conditions were observed at occipital sites, where inter-departure times were significantly more variable in the eyes-open condition. Together, these results suggest that message departure times are indicative of network traffic and capture a novel facet of neural activity.

The brain may be thought of as a network of regions that communicate with each other to produce emergent phenomena such as perception and cognition. Many potentially interesting aspects of brain networks, such as how information is emitted at different nodes, also tend to be of interest in various types of telecommunication systems, such as telephony. Thus, network properties that are relevant in the context of brain function may be important for telecommunication networks in general. Here we show how neural activity can be partitioned into units of information and analyzed from the perspective of a telecommunication system. We demonstrate that the inter-departure times of such units of information have very similar probability distributions across subjects and that they are sensitive both to regional variation and cognitive state. The approach we describe can be applied in a wide variety of experimental paradigms to generate novel indices of neural activity and open new avenues for network analysis of the brain.

Cognitive effort drives workspace configuration of human brain functional networks

Effortful cognitive performance is theoretically expected to depend on the formation of a global neuronal workspace. We tested specific predictions of workspace theory, using graph theoretical measures of network topology and physical distance of synchronization, in magnetoencephalographic data recorded from healthy adult volunteers (N = 13) during performance of a working memory task at several levels of difficulty. We found that greater cognitive effort caused emergence of a more globally efficient, less clustered, and less modular network configuration, with more long-distance synchronization between brain regions. This pattern of task-related workspace configuration was more salient in the β-band (16-32 Hz) and γ-band (32-63 Hz) networks, compared with both lower (α-band; 8-16 Hz) and higher (high γ-band; 63-125 Hz) frequency intervals. Workspace configuration of β-band networks was also greater in faster performing participants (with correct response latency less than the sample median) compared with slower performing participants. Processes of workspace formation and relaxation in relation to time-varying demands for cognitive effort could be visualized occurring in the course of task trials lasting <2 s. These experimental results provide support for workspace theory in terms of complex network metrics and directly demonstrate how cognitive effort breaks modularity to make human brain functional networks transiently adopt a more efficient but less economical configuration.

Abnormal functional connectivity in focal hand dystonia: mutual information analysis in EEG

The aim of the present study was to investigate functional connectivity in focal hand dystonia patients to understand the pathophysiology underlying their abnormality in movement. We recorded EEGs from 58 electrodes in 15 focal hand dystonia patients and 15 healthy volunteers during rest and a simple finger-tapping task that did not induce any dystonic symptoms. We investigated mutual information, which provides a quantitative measure of linear and nonlinear coupling, in the alpha, beta, and gamma bands. Mean mutual information of all 58 channels and mean of the channels of interest representative of regional functional connectivity over sensorimotor areas (C3, CP3, C4, CP4, FCz, and Cz) were evaluated. For both groups, we found enhanced mutual information during the task compared with the rest condition, specifically in the beta and gamma bands for mean mutual information of all channels, and in all bands for mean mutual information of channels of interest. Comparing the focal hand dystonia patients with the healthy volunteers for both rest and task, there was reduced mutual information in the beta band for both mean mutual information of all channels and mean mutual information of channels of interest. Regarding the properties of the connectivity in the beta band, we found that the majority of the mutual information differences were from linear connectivity. The abnormal beta-band functional connectivity in focal hand dystonia patients suggests deficient brain connectivity.

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.

Automated discrimination of brain pathological state attending to complex structural brain network properties: the shiverer mutant mouse case

Neuroimaging classification procedures between normal and pathological subjects are sparse and highly dependent of an expert's clinical criterion. Here, we aimed to investigate whether possible brain structural network differences in the shiverer mouse mutant, a relevant animal model of myelin related diseases, can reflect intrinsic individual brain properties that allow the automatic discrimination between the shiverer and normal subjects. Common structural networks properties between shiverer (C3Fe.SWV Mbp(shi)/Mbp(shi), n = 6) and background control (C3HeB.FeJ, n = 6) mice are estimated and compared by means of three diffusion weighted MRI (DW-MRI) fiber tractography algorithms and a graph framework. Firstly, we found that brain networks of control group are significantly more clustered, modularized, efficient and optimized than those of the shiverer group, which presented significantly increased characteristic path length. These results are in line with previous structural/functional complex brain networks analysis that have revealed topologic differences and brain network randomization associated to specific states of human brain pathology. In addition, by means of network measures spatial representations and discrimination analysis, we show that it is possible to classify with high accuracy to which group each subject belongs, providing also a probability value of being a normal or shiverer subject as an individual anatomical classifier. The obtained correct predictions (e.g., around 91.6-100%) and clear spatial subdivisions between control and shiverer mice, suggest that there might exist specific network subspaces corresponding to specific brain disorders, supporting also the point of view that complex brain network analyses constitutes promising tools in the future creation of interpretable imaging biomarkers.

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes--flexibility and selection--must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we investigate the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes--flexibility and selection--must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we investigate the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.

Understanding complexity in the human brain

Although the ultimate aim of neuroscientific enquiry is to gain an understanding of the brain and how its workings relate to the mind, the majority of current efforts are largely focused on small questions using increasingly detailed data. However, it might be possible to successfully address the larger question of mind-brain mechanisms if the cumulative findings from these neuroscientific studies are coupled with complementary approaches from physics and philosophy. The brain, we argue, can be understood as a complex system or network, in which mental states emerge from the interaction between multiple physical and functional levels. Achieving further conceptual progress will crucially depend on broad-scale discussions regarding the properties of cognition and the tools that are currently available or must be developed in order to study mind-brain mechanisms.

Reorganization of brain functional small-world networks during finger movements

A functional measure of brain organization is the efficiency of functional connectivity. The degree of functional connectivity can differ during a task compared to the rest, and to study this issue, we investigated the functional connectivity networks in healthy subjects during a simple, right-handed, sequential finger-tapping task using graph theoretic measures. EEGs were recorded from 58 channels in 15 healthy subjects at rest and during a motor task. We estimated mutual information values of wavelet coefficients to create an association matrix between EEG electrodes and produced a series of adjacency matrices or graphs, A, by thresholding with network cost. These graphs are called small-world networks, and we assessed their efficiency measures. We found economical small-world properties in brain functional connectivity networks in the alpha and beta band networks. The efficiency of the brain networks was enhanced during the task in the beta band networks, but not in the alpha band networks. A regional efficiency analysis during the task showed that the bilateral primary motor and left sensory areas showed increased nodal efficiency, Enodal, whereas decreased Enodal was found over the posterior parietal areas. The present study provides evidence for the reorganization of brain functional connectivity networks in a motor task with the greatest increase in Enodal in motor executive areas.

Large-scale cortical networks estimated from scalp EEG signals during performance of goal-directed motor tasks

The evaluation of the topological properties of brain networks is an emergent research topic, since the estimated cerebral connectivity patterns often have relatively large size and complex structure. Since a graph is a mathematical representation of a network, the use of a theoretical graph approach would describe concisely the topological features of the functional brain connectivity network estimated using neuroimaging techniques. In the present study, we analyze the changes in brain synchronization networks using high-resolution EEG signals obtained during performance of a complex goal-directed visuomotor task. Our results show that the cortical network is more stable when subjects reach the goal than when they fail by hitting an obstacle. These findings suggest the presence of a possible cerebral "marker" for motor actions that result in successful reaching of a target.

Diffusion tensor-based fast marching for modeling human brain connectivity network

Diffusion tensor imaging (DTI) is an effective modality in studying the connectivity of the brain. To eliminate possible biases caused by fiber extraction approaches due to low spatial resolution of DTI and the number of fibers obtained, the fast marching (FM) algorithm based on the whole diffusion tensor information is proposed to model and study the brain connectivity network. Our observation is that the connectivity extracted from the whole tensor field would be more robust and reliable for constructing brain connectivity network using DTI data. To construct the connectivity network, in this paper, the arrival time map and the velocity map generated by the FM algorithm are combined to define the connectivity strength among different brain regions. The conventional fiber tracking-based and the proposed tensor-based FM connectivity methods are compared, and the results indicate that the connectivity features obtained using the FM-based method agree better with the neuromorphical studies of the human brain.

Non-parametric model selection for subject-specific topological organization of resting-state functional connectivity

In recent years, graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain. Most of these networks have shown small-world topological characteristics: high efficiency in long distance communication between nodes, combined with highly interconnected local clusters of nodes. Moreover, functional studies performed at high resolutions have presented convincing evidence that resting-state functional connectivity networks exhibits (exponentially truncated) scale-free behavior. Such evidence, however, was mostly presented qualitatively, in terms of linear regressions of the degree distributions on log-log plots. Even when quantitative measures were given, these were usually limited to the r(2) correlation coefficient. However, the r(2) statistic is not an optimal estimator of explained variance, when dealing with (truncated) power-law models. Recent developments in statistics have introduced new non-parametric approaches, based on the Kolmogorov-Smirnov test, for the problem of model selection. In this work, we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest. The analysis, performed at voxel level and in a subject-specific fashion, confirmed the superiority of a truncated power-law model, showing high consistency across subjects. Moreover, the most highly connected voxels were found to be consistently part of the default mode network. Our results provide statistically sound support to the evidence previously presented in literature for a truncated power-law model of resting-state functional connectivity.

The interaction of intrinsic dynamics and network topology in determining network burst synchrony

The pre-Bötzinger complex (pre-BötC), within the mammalian respiratory brainstem, represents an ideal system for investigating the synchronization properties of complex neuronal circuits via the interaction of cell-type heterogeneity and network connectivity. In isolation, individual respiratory neurons from the pre-BötC may be tonically active, rhythmically bursting, or quiescent. Despite this intrinsic heterogeneity, coupled networks of pre-BötC neurons en bloc engage in synchronized bursting that can drive inspiratory motor neuron activation. The region's connection topology has been recently characterized and features dense clusters of cells with occasional connections between clusters. We investigate how the dynamics of individual neurons (quiescent/bursting/tonic) and the betweenness centrality of neurons' positions within the network connectivity graph interact to govern network burst synchrony, by simulating heterogeneous networks of computational model pre-BötC neurons. Furthermore, we compare the prevalence and synchrony of bursting across networks constructed with a variety of connection topologies, analyzing the same collection of heterogeneous neurons in small-world, scale-free, random, and regularly structured networks. We find that several measures of network burst synchronization are determined by interactions of network topology with the intrinsic dynamics of neurons at central network positions and by the strengths of synaptic connections between neurons. Surprisingly, despite the functional role of synchronized bursting within the pre-BötC, we find that synchronized network bursting is generally weakest when we use its specific connection topology, which leads to synchrony within clusters but poor coordination across clusters. Overall, our results highlight the relevance of interactions between topology and intrinsic dynamics in shaping the activity of networks and the concerted effects of connectivity patterns and dynamic heterogeneities.

Graph-theoretical analysis reveals disrupted small-world organization of cortical thickness correlation networks in temporal lobe epilepsy

Temporal lobe epilepsy (TLE) is the most common drug-resistant epilepsy in adults. As morphometric studies have shown widespread structural damage in TLE, this condition is often referred to as a system disorder with disrupted structural networks. Studies based on univariate statistical comparisons can only indirectly test such hypothesis. Graph theory provides a new approach to formally analyze large-scale networks. Using graph-theoretical analysis of magnetic resonance imaging-based cortical thickness correlations, we investigated the structural basis of the organization of such networks in 122 TLE patients and 47 age- and sex-matched healthy controls. Networks in patients and controls were characterized by a short path length between anatomical regions and a high degree of clustering, suggestive of a small-world topology. However, compared with controls, patients showed increased path length and clustering, altered distribution of network hubs, and higher vulnerability to targeted attacks, suggesting a reorganization of cortical thickness correlation networks. Longitudinal analysis demonstrated that network alterations intensify over time. Bootstrap simulations showed high reproducibility of network parameters across random subsamplings, indicating that altered network topology in TLE is a consistent finding. Increased network disruption was associated with unfavorable postoperative seizure outcome, implying adverse effects of epileptogenesis on large-scale network organization.

Altered small-world brain networks in temporal lobe in patients with schizophrenia performing an auditory oddball task

The functional architecture of the human brain has been extensively described in terms of complex networks characterized by efficient small-world features. Recent functional magnetic resonance imaging (fMRI) studies have found altered small-world topological properties of brain functional networks in patients with schizophrenia (SZ) during the resting state. However, little is known about the small-world properties of brain networks in the context of a task. In this study, we investigated the topological properties of human brain functional networks derived from fMRI during an auditory oddball (AOD) task. Data were obtained from 20 healthy controls and 20 SZ; A left and a right task-related network which consisted of the top activated voxels in temporal lobe of each hemisphere were analyzed separately. All voxels were detected by group independent component analysis. Connectivity of the left and right task-related networks were estimated by partial correlation analysis and thresholded to construct a set of undirected graphs. The small-worldness values were decreased in both hemispheres in SZ. In addition, SZ showed longer shortest path length and lower global efficiency only in the left task-related networks. These results suggested small-world attributes are altered during the AOD task-related networks in SZ which provided further evidences for brain dysfunction of connectivity in SZ.

Large-scale cortical functional organization and speech perception across the lifespan

Aging is accompanied by substantial changes in brain function, including functional reorganization of large-scale brain networks. Such differences in network architecture have been reported both at rest and during cognitive task performance, but an open question is whether these age-related differences show task-dependent effects or represent only task-independent changes attributable to a common factor (i.e., underlying physiological decline). To address this question, we used graph theoretic analysis to construct weighted cortical functional networks from hemodynamic (functional MRI) responses in 12 younger and 12 older adults during a speech perception task performed in both quiet and noisy listening conditions. Functional networks were constructed for each subject and listening condition based on inter-regional correlations of the fMRI signal among 66 cortical regions, and network measures of global and local efficiency were computed. Across listening conditions, older adult networks showed significantly decreased global (but not local) efficiency relative to younger adults after normalizing measures to surrogate random networks. Although listening condition produced no main effects on whole-cortex network organization, a significant age group x listening condition interaction was observed. Additionally, an exploratory analysis of regional effects uncovered age-related declines in both global and local efficiency concentrated exclusively in auditory areas (bilateral superior and middle temporal cortex), further suggestive of specificity to the speech perception tasks. Global efficiency also correlated positively with mean cortical thickness across all subjects, establishing gross cortical atrophy as a task-independent contributor to age-related differences in functional organization. Together, our findings provide evidence of age-related disruptions in cortical functional network organization during speech perception tasks, and suggest that although task-independent effects such as cortical atrophy clearly underlie age-related changes in cortical functional organization, age-related differences also demonstrate sensitivity to task domains.

Mapping the Alzheimer's brain with connectomics

Alzheimer's disease (AD) is the most common form of dementia. As an incurable, progressive, and neurodegenerative disease, it causes cognitive and memory deficits. However, the biological mechanisms underlying the disease are not thoroughly understood. In recent years, non-invasive neuroimaging and neurophysiological techniques [e.g., structural magnetic resonance imaging (MRI), diffusion MRI, functional MRI, and EEG/MEG] and graph theory based network analysis have provided a new perspective on structural and functional connectivity patterns of the human brain (i.e., the human connectome) in health and disease. Using these powerful approaches, several recent studies of patients with AD exhibited abnormal topological organization in both global and regional properties of neuronal networks, indicating that AD not only affects specific brain regions, but also alters the structural and functional associations between distinct brain regions. Specifically, disruptive organization in the whole-brain networks in AD is involved in the loss of small-world characters and the re-organization of hub distributions. These aberrant neuronal connectivity patterns were associated with cognitive deficits in patients with AD, even with genetic factors in healthy aging. These studies provide empirical evidence to support the existence of an aberrant connectome of AD. In this review we will summarize recent advances discovered in large-scale brain network studies of AD, mainly focusing on graph theoretical analysis of brain connectivity abnormalities. These studies provide novel insights into the pathophysiological mechanisms of AD and could be helpful in developing imaging biomarkers for disease diagnosis and monitoring.

Modulation of the brain's functional network architecture in the transition from wake to sleep

The transition from quiet wakeful rest to sleep represents a period over which attention to the external environment fades. Neuroimaging methodologies have provided much information on the shift in neural activity patterns in sleep, but the dynamic restructuring of human brain networks in the transitional period from wake to sleep remains poorly understood. Analysis of electrophysiological measures and functional network connectivity of these early transitional states shows subtle shifts in network architecture that are consistent with reduced external attentiveness and increased internal and self-referential processing. Further, descent to sleep is accompanied by the loss of connectivity in anterior and posterior portions of the default-mode network and more locally organized global network architecture. These data clarify the complex and dynamic nature of the transitional period between wake and sleep and suggest the need for more studies investigating the dynamics of these processes.

Reproducibility of graph metrics in FMRI networks

The reliability of graph metrics calculated in network analysis is essential to the interpretation of complex network organization. These graph metrics are used to deduce the small-world properties in networks. In this study, we investigated the test-retest reliability of graph metrics from functional magnetic resonance imaging data collected for two runs in 45 healthy older adults. Graph metrics were calculated on data for both runs and compared using intraclass correlation coefficient (ICC) statistics and Bland–Altman (BA) plots. ICC scores describe the level of absolute agreement between two measurements and provide a measure of reproducibility. For mean graph metrics, ICC scores were high for clustering coefficient (ICC = 0.86), global efficiency (ICC = 0.83), path length (ICC = 0.79), and local efficiency (ICC = 0.75); the ICC score for degree was found to be low (ICC = 0.29). ICC scores were also used to generate reproducibility maps in brain space to test voxel-wise reproducibility for unsmoothed and smoothed data. Reproducibility was uniform across the brain for global efficiency and path length, but was only high in network hubs for clustering coefficient, local efficiency, and degree. BA plots were used to test the measurement repeatability of all graph metrics. All graph metrics fell within the limits for repeatability. Together, these results suggest that with exception of degree, mean graph metrics are reproducible and suitable for clinical studies. Further exploration is warranted to better understand reproducibility across the brain on a voxel-wise basis.