The relationship between structural and functional connectivity: Graph theoretical analysis of an EEG neural mass model

Integrating spatial and temporal features for enhanced artifact removal in multi-channel EEG recordings

Objective.Various artifacts in electroencephalography (EEG) are a big hurdle to prevent brain-computer interfaces from real-life usage. Recently, deep learning-based EEG denoising methods have shown excellent performance. However, existing deep network designs inadequately leverage inter-channel relationships in processing multi-channel EEG signals. Typically, most methods process multi-channel signals in a channel-by-channel way. Considering the correlations among EEG channels during the same brain activity, this paper proposes utilizing channel relationships to enhance denoising performance.Approach.We explicitly model the inter-channel relationships using the self-attention mechanism, hypothesizing that these correlations can support and improve the denoising process. Specifically, we introduce a novel denoising network, named spatial-temporal fusion network (STFNet), which integrates stacked multi-dimension feature extractor to explicitly capture both temporal dependencies and spatial relationships.Main results.The proposed network exhibits superior denoising performance, with a 24.27% reduction in relative root mean squared error compared to other methods on a public benchmark. STFNet proves effective in cross-dataset denoising and downstream classification tasks, improving accuracy by 1.40%, while also offering fast processing on CPU.Significance.The experimental results demonstrate the importance of integrating spatial and temporal characteristics. The computational efficiency of STFNet makes it suitable for real-time applications and a potential tool for deployment in realistic environments.

Disrupted brain structural networks associated with depression and cognitive dysfunction in cerebral small vessel disease with microbleeds

Emerging evidence highlights cerebral microbleeds (CMBs) as hallmarks of cerebral small vessel disease (CSVD) underlying depression and cognitive dysfunction. This study aimed to reveal how depression and cognition-related white matter (WM) abnormalities are topologically presented, and the network-level structural disruptions associated with CMBs in CSVD. We used probabilistic diffusion tractography and graph theory to investigate brain WM network topology in CSVD patients with (n = 64, CSVD-c) and without (n = 138, CSVD-n) CMBs and 90 healthy controls. Then we evaluated the Pearson's correlations between disrupted network metrics and neuropsychological parameters. For global topology, the CSVD-c group exhibited significantly decreased global (Eglob) and local (Eloc) efficiency and increased shortest path length compared with the controls, while no significant difference was found between the CSVD-c and CSVD-n groups. For regional topology, although all groups showed highly similar hub distributions, compare with control group, the CSVD-c group exhibited significantly decreased nodal efficiency mainly in the bilateral supplementary motor area (SMA), median cingulate gyrus (DCG) and right orbital middle frontal gyrus, while the CSVD-n group showed significantly decreased nodal efficiency only in the right SMA. Notably, Eglob, Eloc and nodal efficiency of the right anterior cingulate gyrus, DCG, middle temporal gyrus and left insula showed significantly negative correlations with depression score, significantly positive correlations with Rey auditory verbal learning test and symbol digit modalities test scores in CSVD-n group, as well as significantly negative correlations with Stroop color-word test scores in CSVD-c group. The WM networks of CSVD patients are characterized by decreased global integration and local specialization, and decreased nodal efficiency highly related to depression and cognitive dysfunction in the attention, default mode network and sensorimotor regions. These findings provide new insight into the neurobiological mechanisms of CSVD and concomitant affective and cognitive disorders.

Local signal variability and functional connectivity: Sensitive measures of the excitation-inhibition ratio?

A novel network version of permutation entropy, the inverted joint permutation entropy (JPEinv), holds potential as non-invasive biomarker of abnormal excitation-inhibition (E-I) ratio in Alzheimer's disease (AD). In this computational modelling study, we test the hypotheses that this metric, and related measures of signal variability and functional connectivity, are sensitive to altered E-I ratios. The E-I ratio in each neural mass of a whole-brain computational network model was systematically varied. We evaluated whether JPEinv, local signal variability (by permutation entropy) and functional connectivity (by weighted symbolic mutual information (wsMI)) were related to E-I ratio, on whole-brain and regional level. The hub disruption index can identify regions primarily affected in terms of functional connectivity strength (or: degree) by the altered E-I ratios. Analyses were performed for a range of coupling strengths, filter and time-delay settings. On whole-brain level, higher E-I ratios were associated with higher functional connectivity (by JPEinv and wsMI) and lower local signal variability. These relationships were nonlinear and depended on the coupling strength, filter and time-delay settings. On regional level, hub-like regions showed a selective decrease in functional degree (by JPEinv and wsMI) upon a lower E-I ratio, and non-hub-like regions showed a selective increase in degree upon a higher E-I ratio. These results suggest that abnormal functional connectivity and signal variability, as previously reported in patients across the AD continuum, can inform us about altered E-I ratios.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-10003-x.

Virtual neural network-guided optimization of non-invasive brain stimulation in Alzheimer's disease

Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique with potential for counteracting disrupted brain network activity in Alzheimer's disease (AD) to improve cognition. However, the results of tDCS studies in AD have been variable due to different methodological choices such as electrode placement. To address this, a virtual brain network model of AD was used to explore tDCS optimization. We compared a large, representative set of virtual tDCS intervention setups, to identify the theoretically optimized tDCS electrode positions for restoring functional network features disrupted in AD. We simulated 20 tDCS setups using a computational dynamic network model of 78 neural masses coupled according to human structural topology. AD network damage was simulated using an activity-dependent degeneration algorithm. Current flow modeling was used to estimate tDCS-targeted cortical regions for different electrode positions, and excitability of the pyramidal neurons of the corresponding neural masses was modulated to simulate tDCS. Outcome measures were relative power spectral density (alpha bands, 8-10 Hz and 10-13 Hz), total spectral power, posterior alpha peak frequency, and connectivity measures phase lag index (PLI) and amplitude envelope correlation (AEC). Virtual tDCS performance varied, with optimized strategies improving all outcome measures, while others caused further deterioration. The best performing setup involved right parietal anodal stimulation, with a contralateral supraorbital cathode. A clear correlation between the network role of stimulated regions and tDCS success was not observed. This modeling-informed approach can guide and perhaps accelerate tDCS therapy development and enhance our understanding of tDCS effects. Follow-up studies will compare the general predictions to personalized virtual models and validate them with tDCS-magnetoencephalography (MEG) in a clinical AD patient cohort.

Tau trajectory in Alzheimer's disease: Evidence from the connectome-based computational models

Alzheimer's disease (AD) is a progressive neurodegenerative disorder with an impairment of cognition and memory. Current research on connectomics have now related changes in the network organization in AD to the patterns of accumulation and spread of amyloid and tau, providing insights into the neurobiological mechanisms of the disease. In addition, network analysis and modeling focus on particular use of graphs to provide intuition into key organizational principles of brain structure, that stipulate how neural activity propagates along structural connections. The utility of connectome-based computational models aids in early predicting, tracking the progression of biomarker-directed AD neuropathology. In this article, we present a short review of tau trajectory, the connectome changes in tau pathology, and the dependent recent connectome-based computational modelling approaches for tau spreading, reproducing pragmatic findings, and developing significant novel tau targeted therapies.

Study on the diversity of mental states and neuroplasticity of the brain during human-machine interaction

Introduction

With the increasing demand for human-machine collaboration systems, more and more attention has been paid to the influence of human factors on the performance and security of the entire system. Especially in high-risk, high-precision, and difficult special tasks (such as space station maintenance tasks, anti-terrorist EOD tasks, surgical robot teleoperation tasks, etc.), there are higher requirements for the operator's perception and cognitive level. However, as the human brain is a complex and open giant system, the perception ability and cognitive level of the human are dynamically variable, so that it will seriously affect the performance and security of the whole system.

Methods

The method proposed in this paper innovatively explained this phenomenon from two dimensions of brain space and time and attributed the dynamic changes of perception, cognitive level, and operational skills to the mental state diversity and the brain neuroplasticity. In terms of the mental state diversity, the mental states evoked paradigm and the functional brain network analysis method during work were proposed. In terms of neuroplasticity, the cognitive training intervention paradigm and the functional brain network analysis method were proposed. Twenty-six subjects participated in the mental state evoked experiment and the cognitive training intervention experiment.

Results

The results showed that (1) the mental state of the subjects during work had the characteristics of dynamic change, and due to the influence of stimulus conditions and task patterns, the mental state showed diversity. There were significant differences between functional brain networks in different mental states, the information processing efficiency and the mechanism of brain area response had changed significantly. (2) The small-world attributes of the functional brain network of the subjects before and after the cognitive training experiment were significantly different. The brain had adjusted the distribution of information flow and resources, reducing costs and increasing efficiency as a whole. It was demonstrated that the global topology of the cortical connectivity network was reconfigured and neuroplasticity was altered through cognitive training intervention.

Discussion

In summary, this paper revealed that mental state and neuroplasticity could change the information processing efficiency and the response mechanism of brain area, thus causing the change of perception, cognitive level and operational skills, which provided a theoretical basis for studying the relationship between neural information processing and behavior.

A multiscale brain network model links Alzheimer’s disease-mediated neuronal hyperactivity to large-scale oscillatory slowing

Background

Neuronal hyperexcitability and inhibitory interneuron dysfunction are frequently observed in preclinical animal models of Alzheimer’s disease (AD). This study investigates whether these microscale abnormalities explain characteristic large-scale magnetoencephalography (MEG) activity in human early-stage AD patients.

Methods

To simulate spontaneous electrophysiological activity, we used a whole-brain computational network model comprised of 78 neural masses coupled according to human structural brain topology. We modified relevant model parameters to simulate six literature-based cellular scenarios of AD and compare them to one healthy and six contrast (non-AD-like) scenarios. The parameters include excitability, postsynaptic potentials, and coupling strength of excitatory and inhibitory neuronal populations. Whole-brain spike density and spectral power analyses of the simulated data reveal mechanisms of neuronal hyperactivity that lead to oscillatory changes similar to those observed in MEG data of 18 human prodromal AD patients compared to 18 age-matched subjects with subjective cognitive decline.

Results

All but one of the AD-like scenarios showed higher spike density levels, and all but one of these scenarios had a lower peak frequency, higher spectral power in slower (theta, 4–8Hz) frequencies, and greater total power. Non-AD-like scenarios showed opposite patterns mainly, including reduced spike density and faster oscillatory activity. Human AD patients showed oscillatory slowing (i.e., higher relative power in the theta band mainly), a trend for lower peak frequency and higher total power compared to controls. Combining model and human data, the findings indicate that neuronal hyperactivity can lead to oscillatory slowing, likely due to hyperexcitation (by hyperexcitability of pyramidal neurons or greater long-range excitatory coupling) and/or disinhibition (by reduced excitability of inhibitory interneurons or weaker local inhibitory coupling strength) in early AD.

Conclusions

Using a computational brain network model, we link findings from different scales and models and support the hypothesis of early-stage neuronal hyperactivity underlying E/I imbalance and whole-brain network dysfunction in prodromal AD.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13195-022-01041-4.

Brain functional and effective connectivity based on electroencephalography recordings: A review

Functional connectivity and effective connectivity of the human brain, representing statistical dependence and directed information flow between cortical regions, significantly contribute to the study of the intrinsic brain network and its functional mechanism. Many recent studies on electroencephalography (EEG) have been focusing on modeling and estimating brain connectivity due to increasing evidence that it can help better understand various brain neurological conditions. However, there is a lack of a comprehensive updated review on studies of EEG-based brain connectivity, particularly on visualization options and associated machine learning applications, aiming to translate those techniques into useful clinical tools. This article reviews EEG-based functional and effective connectivity studies undertaken over the last few years, in terms of estimation, visualization, and applications associated with machine learning classifiers. Methods are explored and discussed from various dimensions, such as either linear or nonlinear, parametric or nonparametric, time-based, and frequency-based or time-frequency-based. Then it is followed by a novel review of brain connectivity visualization methods, grouped by Heat Map, data statistics, and Head Map, aiming to explore the variation of connectivity across different brain regions. Finally, the current challenges of related research and a roadmap for future related research are presented.

Principles and open questions in functional brain network reconstruction

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

Infant functional networks are modulated by state of consciousness and circadian rhythm

Functional connectivity networks are valuable tools for studying development, cognition, and disease in the infant brain. In adults, such networks are modulated by the state of consciousness and the circadian rhythm; however, it is unknown if infant brain networks exhibit similar variation, given the unique temporal properties of infant sleep and circadian patterning. To address this, we analyzed functional connectivity networks calculated from long-term EEG recordings (average duration 20.8 hr) from 19 healthy infants. Networks were subject specific, as intersubject correlations between weighted adjacency matrices were low. However, within individual subjects, both sleep and wake networks were stable over time, with stronger functional connectivity during sleep than wakefulness. Principal component analysis revealed the presence of two dominant networks; visual sleep scoring confirmed that these corresponded to sleep and wakefulness. Lastly, we found that network strength, degree, clustering coefficient, and path length significantly varied with time of day, when measured in either wakefulness or sleep at the group level. Together, these results suggest that modulation of healthy functional networks occurs over ∼24 hr and is robust and repeatable. Accounting for such temporal periodicities may improve the physiological interpretation and use of functional connectivity analysis to investigate brain function in health and disease.

On the Validity of Neural Mass Models

Modeling the dynamics of neural masses is a common approach in the study of neural populations. Various models have been proven useful to describe a plenitude of empirical observations including self-sustained local oscillations and patterns of distant synchronization. We discuss the extent to which mass models really resemble the mean dynamics of a neural population. In particular, we question the validity of neural mass models if the population under study comprises a mixture of excitatory and inhibitory neurons that are densely (inter-)connected. Starting from a network of noisy leaky integrate-and-fire neurons, we formulated two different population dynamics that both fall into the category of seminal Freeman neural mass models. The derivations contained several mean-field assumptions and time scale separation(s) between membrane and synapse dynamics. Our comparison of these neural mass models with the averaged dynamics of the population reveals bounds in the fraction of excitatory/inhibitory neuron as well as overall network degree for a mass model to provide adequate estimates. For substantial parameter ranges, our models fail to mimic the neural network's dynamics proper, be that in de-synchronized or in (high-frequency) synchronized states. Only around the onset of low-frequency synchronization our models provide proper estimates of the mean potential dynamics. While this shows their potential for, e.g., studying resting state dynamics obtained by encephalography with focus on the transition region, we must accept that predicting the more general dynamic outcome of a neural network via its mass dynamics requires great care.

Using structural connectivity to augment community structure in EEG functional connectivity

Recently, EEG recording techniques and source analysis have improved, making it feasible to tap into fast network dynamics. Yet, analyzing whole-cortex EEG signals in source space is not standard, partly because EEG suffers from volume conduction: Functional connectivity (FC) reflecting genuine functional relationships is impossible to disentangle from spurious FC introduced by volume conduction. Here, we investigate the relationship between white matter structural connectivity (SC) and large-scale network structure encoded in EEG-FC. We start by confirming that FC (power envelope correlations) is predicted by SC beyond the impact of Euclidean distance, in line with the assumption that SC mediates genuine FC. We then use information from white matter structural connectivity in order to smooth the EEG signal in the space spanned by graphs derived from SC. Thereby, FC between nearby, structurally connected brain regions increases while FC between nonconnected regions remains unchanged, resulting in an increase in genuine, SC-mediated FC. We analyze the induced changes in FC, assessing the resemblance between EEG-FC and volume-conduction- free fMRI-FC, and find that smoothing increases resemblance in terms of overall correlation and community structure. This result suggests that our method boosts genuine FC, an outcome that is of interest for many EEG network neuroscience questions.

Small World Index in Default Mode Network Predicts Progression from Mild Cognitive Impairment to Dementia

Aim of this study was to explore the EEG functional connectivity in amnesic mild cognitive impairments (MCI) subjects with multidomain impairment in order to characterize the Default Mode Network (DMN) in converted MCI (cMCI), which converted to Alzheimer’s disease (AD), compared to stable MCI (sMCI) subjects. A total of 59 MCI subjects were recruited and divided -after appropriate follow-up- into cMCI or sMCI. They were further divided in MCI with linguistic domain (LD) impairment and in MCI with executive domain (ED) impairment. Small World (SW) index was measured as index of balance between integration and segregation brain processes. SW, computed restricting to nodes of DMN regions for all frequency bands, evaluated how they differ between MCI subgroups assessed through clinical and neuropsychological four-years follow-up. In addition, SW evaluated how this pattern differs between MCI with LD and MCI with ED. Results showed that SW index significantly decreased in gamma band in cMCI compared to sMCI. In cMCI with LD impairment, the SW index significantly decreased in delta band, while in cMCI with ED impairment the SW index decreased in delta and gamma bands and increased in alpha1 band. We propose that the DMN functional alterations in cognitive impairment could reflect an abnormal flow of brain information processing during resting state possibly associated to a status of pre-dementia.

Synaptic Scaling Improves the Stability of Neural Mass Models Capable of Simulating Brain Plasticity

Neural mass models offer a way of studying the development and behavior of large-scale brain networks through computer simulations. Such simulations are currently mainly research tools, but as they improve, they could soon play a role in understanding, predicting, and optimizing patient treatments, particularly in relation to effects and outcomes of brain injury. To bring us closer to this goal, we took an existing state-of-the-art neural mass model capable of simulating connection growth through simulated plasticity processes. We identified and addressed some of the model's limitations by implementing biologically plausible mechanisms. The main limitation of the original model was its instability, which we addressed by incorporating a representation of the mechanism of synaptic scaling and examining the effects of optimizing parameters in the model. We show that the updated model retains all the merits of the original model, while being more stable and capable of generating networks that are in several aspects similar to those found in real brains.

Brain synchronizability, a false friend

Synchronization plays a fundamental role in healthy cognitive and motor function. However, how synchronization depends on the interplay between local dynamics, coupling and topology and how prone to synchronization a network is, given its topological organization, are still poorly understood issues. To investigate the synchronizability of both anatomical and functional brain networks various studies resorted to the Master Stability Function (MSF) formalism, an elegant tool which allows analysing the stability of synchronous states in a dynamical system consisting of many coupled oscillators. Here, we argue that brain dynamics does not fulfil the formal criteria under which synchronizability is usually quantified and, perhaps more importantly, this measure refers to a global dynamical condition that never holds in the brain (not even in the most pathological conditions), and therefore no neurophysiological conclusions should be drawn based on it. We discuss the meaning of synchronizability and its applicability to neuroscience and propose alternative ways to quantify brain networks synchronization.

On the Influence of Structural Connectivity on the Correlation Patterns and Network Synchronization

Since brain structural connectivity is the foundation of its functionality, in order to understand brain abilities, studying the relation between structural and functional connectivity is essential. Several approaches have been applied to measure the role of the structural connectivity in the emergent correlation/synchronization patterns. In this study, we investigates the cross-correlation and synchronization sensitivity to coupling strength between neural regions for different topological networks. We model the neural populations by a neural mass model that express an oscillatory dynamic. The results highlight that coupling between neural ensembles leads to various cross-correlation patterns and local synchrony even on an ordered network. Moreover, as the network departs from an ordered organization to a small-world architecture, correlation patterns, and synchronization dynamics change. Interestingly, at a certain range of the synaptic strength, by fixing the structural conditions, different organized patterns are seen at the different input signals. This variety switches to a bifurcation region by increasing the synaptic strength. We show that topological variations is a major factor of synchronization behavior and lead to alterations in correlated local clusters. We found the coupling strength (between cortical areas) to be especially important at conversions of correlation and synchronization states. Since correlation patterns generate functional connections and transitions of functional connectivity have been related to cognitive operations, these diverse correlation patterns may be considered as different dynamical states corresponding to various cognitive tasks.

A Comparison of Evoked and Non-evoked Functional Networks

The growing interest in brain networks to study the brain's function in cognition and diseases has produced an increase in methods to extract these networks. Typically, each method yields a different network. Therefore, one may ask what the resulting networks represent. To address this issue we consider electrocorticography (ECoG) data where we compare three methods. We derive networks from on-going ECoG data using two traditional methods: cross-correlation (CC) and Granger causality (GC). Next, connectivity is probed actively using single pulse electrical stimulation (SPES). We compare the overlap in connectivity between these three methods as well as their ability to reveal well-known anatomical connections in the language circuit. We find that strong connections in the CC network form more or less a subset of the SPES network. GC and SPES are related more weakly, although GC connections coincide more frequently with SPES connections compared to non-existing SPES connections. Connectivity between the two major hubs in the language circuit, Broca's and Wernicke's area, is only found in SPES networks. Our results are of interest for the use of patient-specific networks obtained from ECoG. In epilepsy research, such networks form the basis for methods that predict the effect of epilepsy surgery. For this application SPES networks are interesting as they disclose more physiological connections compared to CC and GC networks.

Scale-freeness or partial synchronization in neural mass phase oscillator networks: Pick one of two?

Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both.

Combined structural and functional patterns discriminating upper limb motor disability in multiple sclerosis using multivariate approaches

A structural or functional pattern of neuroplasticity that could systematically discriminate between people with impaired and preserved motor performance could help us to understand the brain networks contributing to preservation or compensation of behavior in multiple sclerosis (MS). This study aimed to (1) investigate whether a machine learning-based technique could accurately classify MS participants into groups defined by upper extremity function (i.e. motor function preserved (MP) vs. motor function impaired (MI)) based on their regional grey matter measures (GMM, cortical thickness and deep grey matter volume) and inter-regional functional connection (FC), (2) investigate which features (GMM, FC, or GMM + FC) could classify groups more accurately, and (3) identify the multivariate patterns of GMM and FCs that are most discriminative between MP and MI participants, and between each of these groups and the healthy controls (HCs). With 26 MP, 25 MI, and 21 HCs (age and sex matched) underwent T1-weighted and resting-state functional MRI at 3 T, we applied support vector machine (SVM) based classification to learn discriminant functions indicating regions in which GMM or between which FCs were most discriminative between groups. This study demonstrates that there exist structural and FC patterns sufficient for correct classification of upper limb motor ability of people with MS. The classifier with GMM + FC features yielded the highest accuracy of 85.61 % (p < 0.001) to distinguish between the MS groups using leave-one-out cross-validation. It suggests that a machine-learning approach combining structural and functional features is useful for identifying the specific neural substrates that are necessary and sufficient to preserve motor function among people with MS.

Functional network stability and average minimal distance - A framework to rapidly assess dynamics of functional network representations

BACKGROUND

Recent advances in neurophysiological recording techniques have increased both the spatial and temporal resolution of data. New methodologies are required that can handle large data sets in an efficient manner as well as to make quantifiable, and realistic, predictions about the global modality of the brain from under-sampled recordings.

NEW METHOD

To rectify both problems, we first propose an analytical modification to an existing functional connectivity algorithm, Average Minimal Distance (AMD), to rapidly capture functional network connectivity. We then complement this algorithm by introducing Functional Network Stability (FuNS), a metric that can be used to quickly assess the global network dynamic changes over time, without being constrained by the activities of a specific set of neurons.

RESULTS

We systematically test the performance of AMD and FuNS (1) on artificial spiking data with different statistical characteristics, (2) from spiking data generated using a neural network model, and (3) using in vivo data recorded from mouse hippocampus during fear learning. Our results show that AMD and FuNS are able to monitor the change in network dynamics during memory consolidation.

COMPARISON WITH OTHER METHODS

AMD outperforms traditional bootstrapping and cross-correlation (CC) methods in both significance and computation time. Simultaneously, FuNS provides a reliable way to establish a link between local structural network changes, global dynamics of network-wide representations activity, and behavior.

CONCLUSIONS

The AMD-FuNS framework should be universally useful in linking long time-scale, global network dynamics and cognitive behavior.

Remodeling Functional Connectivity in Multiple Sclerosis: A Challenging Therapeutic Approach

Neurons in the central nervous system are organized in functional units interconnected to form complex networks. Acute and chronic brain damage disrupts brain connectivity producing neurological signs and/or symptoms. In several neurological diseases, particularly in Multiple Sclerosis (MS), structural imaging studies cannot always demonstrate a clear association between lesion site and clinical disability, originating the "clinico-radiological paradox." The discrepancy between structural damage and disability can be explained by a complex network perspective. Both brain networks architecture and synaptic plasticity may play important roles in modulating brain networks efficiency after brain damage. In particular, long-term potentiation (LTP) may occur in surviving neurons to compensate network disconnection. In MS, inflammatory cytokines dramatically interfere with synaptic transmission and plasticity. Importantly, in addition to acute and chronic structural damage, inflammation could contribute to reduce brain networks efficiency in MS leading to worse clinical recovery after a relapse and worse disease progression. These evidence suggest that removing inflammation should represent the main therapeutic target in MS; moreover, as synaptic plasticity is particularly altered by inflammation, specific strategies aimed at promoting LTP mechanisms could be effective for enhancing clinical recovery. Modulation of plasticity with different non-invasive brain stimulation (NIBS) techniques has been used to promote recovery of MS symptoms. Better knowledge of features inducing brain disconnection in MS is crucial to design specific strategies to promote recovery and use NIBS with an increasingly tailored approach.

Altering neuronal excitability to preserve network connectivity in a computational model of Alzheimer's disease

Neuronal hyperactivity and hyperexcitability of the cerebral cortex and hippocampal region is an increasingly observed phenomenon in preclinical Alzheimer's disease (AD). In later stages, oscillatory slowing and loss of functional connectivity are ubiquitous. Recent evidence suggests that neuronal dynamics have a prominent role in AD pathophysiology, making it a potentially interesting therapeutic target. However, although neuronal activity can be manipulated by various (non-)pharmacological means, intervening in a highly integrated system that depends on complex dynamics can produce counterintuitive and adverse effects. Computational dynamic network modeling may serve as a virtual test ground for developing effective interventions. To explore this approach, a previously introduced large-scale neural mass network with human brain topology was used to simulate the temporal evolution of AD-like, activity-dependent network degeneration. In addition, six defense strategies that either enhanced or diminished neuronal excitability were tested against the degeneration process, targeting excitatory and inhibitory neurons combined or separately. Outcome measures described oscillatory, connectivity and topological features of the damaged networks. Over time, the various interventions produced diverse large-scale network effects. Contrary to our hypothesis, the most successful strategy was a selective stimulation of all excitatory neurons in the network; it substantially prolonged the preservation of network integrity. The results of this study imply that functional network damage due to pathological neuronal activity can be opposed by targeted adjustment of neuronal excitability levels. The present approach may help to explore therapeutic effects aimed at preserving or restoring neuronal network integrity and contribute to better-informed intervention choices in future clinical trials in AD.

Novel measure of the weigh distribution balance on the brain network: graph complexity applied to schizophrenia

The aim of this study was to assess brain complexity dynamics in schizophrenia (SCH) patients during an auditory oddball task. For this task, we applied a novel graph measure based on the balance of the node weights distribution. Previous studies applied complexity parameters that were strongly dependent on network topology. This could bias the results, as well as making correction techniques, such as surrogating process, necessary. In the present study, we applied a novel graph complexity measure derived from the information theory: Shannon Graph Complexity (SGC). Complexity patterns from electroencephalographic recordings of 20 healthy controls and 20 SCH patients during an auditory oddball task were analyzed. Results showed a significantly more pronounced decrease of SGC for controls than for SCH patients during the cognitive task. These findings suggest an important change in the brain configuration towards a more balanced network, mainly in the connections related to long-range interactions. Since these changes are significantly more pronounced in controls, a deficit in the neural network reorganization can be associated with SCH. In addition, an accuracy of 72.5% was obtained using a receiver operating characteristic curve with a leave-one-out cross-validation procedure. The independence of network topology has been demonstrated by the novel complexity measure proposed in this study, therefore, it complements traditional graph measures as a means to characterize brain networks.

Deriving theoretical phase locking values of a coupled cortico-thalamic neural mass model using center manifold reduction

Cognitive functions such as sensory processing and memory processes lead to phase synchronization in the electroencephalogram or local field potential between different brain regions. There are a lot of computational researches deriving phase locking values (PLVs), which are an index of phase synchronization intensity, from neural models. However, these researches derive PLVs numerically. To the best of our knowledge, there have been no reports on the derivation of a theoretical PLV. In this study, we propose an analytical method for deriving theoretical PLVs from a cortico-thalamic neural mass model described by a delay differential equation. First, the model for generating neural signals is transformed into a normal form of the Hopf bifurcation using center manifold reduction. Second, the normal form is transformed into a phase model that is suitable for analyzing synchronization phenomena. Third, the Fokker-Planck equation of the phase model is derived and the phase difference distribution is obtained. Finally, the PLVs are calculated from the stationary distribution of the phase difference. The validity of the proposed method is confirmed via numerical simulations. Furthermore, we apply the proposed method to a working memory process, and discuss the neurophysiological basis behind the phase synchronization phenomenon. The results demonstrate the importance of decreasing the intensity of independent noise during the working memory process. The proposed method will be of great use in various experimental studies and simulations relevant to phase synchronization, because it enables the effect of neurophysiological changes on PLVs to be analyzed from a mathematical perspective.

Relationship between brain stem volume and aggression in children diagnosed with autism spectrum disorder

BACKGROUND

Aggressive behaviors are common in individuals diagnosed with autism spectrum disorder (ASD) and may be phenotypic indicators of different subtypes within ASD. In current research literature for non-ASD samples, aggression has been linked to several brain structures associated with emotion and behavioral control. However, few if any studies exist investigating brain volume differences in individuals with ASD who have comorbid aggression as indicated by standardized diagnostic and behavioral measures.

METHOD

We examined neuroimaging data from individuals rigorously diagnosed with ASD versus typically developing (TD) controls. We began with data from brain volume regions of interest (ROI) taken from previous literature on aggression including the brainstem, amygdala, orbitofrontal cortex, anterior cingulate cortex, and dorsolateral prefrontal cortex. We defined aggression status using the Irritability subscale of the Aberrant Behavior Checklist and used lasso logistic regression to select among these predictor variables. Brainstem volume was the only variable shown to be a predictor of aggression status.

RESULTS

We found that smaller brainstem volumes are associated with higher odds of being in the high aggression group.

CONCLUSIONS

Understanding brain differences in individuals with ASD who engage in aggressive behavior from those with ASD who do not can inform treatment approaches. Future research should investigate brainstem structure and function in ASD to identify possible mechanisms related to arousal and aggression.

Comparison of Local Information Indices Applied in Resting State Functional Brain Network Connectivity Prediction

Anatomical distance has been widely used to predict functional connectivity because of the potential relationship between structural connectivity and functional connectivity. The basic implicit assumption of this method is “distance penalization.” But studies have shown that one-parameter model (anatomical distance) cannot account for the small-worldness, modularity, and degree distribution of normal human brain functional networks. Two local information indices–common neighbor (CN) and preferential attachment index (PA), are introduced into the prediction model as another parameter to emulate many key topological of brain functional networks in the previous study. In addition to these two indices, many other local information indices can be chosen for investigation. Different indices evaluate local similarity from different perspectives. Currently, we still have no idea about how to select local information indices to achieve higher predicted accuracy of functional connectivity. Here, seven local information indices are chosen, including CN, hub depressed index (HDI), hub promoted index (HPI), Leicht-Holme-Newman index (LHN-I), Sørensen index (SI), PA, and resource allocation index (RA). Statistical analyses were performed on eight network topological properties to evaluate the predictions. Analysis shows that different prediction models have different performances in terms of simulating topological properties and most of the predicted network properties are close to the real data. There are four topological properties whose average relative error is less than 5%, including characteristic path length, clustering coefficient, global efficiency, and local efficiency. CN model shows the most accurate predictions. Statistical analysis reveals that five properties within the CN-predicted network do not differ significantly from the real data (P > 0.05, false-discovery rate method corrected for seven comparisons). PA model shows the worst prediction performance which was first applied in models of growth networks. Our results suggest that PA is not suitable for predicting connectivity in a small-world network. Furthermore, in order to evaluate the predictions rapidly, prediction power was proposed as an evaluation metric. The current study compares the predictions of functional connectivity with seven local information indices and provides a reference of method selection for construction of prediction models.

Controllability Analysis of the Neural Mass Model with Dynamic Parameters

The development of control technology for the brain is of potential significance to the prevention and treatment of neuropsychiatric disorders and the improvement of humans' mental health. A controllability analysis of the brain is necessary to ensure the feasibility of the brain control. In this letter, we investigate the influences of dynamical parameters on the controllability in the neural mass model by using controllability indices as quantitative indicators. The indices are obtained by computing Lie brackets and condition numbers of the system model. We show how controllability changes with important parameters of our dynamical (neuronal) model. Our results suggest that the underlying dynamical parameters have certain ranges with better controllability. We hope it can play potential roles in therapy for brain nervous disorder disease.

Brain networks under attack: robustness properties and the impact of lesions

A growing number of studies approach the brain as a complex network, the so-called 'connectome'. Adopting this framework, we examine what types or extent of damage the brain can withstand-referred to as network 'robustness'-and conversely, which kind of distortions can be expected after brain lesions. To this end, we review computational lesion studies and empirical studies investigating network alterations in brain tumour, stroke and traumatic brain injury patients. Common to these three types of focal injury is that there is no unequivocal relationship between the anatomical lesion site and its topological characteristics within the brain network. Furthermore, large-scale network effects of these focal lesions are compared to those of a widely studied multifocal neurodegenerative disorder, Alzheimer's disease, in which central parts of the connectome are preferentially affected. Results indicate that human brain networks are remarkably resilient to different types of lesions, compared to other types of complex networks such as random or scale-free networks. However, lesion effects have been found to depend critically on the topological position of the lesion. In particular, damage to network hub regions-and especially those connecting different subnetworks-was found to cause the largest disturbances in network organization. Regardless of lesion location, evidence from empirical and computational lesion studies shows that lesions cause significant alterations in global network topology. The direction of these changes though remains to be elucidated. Encouragingly, both empirical and modelling studies have indicated that after focal damage, the connectome carries the potential to recover at least to some extent, with normalization of graph metrics being related to improved behavioural and cognitive functioning. To conclude, we highlight possible clinical implications of these findings, point out several methodological limitations that pertain to the study of brain diseases adopting a network approach, and provide suggestions for future research.

Analysis of spontaneous EEG activity in Alzheimer's disease using cross-sample entropy and graph theory

The aim of this pilot study was to analyze spontaneous electroencephalography (EEG) activity in Alzheimer's disease (AD) by means of Cross-Sample Entropy (Cross-SampEn) and two local measures derived from graph theory: clustering coefficient (CC) and characteristic path length (PL). Five minutes of EEG activity were recorded from 37 patients with dementia due to AD and 29 elderly controls. Our results showed that Cross-SampEn values were lower in the AD group than in the control one for all the interactions among EEG channels. This finding indicates that EEG activity in AD is characterized by a lower statistical dissimilarity among channels. Significant differences were found mainly for fronto-central interactions (p <; 0.01, permutation test). Additionally, the application of graph theory measures revealed diverse neural network changes, i.e. lower CC and higher PL values in AD group, leading to a less efficient brain organization. This study suggests the usefulness of our approach to provide further insights into the underlying brain dynamics associated with AD.

Shared Brain Connectivity Issues, Symptoms, and Comorbidities in Autism Spectrum Disorder, Attention Deficit/Hyperactivity Disorder, and Tourette Syndrome

The prevalence of neurodevelopmental disorders, including autism spectrum disorder (ASD), attention deficit/hyperactivity disorder (ADHD), and Tourette syndrome (TS), has increased over the past two decades. Currently, about one in six children in the United States is diagnosed as having a neurodevelopmental disorder. Evidence suggests that ASD, ADHD, and TS have similar neuropathology, which includes long-range underconnectivity and short-range overconnectivity. They also share similar symptomatology with considerable overlap in their core and associated symptoms and a frequent overlap in their comorbid conditions. Consequently, it is apparent that ASD, ADHD, and TS diagnoses belong to a broader spectrum of neurodevelopmental illness. Biologically, long-range underconnectivity and short-range overconnectivity are plausibly related to neuronal insult (e.g., neurotoxicity, neuroinflammation, excitotoxicity, sustained microglial activation, proinflammatory cytokines, toxic exposure, and oxidative stress). Therefore, these disorders may a share a similar etiology. The main purpose of this review is to critically examine the evidence that ASD, ADHD, and TS belong to a broader spectrum of neurodevelopmental illness, an abnormal connectivity spectrum disorder, which results from neural long-range underconnectivity and short-range overconnectivity. The review also discusses the possible reasons for these neuropathological connectivity findings. In addition, this review examines the role and issue of axonal injury and regeneration in order to better understand the neuropathophysiological interplay between short- and long-range axons in connectivity issues.

Statistical detection of EEG synchrony using empirical bayesian inference

There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.

A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model

We introduce a new formalism for evaluating analytically the cross-correlation structure of a finite-size firing-rate network with recurrent connections. The analysis performs a first-order perturbative expansion of neural activity equations that include three different sources of randomness: the background noise of the membrane potentials, their initial conditions, and the distribution of the recurrent synaptic weights. This allows the analytical quantification of the relationship between anatomical and functional connectivity, i.e. of how the synaptic connections determine the statistical dependencies at any order among different neurons. The technique we develop is general, but for simplicity and clarity we demonstrate its efficacy by applying it to the case of synaptic connections described by regular graphs. The analytical equations so obtained reveal previously unknown behaviors of recurrent firing-rate networks, especially on how correlations are modified by the external input, by the finite size of the network, by the density of the anatomical connections and by correlation in sources of randomness. In particular, we show that a strong input can make the neurons almost independent, suggesting that functional connectivity does not depend only on the static anatomical connectivity, but also on the external inputs. Moreover we prove that in general it is not possible to find a mean-field description à la Sznitman of the network, if the anatomical connections are too sparse or our three sources of variability are correlated. To conclude, we show a very counterintuitive phenomenon, which we call stochastic synchronization, through which neurons become almost perfectly correlated even if the sources of randomness are independent. Due to its ability to quantify how activity of individual neurons and the correlation among them depends upon external inputs, the formalism introduced here can serve as a basis for exploring analytically the computational capability of population codes expressed by recurrent neural networks.

Cross-frequency transfer in a stochastically driven mesoscopic neuronal model

The brain is known to operate in multiple coexisting frequency bands. Increasing experimental evidence suggests that interactions between those distinct bands play a crucial role in brain processes, but the dynamical mechanisms underlying this cross-frequency coupling are still under investigation. Two approaches have been proposed to address this issue. In the first one distinct nonlinear oscillators representing the brain rhythms involved are coupled actively (bidirectionally), whereas in the second one the oscillators are coupled unidirectionally and thus the driving between them is passive. Here we elaborate the latter approach by implementing a stochastically driven network of coupled neural mass models that operate in the alpha range. This model exhibits a broadband power spectrum with 1/f^b form, similar to those observed experimentally. Our results show that such a model is able to reproduce recent experimental observations on the effect of slow rocking on the alpha activity associated with sleep. This suggests that passive driving can account for cross-frequency transfer in the brain, as a result of the complex nonlinear dynamics of its underlying oscillators.

The relation between structural and functional connectivity patterns in complex brain networks

OBJECTIVE

An important problem in systems neuroscience is the relation between complex structural and functional brain networks. Here we use simulations of a simple dynamic process based upon the susceptible-infected-susceptible (SIS) model of infection dynamics on an empirical structural brain network to investigate the extent to which the functional interactions between any two brain areas depend upon (i) the presence of a direct structural connection; and (ii) the degree product of the two areas in the structural network.

METHODS

For the structural brain network, we used a 78×78 matrix representing known anatomical connections between brain regions at the level of the AAL atlas (Gong et al., 2009). On this structural network we simulated brain dynamics using a model derived from the study of epidemic processes on networks. Analogous to the SIS model, each vertex/brain region could be in one of two states (inactive/active) with two parameters β and δ determining the transition probabilities. First, the phase transition between the fully inactive and partially active state was investigated as a function of β and δ. Second, the statistical interdependencies between time series of node states were determined (close to and far away from the critical state) with two measures: (i) functional connectivity based upon the correlation coefficient of integrated activation time series; and (ii) effective connectivity based upon conditional co-activation at different time intervals.

RESULTS

We find a phase transition between an inactive and a partially active state for a critical ratio τ=β/δ of the transition rates in agreement with the theory of SIS models. Slightly above the critical threshold, node activity increases with degree, also in line with epidemic theory. The functional, but not the effective connectivity matrix closely resembled the underlying structural matrix. Both functional connectivity and, to a lesser extent, effective connectivity were higher for connected as compared to disconnected (i.e.: not directly connected) nodes. Effective connectivity scaled with the degree product. For functional connectivity, a weaker scaling relation was only observed for disconnected node pairs. For random networks with the same degree distribution as the original structural network, similar patterns were seen, but the scaling exponent was significantly decreased especially for effective connectivity.

CONCLUSIONS

Even with a very simple dynamical model it can be shown that functional relations between nodes of a realistic anatomical network display clear patterns if the system is studied near the critical transition. The detailed nature of these patterns depends on the properties of the functional or effective connectivity measure that is used. While the strength of functional interactions between any two nodes clearly depends upon the presence or absence of a direct connection, this study has shown that the degree product of the nodes also plays a large role in explaining interaction strength, especially for disconnected nodes and in combination with an effective connectivity measure. The influence of degree product on node interaction strength probably reflects the presence of large numbers of indirect connections.

Mesoscopic segregation of excitation and inhibition in a brain network model

Neurons in the brain are known to operate under a careful balance of excitation and inhibition, which maintains neural microcircuits within the proper operational range. How this balance is played out at the mesoscopic level of neuronal populations is, however, less clear. In order to address this issue, here we use a coupled neural mass model to study computationally the dynamics of a network of cortical macrocolumns operating in a partially synchronized, irregular regime. The topology of the network is heterogeneous, with a few of the nodes acting as connector hubs while the rest are relatively poorly connected. Our results show that in this type of mesoscopic network excitation and inhibition spontaneously segregate, with some columns acting mainly in an excitatory manner while some others have predominantly an inhibitory effect on their neighbors. We characterize the conditions under which this segregation arises, and relate the character of the different columns with their topological role within the network. In particular, we show that the connector hubs are preferentially inhibitory, the more so the larger the node's connectivity. These results suggest a potential mesoscale organization of the excitation-inhibition balance in brain networks.

EEG functional connectivity is partially predicted by underlying white matter connectivity

Over the past decade, networks have become a leading model to illustrate both the anatomical relationships (structural networks) and the coupling of dynamic physiology (functional networks) linking separate brain regions. The relationship between these two levels of description remains incompletely understood and an area of intense research interest. In particular, it is unclear how cortical currents relate to underlying brain structural architecture. In addition, although theory suggests that brain communication is highly frequency dependent, how structural connections influence overlying functional connectivity in different frequency bands has not been previously explored. Here we relate functional networks inferred from statistical associations between source imaging of EEG activity and underlying cortico-cortical structural brain connectivity determined by probabilistic white matter tractography. We evaluate spontaneous fluctuating cortical brain activity over a long time scale (minutes) and relate inferred functional networks to underlying structural connectivity for broadband signals, as well as in seven distinct frequency bands. We find that cortical networks derived from source EEG estimates partially reflect both direct and indirect underlying white matter connectivity in all frequency bands evaluated. In addition, we find that when structural support is absent, functional connectivity is significantly reduced for high frequency bands compared to low frequency bands. The association between cortical currents and underlying white matter connectivity highlights the obligatory interdependence of functional and structural networks in the human brain. The increased dependence on structural support for the coupling of higher frequency brain rhythms provides new evidence for how underlying anatomy directly shapes emergent brain dynamics at fast time scales.

Decreased Functional Connectivity and Disturbed Directionality of Information Flow in the Electroencephalography of Intensive Care Unit Patients with Delirium after Cardiac Surgery

Background:

In this article, the authors explore functional connectivity and network topology in electroencephalography recordings of patients with delirium after cardiac surgery, aiming to improve the understanding of the pathophysiology and phenomenology of delirium. The authors hypothesize that disturbances in attention and consciousness in delirium may be related to alterations in functional neural interactions.

Methods:

Electroencephalography recordings were obtained in postcardiac surgery patients with delirium (N = 25) and without delirium (N = 24). The authors analyzed unbiased functional connectivity of electroencephalography time series using the phase lag index, directed phase lag index, and functional brain network topology using graph analysis.

Results:

The mean phase lag index was lower in the α band (8 to 13 Hz) in patients with delirium (median, 0.120; interquartile range, 0.113 to 0.138) than in patients without delirium (median, 0.140; interquartile range, 0.129 to 0.168; P &lt; 0.01). Network topology in delirium patients was characterized by lower normalized weighted shortest path lengths in the α band (t = −2.65; P = 0.01). δ Band–directed phase lag index was lower in anterior regions and higher in central regions in delirium patients than in nondelirium patients (F = 4.53; P = 0.04, and F = 7.65; P &lt; 0.01, respectively).

Conclusions:

Loss of α band functional connectivity, decreased path length, and increased δ band connectivity directed to frontal regions characterize the electroencephalography during delirium after cardiac surgery. These findings may explain why information processing is disturbed in delirium.

Synchronization and stochastic resonance of the small-world neural network based on the CPG

According to biological knowledge, the central nervous system controls the central pattern generator (CPG) to drive the locomotion. The brain is a complex system consisting of different functions and different interconnections. The topological properties of the brain display features of small-world network. The synchronization and stochastic resonance have important roles in neural information transmission and processing. In order to study the synchronization and stochastic resonance of the brain based on the CPG, we establish the model which shows the relationship between the small-world neural network (SWNN) and the CPG. We analyze the synchronization of the SWNN when the amplitude and frequency of the CPG are changed and the effects on the CPG when the SWNN's parameters are changed. And we also study the stochastic resonance on the SWNN. The main findings include: (1) When the CPG is added into the SWNN, there exists parameters space of the CPG and the SWNN, which can make the synchronization of the SWNN optimum. (2) There exists an optimal noise level at which the resonance factor Q gets its peak value. And the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the noise intensity. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.

Neural network modeling of EEG patterns in encephalopathy

The EEG is an accessible tool for detecting encephalopathy, which usually manifests as delirium and sometimes as coma. Several disturbances have been described in the EEG of patients with encephalopathy, including diffuse slowing and periodic discharges. The pathophysiology of these EEG alterations, however, is poorly understood. This article shows that simulating activity of large populations of neurons, using neural mass models and neural network analysis, may increase our understanding of EEG disturbances in encephalopathy. We provide a brief introduction on the concepts of neural mass modeling and graph theoretical network analysis, and insights from this approach in previous work on neurologic disease, with a focus on encephalopathy. Finally, we speculate how anatomically coupled neural mass modeling combined with network analysis could provide new insights in pathophysiology of encephalopathy.

Structural degree predicts functional network connectivity: a multimodal resting-state fMRI and MEG study

Communication between neuronal populations in the human brain is characterized by complex functional interactions across time and space. Recent studies have demonstrated that these functional interactions depend on the underlying structural connections at an aggregate level. Multiple imaging modalities can be used to investigate the relation between the structural connections between brain regions and their functional interactions at multiple timescales. We investigated if consistent modality-independent functional interactions take place between brain regions, and whether these can be accounted for by underlying structural properties. We used functional MRI (fMRI) and magnetoencephalography (MEG) recordings from a population of healthy adults together with a previously described structural network. A high overlap in resting-state functional networks was found in fMRI and especially alpha band MEG recordings. This overlap was characterized by a strongly interconnected functional core network in temporo-posterior brain regions. Anatomically realistically coupled neural mass models revealed that this strongly interconnected functional network emerges near the threshold for global synchronization. Most importantly, this functional core network could be explained by a trade-off between the product of the degrees of structurally-connected regions and the Euclidean distance between them. For both fMRI and MEG, the product of the degrees of connected regions was the most important predictor for functional network connectivity. Therefore, irrespective of the modality, these results indicate that a functional core network in the human brain is especially shaped by communication between high degree nodes of the structural network.

Network diffusion accurately models the relationship between structural and functional brain connectivity networks

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain's long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways.

Potential use and challenges of functional connectivity mapping in intractable epilepsy

This review focuses on the use of resting-state functional magnetic resonance imaging data to assess functional connectivity in the human brain and its application in intractable epilepsy. This approach has the potential to predict outcomes for a given surgical procedure based on the pre-surgical functional organization of the brain. Functional connectivity can also identify cortical regions that are organized differently in epilepsy patients either as a direct function of the disease or through indirect compensatory responses. Functional connectivity mapping may help identify epileptogenic tissue, whether this is a single focal location or a network of seizure-generating tissues. This review covers the basics of connectivity analysis and discusses particular issues associated with analyzing such data. These issues include how to define nodes, as well as differences between connectivity analyses of individual nodes, groups of nodes, and whole-brain assessment at the voxel level. The need for arbitrary thresholds in some connectivity analyses is discussed and a solution to this problem is reviewed. Overall, functional connectivity analysis is becoming an important tool for assessing functional brain organization in epilepsy.

Activity dependent degeneration explains hub vulnerability in Alzheimer's disease

Brain connectivity studies have revealed that highly connected 'hub' regions are particularly vulnerable to Alzheimer pathology: they show marked amyloid-β deposition at an early stage. Recently, excessive local neuronal activity has been shown to increase amyloid deposition. In this study we use a computational model to test the hypothesis that hub regions possess the highest level of activity and that hub vulnerability in Alzheimer's disease is due to this feature. Cortical brain regions were modeled as neural masses, each describing the average activity (spike density and spectral power) of a large number of interconnected excitatory and inhibitory neurons. The large-scale network consisted of 78 neural masses, connected according to a human DTI-based cortical topology. Spike density and spectral power were positively correlated with structural and functional node degrees, confirming the high activity of hub regions, also offering a possible explanation for high resting state Default Mode Network activity. 'Activity dependent degeneration' (ADD) was simulated by lowering synaptic strength as a function of the spike density of the main excitatory neurons, and compared to random degeneration. Resulting structural and functional network changes were assessed with graph theoretical analysis. Effects of ADD included oscillatory slowing, loss of spectral power and long-range synchronization, hub vulnerability, and disrupted functional network topology. Observed transient increases in spike density and functional connectivity match reports in Mild Cognitive Impairment (MCI) patients, and may not be compensatory but pathological. In conclusion, the assumption of excessive neuronal activity leading to degeneration provides a possible explanation for hub vulnerability in Alzheimer's disease, supported by the observed relation between connectivity and activity and the reproduction of several neurophysiologic hallmarks. The insight that neuronal activity might play a causal role in Alzheimer's disease can have implications for early detection and interventional strategies.

Emergence of stable functional networks in long-term human electroencephalography

Functional connectivity networks have become a central focus in neuroscience because they reveal key higher-dimensional features of normal and abnormal nervous system physiology. Functional networks reflect activity-based coupling between brain regions that may be constrained by relatively static anatomical connections, yet these networks appear to support tremendously dynamic behaviors. Within this growing field, the stability and temporal characteristics of functional connectivity brain networks have not been well characterized. We evaluated the temporal stability of spontaneous functional connectivity networks derived from multi-day scalp encephalogram (EEG) recordings in five healthy human subjects. Topological stability and graph characteristics of networks derived from averaged data epochs ranging from 1 s to multiple hours across different states of consciousness were compared. We show that, although functional networks are highly variable on the order of seconds, stable network templates emerge after as little as ∼100 s of recording and persist across different states and frequency bands (albeit with slightly different characteristics in different states and frequencies). Within these network templates, the most common edges are markedly consistent, constituting a network "core." Although average network topologies persist across time, measures of global network connectivity, density and clustering coefficient, are state and frequency specific, with sparsest but most highly clustered networks seen during sleep and in the gamma frequency band. These findings support the notion that a core functional organization underlies spontaneous cortical processing and may provide a reference template on which unstable, transient, and rapidly adaptive long-range assemblies are overlaid in a frequency-dependent manner.

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.

Epilepsy as a disorder of cortical network organization

The brain is naturally considered as a network of interacting elements which, when functioning properly, produces an enormous range of dynamic, adaptable behavior. However, when elements of this network fail, pathological changes ensue, including epilepsy, one of the most common brain disorders. This review examines some aspects of cortical network organization that distinguish epileptic cortex from normal brain as well as the dynamics of network activity before and during seizures, focusing primarily on focal seizures. The review is organized around four phases of the seizure: the interictal period, onset, propagation, and termination. For each phase, the authors discuss the most common rhythmic characteristics of macroscopic brain voltage activity and outline the observed functional network features. Although the characteristics of functional networks that support the epileptic seizure remain an area of active research, the prevailing trends point to a complex set of network dynamics between, before, and during seizures.