Topographic organization of nonlinear interdependence in multichannel human EEG

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.

Testing nonlinearity in topological organization of functional brain networks

Aiming to provide an argumentation on the underlying nonlinearity of the overall functional brain network via surrogate data method and graph theory. Taking the functional magnetic resonance imaging data as original data set and then shuffled the time series of each region of interest to generate surrogate data sets, corresponding original network and its 400 surrogates were obtained via computing connectivity matrixes. The results show that both the global correlation level and corresponding small-world topological characters exhibited obvious differences between the original network and its surrogates. And the following statistical testing results demonstrate their significant distinction, and this topological difference has been proved to be caused by the intrinsic nonlinear dynamics. Accordingly, the nonlinearity of the original functional network and its superior dynamical complexity have been confirmed. The results of this study could provide a novel angle into exploring the underlying mechanism of the neural brain system and offer an essential evidence in explaining complex brain activities.

Nonlinear dynamics underlying sensory processing dysfunction in schizophrenia

Natural systems, including the brain, often seem chaotic, since they are typically driven by complex nonlinear dynamical processes. Disruption in the fluid coordination of multiple brain regions contributes to impairments in information processing and the constellation of symptoms observed in neuropsychiatric disorders. Schizophrenia (SZ), one of the most debilitating mental illnesses, is thought to arise, in part, from such a network dysfunction, leading to impaired auditory information processing as well as cognitive and psychosocial deficits. Current approaches to neurophysiologic biomarker analyses predominantly rely on linear methods and may, therefore, fail to capture the wealth of information contained in whole EEG signals, including nonlinear dynamics. In this study, delay differential analysis (DDA), a nonlinear method based on embedding theory from theoretical physics, was applied to EEG recordings from 877 SZ patients and 753 nonpsychiatric comparison subjects (NCSs) who underwent mismatch negativity (MMN) testing via their participation in the Consortium on the Genetics of Schizophrenia (COGS-2) study. DDA revealed significant nonlinear dynamical architecture related to auditory information processing in both groups. Importantly, significant DDA changes preceded those observed with traditional linear methods. Marked abnormalities in both linear and nonlinear features were detected in SZ patients. These results illustrate the benefits of nonlinear analysis of brain signals and underscore the need for future studies to investigate the relationship between DDA features and pathophysiology of information processing.

Detecting switching and intermittent causalities in time series

During the last decade, complex network representations have emerged as a powerful instrument for describing the cross-talk between different brain regions both at rest and as subjects are carrying out cognitive tasks, in healthy brains and neurological pathologies. The transient nature of such cross-talk has nevertheless by and large been neglected, mainly due to the inherent limitations of some metrics, e.g., causality ones, which require a long time series in order to yield statistically significant results. Here, we present a methodology to account for intermittent causal coupling in neural activity, based on the identification of non-overlapping windows within the original time series in which the causality is strongest. The result is a less coarse-grained assessment of the time-varying properties of brain interactions, which can be used to create a high temporal resolution time-varying network. We apply the proposed methodology to the analysis of the brain activity of control subjects and alcoholic patients performing an image recognition task. Our results show that short-lived, intermittent, local-scale causality is better at discriminating both groups than global network metrics. These results highlight the importance of the transient nature of brain activity, at least under some pathological conditions.

Electroencephalogram characteristics in patients with chronic fatigue syndrome

OBJECTIVE

To explore the electroencephalogram (EEG) characteristics in patients with chronic fatigue syndrome (CFS) using brain electrical activity mapping (BEAM) and EEG nonlinear dynamical analysis.

METHODS

Forty-seven outpatients were selected over a 3-month period and divided into an observation group (24 outpatients) and a control group (23 outpatients) by using the non-probability sampling method. All the patients were given a routine EEG. The BEAM and the correlation dimension changes were analyzed to characterize the EEG features.

RESULTS

1) BEAM results indicated that the energy values of δ, θ, and α1 waves significantly increased in the observation group, compared with the control group (P<0.05, P<0.01, respectively), which suggests that the brain electrical activities in CFS patients were significantly reduced and stayed in an inhibitory state; 2) the increase of δ, θ, and α1 energy values in the right frontal and left occipital regions was more significant than other encephalic regions in CFS patients, indicating the region-specific encephalic distribution; 3) the correlation dimension in the observation group was significantly lower than the control group, suggesting decreased EEG complexity in CFS patients.

CONCLUSION

The spontaneous brain electrical activities in CFS patients were significantly reduced. The abnormal changes in the cerebral functions were localized at the right frontal and left occipital regions in CFS patients.

EEG oscillatory states: universality, uniqueness and specificity across healthy-normal, altered and pathological brain conditions

For the first time the dynamic repertoires and oscillatory types of local EEG states in 13 diverse conditions (examined over 9 studies) that covered healthy-normal, altered and pathological brain states were quantified within the same methodological and conceptual framework. EEG oscillatory states were assessed by the probability-classification analysis of short-term EEG spectral patterns. The results demonstrated that brain activity consists of a limited repertoire of local EEG states in any of the examined conditions. The size of the state repertoires was associated with changes in cognition and vigilance or neuropsychopathologic conditions. Additionally universal, optional and unique EEG states across 13 diverse conditions were observed. It was demonstrated also that EEG oscillations which constituted EEG states were characteristic for different groups of conditions in accordance to oscillations' functional significance. The results suggested that (a) there is a limit in the number of local states available to the cortex and many ways in which these local states can rearrange themselves and still produce the same global state and (b) EEG individuality is determined by varying proportions of universal, optional and unique oscillatory states. The results enriched our understanding about dynamic microstructure of EEG-signal.

EEG oscillatory states: universality, uniqueness and specificity across healthy-normal, altered and pathological brain conditions

For the first time the dynamic repertoires and oscillatory types of local EEG states in 13 diverse conditions (examined over 9 studies) that covered healthy-normal, altered and pathological brain states were quantified within the same methodological and conceptual framework. EEG oscillatory states were assessed by the probability-classification analysis of short-term EEG spectral patterns. The results demonstrated that brain activity consists of a limited repertoire of local EEG states in any of the examined conditions. The size of the state repertoires was associated with changes in cognition and vigilance or neuropsychopathologic conditions. Additionally universal, optional and unique EEG states across 13 diverse conditions were observed. It was demonstrated also that EEG oscillations which constituted EEG states were characteristic for different groups of conditions in accordance to oscillations' functional significance. The results suggested that (a) there is a limit in the number of local states available to the cortex and many ways in which these local states can rearrange themselves and still produce the same global state and (b) EEG individuality is determined by varying proportions of universal, optional and unique oscillatory states. The results enriched our understanding about dynamic microstructure of EEG-signal.

Spatially Nonlinear Interdependence of Alpha-Oscillatory Neural Networks under Chan Meditation

This paper reports the results of our investigation of the effects of Chan meditation on brain electrophysiological behaviors from the viewpoint of spatially nonlinear interdependence among regional neural networks. Particular emphasis is laid on the alpha-dominated EEG (electroencephalograph). Continuous-time wavelet transform was adopted to detect the epochs containing substantial alpha activities. Nonlinear interdependence quantified by similarity index S(X∣Y), the influence of source signal Y on sink signal X, was applied to the nonlinear dynamical model in phase space reconstructed from multichannel EEG. Experimental group involved ten experienced Chan-Meditation practitioners, while control group included ten healthy subjects within the same age range, yet, without any meditation experience. Nonlinear interdependence among various cortical regions was explored for five local neural-network regions, frontal, posterior, right-temporal, left-temporal, and central regions. In the experimental group, the inter-regional interaction was evaluated for the brain dynamics under three different stages, at rest (stage R, pre-meditation background recording), in Chan meditation (stage M), and the unique Chakra-focusing practice (stage C). Experimental group exhibits stronger interactions among various local neural networks at stages M and C compared with those at stage R. The intergroup comparison demonstrates that Chan-meditation brain possesses better cortical inter-regional interactions than the resting brain of control group.

Drug polyconsumption is associated with increased synchronization of brain electrical-activity at rest and in a counting task

Drug abusers typically consume not just one but several types of drugs, starting from alcohol and marijuana consumption, and then dramatically lapsing into addiction to harder drugs, such as cocaine, heroin, or amphetamine. The brain of drug abusers presents various structural and neurophysiological abnormalities, some of which may predate drug consumption onset. However, how these changes translate into modifications in functional brain connectivity is still poorly understood. To characterize functional connectivity patterns, we recorded Electroencephalogram (EEG) activity from 21 detoxified drug abusers and 20 age-matched control subjects performing a simple counting task and at rest activity. To evaluate the cortical brain connectivity network we applied the Synchronization Likelihood algorithm. The results showed that drug abusers had higher synchronization levels at low frequencies, mainly in the θ band (4-8 Hz) between frontal and posterior cortical regions. During the counting task, patients showed increased synchronization in the β (14-35 Hz), and γ (35-45 Hz) frequency bands, in fronto-posterior and interhemispheric temporal regions. Taken together 'slow-down' at rest and task-related 'over-exertion' could indicate that the brain of drug abusers is suffering from a premature form of ageing. Future studies will clarify whether this condition can be reversed following prolonged periods of abstinence.

Neural masses and fields in dynamic causal modeling

Dynamic causal modeling (DCM) provides a framework for the analysis of effective connectivity among neuronal subpopulations that subtend invasive (electrocorticograms and local field potentials) and non-invasive (electroencephalography and magnetoencephalography) electrophysiological responses. This paper reviews the suite of neuronal population models including neural masses, fields and conductance-based models that are used in DCM. These models are expressed in terms of sets of differential equations that allow one to model the synaptic underpinnings of connectivity. We describe early developments using neural mass models, where convolution-based dynamics are used to generate responses in laminar-specific populations of excitatory and inhibitory cells. We show that these models, though resting on only two simple transforms, can recapitulate the characteristics of both evoked and spectral responses observed empirically. Using an identical neuronal architecture, we show that a set of conductance based models-that consider the dynamics of specific ion-channels-present a richer space of responses; owing to non-linear interactions between conductances and membrane potentials. We propose that conductance-based models may be more appropriate when spectra present with multiple resonances. Finally, we outline a third class of models, where each neuronal subpopulation is treated as a field; in other words, as a manifold on the cortical surface. By explicitly accounting for the spatial propagation of cortical activity through partial differential equations (PDEs), we show that the topology of connectivity-through local lateral interactions among cortical layers-may be inferred, even in the absence of spatially resolved data. We also show that these models allow for a detailed analysis of structure-function relationships in the cortex. Our review highlights the relationship among these models and how the hypothesis asked of empirical data suggests an appropriate model class.

Cross-frequency power coupling between hierarchically organized face-selective areas

Neural oscillations are linked to perception and behavior and may reflect mechanisms for long-range communication between brain areas. We developed a causal model of oscillatory dynamics in the face perception network using magnetoencephalographic data from 51 normal volunteers. This model predicted induced responses to faces by estimating oscillatory power coupling between source locations corresponding to bilateral occipital and fusiform face areas (OFA and FFA) and the right superior temporal sulcus (STS). These sources showed increased alpha and theta and decreased beta power as well as selective responses to fearful facial expressions. We then used Bayesian model comparison to compare hypothetical models, which were motivated by previous connectivity data and a well-known theory of temporal lobe function. We confirmed this theory in detail by showing that the OFA bifurcated into 2 independent, hierarchical, feedforward pathways, with fearful expressions modulating power coupling only in the more dorsal (STS) pathway. The power coupling parameters showed a common pattern over connections. Low-frequency bands showed same-frequency power coupling, which, in the dorsal pathway, was modulated by fearful faces. Also, theta power showed a cross-frequency suppression of beta power. This combination of linear and nonlinear mechanisms could reflect computational mechanisms in hierarchical feedforward networks.

A canonical model of multistability and scale-invariance in biological systems

Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations arise when there is an approximately constant ratio between the mean and standard deviation of a system's fluctuations. Both are an important property of human perception, movement, decision making and computation and they occur together in the human alpha rhythm, imparting it with complex dynamical behavior. Here, we elucidate their fundamental dynamical mechanisms in a canonical model of nonlinear bifurcations under stochastic fluctuations. We find that the co-occurrence of multistability and scale-invariant fluctuations mandates two important dynamical properties: Multistability arises in the presence of a subcritical Hopf bifurcation, which generates co-existing attractors, whilst the introduction of multiplicative (state-dependent) noise ensures that as the system jumps between these attractors, fluctuations remain in constant proportion to their mean and their temporal statistics become long-tailed. The simple algebraic construction of this model affords a systematic analysis of the contribution of stochastic and nonlinear processes to cortical rhythms, complementing a recently proposed biophysical model. Similar dynamics also occur in a kinetic model of gene regulation, suggesting universality across a broad class of biological phenomena.

Biological systems are able to adapt to rapidly and widely changing environments. Many biological organisms employ two distinct mechanisms that improve their survival in these circumstances: Firstly they exhibit rapid, qualitative changes in their internal dynamics; secondly they possess the ability to respond to change that is not absolute, but scales in proportion to the underlying intensity of the environment. In this paper, we study a simple class of noisy, dynamical systems that mathematically represent a very broad range of more complex models. We hence show how a combination of nonlinear instabilities and state-dependent noise in this model is able to unify these two apparently distinct biological phenomena. To illustrate its unifying potential, this simple model is applied to two very distinct biological processes – the spontaneous activity of the human cortex (i.e. when subjects are at rest), and genetic regulation in a bacteriophage. We also provide proof of principle that our model can be inverted from empirical data, allowing estimation of the parameters that express the nonlinear and stochastic influences at play in the underlying system.

Hemispheric asymmetry in non-linear interdependence of EEG in post-traumatic stress disorder

AIM

While volumetric and metabolic imaging on post-traumatic stress disorder (PTSD) patients has been intensively performed, few studies using electroencephalograms (EEG) have been done as yet. The aim of the present study was to investigate abnormalities in functional connectivity of cortical networks in PTSD.

METHODS

Non-linear interdependence (NI), a measure of bidirectional, non-linear information transmission between two time series, was used. Resting EEG were recorded for 18 PTSD patients and 18 sex-matched healthy subjects on 16 channels with their eyes closed.

RESULTS

The NI patterns in PTSD patients were hemisphere asymmetric: an increase in NI in the fronto-parieto-temporal regions of the left hemisphere (F7, F3, T3, C3, T5 and P3) and a decrease in the fronto-parieto-occipital regions of the right hemisphere (F4, C4, P4 and O2). The non-linearity of NI in EEG, estimated from the surrogate data method, exhibited an increase in the PTSD patients as compared with that of healthy subjects, particularly in the left hemispheric cortex.

CONCLUSION

Abnormal functional connectivity in PTSD can be assessed using NI, a measure of multi-channel EEG.

Transfer entropy in magnetoencephalographic data: quantifying information flow in cortical and cerebellar networks

The analysis of cortical and subcortical networks requires the identification of their nodes, and of the topology and dynamics of their interactions. Exploratory tools for the identification of nodes are available, e.g. magnetoencephalography (MEG) in combination with beamformer source analysis. Competing network topologies and interaction models can be investigated using dynamic causal modelling. However, we lack a method for the exploratory investigation of network topologies to choose from the very large number of possible network graphs. Ideally, this method should not require a pre-specified model of the interaction. Transfer entropy--an information theoretic implementation of Wiener-type causality--is a method for the investigation of causal interactions (or information flow) that is independent of a pre-specified interaction model. We analysed MEG data from an auditory short-term memory experiment to assess whether the reconfiguration of networks implied in this task can be detected using transfer entropy. Transfer entropy analysis of MEG source-level signals detected changes in the network between the different task types. These changes prominently involved the left temporal pole and cerebellum--structures that have previously been implied in auditory short-term or working memory. Thus, the analysis of information flow with transfer entropy at the source-level may be used to derive hypotheses for further model-based testing.

Quantifying auditory event-related responses in multichannel human intracranial recordings

Multichannel intracranial recordings are used increasingly to study the functional organization of human cortex. Intracranial recordings of event-related activity, or electrocorticography (ECoG), are based on high density electrode arrays implanted directly over cortex, combining good temporal and spatial resolution. Developing appropriate statistical methods for analyzing event-related responses in these high dimensional ECoG datasets remains a major challenge for clinical and systems neuroscience. We present a novel methodological framework that combines complementary, existing methods adapted for statistical analysis of auditory event-related responses in multichannel ECoG recordings. This analytic framework integrates single-channel (time-domain, time–frequency) and multichannel analyses of event-related ECoG activity to determine statistically significant evoked responses, induced spectral responses, and effective (causal) connectivity. Implementation of this quantitative approach is illustrated using multichannel ECoG data from recent studies of auditory processing in patients with epilepsy. Methods described include a time–frequency matching pursuit algorithm adapted for modeling brief, transient cortical spectral responses to sound, and a recently developed method for estimating effective connectivity using multivariate autoregressive modeling to measure brief event-related changes in multichannel functional interactions. A semi-automated spatial normalization method for comparing intracranial electrode locations across patients is also described. The individual methods presented are published and readily accessible. We discuss the benefits of integrating multiple complementary methods in a unified and comprehensive quantitative approach. Methodological considerations in the analysis of multichannel ECoG data, including corrections for multiple comparisons are discussed, as well as remaining challenges in the development of new statistical approaches.

Bistability and non-Gaussian fluctuations in spontaneous cortical activity

The brain is widely assumed to be a paradigmatic example of a complex, self-organizing system. As such, it should exhibit the classic hallmarks of nonlinearity, multistability, and "nondiffusivity" (large coherent fluctuations). Surprisingly, at least at the very large scale of neocortical dynamics, there is little empirical evidence to support this, and hence most computational and methodological frameworks for healthy brain activity have proceeded very reasonably from a purely linear and diffusive perspective. By studying the temporal fluctuations of power in human resting-state electroencephalograms, we show that, although these simple properties may hold true at some temporal scales, there is strong evidence for bistability and nondiffusivity in key brain rhythms. Bistability is manifest as nonclassic bursting between high- and low-amplitude modes in the alpha rhythm. Nondiffusivity is expressed through the irregular appearance of high amplitude "extremal" events in beta rhythm power fluctuations. The statistical robustness of these observations was confirmed through comparison with Gaussian-rendered phase-randomized surrogate data. Although there is a good conceptual framework for understanding bistability in cortical dynamics, the implications of the extremal events challenge existing frameworks for understanding large-scale brain systems.

Small-world properties of nonlinear brain activity in schizophrenia

A disturbance in the interactions between distributed cortical regions may underlie the cognitive and perceptual dysfunction associated with schizophrenia. In this article, nonlinear measures of cortical interactions and graph-theoretical metrics of network topography are combined to investigate this schizophrenia "disconnection hypothesis." This is achieved by analyzing the spatiotemporal structure of resting state scalp EEG data previously acquired from 40 young subjects with a recent first episode of schizophrenia and 40 healthy matched controls. In each subject, a method of mapping the topography of nonlinear interactions between cortical regions was applied to a widely distributed array of these data. The resulting nonlinear correlation matrices were converted to weighted graphs. The path length (a measure of large-scale network integration), clustering coefficient (a measure of "cliquishness"), and hub structure of these graphs were used as metrics of the underlying brain network activity. The graphs of both groups exhibited high levels of local clustering combined with comparatively short path lengths--features consistent with a "small-world" topology--as well as the presence of strong, central hubs. The graphs in the schizophrenia group displayed lower clustering and shorter path lengths in comparison to the healthy group. Whilst still "small-world," these effects are consistent with a subtle randomization in the underlying network architecture--likely associated with a greater number of links connecting disparate clusters. This randomization may underlie the cognitive disturbances characteristic of schizophrenia.

Dynamics of event-related causality in brain electrical activity

A new method (Event-Related Causality, ERC) is proposed for the investigation of functional interactions between brain regions during cognitive processing. ERC estimates the direction, intensity, spectral content, and temporal course of brain activity propagation within a cortical network. ERC is based upon the short-time directed transfer function (SDTF), which is measured in short EEG epochs during multiple trials of a cognitive task, as well as the direct directed transfer function (dDTF), which distinguishes direct interactions between brain regions from indirect interactions via brain regions. ERC uses new statistical methods for comparing estimates of causal interactions during prestimulus "baseline" epochs and during poststimulus "activated" epochs in order to estimate event-related increases and decreases in the functional interactions between cortical network components during cognitive tasks. The utility of the ERC approach is demonstrated through its application to human electrocorticographic recordings (ECoG) of a simple language task. ERC analyses of these ECoG recordings reveal frequency-dependent interactions, particularly in high gamma (>60 Hz) frequencies, between brain regions known to participate in the recorded language task, and the temporal evolution of these interactions is consistent with the putative processing stages of this task. The method may be a useful tool for investigating the dynamics of causal interactions between various brain regions during cognitive task performance.

Brain-mind operational architectonics imaging: technical and methodological aspects

This review paper deals with methodological and technical foundations of the Operational Architectonics framework of brain and mind functioning. This theory provides a framework for mapping and understanding important aspects of the brain mechanisms that constitute perception, cognition, and eventually consciousness. The methods utilized within Operational Architectonics framework allow analyzing with an incredible detail the operational behavior of local neuronal assemblies and their joint activity in the form of unified and metastable operational modules, which constitute the whole hierarchy of brain operations, operations of cognition and phenomenal consciousness.

Evaluation of cortical connectivity during real and imagined rhythmic finger tapping

Accumulating evidence suggests the existence of a shared neural substrate between imagined and executed movements. However, a better understanding of the mechanisms involved in the motor execution and motor imagery requires knowledge of the way the co-activated brain regions interact to each other during the particular (real or imagined) motor task. Within this general framework, the aim of the present study is to investigate the cortical activation and connectivity sub-serving real and imaginary rhythmic finger tapping, from the analysis of multi-channel electroencephalogram (EEG) scalp recordings. A sequence of 250 auditory pacing stimuli has been used for both the real and imagined right finger tapping task, with a constant inter-stimulus interval of 1.5 s length. During the motor execution, healthy subjects were asked to tap in synchrony with the regular sequence of stimulus events, whereas in the imagery condition subjects imagined themselves tapping in time with the auditory cue. To improve the spatial resolution of the scalp fields and suppress unwanted interferences, the EEG data have been spatially filtered. Further, event related synchronization and desynchronization phenomena and phase synchronization analysis have been employed for the study of functionally active brain areas and their connectivity during real and imagery finger tapping. Our results show a fronto-parietal co-activation during both real and imagined movements and similar connectivity patterns among contralateral brain areas. The results support the hypothesis that functional connectivity over the contralateral hemisphere during finger tapping is preserved in imagery. The approach and results can be regarded as indicative evidences of a new strategy for recognizing imagined movements in EEG-based brain computer interface research.

Dynamics of spontaneous transitions between global brain states

Phase patterns of human scalp alpha EEG activity show spontaneous transitions between different globally phase-synchronized states. We studied the dynamical properties of these transitions using the method of symbolic dynamics. We found greater predictability (deterministicity) and heterogeneity in the dynamics than what was expected from corresponding surrogate series in which linear correlations are retained. A possible explanation of these observations within the framework of chaotic itinerancy is discussed.

Opioid withdrawal results in an increased local and remote functional connectivity at EEG alpha and beta frequency bands

Withdrawal may be a natural model to study craving and compulsive drug seeking, since craving can be viewed as a conditioned dysphoric state. It has been suggested that functional connectivity between brain areas may be of major value in explaining excessive craving and compulsive drug seeking by providing essential link between psychological and biological processes. Considering that withdrawal initiates a widespread activation of cortical regions responsible for compulsive drug seeking and desire for the drug, we predict that withdrawal would result in a significant increase in functional cortical connectivity. We applied the novel operational architectonics approach that enables us to estimate both local and remote functional cortical connectivity by means of EEG structural synchrony measure. In 13 withdrawal opioid-dependent patients we found the evidence that local and remote cortical functional connectivity was indeed significantly enhanced (for both alpha and beta frequency oscillations). Additionally, statistical relationship between functional connectivity and the severity of opioid withdrawal has been found.

Impaired functional connectivity at EEG alpha and theta frequency bands in major depression

Recent reports on functional brain imaging in major depression have lead to an assumption that observed psychopathology might be related to an altered brain functional connectivity. Our hypothesis was that an increase in brain functional connectivity occurs in major depression. As a measure of functional connectivity, the electroencephalogram (EEG) structural synchrony approach was used in 12 medication-free depressive outpatients and 10 control subjects. Differences in the number and strength of structurally synchronized EEG patterns were compared between groups. In depressive patients the number and strength of short cortex functional connections were significantly larger for the left than for the right hemisphere, while the number and strength of long functional connections were significantly larger for the right than for the left hemisphere. Some of the functional connections were positively correlated with the severity of depression, thus being predictive. These were short-range anterior, posterior, and left hemisphere functional connections for the alpha frequency band and short-range anterior functional connections for the theta frequency band. The topology of the most representative functional connections among all patients with major depression indicated that the right anterior and left posterior brain parts may discriminate depressive patients from healthy controls. The obtained data support our hypothesis that there is an increase in brain functional connectivity in major depression. This finding was interpreted within the semantic framework, where different specialization of left (monosemantic context) and right (polysemantic context) hemispheres is functionally insufficient in patients with depression.

Increased local and decreased remote functional connectivity at EEG alpha and beta frequency bands in opioid-dependent patients

RATIONALE

Although researchers now have a working knowledge of key brain structures involved in realization of actions of substance abuse and addiction, deeper understanding will require examination of network interactions between cortical neuronal assemblies and their subcortical tails in the effects of opioid dependence.

OBJECTIVES

Given that repeated exposure to opiates initiates a widespread reorganization of cortical regions, we predict that opioid dependence would result in a considerable reorganization of local and remote functional connectivity in the neocortex.

METHODS

We applied the novel operational architectonics approach that enables us to estimate two local and remote functional cortex connectivities by means of electroencephalogram structural synchrony measure.

RESULTS

In 22 opioid-dependent patients, we found the evidence that brain functional connectivity was indeed disrupted by chronic opioid abuse (i.e., the local functional connectivity increased and remote functional connectivity decreased in opioid abusers). This significant difference between "opioid" and "control" populations was the same for alpha and beta frequency bands. Additionally, significant negative relations between duration (years) of daily opioid abuse and the number/strength of functional connections in the posterior section of the cortex were found.

Frequency flows and the time-frequency dynamics of multivariate phase synchronization in brain signals

The quantification of phase synchrony between brain signals is of crucial importance for the study of large-scale interactions in the brain. Current methods are based on the estimation of the stability of the phase difference between pairs of signals over a time window, within successive frequency bands. This paper introduces a new approach to study the dynamics of brain synchronies, Frequency Flows Analysis (FFA). It allows direct tracking and characterization of the nonstationary time-frequency dynamics of phase synchrony among groups of signals. It is based on the use of the one-to-one relationship between frequency locking and phase synchrony, which applies when the concept of phase synchrony is not taken in an extended 'statistical' sense of a bias in the distribution of phase differences, but in the sense of a continuous phase difference conservation during a short period of time. In such a case, phase synchrony implies identical instantaneous frequencies among synchronized signals, with possible time varying frequencies of synchronization. In this framework, synchronous groups of signals or neural assemblies can be identified as belonging to common frequency flows, and the problem of studying synchronization becomes the problem of tracking frequency flows. We use the ridges of the analytic wavelet transforms of the signals of interest in order to estimate maps of instantaneous frequencies and reveal sustained periods of common instantaneous frequency among groups of signal. FFA is shown to track complex dynamics of synchrony in coupled oscillator models, reveal the time-frequency and spatial dynamics of synchrony convergence and divergence in epileptic seizures, and in MEG data the large-scale ongoing dynamics of synchrony correlated with conscious perception during binocular rivalry.

The nonlinear theory of schizophrenia

OBJECTIVE

Nonlinear properties exist within the brain across a hierarchy of scales and within a variety of critical neural processes. Only a few studies of brain activity in schizophrenia, however, have used nonlinear methods. This review paper evaluates the contribution of the nonlinear sciences towards understanding schizophrenia.

METHOD

Applications of nonlinear methods to the study of schizophrenia symptoms and to healthy and schizophrenia functional neuroscience data are reviewed. The main flaws of nonlinear algorithms and recent methods to correct these are also appraised.

RESULTS

Initial research methods utilized in the study of nonlinearity in schizophrenia have fundamental methodological limitations. In the last decade, many of these problems have been addressed, facilitating future progress. Research incorporating these improvements has been applied to normal electroencephalogram (EEG) data and to the symptoms of schizophrenia, but not systematically to brain imaging data collected from patients with schizophrenia.

CONCLUSION

There is strong statistical evidence for weak nonlinearity in normal EEG and in the fluctuations of the symptoms of schizophrenia. However, the contribution of nonlinear processes to brain dysfunction in schizophrenia is yet to be properly established or accurately quantified. Despite this, recent methodological advances suggest that a 'nonlinear theory' of schizophrenia may be helpful in understanding this disorder.

Nonlinear dynamical analysis of EEG and MEG: review of an emerging field

Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called 'chaos theory', has now progressed to a stage, where it becomes possible to study self-organization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of EEG or MEG, an attractor of the underlying dynamical system, and characterizing it in terms of its dimension (an estimate of the degrees of freedom of the system), or its Lyapunov exponents and entropy (reflecting unpredictability of the dynamics due to the sensitive dependence on initial conditions). More recently developed nonlinear measures characterize other features of local brain dynamics (forecasting, time asymmetry, determinism) or the nonlinear synchronization between recordings from different brain regions. Nonlinear time series has been applied to EEG and MEG of healthy subjects during no-task resting states, perceptual processing, performance of cognitive tasks and different sleep stages. Many pathologic states have been examined as well, ranging from toxic states, seizures, and psychiatric disorders to Alzheimer's, Parkinson's and Cre1utzfeldt-Jakob's disease. Interpretation of these results in terms of 'functional sources' and 'functional networks' allows the identification of three basic patterns of brain dynamics: (i) normal, ongoing dynamics during a no-task, resting state in healthy subjects; this state is characterized by a high dimensional complexity and a relatively low and fluctuating level of synchronization of the neuronal networks; (ii) hypersynchronous, highly nonlinear dynamics of epileptic seizures; (iii) dynamics of degenerative encephalopathies with an abnormally low level of between area synchronization. Only intermediate levels of rapidly fluctuating synchronization, possibly due to critical dynamics near a phase transition, are associated with normal information processing, whereas both hyper-as well as hyposynchronous states result in impaired information processing and disturbed consciousness.

EEG responses to long-term audio-visual stimulation

In this study, linear and nonlinear electroencephalogram (EEG) changes due to long-term audio-visual stimulation (AVS) were investigated. In the course of 2 months, 25 repetitions of a 20-min AVS program with stimulation frequencies in the range 2-18 Hz were applied to six healthy volunteers. EEG data were recorded from six head locations during relaxed wakefulness prior to AVS. Then linear spectral measures (total power, frequency band powers, spectral edge frequency, and spectral entropy), nonlinear measures of complexity (histogram-based entropy and correlation dimension), interdependency measures (linear correlation coefficient, mutual information, and coherence), and measures of subjective assessment were estimated. Evolution of these measures during the whole experiment period was analyzed with respect to the significance of their linear regression. Our results confirm that repetitive training with audio-visual stimulation does induce changes in the electro-cortical activity of the brain. Long-term AVS significantly increased power in theta-1, theta-2, and alpha-1 bands in the frontal and central cortex locations. Total power increased in the right central region. Interhemispheric coherence in alpha-1 band displayed a significant increase between frontal parts in contrast to the decrease of both linear correlation and mutual information. Correlation dimension significantly decreased in some locations while entropy displayed an ascending trend.

Assessing interactions of linear and nonlinear neuronal sources using MEG beamformers: a proof of concept

OBJECTIVE

This study aimed to explore methods of assessing interactions between neuronal sources using MEG beamformers. However, beamformer methodology is based on the assumption of no linear long-term source interdependencies [VanVeen BD, vanDrongelen W, Yuchtman M, Suzuki A. Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 1997;44:867-80; Robinson SE, Vrba J. Functional neuroimaging by synthetic aperture magnetometry (SAM). In: Recent advances in Biomagnetism. Sendai: Tohoku University Press; 1999. p. 302-5]. Although such long-term correlations are not efficient and should not be anticipated in a healthy brain [Friston KJ. The labile brain. I. Neuronal transients and nonlinear coupling. Philos Trans R Soc Lond B Biol Sci 2000;355:215-36], transient correlations seem to underlie functional cortical coordination [Singer W. Neuronal synchrony: a versatile code for the definition of relations? Neuron 1999;49-65; Rodriguez E, George N, Lachaux J, Martinerie J, Renault B, Varela F. Perception's shadow: long-distance synchronization of human brain activity. Nature 1999;397:430-3; Bressler SL, Kelso J. Cortical coordination dynamics and cognition. Trends Cogn Sci 2001;5:26-36].

METHODS

Two periodic sources were simulated and the effects of transient source correlation on the spatial and temporal performance of the MEG beamformer were examined. Subsequently, the interdependencies of the reconstructed sources were investigated using coherence and phase synchronization analysis based on Mutual Information. Finally, two interacting nonlinear systems served as neuronal sources and their phase interdependencies were studied under realistic measurement conditions.

RESULTS

Both the spatial and the temporal beamformer source reconstructions were accurate as long as the transient source correlation did not exceed 30-40 percent of the duration of beamformer analysis. In addition, the interdependencies of periodic sources were preserved by the beamformer and phase synchronization of interacting nonlinear sources could be detected.

CONCLUSIONS

MEG beamformer methods in conjunction with analysis of source interdependencies could provide accurate spatial and temporal descriptions of interactions between linear and nonlinear neuronal sources.

SIGNIFICANCE

The proposed methods can be used for the study of interactions between neuronal sources.

Respiration and postural sway: detection of phase synchronizations and interactions

The aim of the central nervous system in upright stance is to control an intrinsically unstable plant. Internal disturbances, such as haemodynamics and respiration, constitute an endogenous threat to equilibrium. The way CNS reacts to those perturbations was studied in this work, through the analysis of summary scores taken from posturographic and pneumographic data. Signals were recorded simultaneously during trials administered on a sample population of healthy young adults, while sitting and standing and at paced and spontaneous uncontrolled breathing. The extraction of posturographic and pneumographic parameters was accompanied by the utilization of techniques for the detection of phase synchronization in bivariate data, and the extraction of an interaction index, the mutual information MI. The effects of the biomechanical condition and respiratory amplitude on MI and summary measures were tested with a two-way ANOVA. Summary scores clearly depend on posture condition. Synchronization between breath and postural sway is always present, depends on both biomechanical condition and respiratory threat, and cannot be reduced to a simple linear relation.

Detection of weak directional coupling: phase-dynamics approach versus state-space approach

We compare two conceptually different approaches to the detection of weak directional couplings between two oscillatory systems from bivariate time series. The first approach is based on the analysis of the systems' phase dynamics, whereas the other one tests for interdependencies in the reconstructed state spaces of the systems. We analyze the sensitivity of both techniques to weak couplings in numerical experiments by considering couplings between almost identical as well as between significantly different nonlinear systems. We study different degrees of phase diffusion, test the robustness of the two techniques against observational noise, and investigate the influence of the time series length. Our results show that none of the two approaches is generally superior to the other, and we conclude that it is probably the combination of both techniques that would allow the most comprehensive and reliable characterization of coupled systems.

Spatiotemporal wavelet resampling for functional neuroimaging data

The study of dynamic interdependences between brain regions is currently a very active research field. For any connectivity study, it is important to determine whether correlations between two selected brain regions are statistically significant or only chance effects due to non-specific correlations present throughout the data. In this report, we present a wavelet-based non-parametric technique for testing the null hypothesis that the correlations are typical of the data set and not unique to the regions of interest. This is achieved through spatiotemporal resampling of the data in the wavelet domain. Two functional MRI data sets were analysed: (1) Data from 8 healthy human subjects viewing a checkerboard image, and (2) "Null" data obtained from 3 healthy human subjects, resting with eyes closed. It was demonstrated that constrained resampling of the data in the wavelet domain allows construction of bootstrapped data with four essential properties: (1) Spatial and temporal correlations within and between slices are preserved, (2) The irregular geometry of the intracranial images is maintained, (3) There is adequate type I error control, and (4) Expected experiment-induced correlations are identified. The limitations and possible extensions of the proposed technique are discussed.

"Dynamic" connectivity in neural systems: theoretical and empirical considerations

The study of functional interdependences between brain regions is a rapidly growing focus of neuroscience research. This endeavor has been greatly facilitated by the appearance of a number of innovative methodologies for the examination of neurophysiological and neuroimaging data. The aim of this article is to present an overview of dynamical measures of interdependence and contrast these with statistical measures that have been more widely employed. We first review the motivation, conceptual basis, and experimental approach of dynamical measures of interdependence and their application to the study of neural systems. A consideration of boot-strap "surrogate data" techniques, which facilitate hypothesis testing of dynamical measures, is then used to clarify the difference between dynamical and statistical measures of interdependence. An overview of some of the most active research areas such as the study of the "synchronization manifold," dynamical interdependence in neurophysiology data and the putative role of nonlinear desynchronization is then given. We conclude by suggesting that techniques based on dynamical interdependence--or "dynamical connectivity"--show significant potential for extracting meaningful information from functional neuroimaging data.

Nonlinear analysis of EEG during NREM sleep reveals changes in functional connectivity due to natural aging

The spatial organization of nonlinear interactions between different brain regions during the first NREM sleep stage is investigated. This is achieved via consideration of four bipolar electrode derivations, Fp1F3, Fp2F4, O1P3, O2P4, which are used to compare anterior and posterior interhemispheric interactions and left and right intrahemispheric interactions. Nonlinear interdependence is detected via application of a previously written algorithm, along with appropriately generated surrogate data sets. It is now well understood that the output of neural systems does not scale linearly with inputs received and, thus, the study of nonlinear interactions in EEG is crucial. This approach also offers significant advantages over standard linear techniques, in that the strength, direction, and topography of the interdependencies can all be calculated and considered. Previous research has linked delta activity during the first NREM sleep stage to performance on frontally activating tasks during waking hours. We demonstrate that nonlinear mechanisms are the driving force behind this delta activity. Furthermore, evidence is presented to suggest that the aging brain calls upon the right parietal region to assist the pre-frontal cortex. This is highlighted by statistically significant differences in the rates of interdependencies between the left pre-frontal cortex and the right parietal region when comparing younger subjects (<23 years) with older subjects (>60 years). This assistance has been observed in brain-imaging studies of sleep-deprived young adults, suggesting that similar mechanisms may play a role in the event of healthy aging. Additionally, the contribution to the delta rhythm via nonlinear mechanisms is observed to be greater in older subjects.

Local and remote functional connectivity of neocortex under the inhibition influence

The current paper focuses on a relatively new and promising area of the study of EEG transformations during brain information processing based on the reduction of the signal to the discrete quasi-stationary segment sequences which may reflect individual brain microstates or discrete operations. In this framework, the complex brain functions require integration of several operations throughout the whole neocortex. However, the role of inhibitory brain systems in such processes is still unsettled. The effects of a single dose (30 microg/kg) of lorazepam on the operational activity of neuronal populations and on the temporal binding between them were examined in a double-blind randomized crossover placebo-controlled study with eight healthy volunteers. EEG measures at 20 channels were evaluated on two occasions: (1) eyes closed, (2) eyes open. In short, we conducted a two-by-two factorial study where one factor manipulated GABAergic neurotransmission (lorazepam vs. placebo), and the other factor was simply brain state (eyes closed vs. eyes opened). We were primarily interested in the main effect of lorazepam. In the present study, a connection between the mesoscopic level, described by the local functional processes (neuronal assemblies or populations) and the macroscopic level, described as a sequence of metastable brain states (remote functionally synchronized neuronal populations) was established. The role of inhibitory brain systems facilitated by lorazepam in the operational dynamics of neuronal populations and in the process of EEG structural synchrony (SS) (topological peculiarities) was addressed for the first time. It was shown that GABA signaling reorganized the dynamics of local neuronal populations and the remote functional connectivity between them.

A novel method for the topographic analysis of neural activity reveals formation and dissolution of 'Dynamic Cell Assemblies'

The study of synchronous oscillations in neural systems is a very active area of research. However, cognitive function may depend more crucially upon a dynamic alternation between synchronous and desynchronous activity rather than synchronous behaviour per se. The principle aim of this study is to develop and validate a novel method of quantifying this complex process. The method permits a direct mapping of phase synchronous dynamics and desynchronizing bursts in the spatial and temporal domains. Two data sets are analyzed: Numeric data from a model of a sparsely coupled neural cell assembly and experimental data consisting of scalp-recorded EEG from 40 human subjects. In the numeric data, the approach enables the demonstration of complex relationships between cluster size and temporal duration that cannot be detected with other methods. Dynamic patterns of phase-clustering and desynchronization are also demonstrated in the experimental data. It is further shown that in a significant proportion of the recordings, the pattern of dynamics exhibits nonlinear structure. We argue that this procedure provides a 'natural partitioning' of ongoing brain dynamics into topographically distinct synchronous epochs which may be integral to the brain's adaptive function. In particular, the character of transitions between consecutive synchronous epochs may reflect important aspects of information processing and cognitive flexibility.

Bivariate surrogate techniques: necessity, strengths, and caveats

The concept of surrogates allows testing results from time series analysis against specified null hypotheses. In application to bivariate model dynamics we here compare different types of surrogates, each designed to test against a different null hypothesis, e.g., an underlying bivariate linear stochastic process. Two measures that aim at a characterization of interdependence between nonlinear deterministic dynamics were used as discriminating statistics. We analyze eight different stochastic and deterministic models not only to demonstrate the power of the surrogates, but also to reveal some pitfalls and limitations.

A disturbance of nonlinear interdependence in scalp EEG of subjects with first episode schizophrenia

It has been proposed that schizophrenia arises through a disturbance of coupling between large-scale cortical systems. This "disconnection hypothesis" is tested by applying a measure of dynamical interdependence to scalp EEG data. EEG data were collected from 40 subjects with a first episode of schizophrenia and 40 matched healthy controls. An algorithm for the detection of dynamical interdependence was applied to six pairs of bipolar electrodes in each subject. The topographic organization of the interdependence was calculated and served as the principle measure of cortical integration. The rate of occurrence of dynamical interdependence did not statistically differ between subject groups at any of the sites. However, the topography across the scalp was significantly different between the two groups. Specifically, nonlinear interdependence tended to occur in larger concurrent "clusters" across the scalp in schizophrenia than in the healthy subjects. This disturbance was reflected most strongly in left intrahemispheric coupling and did not differ significantly according to symptomatology. Medication dose and subject arousal were not observed to be confounding factors. The study of dynamical interdependence in scalp EEG data does not support a straightforward interpretation of the disconnection hypothesis-that there is a decrease in the strength of functional coupling between adjacent cortical regions. Rather, it suggests a dysregulation in the organization of dynamical interactions across supraregional brain systems.