Functional modularity of background activities in normal and epileptic brain networks

We analyze the connectivity structure of weighted brain networks extracted from spontaneous magnetoencephalographic signals of healthy subjects and epileptic patients (suffering from absence seizures) recorded at rest. We find that, for the activities in the 5-14 Hz range, healthy brains exhibit a sparse connectivity, whereas the brain networks of patients display a rich connectivity with a clear modular structure. Our results suggest that modularity plays a key role in the functional organization of brain areas during normal and pathological neural activities at rest.

Complex modular structure of large-scale brain networks

Modular structure is ubiquitous among real-world networks from related proteins to social groups. Here we analyze the modular organization of brain networks at a large scale (voxel level) extracted from functional magnetic resonance imaging signals. By using a random-walk-based method, we unveil the modularity of brain webs and show modules with a spatial distribution that matches anatomical structures with functional significance. The functional role of each node in the network is studied by analyzing its patterns of inter- and intramodular connections. Results suggest that the modular architecture constitutes the structural basis for the coexistence of functional integration of distant and specialized brain areas during normal brain activities at rest.

Dynamic small-world behavior in functional brain networks unveiled by an event-related networks approach

There is growing interest in studying the role of connectivity patterns in brain functions. In recent years, functional brain networks were found to exhibit small-world properties during different brain states. In previous studies, time-independent networks were recovered from long time periods of brain activity. In this paper, we propose an approach, the event-related networks, that allows one to characterize the dynamical evolution of functional brain networks in time-frequency space. We illustrate this approach by characterizing connectivity patterns in magnetoencephalographic signals recorded during a visual stimulus paradigm. When compared with equivalent random and regular networks, the results reveal that functional connectivity varies with time and frequency during the processing of the stimulus, while maintaining a small-world structure. This approach may provide insights into the connectivity of other complex and spatially extended nonstationary systems.

Loss of phase synchrony in an animal model of partial status epilepticus

Interrupting a focal, chronic infusion of GABA to the rat motor cortex initiates the progressive emergence of a sustained spiking electroencephalographic (EEG) activity, associated with myoclonic jerks of the corresponding body territory. This activity is maintained over several hours, has an average frequency of 1.5 Hz, is localized to the infusion site and never generalizes. The GABA withdrawal syndrome (GWS) has therefore features of partial status epilepticus. Changes in EEG signals associated with the GWS were studied in freely moving rats by measuring the phase synchrony between bilateral epidural records from the neocortex. Our results showed (i) epileptic activity was associated with a striking decrease in phase synchrony between all pairs of electrodes including the focus, predominantly in the 1-6 Hz frequency range. There was a mean decrease of 75.34+/-5.26% in phase synchrony levels between the period before GABA interruption and the period after epileptic activity appeared. (ii) This reduction in synchrony contrasted with an increase of power spectral density in the corresponding EEG channels over the same 1-6 Hz frequency range, (iii) neither changes in synchrony nor in nonlinear dynamics were detected before the first EEG spikes, (iv) systemic injection of ketamine, an antagonist of N-methyl-d-aspartic acid (NMDA) receptors, modified transiently both epileptic activity and the synchrony profile. (v) Spiking activity and synchrony changes were suppressed by reperfusion of GABA. Our data suggest that, during a partial status epilepticus, interactions between the epileptic focus and connected neocortical neuronal populations are dramatically decreased in low frequencies.

Degree mixing and the enhancement of synchronization in complex weighted networks

Real networks often consist of local units interacting with each other by means of heterogeneous connections. In many cases, furthermore, such networks feature degree mixing properties, i.e., the tendency of nodes with high degree (with low degree) to connect with connectivity peers (with highly connected nodes). Such degree-degree correlations may have an important influence in the spreading of information or infectious agents on a network. We explore the role played by these correlations for the synchronization of networks of coupled dynamical systems. Using a stochastic optimization technique, we find that the value of degree mixing providing optimal conditions for synchronization depends on the weighted coupling scheme. We also show that a minimization of the assortative coefficient may induce a strong destabilization of the synchronous state. We illustrate our findings for weighted networks with scale free and random topologies.

Towards a proper estimation of phase synchronization from time series

In experimental synchronization studies a continuous phase variable is commonly estimated from a scalar time series by means of its representation on the complex plane. The aim is to obtain a pair of functions [A(t), phi(t)] defining its instantaneous amplitude and phase, respectively. However, any arbitrary pair of functions cannot be considered as the amplitude and the phase of the real observable. Here, we point out some criteria that the pair [A(t), phi(t)] must observe to unambiguously define the instantaneous amplitude and phase of the observed signal. In this work, we illustrate how the complex representation may fail if the signal possesses a multi-component or a broadband spectra. We also point out a practical procedure to test whether a signal, not displaying a single oscillation at a unique frequency, has a narrow-band behavior. Implications for the study of phase interdependencies are illustrated and discussed. Phase dynamics estimated from electric brain activities recorded from an epileptic patient are also discussed.

Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony

The quantification of phase synchrony between neuronal signals is of crucial importance for the study of large-scale interactions in the brain. Two methods have been used to date in neuroscience, based on two distinct approaches which permit a direct estimation of the instantaneous phase of a signal [Phys. Rev. Lett. 81 (1998) 3291; Human Brain Mapping 8 (1999) 194]. The phase is either estimated by using the analytic concept of Hilbert transform or, alternatively, by convolution with a complex wavelet. In both methods the stability of the instantaneous phase over a window of time requires quantification by means of various statistical dependence parameters (standard deviation, Shannon entropy or mutual information). The purpose of this paper is to conduct a direct comparison between these two methods on three signal sets: (1) neural models; (2) intracranial signals from epileptic patients; and (3) scalp EEG recordings. Levels of synchrony that can be considered as reliable are estimated by using the technique of surrogate data. Our results demonstrate that the differences between the methods are minor, and we conclude that they are fundamentally equivalent for the study of neuroelectrical signals. This offers a common language and framework that can be used for future research in the area of synchronization.

Nonlinear analysis of orthostatic posture in patients with vertigo or balance disorders

The stabilometry signals involve irregular and unpredictable components. In order to identify the hidden dynamics that underlie the multi-link networks consisted of the multiple sensory systems, motor components and central integration, we applied a nonlinear analysis to these signals. We evaluated the postural control differences between eyes open and closed by means of the dynamical closeness between two states, known as similarity index, for the patients with vestibular disorders. We were able to demonstrate that some patients (eight of 21) showed a difference between the conventional and nonlinear measures. Especially, the similarity index tended to reflect the clinical course of the vestibular compensation and the findings in the patients with benign paroxysmal positional vertigo (BPPV) demonstrated that its vestibular function may include various pathologies besides canalithiasis. These results suggest that nonlinear analysis can elucidate the complex postural control networks and this procedure may also be able to provide the new findings of the stabilometry examinations.

Characterizing neurodynamic changes before seizures

The study of dynamic changes in neural activity preceding epileptic seizure allows the characterization of a preictal state several minutes before seizure onset. This opens up new perspectives for studying the mechanisms of epileptogenesis as well as for possible therapeutic interventions, which represent a major breakthrough. In this review the authors present and discuss the results from their group in this domain using nonlinear analysis of brain signals, as well as the limitations of this topic and current questions.

The brainweb: phase synchronization and large-scale integration

The emergence of a unified cognitive moment relies on the coordination of scattered mosaics of functionally specialized brain regions. Here we review the mechanisms of large-scale integration that counterbalance the distributed anatomical and functional organization of brain activity to enable the emergence of coherent behaviour and cognition. Although the mechanisms involved in large-scale integration are still largely unknown, we argue that the most plausible candidate is the formation of dynamic links mediated by synchrony over multiple frequency bands.

Anticipation of epileptic seizures from standard EEG recordings

BACKGROUND

New methods derived from non-linear analysis of intracranial recordings permit the anticipation of an epileptic seizure several minutes before the seizure. Nevertheless, anticipation of seizures based on standard scalp electroencephalographical (EEG) signals has not been reported yet. The accessibility to preictal changes from standard EEGs is essential for expanding the clinical applicability of these methods.

METHODS

We analysed 26 scalp-EEG/video recordings, from 60 min before a seizure, in 23 patients with temporal-lobe epilepsy. For five patients, simultaneous scalp and intracranial EEG recordings were assessed. Long-term changes before seizure onset were identified by a measure of non-linear similarity, which is very robust in spite of large artifacts and runs in real-time.

FINDINGS

In 25 of 26 recordings, measurement of non-linear changes in EEG signals allowed the anticipation of a seizure several minutes before it occurred (mean 7 min). These preictal changes in the scalp EEG correspond well with concurrent changes in depth recordings.

INTERPRETATION

Scalp-EEG recordings retain sufficient dynamical information which can be used for the analysis of preictal changes leading to seizures. Seizure anticipation strategies in real-time can now be envisaged for diverse clinical applications, such as devices for patient warning, for efficacy of ictal-single photon emission computed tomography procedures, and eventual treatment interventions for preventing seizures.

A quantitative study of gamma-band activity in human intracranial recordings triggered by visual stimuli

This paper studies gamma-band responses from two implanted epileptic patients during a simple visual discrimination task. Our main aim was to ascertain, in a reliable manner, whether evoked (stimulus-locked) and induced (triggered by, but not locked to, stimuli) responses are present in intracranial recordings. For this purpose, we introduce new methods adapted to detect the presence of gamma responses at this level of recording, intermediary between EEG-scalp and unicellular responses. The analysis relies on a trial-by-trial time-frequency analysis and on the use of surrogate data for statistical testing. We report that visual stimulation reliably elicits evoked and induced responses in human intracranial recordings. Induced intracranial gamma activity is significantly present in short oscillatory bursts (a few cycles) following visual stimulation. These responses are highly variable from trial to trial, beginning after 200 ms and lasting up to 500 ms. In contrast, intracranial-evoked gamma responses concentrate around 100 ms latencies corresponding to evoked responses observed on the scalp. We discuss our results in relation to scalp gamma response in a similar protocol [Tallon-Baudry et al. (1996) J. Neurosci., 16, 4240-4249] and draw some conclusions for bridging the gap between gamma oscillations observed on the scalp surface and their possible cortical sources.

Spatio-temporal characterizations of non-linear changes in intracranial activities prior to human temporal lobe seizures

Recent studies have shown that non-linear analysis of intracranial activities can detect a 'pre-ictal phase' preceding the epileptic seizure. Nevertheless, the dynamical nature of the underlying neuronal process and the spatial extension of this pre-ictal phase still remain unknown. In this paper, we address these aspects using a new non-linear measure of dynamic similarity between different parts of intracranial recordings of nine patients with medial temporal lobe epilepsy recorded during transitions to seizure. Our results confirm that non-linear changes in neuronal dynamics allow, in most cases (16 out of 17), a seizure anticipation several minutes in advance. Furthermore, we show that the spatial distribution of pre-ictal changes often involves an extended network projecting beyond the limits of the epileptogenic region. Finally, the pre-ictal phase could frequently (13 out of 17) be characterized with a marked shift toward slower frequencies in upper delta or theta frequency range.

Anticipating epileptic seizures in real time by a non-linear analysis of similarity between EEG recordings

In a previous publication we showed that non-linear analysis can extract spatio-temporal changes of brain electrical activity prior to epileptic seizures. Here we describe a new method to analyze this long-term non-stationarity in the EEG by a measure of dynamical similarity between different parts of the time series. We apply this method to the study of a group of patients with temporal lobe epilepsy recorded intracranially during transitions to seizure. We show that the method, which can be implemented on a personal computer, can track in real time spatio-temporal changes in brain dynamics several minutes prior to seizure.

[Interactions between the epileptic network and brain function: an approach by nonlinear analysis of intracranial EEG]

Recent advances in the non-linear dynamics analysis have made it possible to identify hidden recurrences in EEG signals that could be missed by more traditional linear techniques such as power spectrum or coherence analysis. This is particularly true for epileptic EEG recordings either in animals or in humans as epileptic phenomena are usually concomitant with the emergence a strong non-linear EEG behavior. Non-linear dynamical analysis techniques quantify the relations between EEG signals. The literature concerning the spatio-temporal characteristics of the epileptic processes during seizures and interictal periods is reviewed. Our attention has been mainly focused on the interdependences between brain structures or on the dynamical changes of one particular brain region during intracranial recordings. These data could explain in part the dysfunctioning of the cerebral cortex induced by epileptic activities and provide an insight into the spatio-temporal organization of the epileptic network. Futhermore, by tracking the time variation of non-linear indices, one can anticipate the occurrence of seizures in temporal lobe epilepsies. All this information could contribute to improve definitions of the epileptogenic zone in partial epilepsy and also open the way to preventive interventions.

Why bother to spatially embed EEG? Comments on Pritchard et al., Psychophysiology, 33, 362-368, 1996

In a recent paper, Pritchard, Krieble, and Duke (Psychophysiology, 33, 362-368, 1996) studied the validity of spatial embedding of electroencephalographic (EEG) data and rejected this method in favor of time-delay embedding. The present paper describes the nonlinear characterization of brain dynamics using either spatial or time-delay embedding. We discuss the arguments published in Pritchard et al. (1996) and demonstrate that the spatial embedding cannot be rejected on this basis. We also point out the limitations of both spatial and time-delay embeddings related to the spatial extension and the high-dimensional dynamics of brain activity.

Perception's shadow: long-distance synchronization of human brain activity

Transient periods of synchronization of oscillating neuronal discharges in the frequency range 30-80 Hz (gamma oscillations) have been proposed to act as an integrative mechanism that may bring a widely distributed set of neurons together into a coherent ensemble that underlies a cognitive act. Results of several experiments in animals provide support for this idea. In humans, gamma oscillations have been described both on the scalp (measured by electroencephalography and magnetoencephalography) and in intracortical recordings, but no direct participation of synchrony in a cognitive task has been demonstrated so far. Here we record electrical brain activity from subjects who are viewing ambiguous visual stimuli (perceived either as faces or as meaningless shapes). We show for the first time, to our knowledge, that only face perception induces a long-distance pattern of synchronization, corresponding to the moment of perception itself and to the ensuing motor response. A period of strong desynchronization marks the transition between the moment of perception and the motor response. We suggest that this desynchronization reflects a process of active uncoupling of the underlying neural ensembles that is necessary to proceed from one cognitive state to another.

Epileptic seizures can be anticipated by non-linear analysis

Epileptic seizures are a principal brain dysfunction with important public health implications, as they affect 0.8% of humans. Many of these patients (20%) are resistant to treatment with drugs. The ability to anticipate the onset of seizures in such cases would permit clinical interventions. The view of chronic focal epilepsy now is that abnormally discharging neurons act as pacemakers to recruit and entrain other normal neurons by loss of inhibition and synchronization into a critical mass. Thus, preictal changes should be detectable during the stages of recruitment. Traditional signal analyses, such as the count of focal spike density, the frequency coherence or spectral analyses are not reliable predictors. Non-linear indicators may undergo consistent changes around seizure onset. Our objective was to follow the transition into seizure by reconstructing intracranial recordings in implanted patients as trajectories in a phase space and then introduce non-linear indicators to characterize them. These indicators take into account the extended spatio-temporal nature of the epileptic recruitment processes and the corresponding physiological events governed by short-term causalities in the time series. We demonstrate that in most cases (17 of 19), seizure onset could be anticipated well in advance (between 2-6 minutes beforehand), and that all subjects seemed to share a similar 'route' towards seizure.

Entropy maps characterize drug effects on brain dynamics in Alzheimer's disease

Non-linear quantifiers of brain electrical dynamics (entropy maps computed from the degradation of temporal forecasting of EEG signals) were studied in relation to drug treatment of Alzheimer's disease. A placebo condition was compared to three drug doses (50, 100 and 200 mg). A significant general effect of the drug was found when compared to placebo and specific contrasts between placebo and each of the three drug doses only reveal a significant entropy increase for the highest dose. These effects were localized bilaterally in fronto-temporal areas and support changes in the dynamics of the cerebral structures involved in memory processes.

[Static balance is controlled by a non-linear dynamic system]

Different techniques of stabilometric signal analysis have been used in order to study the adaptation of the fine postural control system to the wearing of corrective glasses with or without prisms. The comparison between the results obtained with conventional techniques and those obtained with non-linear dynamic methods demonstrates the better efficiency of the latter. These results confirm that the postural system behaves as a non-linear dynamical system and may explain the outstanding sensitivity of the fine postural system to small perturbations.

Nonlinear interdependencies of EEG signals in human intracranially recorded temporal lobe seizures

The degree of interdependence between intracranial EEG channels was investigated in four epileptic patients with complex partial seizures of mesial temporal lobe origin. With a new method to characterize nonlinear dynamical interdependence-the mutual nonlinear prediction-we demonstrated here a possibility to quantify, during epileptic seizures, the relationships between EEG signals of electrode contacts in the epileptogenic area. During the interictal period, the degree of nonlinear interdependences were very low or absent. In contrast, it was found that transient patterns of nonlinear interdependences emerge at the initial spread of the seizure, during essential parts of its development, and at seizure end, but the maintenance of these interactions are not observed throughout the seizure activity. These results suggest that the nonlinear associations plays an important role in epileptogenesis, and that the process of neuronal entrainment during seizure onset involves a transient interaction between a distributed network of neuronal aggregates, but the maintenance of this interaction is not required for sustained seizure activity. Furthermore, this technique can describe properly the spatio-temporal organisation of the seizures of medio-temporal lobe origin and could become a very useful tool to aid the localization of the epileptogenic regions at the origin of epileptic seizures and their pathways of propagation.

Temporal patterns in human epileptic activity are modulated by perceptual discriminations

We studied subdural recordings from a patient with an unusually focal and stable occipito-temporal epileptic discharge under four experimental conditions. The series of time intervals between successive spike discharges displayed a few (3-5) clusters of periodic values representing statistically significant short-term periodicities when tested against surrogate data. This short-term predictability was modulated during the different experimental conditions by periodicity shifts of the order of 15-30 ms. Correspondingly, there was an increased gamma-band (30-70 Hz) coherence between the epileptic focus and surrounding recording sites. We conclude that the focal epileptic activity is part of an extended network of neural activities which exert a fast modulation reflected in changes of transiently periodic activities.

Depression as a dynamical disease

Mathematical models are helpful in the understanding of diseases through the use of dynamical indicators. A previous study has shown that brain activity can be characterized by a decrease of dynamical complexity in depressive subjects. The present paper confirms and extends these conclusions through the use of recent methodological advances: first episode and recurrent patients strongly differ in their dynamical response to therapeutic interventions. These results emphasize the need for clinical follow-ups to avoid recurrence and the necessity of specific therapeutic intervention in the case of recurrent patients.

Non-linear forecasting measurements of multichannel EEG dynamics

This work presents a new method for studying the underlying dynamics of multichannel EEG on the basis of the mathematical theory of dynamical systems. It computes the local loss of predictability and Kolmogorov entropy of the dynamics reconstructed from brain electrical activity. This reconstruction uses multichannel recordings in order to quantify an equivalent of spatio-temporal mapping. Five experimental conditions have been studied: closed eyes at rest, closed eyes and counting even numbers, staring at a spotlight, passive and active auditive odd-ball tasks. The entropy is positive for all the experimental conditions which proves that the underlying EEG dynamics are chaotic. Moreover, on the basis of the dynamical signature it is possible to differentiate 3 types of EEG activity: the rest closed eyes activity, the task closed eyes activity (counting and odd-ball tasks) and the open eyes activity (staring at a spotlight). It is inferred that this index could characterize task-related changes in brain activity.

Loss of control of pre-motor activation in anxious agitated and impulsive depressives. A clinical and ERP study

1. Current research uses a variety of traditional validation methods in order to test the clinical expression of biological models in psychiatry. The application of these methods has resulted in a paradoxical situation which requires the definition of new objectives in biological and pharmacoclinical research: the biological specificity of new psychotropic drugs does not assume any congruence between their pharmacological and their therapeutic effects, but raises the question of the relationship between biological systems and clinical symptomatology. The dimensional description of psychopathological disorders may be more appropriate to biological studies in psychiatry. 2. A study was undertaken on a population of twenty-one in-patients fulfilling the DSM III-R criteria for major depressive episode. They were divided into two groups on the basis of contrasting clinical dimensions: anxious-agitation and impulsiveness versus retardation and affective blunting. 3. Significant clinical differences between the two groups on mood profiles were echoed by contrasts in event-related potentials during a go-nogo task: only anxious agitated and impulsive patients developed an abnormal cortical activity, as measured by contingent negative variation (CNV), in the nogo condition. 4. This paper suggests how a paradigm with control of motor action leads to specify premotor activation abnormalities in the agitated impulsive depression subtype.

Decrease of complexity in EEG as a symptom of depression

Nonlinear dynamic analysis provides new methods for the processing of the electroencephalogram (EEG). We demonstrate here that the EEG dynamics of major depressive subjects is more predictable, that is less complex, than that of control subjects. Moreover, the consequence of treatment upon the EEG dynamics seems to be dependent on the appearance of the illness. Although the specificity of this dynamic signature for different stages of depression is to be confirmed, the assumption of a strong link between a healthy system and a high level of complexity in dynamics is further supported.

A dynamical analysis of oscillatory responses in the optic tectum

Multi-unit recordings from the optic tectum of an awake pigeon displaying oscillatory behavior evoked by visual stimulus are highly non-stationary and contain a broad band of frequencies under a time-window analysis. Here we extend these observations by a non-linear dynamical analysis of these oscillatory signals (local fields potentials) in successive epochs during background activity and visual responses. Two numerical estimates have been obtained from the original data every 200 ms: (1) correlation dimension and (2) non-linear forecasting of the trajectories. Results from eight different recording sites analyzed are consistent and indicate, in the average, an increase in complexity of the signal during the oscillatory periods.

Computerized detection of rapid eye movements during paradoxical sleep

A technique for automatically analysing rapid eye movements in sleep EOG is described, in which time of occurrence, amplitude and duration of each REM are measured. This method is based on the pattern recognition algorithm that simulates visual analysis.