Performance of different synchronization measures in real data: a case study on electroencephalographic signals

Fluctuation of gamma-band phase synchronization within the auditory cortex in schizophrenia

OBJECTIVE

To study the phase stability of the 40Hz auditory steady-state response (ASSR) in Sz, and in addition, to investigate inter-hemispheric phase synchronization using ipsilateral and contralateral hemisphere gamma band ASSRs.

METHODS

Whole head magnetoencephalography (MEG) was used to detect ASSR from both hemispheres in Sz patients and their control counterparts. Source localization, spatial and temporal filtering were performed to infer gamma band activity from the neural generators of the ASSR. The response gamma band phase stability relative to a reference signal was quantified using the phase synchronization index (PSI).

RESULTS

Results indicated reduced phase synchronization of the ASSR and the stimulus reference signal in Sz patients compared to control subjects, in addition to reduced inter-hemispheric phase synchronization between contralateral and ipsilateral hemispheric responses in Sz patients.

CONCLUSIONS

Greater intra and inter hemispheric fluctuations of ASSR gamma band phase synchronization in Sz add to previous studies suggesting timing deficiencies within neural populations, possibly caused by impairments of neural network parameters.

SIGNIFICANCE

This study provides experimental support that may aid in understanding the dynamics of neural phase synchrony caused by modifications of underlying neurotransmitter systems, as reflected in disease states such as schizophrenia.

EEG recording in rodents, with a focus on epilepsy

This unit describes the materials, methods, and analytical techniques available for the study of electrical activity of neural tissue in rodents in both homeostatic and disease states, with emphasis on epileptogenesis. A table containing a list of suppliers of relevant materials and equipment is also provided.

Influences of bilateral ischemic stroke on the cortical synchronization

Stroke has been one of the leading causes of mortality and long-term morbidity around the world. Describing the cortical synchrony has been useful in understanding of central nervous system disorders after brain injury. In this paper, we investigated the large scale cortical phase synchronization derived from multichannel electroencephalogram (EEG) recordings of bilateral ischemic stroke patients(n = 9). Compared with the results from the age- and gender-matched control subjects (n = 8), stroke patients showed 1) there were not significant changes of the intra-hemispheric synchronization after the bilateral stroke; and however, 2) both global and inter-hemispheric synchronization are vulnerable to the ischemic injury. Our preliminary results indicated that synchrony analysis of the spontaneous scalp EEG during at resting state provided new insight into cortical functional disorder following stroke.

Adaptive tracking of EEG oscillations

Neuronal oscillations are an important aspect of EEG recordings. These oscillations are supposed to be involved in several cognitive mechanisms. For instance, oscillatory activity is considered a key component for the top-down control of perception. However, measuring this activity and its influence requires precise extraction of frequency components. This processing is not straightforward. Particularly, difficulties with extracting oscillations arise due to their time-varying characteristics. Moreover, when phase information is needed, it is of the utmost importance to extract narrow-band signals. This paper presents a novel method using adaptive filters for tracking and extracting these time-varying oscillations. This scheme is designed to maximize the oscillatory behavior at the output of the adaptive filter. It is then capable of tracking an oscillation and describing its temporal evolution even during low amplitude time segments. Moreover, this method can be extended in order to track several oscillations simultaneously and to use multiple signals. These two extensions are particularly relevant in the framework of EEG data processing, where oscillations are active at the same time in different frequency bands and signals are recorded with multiple sensors. The presented tracking scheme is first tested with synthetic signals in order to highlight its capabilities. Then it is applied to data recorded during a visual shape discrimination experiment for assessing its usefulness during EEG processing and in detecting functionally relevant changes. This method is an interesting additional processing step for providing alternative information compared to classical time-frequency analyses and for improving the detection and analysis of cross-frequency couplings.

Increased phase synchronization and decreased cerebral autoregulation during fainting in the young

Vasovagal syncope may be due to a transient cerebral hypoperfusion that accompanies frequency entrainment between arterial pressure (AP) and cerebral blood flow velocity (CBFV). We hypothesized that cerebral autoregulation fails during fainting; a phase synchronization index (PhSI) between AP and CBFV was used as a nonlinear, nonstationary, time-dependent measurement of cerebral autoregulation. Twelve healthy control subjects and twelve subjects with a history of vasovagal syncope underwent 10-min tilt table testing with the continuous measurement of AP, CBFV, heart rate (HR), end-tidal CO2 (ETCO2), and respiratory frequency. Time intervals were defined to compare physiologically equivalent periods in fainters and control subjects. A PhSI value of 0 corresponds to an absence of phase synchronization and efficient cerebral autoregulation, whereas a PhSI value of 1 corresponds to complete phase synchronization and inefficient cerebral autoregulation. During supine baseline conditions, both control and syncope groups demonstrated similar oscillatory changes in phase, with mean PhSI values of 0.58+/-0.04 and 0.54+/-0.02, respectively. Throughout tilt, control subjects demonstrated similar PhSI values compared with supine conditions. Approximately 2 min before fainting, syncopal subjects demonstrated a sharp decrease in PhSI (0.23+/-0.06), representing efficient cerebral autoregulation. Immediately after this period, PhSI increased sharply, suggesting inefficient cerebral autoregulation, and remained elevated at the time of faint (0.92+/-0.02) and during the early recovery period (0.79+/-0.04) immediately after the return to the supine position. Our data demonstrate rapid, biphasic changes in cerebral autoregulation, which are temporally related to vasovagal syncope. Thus, a sudden period of highly efficient cerebral autoregulation precedes the virtual loss of autoregulation, which continued during and after the faint.

Unified framework for detecting phase synchronization in coupled time series

Phase synchronization (PS) has drawn increasing attention in recent years for its extensive applications in analyzing time series observed from coupled systems. In this paper, we examine the detection of PS in bivariate time series from the viewpoints of signal processing and circular statistics. Several definitions of instantaneous phase (IP) are first revisited and further unified into a framework, which defines IP as the argument of the signal with a specific bandpass filter applied. With this framework, the constraints for IP definition are discussed and the effect of noise in IP estimation is studied. The estimate error of IP, which is due to noise, is shown to obey a scale mixture of normal (SMN) distributions. Further, under the assumption that the SMN of IP error can be approximated by a particular normal distribution, the estimate of mean phase coherence of bivariate time series is shown to be degraded by a factor, which is determined by only the level of in-band noise. Finally, simulations are provided to support the theoretical results.

Quantifying statistical interdependence by message passing on graphs-part II: multidimensional point processes

Stochastic event synchrony is a technique to quantify the similarity of pairs of signals. First, events are extracted from the two given time series. Next, one tries to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. In Part I, the companion letter in this issue, one-dimensional events are considered; this letter concerns multidimensional events. Although the basic idea is similar, the extension to multidimensional point processes involves a significantly more difficult combinatorial problem and therefore is nontrivial. Also in the multidimensional case, the problem of jointly computing the pairwise alignment and SES parameters is cast as a statistical inference problem. This problem is solved by coordinate descent, more specifically, by alternating the following two steps: (1) estimate the SES parameters from a given pairwise alignment; (2) with the resulting estimates, refine the pairwise alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (step 1), in analogy to the one-dimensional case. The pairwise alignment (step 2) can no longer be obtained through dynamic programming, since the state space becomes too large. Instead it is determined by applying the max-product algorithm on a cyclic graphical model. In order to test the robustness and reliability of the SES method, it is first applied to surrogate data. Next, it is applied to detect anomalies in EEG synchrony of mild cognitive impairment (MCI) patients. Numerical results suggest that SES is significantly more sensitive to perturbations in EEG synchrony than a large variety of classical synchrony measures.

Quantifying statistical interdependence by message passing on graphs-part I: one-dimensional point processes

We present a novel approach to quantify the statistical interdependence of two time series, referred to as stochastic event synchrony (SES). The first step is to extract the two given time series. The next step is to try to align events from one time series with events from the other. The better the alignment the more similar the two series are considered to be. More precisely, the similarity is quantified by the following parameters: time delay, variance of the time jitter, fraction of noncoincident events, and average similarity of the aligned events. The pairwise alignment and SES parameters are determined by statistical inference. In particular, the SES parameters are computed by maximum a posteriori (MAP) estimation, and the pairwise alignment is obtained by applying the max product algorithm. This letter deals with one-dimensional point processes; the extension to multidimensional point processes is considered in a companion letter in this issue. By analyzing surrogate data, we demonstrate that SES is able to quantify both timing precision and event reliability more robustly than classical measures can. As an illustration, neuronal spike data generated by Morris-Lecar neuron model are considered.

Synchronization of low-frequency oscillations in the human cardiovascular system

We investigate synchronization between the low-frequency oscillations of heart rate and blood pressure having in humans a basic frequency close to 0.1 Hz. A method is proposed for quantitative estimation of synchronization between these oscillating processes based on calculation of relative time of phase synchronization of oscillations. It is shown that healthy subjects exhibit on average substantially longer epochs of internal synchronization between the low-frequency oscillations in heart rate and blood pressure than patients after acute myocardial infarction.

Nonlinear dynamical analysis of the interdependence between central and autonomic nervous systems in neonates during sleep

We present in this paper the results of a study of the interdependence between signal characteristic of the central nervous system (electroencephalography) and the autonomic nervous system (heart rate and respiration) in human neonates during sleep. By using methods from nonlinear dynamical systems theory, we show that there exist significant differences in this interdependence with the sleep stage and the electrodes considered. This paves the way for the application of this methodology in clinical practice to study pathologies where this interdependence is altered, such as the sudden infant death syndrome.

Reliable detection of directional couplings using rank statistics

To detect directional couplings from time series various measures based on distances in reconstructed state spaces were introduced. These measures can, however, be biased by asymmetries in the dynamics' structure, noise color, or noise level, which are ubiquitous in experimental signals. Using theoretical reasoning and results from model systems we identify the various sources of bias and show that most of them can be eliminated by an appropriate normalization. We furthermore diminish the remaining biases by introducing a measure based on ranks of distances. This rank-based measure outperforms existing distance-based measures concerning both sensitivity and specificity for directional couplings. Therefore, our findings are relevant for a reliable detection of directional couplings from experimental signals.

Duration of coherence intervals in electrical brain activity in perceptual organization

We investigated the relationship between visual experience and temporal intervals of synchronized brain activity. Using high-density scalp electroencephalography, we examined how synchronized activity depends on visual stimulus information and on individual observer sensitivity. In a perceptual grouping task, we varied the ambiguity of visual stimuli and estimated observer sensitivity to this variation. We found that durations of synchronized activity in the beta frequency band were associated with both stimulus ambiguity and sensitivity: the lower the stimulus ambiguity and the higher individual observer sensitivity the longer were the episodes of synchronized activity. Durations of synchronized activity intervals followed an extreme value distribution, indicating that they were limited by the slowest mechanism among the multiple neural mechanisms engaged in the perceptual task. Because the degree of stimulus ambiguity is (inversely) related to the amount of stimulus information, the durations of synchronous episodes reflect the amount of stimulus information processed in the task. We therefore interpreted our results as evidence that the alternating episodes of desynchronized and synchronized electrical brain activity reflect, respectively, the processing of information within local regions and the transfer of information across regions.

Network inference with confidence from multivariate time series

Networks--collections of interacting elements or nodes--abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions, it is common to include edges between those nodes whose time series exhibit sufficient functional connectivity, typically defined as a measure of coupling exceeding a predetermined threshold. However, when uncertainty exists in the original network measurements, uncertainty in the inferred network is likely, and hence a statistical propagation of error is needed. In this manuscript, we describe a principled and systematic procedure for the inference of functional connectivity networks from multivariate time series data. Our procedure yields as output both the inferred network and a quantification of uncertainty of the most fundamental interest: uncertainty in the number of edges. To illustrate this approach, we apply a measure of linear coupling to simulated data and electrocorticogram data recorded from a human subject during an epileptic seizure. We demonstrate that the procedure is accurate and robust in both the determination of edges and the reporting of uncertainty associated with that determination.

Functional connectivity through nonlinear modeling: an application to the rat hippocampus

Implementation of neuroprosthetic devices requires a reliable and accurate quantitative representation of the input-output transformations performed by the involved neuronal populations. Nonparametric, data driven models with predictive capabilities are excellent candidates for these purposes. When modeling input-output relations in multi-input neuronal systems, it is important to select the subset of inputs that are functionally and causally related to the output. Inputs that do not convey information about the actual transformation not only increase the computational burden but also affect the generalization of the model. Moreover, a reliable functional connectivity measure can provide patterns of information flow that can be linked to physiological and anatomical properties of the system. We propose a method based on the Volterra modeling approach that selects distinct subsets of inputs for each output based on the prediction of the respective models and its statistical evaluation. The algorithm builds successive models with increasing number of inputs and examines whether the inclusion of additional inputs benefits the predictive accuracy of the overall model. It also explores possible second-order (inter-modulatory) interactions among the inputs. The method was applied to multi-unit recordings from the CA3 (input) and CA1 (output) regions of the hippocampus in behaving rats, in order to reveal spatiotemporal connectivity maps of the input-output transformation taking place in the CA3-CA1 synapse.

Assessment of neural dynamic coupling and causal interactions between independent EEG components from cognitive tasks using linear and nonlinear methods

Over the past few years there has been an increased interest in studying the underlying neural mechanism of cognitive brain activity. In this direction, we study the brain activity based on its independent components instead of the EEG signal itself. Both linear and nonlinear synchronization measures are applied to EEG components, which are free of volume conduction effects and background noise. More specifically, a robust nonlinear state-space generalized synchronization assessment method and the recently introduced partial directed coherence are investigated in a working memory paradigm, during mental rehearsal of pictures. The latter is a linear method able to assess not only the independence of the brain regions, but also the direction of the statistically significant relationships. The results are in accordance with previous psychophysiology studies suggesting increased synchrony between prefrontal and parietal components during the rehearsal process, most prominently in gamma (ca. 40 Hz) band. This study indicates that functional connectivity during cognitive processes may be successfully assessed using independent components, which reflect distinct spatial patterns of activity.

Assessing causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods

We investigated the ability of mutual nonlinear prediction methods to assess causal interactions in short-term cardiovascular variability during normal and impaired conditions. Directional interactions between heart period (RR interval of the ECG) and systolic arterial pressure (SAP) short-term variability series were quantified as the cross-predictability (CP) of one series given the other, and as the predictability improvement (PI) yielded by the inclusion of samples of one series into the prediction of the other series. Nonlinear prediction was performed through global approximation (GA), approximation with locally constant models (LA0) and approximation with locally linear models (LA1) of the nonlinear function linking the samples of the two series, on patients with neurally mediated syncope and control subjects. Causality measures were evaluated in the two directions (from SAP to RR and from RR to SAP) in the supine (SU) position, in the upright position after head-up tilt (early tilt, ET) and after prolonged upright posture (late tilt, LT). While the trends for the GA, LA0 and LA1 methods were substantially superimposable, PI elicited better than CP the prevalence of causal coupling from RR to SAP during SU. Both CP and PI noted a marked decrease in coupling in both causal directions in syncope subjects during LT, documenting the impairment of cardiovascular regulation in the minutes just preceding syncope.

Identifying neural drivers with functional MRI: an electrophysiological validation

Whether functional magnetic resonance imaging (fMRI) allows the identification of neural drivers remains an open question of particular importance to refine physiological and neuropsychological models of the brain, and/or to understand neurophysiopathology. Here, in a rat model of absence epilepsy showing spontaneous spike-and-wave discharges originating from the first somatosensory cortex (S1BF), we performed simultaneous electroencephalographic (EEG) and fMRI measurements, and subsequent intracerebral EEG (iEEG) recordings in regions strongly activated in fMRI (S1BF, thalamus, and striatum). fMRI connectivity was determined from fMRI time series directly and from hidden state variables using a measure of Granger causality and Dynamic Causal Modelling that relates synaptic activity to fMRI. fMRI connectivity was compared to directed functional coupling estimated from iEEG using asymmetry in generalised synchronisation metrics. The neural driver of spike-and-wave discharges was estimated in S1BF from iEEG, and from fMRI only when hemodynamic effects were explicitly removed. Functional connectivity analysis applied directly on fMRI signals failed because hemodynamics varied between regions, rendering temporal precedence irrelevant. This paper provides the first experimental substantiation of the theoretical possibility to improve interregional coupling estimation from hidden neural states of fMRI. As such, it has important implications for future studies on brain connectivity using functional neuroimaging.

Our understanding of how the brain works relies on the development of neuropsychological models, which describe how brain activity is coordinated among different regions during the execution of a given task. Knowing the directionality of information transfer between connected regions, and in particular distinguishing neural drivers, or the source of forward connections in the brain, from other brain regions, is critical to refine models of the brain. However, whether functional magnetic resonance imaging (fMRI), the most common technique for imaging brain function, allows one to identify neural drivers remains an open question. Here, we used a rat model of absence epilepsy, a form of nonconvulsive epilepsy that occurs during childhood in humans, showing spontaneous spike-and-wave discharges (nonconvulsive seizures) originating from the first somatosensory cortex, to validate several functional connectivity measures derived from fMRI. Standard techniques estimating interactions directly from fMRI data failed because blood flow dynamics varied between regions. However, we were able to identify the neural driver of spike-and-wave discharges when hemodynamic effects were explicitly removed using appropriate modelling. This study thus provides the first experimental substantiation of the theoretical possibility to improve interregional coupling estimation from hidden neural states of fMRI. As such, it has important implications for future studies on connectivity in the functional neuroimaging literature.

Neural long-range interactions can be distinguished from hemodynamic confounds in functional magnetic resonance imaging using new data analysis techniques that will allow experimental validation of models of brain function.

An investigation of the phase locking index for measuring of interdependency of cortical source signals recorded in the EEG

The phase locking index (PLI) was introduced to quantify in a statistical sense the phase synchronization of two signals. It has been commonly used to process biosignals. In this article, we investigate the PLI for measuring the interdependency of cortical source signals (CSSs) recorded in the Electroencephalogram (EEG). To this end, we consider simple analytical models for the mapping of simulated CSSs into the EEG. For these models, the PLI is investigated analytically and through numerical simulations. An evaluation is made of the sensitivity of the PLI to the amount of crosstalk between the sources through biological tissues of the head. It is found that the PLI is a useful interdependency measure for CSSs, especially when the amount of crosstalk is small. Another common interdependency measure is the coherence. A direct comparison of both measures has not been made in the literature so far. We assess the performance of the PLI and coherence for estimation and detection purposes based on, respectively, a normalized variance and a novel statistical measure termed contrast. Based on these performance measures, it is found that the PLI is similar or better than the CM in most cases. This result is also confirmed through analysis of EEGs recorded from epileptic patients.

Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer's disease

The aim of the present study is to show the usefulness of nonlinear methods to analyse the electroencephalogram (EEG) and magnetoencephalogram (MEG) in patients with Alzheimer's disease (AD). The following nonlinear methods have been applied to study the EEG and MEG background activity in AD patients and control subjects: approximate entropy, sample entropy, multiscale entropy, auto-mutual information and Lempel-Ziv complexity. We discuss why these nonlinear methods are appropriate to analyse the EEG and MEG. Furthermore, the performance of all these methods has been compared when applied to the same databases of EEG and MEG recordings. Our results show that EEG and MEG background activities in AD patients are less complex and more regular than in healthy control subjects. In line with previous studies, our work suggests that nonlinear analysis techniques could be useful in AD diagnosis.

Use of piecewise stationary segmentation as a pre-treatment for synchronization measures

The analysis of the synchronization between biological signals can be helpful for the characterization of biological functions. Biological signals are however often strongly non stationary. This is in contradiction to the assumption of commonly used synchronization measures which assume that the signal is stationary. We propose to use a piecewise stationary pre-segmentation (PSP) of the signals of interest, before the computation of synchronization measures. We show on synthetic as well as real biological signals (EEG and uterine EMG) that the proposed piecewise stationary pre-segmentation approach increases the accuracy of the measures by making a good tradeoff between the stationary assumption and length of the analyzed segments, when compared to the classical windowing method.

Antiepileptic drug intervention decouples electroencephalogram (EEG) signals: a case study in Unverricht-Lundborg Disease

Change in severity of myoclonus as an outcome measure of antiepileptic drug (AED) treatment in patients with Unverricht-Lundborg Disease (ULD) has been estimated by utilizing the Unified Myoclonus Rating Scale (UMRS). In this study, we measure treatment effects through EEG analysis using mutual information approach to quantify interdependence/coupling strength among different electrode sites. Mutual information is known to have the ability to capture linear and non-linear dependencies between EEG time series with superior performance over the traditional linear measures. One subject with ULD participated in this study and 1-hour EEG recordings were acquired before and after treatment of AED. Our results indicate that the mutual information is significantly lower after taking the add-on AED for four weeks at least. This finding could lead to a new insight for developing a new outcome measure for patient with ULD, when UMRS could potentially fail to detect a significant difference.

Interpretation of the auto-mutual information rate of decrease in the context of biomedical signal analysis. Application to electroencephalogram recordings

The mutual information (MI) is a measure of both linear and nonlinear dependences. It can be applied to a time series and a time-delayed version of the same sequence to compute the auto-mutual information function (AMIF). Moreover, the AMIF rate of decrease (AMIFRD) with increasing time delay in a signal is correlated with its entropy and has been used to characterize biomedical data. In this paper, we aimed at gaining insight into the dependence of the AMIFRD on several signal processing concepts and at illustrating its application to biomedical time series analysis. Thus, we have analysed a set of synthetic sequences with the AMIFRD. The results show that the AMIF decreases more quickly as bandwidth increases and that the AMIFRD becomes more negative as there is more white noise contaminating the time series. Additionally, this metric detected changes in the nonlinear dynamics of a signal. Finally, in order to illustrate the analysis of real biomedical signals with the AMIFRD, this metric was applied to electroencephalogram (EEG) signals acquired with eyes open and closed and to ictal and non-ictal intracranial EEG recordings.

BrainNetVis: analysis and visualization of brain functional networks

BrainNetVis is an application, written in Java, that displays and analyzes synchronization networks from brain signals. The program implements a number of network indices and visualization techniques. We demonstrate its use through a case study of left hand and foot motor imagery. The data sets were provided by the Berlin BCI group. Using this program we managed to find differences between the average left hand and foot synchronization networks by comparing them with the average idle state synchronization network.

Chaotic communication via temporal transfer entropy

We propose a new perspective on communication using chaos. A binary message is encoded into the temporally causal relations on a coupled maps ring of N chaotic nodes. From the analysis of temporal transfer entropy, the masked information can be recovered from transmitted signals at the receiver. The communication scheme has been demonstrated to be robust against external noise and some traditional attacks.

Data-driven estimates of the number of clusters in multivariate time series

An important problem in unsupervised data clustering is how to determine the number of clusters. Here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series. Two nonparametric and purely data driven algorithms are expounded and compared. The first exploits the eigenvalue spectra of surrogate data, while the second employs the eigenvector components of the interrelation matrix. Compared to the first algorithm, the second approach is computationally faster and not limited to linear interrelation measures.

Characterizing dynamic functional connectivity across sleep stages from EEG

Following a nonlinear dynamics approach, we investigated the emergence of functional clusters which are related with spontaneous brain activity during sleep. Based on multichannel EEG traces from 10 healthy subjects, we compared the functional connectivity across different sleep stages. Our exploration commences with the conjecture of a small-world patterning, present in the scalp topography of the measured electrical activity. The existence of such a communication pattern is first confirmed for our data and then precisely determined by means of two distinct measures of non-linear interdependence between time-series. A graph encapsulating the small-world network structure along with the relative interdependence strength is formed for each sleep stage and subsequently fed to a suitable clustering procedure. Finally the delineated graph components are comparatively presented for all stages revealing novel attributes of sleep architecture. Our results suggest a pivotal role for the functional coupling during the different stages and indicate interesting dynamic characteristics like its variable hemispheric asymmetry and the isolation between anterior and posterior cortical areas during REM.

Nonlinear modeling of causal interrelationships in neuronal ensembles

The increasing availability of multiunit recordings gives new urgency to the need for effective analysis of "multidimensional" time-series data that are derived from the recorded activity of neuronal ensembles in the form of multiple sequences of action potentials--treated mathematically as point-processes and computationally as spike-trains. Whether in conditions of spontaneous activity or under conditions of external stimulation, the objective is the identification and quantification of possible causal links among the neurons generating the observed binary signals. A multiple-input/multiple-output (MIMO) modeling methodology is presented that can be used to quantify the neuronal dynamics of causal interrelationships in neuronal ensembles using spike-train data recorded from individual neurons. These causal interrelationships are modeled as transformations of spike-trains recorded from a set of neurons designated as the "inputs" into spike-trains recorded from another set of neurons designated as the "outputs." The MIMO model is composed of a set of multiinput/single-output (MISO) modules, one for each output. Each module is the cascade of a MISO Volterra model and a threshold operator generating the output spikes. The Laguerre expansion approach is used to estimate the Volterra kernels of each MISO module from the respective input-output data using the least-squares method. The predictive performance of the model is evaluated with the use of the receiver operating characteristic (ROC) curve, from which the optimum threshold is also selected. The Mann-Whitney statistic is used to select the significant inputs for each output by examining the statistical significance of improvements in the predictive accuracy of the model when the respective inputs is included. Illustrative examples are presented for a simulated system and for an actual application using multiunit data recordings from the hippocampus of a behaving rat.

Comparison of power spectrum predictors in computing coherence functions for intracortical EEG signals

The present study compares two Auto-Regressive (AR) model based (Burg Method (BM) and Yule Walker Method) and two subspace based (Eigen Method and Multiple Signal Classification Method) power spectral density predictors in computing the Coherence Function (CF) to observe EEG synchronization between right and left hemispheres. For this purpose, two channels intracortical EEG series recorded from WAG/Rij rats (a genetic model for human absence epilepsy) are analyzed. In tests, AR model-based predictors result the close performance such that the CF estimations are sensitive to the AR model order. Dealing with the subspace-based predictors; certain peaks in CF estimations can also be detected in case of low noise subspace dimension. Besides, they are more computational complexity. In conclusion, high order BM is proposed in EEG synchronization. The results support that each EEG sequence probably meets a high order AR model where the dimension of the related noise subspace is relatively low in comparison to the model order.

Inferring coupling strength from event-related dynamics

We propose an approach for inferring strength of coupling between two systems from their transient dynamics. This is of vital importance in cases where most information is carried by the transients, for instance, in evoked potentials measured commonly in electrophysiology. We show viability of our approach using nonlinear and linear measures of synchronization on a population model of thalamocortical loop and on a system of two coupled Rössler-type oscillators in nonchaotic regime.

Evolving functional network properties and synchronizability during human epileptic seizures

We assess electrical brain dynamics before, during, and after 100 human epileptic seizures with different anatomical onset locations by statistical and spectral properties of functionally defined networks. We observe a concave-like temporal evolution of characteristic path length and cluster coefficient indicative of a movement from a more random toward a more regular and then back toward a more random functional topology. Surprisingly, synchronizability was significantly decreased during the seizure state but increased already prior to seizure end. Our findings underline the high relevance of studying complex systems from the viewpoint of complex networks, which may help to gain deeper insights into the complicated dynamics underlying epileptic seizures.

Event-related EEG time-frequency analysis: an overview of measures and an analysis of early gamma band phase locking in schizophrenia

An increasing number of schizophrenia studies have been examining electroencephalography (EEG) data using time-frequency analysis, documenting illness-related abnormalities in neuronal oscillations and their synchronization, particularly in the gamma band. In this article, we review common methods of spectral decomposition of EEG, time-frequency analyses, types of measures that separately quantify magnitude and phase information from the EEG, and the influence of parameter choices on the analysis results. We then compare the degree of phase locking (ie, phase-locking factor) of the gamma band (36-50 Hz) response evoked about 50 milliseconds following the presentation of standard tones in 22 healthy controls and 21 medicated patients with schizophrenia. These tones were presented as part of an auditory oddball task performed by subjects while EEG was recorded from their scalps. The results showed prominent gamma band phase locking at frontal electrodes between 20 and 60 milliseconds following tone onset in healthy controls that was significantly reduced in patients with schizophrenia (P = .03). The finding suggests that the early-evoked gamma band response to auditory stimuli is deficiently synchronized in schizophrenia. We discuss the results in terms of pathophysiological mechanisms compromising event-related gamma phase synchrony in schizophrenia and further attempt to reconcile this finding with prior studies that failed to find this effect.

Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: comparison among different strategies based on k nearest neighbors

We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of k -nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application during known conditions of interaction-i.e., the analysis of the interdependence between heart rate and arterial pressure variability in healthy humans during supine resting and passive head-up tilting. Based on both simulation results and physiological interpretability of cardiovascular results, we conclude that cross prediction is valuable to quantify the coupling strength and predictability improvement to elicit directionality of the interactions in short and noisy bivariate time series.

Enhanced EEG functional connectivity in mesial temporal lobe epilepsy

PURPOSE

To analyze and compare spectral properties and interdependencies of intracerebral EEG signals recorded during interictal periods from mesial temporal lobe structures in two groups of epileptic patients defined according to the involvement of these structures in the epileptogenic zone (EZ).

METHODS

Interictal EEG activity in mesial temporal lobe (MTL) structures (hippocampus, entorhinal cortex and amygdala) was obtained from intracerebral recordings performed in 21 patients with drug-resistant mesial temporal lobe epilepsy (MTLE group). This group was compared with a "control" group of patients (non-MTLE group) in whom depth-EEG recordings of MTL show that seizures did not start from the MTL. Comparison criteria were based on spectral properties and statistical coupling (nonlinear correlation coefficient h(2)) of MTL signals.

RESULTS

Power spectral density analysis showed a significant decrease in the theta frequency sub-band (p=0.01) in the MTLE group. Nonlinear correlation (h(2)) values were found to be higher in the MTLE group than in the NMTLE group (p=0.0014). This effect was significant for theta, alpha, beta and gamma frequencies. Correlation values were not correlated with the frequency of interictal spikes (IS) and significant differences between groups were still measureable even when spikes were suppressed from analyzed EEG periods.

DISCUSSION

This study shows that, during the interictal state, the EZ in MTLE is characterized by a decrease of oscillations in the theta sub-band and by a general increase of signal interdependencies. This last finding suggests that the EZ is characterized by network of neuronal assemblies with a reinforced functional connectivity.

Phase dynamics of coupled oscillators reconstructed from data

We systematically develop a technique for reconstructing the phase dynamics equations for coupled oscillators from data. For autonomous oscillators and for two interacting oscillators we demonstrate how phase estimates obtained from general scalar observables can be transformed to genuine phases. This allows us to obtain an invariant description of the phase dynamics in terms of the genuine, observable-independent phases. We discuss the importance of this transformation for characterization of strength and directionality of interaction from bivariate data. Moreover, we demonstrate that natural (autonomous) frequencies of oscillators can be recovered if several observations of coupled systems at different, yet unknown coupling strengths are available. We illustrate our method by several numerical examples and apply it to a human electrocardiogram and to a physical experiment with coupled metronomes.

Gastrointestinal arrhythmias are associated with statistically significant fluctuations in systemic information dimension

Although cardiac arrhythmias have been studied extensively, little is known about arrhythmic phenomena in the gastrointestinal (GI) system. In this study, we demonstrate for the first time that the onset of GI arrhythmias is associated with statistically significant fluctuations in the information dimension of the associated systems. We induced gastric and intestinal arrhythmias in pigs using surgical stomach division and mesenteric artery ligation, respectively. Both conditions lead to a decreased supply of blood to the GI tract, which is associated in humans with various potentially lethal conditions including chronic mesenteric ischemia, whose mortality rate is over 60%. During our experiments, we recorded simultaneous magnetocardiographic, magnetogastrographic and magnetoenterographic signals and concluded that, when GI circulation is compromised, the information dimensionality of the system fluctuates significantly. In conclusion, dimensionality may be an important diagnostic factor for the characterization of arrhythmias in the context of GI pathophysiology.

Kernel method for nonlinear granger causality

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

Optimal brain network synchrony visualization: application in an alcoholism paradigm

Although Electroencephalographic (EEG) signal synchronization studies have been a topic of increasing interest lately, there is no similar effort in the visualization of such measures. In this direction a graph-theoretic approach devised to study and stress the coupling dynamics of task-performing dynamical networks is proposed. Both linear and nonlinear interdependence measures are investigated in an alcoholism paradigm during mental rehearsal of pictures, which is known to reflect synchronization impairment. More specifically, the widely used magnitude squared coherence; phase synchronization and a robust nonlinear state-space generalized synchronization assessment method are investigated. This paper mostly focuses on a signal-based technique of selecting the optimal visualization threshold using surrogate datasets to correctly identify the most significant correlation patterns. Furthermore, a graph statistical parameter attempts to capture and quantify collective motifs present in the functional brain network. The results are in accordance with previous psychophysiology studies suggesting that an alcoholic subject has impaired synchronization of brain activity and loss of lateralization during the rehearsal process, most prominently in alpha (8-12 Hz) band, as compared to a control subject. Lower beta (13-30 Hz) synchronization was also evident in the alcoholic subject.

Analysis of the phase locking index for measuring of interdependency of cortical signals recorded in the EEG

The phase locking index (PLI) was introduced to quantify in a statistical sense the phase synchronization of two signals. It has been commonly used to process biosignals. In this paper, we analyze the PLI for measuring the interdependency of cortical source signals (CSSs) recorded in the Electroencephalogram (EEG). The main focus of the analysis is the probability density function, which describes the sensitivity of the PLI to the joint noise ensemble in the CSSs. Since this function is mathematically intractable, we derive approximations and analyze them for a simple analytical model of the CSS mixture in the EEG. The accuracies of the approximate probability density functions (APDFs) are evaluated using simulations for the model. The APDFs are found sufficiently accurate and thus are applicable for practical intents and purposes. They can hence be used to determine the confidence intervals and significance levels for detection methods for interdependencies, e.g., between cortical signals recorded in the EEG.

Detecting phase synchronization in noisy data from coupled chaotic oscillators

Two schemes are proposed to detect phase synchronization from chaotic data contaminated by noise. The first is a neighborhood-based method which links time delay embedding with instantaneous phase estimation. The second adopts the local projection method as a preprocessing filter to noisy data. Both schemes utilize the state recurrence, an important feature of chaotic data. The proposed schemes are applied to data measured from two typical chaotic systems, i.e., the coupled Rössler systems and the coupled Lorenz systems, respectively. The results show that phase synchronization, which may be buried by noise, is detected even when the noise level is high. Moreover, the overestimation of the degree of phase synchronization, which may be introduced by the Hilbert transform combined with a traditional linear bandpass filter, can be avoided when the data are contaminated by only measurement noise.

Dynamic causal modelling of induced responses

This paper describes a dynamic causal model (DCM) for induced or spectral responses as measured with the electroencephalogram (EEG) or the magnetoencephalogram (MEG). We model the time-varying power, over a range of frequencies, as the response of a distributed system of coupled electromagnetic sources to a spectral perturbation. The model parameters encode the frequency response to exogenous input and coupling among sources and different frequencies. The Bayesian inversion of this model, given data enables inferences about the parameters of a particular model and allows us to compare different models, or hypotheses. One key aspect of the model is that it differentiates between linear and non-linear coupling; which correspond to within and between-frequency coupling respectively. To establish the face validity of our approach, we generate synthetic data and test the identifiability of various parameters to ensure they can be estimated accurately, under different levels of noise. We then apply our model to EEG data from a face-perception experiment, to ask whether there is evidence for non-linear coupling between early visual cortex and fusiform areas.

Synchronization Clusters of Interictal Activity in the Lateral Temporal Cortex of Epileptic Patients: Intraoperative Electrocorticographic Analysis

OBJECTIVE

Drug-resistant temporal lobe epilepsy (TLE) can be treated by tailored surgery guided by electrocorticography (ECoG). Although its value is still controversial, ECoG activity can provide continuous information on intracortical interactions that may be useful to understand the pathophysiology of TLE. The goal of this study is to characterize local interactions in multichannel ECoG recordings of the lateral cortex of TLE patients using three synchronization measures and to link this information with surgical outcome.

METHODS

Intraoperative ECoG recordings from 29 TLE patients were obtained using grids of 20 electrodes (4 x 5) covering regions T1, T2, and T3 of the lateral temporal lobe. Linear correlation, mutual information, and phase synchronization were calculated to quantify lateral intracortical interactions. Surrogate data files were generated to test results statistically.

RESULTS

By distributing locally the interactions between the electrodes, we characterized the spatial patterns of ECoG activity. We found clusters of synchronized activity at specific areas of the lateral temporal cortex in most patients. Methodologically, linear correlation and phase synchronization performed better than mutual information for cluster discrimination. ROC analysis suggested that surgical removal of sharply defined synchronization clusters correlated with seizure control.

CONCLUSIONS

Our results show that synchronous intraoperative ECoG activity emerges from specific cortical areas that are highly differentiated from the rest of the temporal cortex. This suggests that synchronization analysis could be used to functionally map into the temporal cortex of TLE patients. Moreover, our results suggest that these sites might be involved in the circuits that participate in clinical seizures.

Estimating interdependences in networks of weakly coupled deterministic systems

The extraction of information from measured data about the interactions taking place in a network of systems is a key topic in modern applied sciences. This topic has been traditionally addressed by considering bivariate time series, providing methods which are sometimes difficult to extend to multivariate data, the limiting factor being the computational complexity. Here, we present a computationally viable method based on black-box modeling which, while theoretically applicable only when a deterministic hypothesis about the processes behind the recordings is plausible, proves to work also when this assumption is severely affected. Conceptually, the method is very simple and is composed of three independent steps: in the first step a state-space reconstruction is performed separately on each measured signal; in the second step, a local model, i.e., a nonlinear dynamical system, is fitted separately on each (reconstructed) measured signal; afterward, a linear model of the dynamical interactions is obtained by cross-relating the (reconstructed) measured variables to the dynamics unexplained by the local models. The method is successfully validated on numerically generated data. An assessment of its sensitivity to data length and modeling and measurement noise intensity, and of its applicability to large-scale systems, is also provided.

On the application of the auto mutual information rate of decrease to biomedical signals

The auto mutual information function (AMIF) evaluates the signal predictability by assessing linear and non-linear dependencies between two measurements taken from a single time series. Furthermore, the AMIF rate of decrease (AMIFRD) is correlated with signal entropy. This metric has been used to analyze biomedical data, including cardiac and brain activity recordings. Hence, the AMIFRD can be a relevant parameter in the context of biomedical signal analysis. Thus, in this pilot study, we have analyzed a synthetic sequence (a Lorenz system) and real biosignals (electroencephalograms recorded with eyes open and closed) with the AMIFRD. We aimed at illustrating the application of this parameter to biomedical time series. Our results show that the AMIFRD can detect changes in the non-linear dynamics of a sequence and that it can distinguish different physiological conditions.