Quantitative analysis of directional strengths in jointly stationary linear multivariate processes

Identification and analysis of directed influences in multivariate systems is an important problem in many scientific areas. Recent studies in neuroscience have provided measures to determine the network structure of the process and to quantify the total effect in terms of energy transfer. These measures are based on joint stationary representations of a multivariate process using vector auto-regressive (VAR) models. A few important issues remain unaddressed though. The primary outcomes of this study are (i) a theoretical proof that the total coupling strength consists of three components, namely, the direct, indirect, and the interference produced by the direct and indirect effects, (ii) expressions to estimate/calculate these effects, and (iii) a result which shows that the well-known directed measure for linear systems, partial directed coherence (PDC) only aids in structure determination but does not provide a normalized measure of the direct energy transfer. Simulation case studies are shown to illustrate the theoretical results.     

Quantitative measures of cortical functional connectivity: A state-of-the-art brief survey

The modern concepts of quantitative measurement of the strength of functional and effective cortical connectivity in neurocognitive networks (large-scale distributed brain systems of interacting neuronal populations that are believed to underlie cognitive processing) are reviewed. The two main classes of the methods of connectivity assessment (linear and nonlinear) are discussed. In the class of linear methods, in addition to coherence routinely used to measure the strength of functional links, the vector autoregressive modeling of multichannel EEG is discussed in detail. The latter technique allows the estimation of both functional and effective connectivity, i.e., the measures such as directed transfer function (DTF) and direct partial coherence (PDC) extensively used in cognitive neuroscience. The impact of volume conduction on different estimates of connectivity is considered and the imaginary part of complex-valued coherence as a way to reduce the artificial influence of volume conduction is discussed. Independent component analysis (ICA) and transfer entropy as a method of estimating direct influence are reviewed in the class of nonlinear methods.     

Electrophysiological measures of regional neural interactive coupling. Linear and non-linear dependence relationships among multiple channel electroencephalographic recordings

Linear spectral coherence (Sklat et al., 1973) measures have been used in the neurosciences to test hypotheses which address the question of whether multiple EEG recording sites are independent or whether they are activated by common sources of neurophysiological activity. This measure is appropriate when regional neural sources interact and thereby electrically activate several recording sites through linear transmission pathways which may or may not be different in their linear transformation properties. However, if the transmission media are non-linear, then interactive dependency is not necessarily revealed by a linear coherence test. Therefore, if common sources are activating EEG recording sites through nonlinear media, evaluating the resulting relationships among the signals recorded from these sites requires a test which reveals the presence of such nonlinear relationships. In neurophysiological applications, a polycoherence cross-spectral measure provides such a test for nonlinear dependency (similar to the linear coherence test) among EEG recording sites. The data requirements and statistical properties of these linear and non-linear measures are described and results of a linear coherence analysis are presented in the context of an EEG pilot study of learning diabled children.     

The research of constructing dynamic cognition model based on brain network

Estimating the functional interactions and connections between brain regions to corresponding process in cognitive, behavioral and psychiatric domains is a central pursuit for understanding the human connectome. Few studies have examined the effects of dynamic evolution on cognitive processing and brain activation using brain network model in scalp electroencephalography (EEG) data. Aim of this study was to investigate the brain functional connectivity and construct dynamic programing model from EEG data and to evaluate a possible correlation between topological characteristics of the brain connectivity and cognitive evolution processing. Here, functional connectivity between brain regions is defined as the statistical dependence between EEG signals in different brain areas and is typically determined by calculating the relationship between regional time series using wavelet coherence. We present an accelerated dynamic programing algorithm to construct dynamic cognitive model that we found that spatially distributed regions coherence connection difference, the topologic characteristics with which they can transfer information, producing temporary network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time after variation audio stimulation, dynamic programing model gives the dynamic evolution processing at different time and frequency. In this paper, by applying a new construct approach to understand whole brain network dynamics, firstly, brain network is constructed by wavelet coherence, secondly, different time active brain regions are selected by network topological characteristics and minimum spanning tree. Finally, dynamic evolution model is constructed to understand cognitive process by dynamic programing algorithm, this model is applied to the auditory experiment, results showed that, quantitatively, more correlation was observed after variation audio stimulation, the EEG function connection dynamic evolution model on cognitive processing is feasible with wavelet coherence EEG recording.     

Face to phase: pitfalls in time delay estimation from coherency phase

Coherency phase is often interpreted as a time delay reflecting a transmission delay between spatially separated neural populations. However, time delays estimated from corticomuscular coherency are conflicting and often shorter than expected physiologically. Recent work suggests that corticomuscular coherence is influenced by afferent sensory feedback and bidirectional interactions. We investigated how bidirectional interaction affects time delay estimated from coherency, using a feedback model of the corticomuscular system. We also evaluated the effect of bidirectional interaction on two popular directed connectivity measures: directed transfer function (DTF) and partial directed coherence (PDC). The model is able to reproduce the range of time delays found experimentally from coherency phase by varying the strengths of the efferent and afferent pathways and the recording of sensory feedback in the cortical signal. Both coherency phase and DTF phase were affected by sensory feedback, resulting in an underestimation of the transmission delay. Coherency phase was altered by the recording of sensory feedback in the cortical signals and both measures were affected by the presence of a closed loop feedback system. Only PDC phase led to the correct estimation of efferent transmission delay in all simulated model configurations. Coherency and DTF phase should not be used to estimate transmission delays in neural networks as the estimated time delays are meaningless in the presence of sensory feedback and closed feedback loops.     

Information theoretic interpretation of frequency domain connectivity measures

In order to provide adequate multivariate measures of information flow between neural structures, modified expressions of partial directed coherence (PDC) and directed transfer function (DTF), two popular multivariate connectivity measures employed in neuroscience, are introduced and their formal relationship to mutual information rates are proved.     

Characteristics of the interhemispheric EEG relationships in assessing the functional state of the human brain

In healthy subjects (11 right-handed men) reorganization was studied of intra- and interhemispheric correlation of the electrical brain activity at transition from the state of alertness to drowsiness. At the lowering of alertness level, the coherence of hemispheres symmetrical points changed not abruptly, with a tendency towards an increase at differently directed character of changes of combinations of separate physiological rhythms ranges. Comparison of the EEG coherence changes within the right and left hemispheres revealed a greater reactivity of the left (dominant) hemisphere. The reduction of the predominance (observed in the dominant hemisphere in alertness) of the degree of EEG conjunction, at transition to drowsiness, leads to smoothing of interhemispheric asymmetry in the organization of electrical brain processes.     

Early Adolescent Cognitive Gains Are Marked by Increased Sleep EEG Coherence

Although the increases in cognitive capacities of adolescent humans are concurrent with significant cortical restructuring, functional associations between these phenomena are unclear. We examined the association between cortical development, as measured by the sleep EEG, and cognitive performance in a sample of 9/10 year olds followed up 1 to 3 years later. Our cognitive measures included a response inhibition task (Stroop), an executive control task (Trail Making), and a verbal fluency task (FAS). We correlated sleep EEG measures of power and intra-hemispheric coherence at the initial assessment with performance at that assessment. In addition we correlated the rate of change across assessments in sleep EEG measures with the rate of change in performance. We found no correlation between sleep EEG power and performance on cognitive tasks for the initial assessment. In contrast, we found a significant correlation of the rate of change in intra-hemispheric coherence for the sigma band (11 to 16 Hz) with rate of change in performance on the Stroop (r = 0.61; p<0.02) and Trail Making (r = −0.51; p<0.02) but no association for the FAS. Thus, plastic changes in connectivity (i.e., sleep EEG coherence) were associated with improvement in complex cognitive function.     

Linear and nonlinear causality between signals: methods, examples and neurophysiological applications

In this paper, we will present and review the most usual methods to detect linear and nonlinear causality between signals: linear Granger causality test (Geweke in J Am Stat Assoc 77:304–313, 1982) extended to direct causality in multivariate case (LGC), directed coherence (DCOH, Saito and Harashima in Recent advances in EEG and EMG data processing, Elsevier, Amsterdam, 1981), partial directed coherence (PDC, Sameshima and Baccala 1999) and nonlinear Granger causality test of Baek and Brock (in Working Paper University of Iowa, 1992) extended to direct causality in multivariate case (partial nonlinear Granger causality, PNGC). All these methods are tested and compared on several ARX, Poisson and nonlinear models, and on neurophysiological data (depth EEG). The results show that LGC, DCOH and PDC are not very robust in relation to nonlinear linkages but they seem to correctly find linear linkages if only the autoregressive parts are nonlinear. PNGC is extremely dependent on the choice of parameters. Moreover, LGC and PNGC may give misleading results in the case of causality on a spectral band, which is illustrated by our neurophysiological database.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

Gender differences in EEG coherence during memorization of dichotically and monaurally presented verbal stimuli

Gender differences in changes of coherence values in the theta and alpha frequency bands during encoding of dichotically and monaurally presented verbal information were studied. Right-handed students (14 male and 14 female subjects) participated in experiments. The EEG was recorded from 16 electrodes placed at homologous sites of the left and the right hemispheres. In male subjects, numerous differences in coherence values between conditions of dichotical and monaural word presentation were found in the theta2- and alpha1-bands, in females, the differences were most pronounced in the theta1- and theta2-frequency bands. Numerous differences in coherence values differentiated between dichotic and left-sided monaural presentations in males and between dichotic and right-sided monaural presentations in females. As compared to dichotic presentation, in condition of the monaural presentation, higher coherence values were observed in men and lower in women. The features of gender differences in frequency-spatial patterns of changes in EEG coherence values under conditions of bilaterally and unilaterally directed attention in male and female groups may testify that female subjects predominantly use right-hemispheric processing strategy, whereas male subjects use, mainly, left-hemispheric strategy for selection and memorization of concrete nouns.     

第一和第二语言Stroop任务中EEG同步化分析

采用基于多元自回归的瞬时EEG相干方法研究了十位汉英双语者执行Stroop任务时脑神经电活动及其功能皮层区的协同作用。结果显示：在β1(13-18Hz)频段,无论是汉语(第一语言,L1)还是英语(第二语言,L2)呈现的刺激,不一致条件的EEG相干值明显大于一致条件的EEG相干值,表明β1频段对刺激类型敏感;与L2相比,L1的Stroop任务中,额一顶区的相干值显著增强。EEG相干值反映了不同脑皮层间的相互作用强度。因此研究结果表明：判断和处理冲突信息(如Stroop的不一致条件)时脑功能皮层区之间的协同作用增强;相对于第二语言,第一语言处理过程中额一顶区之间的通信协作增加。     

EEG markers of the stabilotraining effect during the rehabilitation of patients with posttraumatic Korsakoff’s syndrome

Nine patients with posttraumatic Korsakoff syndrome (KS) were examined before and after a rehabilitation course of feedback stability training (ST) using EEG, posturographic and clinical tests (with the FIM and Mayo Portland scales used for estimation). During 7 to 12 sessions, the patients tried to perform static and motor tasks. A group of 18 healthy subjects were examined to provide standard parameters. The results demonstrated a disturbed spatiotemporal EEG pattern in patients with KS before ST in the form of a reduced coherence for short derivation pairs (intrahemispheric, interhemispheric, and diagonal ones) in frontal and parietooccipital areas. Analysis of specific EEG rhythms demonstrated the maximum decrease in coherence in the α band (with the aforementioned regional specificity) and for long diagonal pairs (between the left frontal and right parietooccipital areas). The ST course was accompanied by KS regression (according to clinical scales and posturographic study); an original increase in EEG coherence, especially that of α waves, was recorded in the occipitoparietal and central frontal areas of the right hemisphere; a subsequent increase in coherence of the frontal areas in both hemispheres was observed. Late after the ST course, further positive changes were characteristic of the EEG spatiotemporal pattern. However, comparison with standard data suggested incomplete recovery of various coherence parameters: hypertrophied coherence in intrahemispheric pairs and still reduced values in interhemispheric derivations. This EEG pattern suggested incomplete KS regression, which was confirmed by clinical data.     

EEG differences between resting states with eyes open and closed in darkness

Transition from a resting state with eyes closed (REC) to a resting state with eyes open (REO) is associated with visible changes in EEG, which are traditionally considered to be a sign of reorganization of the brain’s activity in response to visual stimuli. The EEGs recorded in the REC and REO states in complete darkness, when the stimulatory effect of light to the eye’s retina was absent, were compared. Thirty healthy subjects participated in the study. EEG in the range of 1.5–50 Hz was recorded from nineteen zones of the head monopolarly. It was found that, under conditions of complete darkness, the REC and REO states significantly differed in their EEG spectral power and coherence in the Δ, θ, α₁, α₂, β₁, β₂ and γ frequency bands. Under experimental conditions, these changes in the EEG could not be induced by external influence to the visual system. Therefore, we suppose that they are correlates of the switching of involuntary preliminary attention from internally directed attention specific for the REC state to externally directed attention specific for the REO state.     

On the spectral formulation of Granger causality

Spectral measures of causality are used to explore the role of different rhythms in the causal connectivity between brain regions. We study several spectral measures related to Granger causality, comprising the bivariate and conditional Geweke measures, the directed transfer function, and the partial directed coherence. We derive the formulation of dependence and causality in the spectral domain from the more general formulation in the information-theory framework. We argue that the transfer entropy, the most general measure derived from the concept of Granger causality, lacks a spectral representation in terms of only the processes associated with the recorded signals. For all the spectral measures we show how they are related to mutual information rates when explicitly considering the parametric autoregressive representation of the processes. In this way we express the conditional Geweke spectral measure in terms of a multiple coherence involving innovation variables inherent to the autoregressive representation. We also link partial directed coherence with Sims' criterion of causality. Given our results, we discuss the causal interpretation of the spectral measures related to Granger causality and stress the necessity to explicitly consider their specific formulation based on modeling the signals as linear Gaussian stationary autoregressive processes.     

Time Delay and Partial Coherence Analyses to Identify Cortical Connectivities

Recently it has been demonstrated by Albo that partial coherence analysis is sensitive to signal to noise ratio (SNR) and that it will always identify the signal with the highest SNR among the three signals as the main (driving) influence. We propose to use time delay analysis in parallel to partial coherence analysis to identify the connectivities between the multivariate time series. Both are applied to a theoretical model (used by Albo) to analyse the connections introduced in the model. Time delay analysis identifies the connections correctly. We also apply these analyses to the electroencephalogram (EEG) and electromyogram of essential tremor patients and EEG of normal subjects while bimanually tapping their index fingers. Biologically plausible cortico-muscular and cortico-cortical connections are identified by these methods.     

Intercentral EEG relationships in regressive and chronic post-traumatic Korsakoff syndrome.]

Dynamic EEG study of patients with posttraumatic Korsakoff's syndrome (KS) with the application of complex analysis methods revealed a complicated pathological structure of the intercentral relations of cortical electrical activity. The interhemispheric EEG coherence between symmetrical frontal cortical areas are sharply reduced, while the intrahemispheric coherence are increased in comparison with the normal values. The proposed technique of segregation of statistically homogeneous spectro-coherent characteristics made it possible to reveal the earlier intercentral EEG relations formed by stable and variable coherence spectra. The structure formed by the stable and variable coherence spectra in KS differs from that reflected in the mean coherence levels. During the KS regression, the EEG coherence between the right and left frontal areas increased to the normal level, and the variable spectra are revealed. In the chronic KS syndrome, the pathological intercentral relations persist, while the variable relations in the frontal areas are absent. A reduction of pathologically decreased intrahemispheric coherence selectively revealed in the right hemisphere during the KS regression and formation of variable relations in this hemisphere point to a leading role of the right hemisphere in development of compensatory processes in KS. The reciprocal relations between the intra- and interhemispheric coherence and coherence dynamics in the theta rhythm suggest that pathological activity in the basal diencephalic structures plays an important role in formation of the pathological EEG pattern in KS.     

Electroencephalographic characteristic of cognitive-specific alerting attention in verbal learning--III: Localized characteristics of EEG spatial synchronization

Electroencephalograms (EEG) were recorder in 19 standard derivations in 88 healthy subjects, while they were in the states: rest with eyes open; memorization (learning) of verbal bilingual semantic pairs (Latin and Russian languages); the retrieval of the rote information from memory (control). We compared estimates of EEG coherence in these states for the frequency bands theta (4-7 Hz), alpha-1 (7-10 Hz), alpha-2 (10-13 Hz), beta-1 (13-18 Hz), beta-2 (18-30 Hz), gamma (30-40 Hz). When compared with the rest most strongly expressed: for memorization a decrease of coherence in the pairs of derivations from frontal and central areas of the cortex in the EEG frequency bands; for retrieval an increase of coherence in interhemispheric derivation pairs of pariental-occipital region in majority of the frequency bands. For the retrieval also increases of coherence in the beta2 and gamma bands, along with coherence decreases at low frequencies take place in pairs formed by derivations from the parieto-occipital region with derivations from the frontal and the central ones. Dynamics of EEG coherence in comparisons of memorization and retrieval from the rest and each are expressed significantly more in the interhemispheric and crosshemispheric pairs of derivations than in the intrahemispheric pairs. Revealed topographic specificity of the dynamics of EEG coherence by changing the states is considered in terms of ideas about cognitive-specific forms of sustained goal-directed mental attention.     

EEG-MEG Integration Enhances the Characterization of Functional and Effective Connectivity in the Resting State Network

At the sensor level many aspects, such as spectral power, functional and effective connectivity as well as relative-power-ratio ratio (RPR) and spatial resolution have been comprehensively investigated through both electroencephalography (EEG) and magnetoencephalography (MEG). Despite this, differences between both modalities have not yet been systematically studied by direct comparison. It remains an open question as to whether the integration of EEG and MEG data would improve the information obtained from the above mentioned parameters. Here, EEG (64-channel system) and MEG (275 sensor system) were recorded simultaneously in conditions with eyes open (EO) and eyes closed (EC) in 29 healthy adults. Spectral power, functional and effective connectivity, RPR, and spatial resolution were analyzed at five different frequency bands (delta, theta, alpha, beta and gamma). Networks of functional and effective connectivity were described using a spatial filter approach called the dynamic imaging of coherent sources (DICS) followed by the renormalized partial directed coherence (RPDC). Absolute mean power at the sensor level was significantly higher in EEG than in MEG data in both EO and EC conditions. At the source level, there was a trend towards a better performance of the combined EEG+MEG analysis compared with separate EEG or MEG analyses for the source mean power, functional correlation, effective connectivity for both EO and EC. The network of coherent sources and the spatial resolution were similar for both the EEG and MEG data if they were analyzed separately. Results indicate that the combined approach has several advantages over the separate analyses of both EEG and MEG. Moreover, by a direct comparison of EEG and MEG, EEG was characterized by significantly higher values in all measured parameters in both sensor and source level. All the above conclusions are specific to the resting state task and the specific analysis used in this study to have general conclusion multi-center studies would be helpful.     

Dextrals and sinistrals (right-handers and left-handers): specificity of interhemispheric brain asymmetry and EEG coherence parameters

Data of literature about morphological, functional and biochemical specificity of the brain interhemispheric asymmetry of healthy right-handers and left-handers and about peculiarity of dynamics of cerebral pathology in patients with different individual asymmetry profiles are presented at the present article. Results of our investigation by using coherence parameters of electroencephalogram (EEG) in healthy right-handers and left-handers in state of rest, during functional tests and sleeping and in patients with different forms of the brain organic damage were analyzed too. EEG coherence analysis revealed the reciprocal changing of alpha-beta and theta-delta spectral bands in right-handers whilein left-handers synchronous changing of all EEG spectral bands were observed. Data about regional-frequent specificity of EEG coherence, peculiarity of EEG asymmetry in right-handers and left-handers, aslo about specificity of EEG spectral band genesis and point of view about a role of the brain regulator systems in forming of interhemispheric asymmetry in different functional states allowed to propose the conception about principle of interhermispheric brain asymmetry formation in left-handers and left-handers. Following this conception in dextrals elements of concurrent (summary-reciprocal) cooperation are predominant at the character of interhemispheric and cortical-subcortical interaction while in sinistrals a principle of concordance (supplementary) is preferable. These peculiarities the brain organization determine, from the first side, the quicker revovery of functions damaged after cranio-cerebral trauma in left-handers in comparison right-handers and from the other side - they determine the forming of the more expressed pathology in the remote terms after exposure the low dose of radiation.     

Changes in EEG coherence during tests for nonverbal (Figurative) creativity

Brain neurodynamics was studied by the EEG method during the performance of a task for figurative (or imaginative) creativity. The EEG was recorded in 19 standard derivations according to the international 10–20 system in 30 subjects. The following creative tasks were presented to subjects to involve them in the creative process: (Crl) thinking up and drawing an original picture; (Cr2) drawing a face, a house, and a clown in an original manner; (C1) drawing a picture from memory; and (C2) drawing geometric figures without any system. All the tasks had to be performed using a given set of geometric figures (a circle, semicircle, triangle, and rectangle). Statistical analysis of the EEG coherence function in these states for the frequency bands Δ, θ, α₁, α₂, β₁, β₂, and γ showed that the performance of creative and control tasks was associated with significant coherence changes in all the EEG frequency bands. As compared to the control tasks, performance of creative tasks caused an increase in the coherence of the α₁-and α₂ bands, more pronounced when creative tasks were compared with the second control task. In addition, the performance of the creative tasks (as compared to the control tasks) was accompanied by a decrease in the interhemispheric coherence of high-frequency rhythms (β₂ and γ) and an increase in the intrahemispheric coherence of these rhythms. The findings are compared to the results of previous EEG studies on creative activity.