Global dimensional complexity of multi-channel EEG indicates change of human brain functional state after a single dose of a nootropic drug

Fundamentally altered global- and microstate EEG characteristics in Huntington's disease

OBJECTIVE

Huntington's disease (HD) is characterized by psychiatric, cognitive, and motor disturbances. The study aimed to determine electroencephalography (EEG) global state and microstate changes in HD and their relationship with cognitive and behavioral impairments.

METHODS

EEGs from 20 unmedicated HD patients and 20 controls were compared using global state properties (connectivity and dimensionality) and microstate properties (EEG microstate analysis). For four microstate classes (A, B, C, D), three parameters were computed: duration, occurrence, coverage. Global- and microstate properties were compared between groups and correlated with cognitive test scores for patients.

RESULTS

Global state analysis showed reduced connectivity in HD and an increasing dimensionality with increasing HD severity. Microstate analysis revealed parameter increases for classes A and B (coverage), decreases for C (occurrence) and D (coverage and occurrence). Disease severity and poorer test performances correlated with parameter increases for class A (coverage and occurrence), decreases for C (coverage and duration) and a dimensionality increase.

CONCLUSIONS

Global state changes may reflect higher functional dissociation between brain areas and the complex microstate changes possibly the widespread neuronal death and corresponding functional deficits in brain regions associated with HD symptomatology.

SIGNIFICANCE

Combining global- and microstate analyses can be useful for a better understanding of progressive brain deterioration in HD.

Shape facilitates number: brain potentials and microstates reveal the interplay between shape and numerosity in human vision

Recognition of simple shapes and numerosity estimation for small quantities are often studied independently of each other, but we know that these processes are both rapid and accurate, suggesting that they may be mediated by common neural mechanisms. Here we address this issue by examining how spatial configuration, shape complexity, and luminance polarity of elements affect numerosity estimation. We directly compared the Event Related Potential (ERP) time-course for numerosity estimation under shape and random configurations and found a larger N2 component for shape over lateral-occipital electrodes (250–400 ms), which also increased with higher numbers. We identified a Left Mid Frontal (LMF; 400–650 ms) component over left-lateralised medial frontal sites that specifically separated low and high numbers of elements, irrespective of their spatial configuration. Different luminance-polarities increased N2 amplitude only, suggesting that shape but not numerosity is selective to polarity. Functional microstates confined numerosity to a strict topographic distribution occurring within the LMF time-window, while a microstate responding only to shape-configuration was evidenced earlier, in the N2 time-window. We conclude that shape-coding precedes numerosity estimation, which can be improved when the number of elements and shape vertices are matched. Thus, numerosity estimation around the subitizing range is facilitated by a shape-template matching process.

Functional Near-Infrared Spectroscopy for the Classification of Motor-Related Brain Activity on the Sensor-Level

Sensor-level human brain activity is studied during real and imaginary motor execution using functional near-infrared spectroscopy (fNIRS). Blood oxygenation and deoxygenation spatial dynamics exhibit pronounced hemispheric lateralization when performing motor tasks with the left and right hands. This fact allowed us to reveal biomarkers of hemodynamical response of the motor cortex on the motor execution, and use them for designing a sensing method for classification of the type of movement. The recognition accuracy of real movements is close to 100%, while the classification accuracy of imaginary movements is lower but quite high (at the level of 90%). The advantage of the proposed method is its ability to classify real and imaginary movements with sufficiently high efficiency without the need for recalculating parameters. The proposed system can serve as a sensor of motor activity to be used for neurorehabilitation after severe brain injuries, including traumas and strokes.

Characterization of EEG patterns in brain-injured subjects and controls after a Snoezelen(®) intervention

BACKGROUND AND OBJECTIVE

The aim of this study was to assess the changes induced in electroencephalographic (EEG) activity by a Snoezelen(®) intervention on individuals with brain-injury and control subjects.

METHODS

EEG activity was recorded preceding and following a Snoezelen(®) session in 18 people with cerebral palsy (CP), 18 subjects who have sustained traumatic brain-injury (TBI) and 18 controls. EEG data were analyzed by means of spectral and nonlinear measures: median frequency (MF), individual alpha frequency (IAF), sample entropy (SampEn) and Lempel-Ziv complexity (LZC).

RESULTS

Our results showed decreased values for MF, IAF, SampEn and LZC as a consequence of the therapy. The main changes between pre-stimulation and post-stimulation conditions were found in occipital and parietal brain areas. Additionally, these changes are more widespread in controls than in brain-injured subjects, which can be due to cognitive deficits in TBI and CP groups.

CONCLUSIONS

Our findings support the notion that Snoezelen(®) therapy affects central nervous system, inducing a slowing of oscillatory activity, as well as a decrease of EEG complexity and irregularity. These alterations seem to be related with higher levels of relaxation of the participants.

Migraine — New Perspectives from Chaos Theory

Converging from a number of disciplines, non-linear systems theory and in particular chaos theory offer new descriptive and prescriptive insights into physiological systems. This paper briefly reviews an approach to physiological systems from these perspectives and outlines how these concepts can be applied to the study of migraine. It suggests a wide range of potential applications including new approaches to classification, treatment and pathophysiological mechanisms. A hypothesis is developed that suggests that dysfunctional consequences can result from a mismatch between the complexity of the environment and the system that is seeking to regulate it and that the migraine phenomenon is caused by an incongruity between the complexity of mid brain sensory integration and cortical control networks. Chaos theory offers a new approach to the study of migraine that complements existing frameworks but may more accurately reflect underlying physiological mechanisms.

A study on validity of cortical alpha connectivity for schizophrenia

Abnormalities in schizophrenia are thought to be associated with functional disconnections between different brain regions. Most previous studies on schizophrenia have considered high-band connectivity in preference to the Alpha band, as there has been some uncertainty correlating the latter to the condition. In this paper we attempt to clarify this correlation using an Electroencephalogram (EEG) analysis of the Alpha band from schizophrenic patients. Global, regional Omega and dimensional complexity and local Omega complexity differentials (LCD) of single channel are calculated using 16 channels of resting EEG data from 31 adult patients with schizophrenia and 31 age/sex matched control subjects. It was found that, compared to the controls, anterior alpha Omega and dimensional complexity are higher in schizophrenia patients (p<0.05) with the single channel LCD also increasing at FP1, FP2, F7 and F8 electrodes. Furthermore, higher left hemisphere dimensional complexity and LCD at T3 point was also found. The results suggest there is lower connectivity in the pre-frontal and left temporal regions with respect to the alpha band in schizophrenia patients.

Reliability of resting-state microstate features in electroencephalography

Background

Electroencephalographic (EEG) microstate analysis is a method of identifying quasi-stable functional brain states (“microstates”) that are altered in a number of neuropsychiatric disorders, suggesting their potential use as biomarkers of neurophysiological health and disease. However, use of EEG microstates as neurophysiological biomarkers requires assessment of the test-retest reliability of microstate analysis.

Methods

We analyzed resting-state, eyes-closed, 30-channel EEG from 10 healthy subjects over 3 sessions spaced approximately 48 hours apart. We identified four microstate classes and calculated the average duration, frequency, and coverage fraction of these microstates. Using Cronbach's α and the standard error of measurement (SEM) as indicators of reliability, we examined: (1) the test-retest reliability of microstate features using a variety of different approaches; (2) the consistency between TAAHC and k-means clustering algorithms; and (3) whether microstate analysis can be reliably conducted with 19 and 8 electrodes.

Results

The approach of identifying a single set of “global” microstate maps showed the highest reliability (mean Cronbach's α>0.8, SEM ≈10% of mean values) compared to microstates derived by each session or each recording. There was notably low reliability in features calculated from maps extracted individually for each recording, suggesting that the analysis is most reliable when maps are held constant. Features were highly consistent across clustering methods (Cronbach's α>0.9). All features had high test-retest reliability with 19 and 8 electrodes.

Conclusions

High test-retest reliability and cross-method consistency of microstate features suggests their potential as biomarkers for assessment of the brain's neurophysiological health.

Global synchronization index as a biological correlate of cognitive decline in Alzheimer's disease

OBJECTIVE

The recently developed global synchronization index (GSI) quantifies synchronization between neuronal signals at multiple sites. This study explored the clinical significance of the GSI in Alzheimer's disease (AD) patients.

METHODS

Electroencephalograms were recorded from 25 AD patients and 22 age-matched healthy normal controls (NC). GSI values were computed both across the entire frequency band and separately in the delta, theta, alpha, beta1, beta2, beta3, and gamma bands. The Mini-Mental Status Examination (MMSE) and Clinical Dementia Rating scale (CDR) were used to assess the symptom severity.

RESULTS

GSI values in the beta1, beta2, beta3, and gamma bands were significantly lower in AD patients than in NC. GSI values in the beta and gamma bands were positively correlated with the MMSE scores in all participants (AD and NC). In AD patients, GSI values were negatively correlated with MMSE scores in the delta bands, but positively correlated in the beta1 and gamma band. Also, GSI values were positively correlated with CDR scores in the delta bands, but negatively correlated in the gamma band.

CONCLUSIONS

GSI values of mainly high-frequency bands were significantly lower in AD patients than in NC, they were significantly correlated with scores on symptom severity scales.

SIGNIFICANCE

Our results suggest that GSI values are a useful biological correlate of cognitive decline in AD patients.

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

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

Alzheimer's disease: models of computation and analysis of EEGs

In a recent article the authors presented a comprehensive review of research performed on computational modeling of Alzheimer's disease (AD) and its markers with a focus on computer imaging, classification models, connectionist neural models, and biophysical neural models. The popularity of imaging techniques for detection and diagnosis of possible AD stems from the relative ease with which neurological markers can be converted to visual markers. However, due to the expense of specialized experts and equipment involved in the use of imaging techniques, a subject of significant research interest is detecting markers in EEGs obtained from AD patients. In this article, the authors present a state-of-the-art review of models of computation and analysis of EEGs for diagnosis and detection of AD. This review covers three areas: time-frequency analysis, wavelet analysis, and chaos analysis. The vast number of physiological parameters involved in the poorly understood processes responsible for AD yields a large combination of parameters that can be manipulated and studied. A combination of parameters from different investigation modalities seems to be more effective in increasing the accuracy of detection-and diagnosis.

Changes in Cortical Dynamics in the Preictal Stage of a Migraine Attack

Neurophysiologic studies suggest that migraineurs without aura have a dysfunction of cortical information processing in the pain-free interval. In this study, the advanced method of nonlinear multielectrode sleep-EEG analysis is used to investigate changes of cortical activity in the preictal time span. Five patients (four women, one man; age range, 29 to 58 years) experiencing migraine without aura participated in the study. The patients spent two blocks in the sleep laboratory. The first block was taken in a headache-free interictal time interval, and the second block when the onset of a migraine attack was most likely. After a nocturnal migraine attack, the patient was asked to mark the maximum of migraine pain in a surface-head scheme. The comparison of preictal and interictal EEGs enabled the authors to obtain a topographical view of changes in cortical dynamics. In each patient map, an area was found that displayed a pronounced focus indicating the region of maximum change in dimensional complexity. It shows a clearly recognizable correspondence with the scalp topography of the later pain perception. These findings indicate an association between cortical status and pain lateralization in the preictal time span.

The algorithmic complexity of multichannel EEGs is sensitive to changes in behavior

Symbolic measures of complexity provide a quantitative characterization of the sequential structure of symbol sequences. Promising results from the application of these methods to the analysis of electroencephalographic (EEG) and event-related brain potential (ERP) activity have been reported. Symbolic measures used thus far have two limitations, however. First, because the value of complexity increases with the length of the message, it is difficult to compare signals of different epoch lengths. Second, these symbolic measures do not generalize easily to the multichannel case. We address these issues in studies in which both single and multichannel EEGs were analyzed using measures of signal complexity and algorithmic redundancy, the latter being defined as a sequence-sensitive generalization of Shannon's redundancy. Using a binary partition of EEG activity about the median, redundancy was shown to be insensitive to the size of the data set while being sensitive to changes in the subject's behavioral state (eyes open vs. eyes closed). The covariance complexity, calculated from the singular value spectrum of a multichannel signal, was also found to be sensitive to changes in behavioral state. Statistical separations between the eyes open and eyes closed conditions were found to decrease following removal of the 8- to 12-Hz content in the EEG, but still remained statistically significant. Use of symbolic measures in multivariate signal classification is described.

EEG source localization and global dimensional complexity in high- and low- hypnotizable subjects: a pilot study

Individuals differ in hypnotizability. Information on hypnotizability-related EEG characteristics is controversial and incomplete, particularly on intracerebral source localization and EEG dimensionality. 19-channel, eyes-closed resting EEGs from right-handed, healthy, 8 high- and 4 low-hynotizable subjects (age: 26.7 +/- 7.3 years) were analyzed. Hypnotizability was rated after the subjects' ability to attain a deep hypnotic stage (amnesia). FFT Dipole Approximation analysis in seven EEG frequency bands showed significant differences (p < 0.04) of source gravity center locations for theta (6.5-8 Hz, more posterior and more left for highs), beta-1 and beta-2 frequencies (12.5-18 and 18.5-21 Hz; both more posterior and more right for highs). Low Resolution Electromagnetic Tomography (LORETA) specified the cortical anteriorization of beta-1 and beta-2 in low hypnotizables. Power spectral analysis of Global Field Power time series (curves) showed no overall power differences in any band. Full-band Global Dimensional Complexity was higher in high-hypnotizable subjects (p < 0.02). Thus, before hypnosis, high and low hypnotizables were in different brain electric states, with more posterior brain activity gravity centers (excitatory right, routine or relaxation left) and higher dimensional complexity (higher arousal) in high than low hypnotizables.

Pattern analysis of sleep-deprived human EEG

Progress during the past decade in non-linear dynamics and instability theory has provided useful tools for understanding spatio-temporal pattern formation. Procedures which apply principle component analysis (using the Karhunen-Loeve decomposition technique) to the multichannel electroencephalograph (EEG) time series have been developed. This technique shows localized changes of cortical functioning; it identifies increases and decreases of the activity of localized cortical regions over time while the subject performs a simple task or test. It can be used to demonstrate the change in cortical dynamics in response to a continuous challenge. Using 16 EEG electrodes, the technique provides spatio-temporal information not obtained with power spectrum analysis, and includes the weighted information given with omega complexity. As an application, we performed a pattern analysis of sleep-deprived human EEG data in 20 healthy young men. Electroencephalograph recordings were performed on subjects for <2 min, with eyes closed after normal sleep and after 24 h of experimentally-induced sleep deprivation. The significant changes in the eigenvector components indicated the relative changes of local activity in the brain with progressive sleep deprivation. A sleep deprivation effect was observed, which was hemispherically correlated but with opposite directional dynamics. These changes were seen in the temporo-parietal regions bilaterally. The application of the technique showed that the simple test task was performed with a limited unilateral hemispheric involvement at baseline, but needed a much larger cortical participation with decreased frontal activity and increased coherence and bilateral hemispheric involvement. The calculations performed demonstrated that the same weighted changes as those obtained with omega complexity were shown, but the technique had the added advantage of showing the localized directional changes of the principle eigenvector at each studied electrode, pointing out the cortical localized region affected by the sleep deprivation and toward which direction the environmental challenge induced the spatial change. This methodology may allow the evaluation of changes in local dynamics in brain activity in normal and pathological conditions.

Detection of non-linearity in the EEG of schizophrenic patients

OBJECTIVE

The aim of this study is to detect non-linearity in the EEG of schizophrenia with a modified method of surrogate data. We also want to identify if dimension complexity (correlation dimension using spatial embedding) could be used as a discriminating statistic to demonstrate non-linearity in the EEG. The difference between the attractor dimension of healthy subjects and schizophrenic subjects is expected to be interpreted as reflecting some mechanisms underlying brain wave by views of non-linear dynamics analysis may reflect mechanistic differences.

METHODS

EEGs were recorded with 14 electrodes in 18 healthy male subjects (average age: 26.3; range: 20--35) and 18 male schizophrenic patients (average age: 30.6; range: 24--40) during a resting eye-closed state. Neither of two groups was taking medicines. All artificial epochs in the EEG records were rejected by an experienced doctor's visual inspection.

RESULTS

Testing non-linearity with modified surrogate data, we showed that correlation dimension of EEG data of schizophrenia does refuse the null hypothesis that the data were resulted from a linear dynamic system. A decrease of dimension complexity was found in the EEG of schizophrenia compared with controls. We interpreted it as the result of the psychopath's dysfunction overall brain. The surrogating procedure results in a significant increase in D(s).

CONCLUSIONS

Non-linearity of the EEG in schizophrenia was proven in our study. We think the correlation dimension with spatial embedding as a good discriminating statistic for testing such non-linearity. Moreover, schizophrenic patients' EEGs were compared with controls and a lower dimension complexity was found. The results of our study indicate the possibility of using the methods of non-linear time series analysis to identify the EEGs of schizophrenic patients.

An efficient method for quantifying the multichannel EEG spatial-temporal complexity

The complexity index (delta) quantifies the intrinsic dimensionality of the global complexity of a point set, and was shown to be able to characterize electroencephalogram spatial-temporal features. The complexity index is conceptually comprehensible and easily implemented, yet, it is time consuming. In this paper, we present an efficient computational method based on the projection of the high-dimensional state-space points onto a one-dimensional axis. The computational time decreases by at least 50%, without affecting the measure accuracy.

Investigation of non-linear properties of multichannel EEG in the early stages of Parkinson's disease

OBJECTIVES

Modifications of brain activity in the early stages of Parkinson's disease (PD) are difficult to detect using electroencephalography (EEG) signals and are often biased by L-DOPA treatment. We compare here the performances of both linear and non-linear methods in differentiating EEG of L-DOPA naive PD patients from that of control subjects.

METHODS

Resting multichannel EEG (20 electrodes, 30 s epochs) of 9 patients with PD in Hoehn and Yahr stages 1-2 (4 women, 5 men, mean age 54.3 years, range 48-63 years) were compared with those of 9 control subjects (7 women, two men, mean age 51.3 years, range 43-61 years). The following measurements were computed: theta-, alpha- and beta-band relative powers constituted the linear indices; localized entropy, slope asymmetry and number of non-linear EEG segments constituted the non-linear indices.

RESULTS

In the case of linear quantification, only a decrease in the beta-band was observed for patients. Significant non-linear structures were observed in our EEG data. Non-linear quantifiers demonstrate an increase in entropy and in the number of non-linear EEG segments for the patients.

CONCLUSIONS

Changes in EEG dynamics observed here in L-DOPA naive PD patients may represent early signs of cortical dysfunction produced by subcortical dopamine depletion.

Nonlinear dynamic analysis of the EEG in patients with Alzheimer's disease and vascular dementia

To assess nonlinear EEG activity in patients with Alzheimer's disease (AD) and vascular dementia (VaD), the authors estimated the correlation dimension (D2) and the first positive Lyapunov exponent (L1) of the EEGs in both patients and age-matched healthy control subjects. EEGs were recorded in 15 electrodes from 12 AD patients, 12 VaD patients, and 14 healthy subjects. The AD patients had significantly lower D2 values than the normal control subjects, (P < H > 0.05), except at the F7 and the O1 electrodes, and the VaD patients, except at the C3 and the C4 electrodes. The VaD patients had relatively increased values of D2 and L1 compared with the AD patients, and rather higher values of D2 than the normal control subjects at the F7, F4, F8, Fp2, O1, and O2 electrodes. The L1 values of the EEGs were also lower for the AD patients than for the normal control subjects, except in the O1 and the O2 channels, and for the VaD patients at all electrodes. The L1 values were higher for the VaD patients than for the normal control subjects (F3, F4, F8, O1, and O2). In addition, the authors detected that the VaD patients had an uneven distribution of D2 values over the regions than the AD patients and the normal control subjects, although the statistics do not confirm this. By contrast, AD patients had uniformly lower D2 values in most regions, indicating that AD patients have less complex temporal characteristics of the EEG in entire regions. These nonlinear analyses of the EEG may be helpful in understanding the nonlinear EEG activity in AD and VaD.

Quantitative EEG methods and measures in human psychopharmacological research

The quantitative analysis of electroencephalographic (EEG) signals is an established methodology for objectively describing the central impact of drugs administered to human subjects. This paper outlays the essential objectives and findings of this electrophysiologic measurement model of drug action and addresses the subject, recording, analytical and statistical standards which are required to ensure valid pharmaco-EEG profiling. Copyright 2000 John Wiley & Sons, Ltd.

Low sampling rate induces high correlation dimension on electroencephalograms from healthy subjects

The aim of this paper was to elucidate the influence of sampling parameters in the non-linear analysis of a resting electroencephalogram (EEG) in healthy subjects. Electroencephalograms in 12 healthy volunteers were recorded and the signal digitized at 128, 256, 512 and 1024 Hz, respectively, with the resolution of 8 bits, 12 bits and 16 bits for each sampling rate. Correlation dimension was calculated on each data set. Results were demonstrated on brain maps and examined by analysis of variance (ANOVA). Correlation integral functions demonstrated four parts separated by critical points. The data showed that sampling rate significantly affected the estimation, while resolution did not influence the results. The correlation dimensions calculated with the sampling rate at or below 256 Hz were apparently higher than the results obtained at 1024 Hz. The values at 512 Hz and 1024 Hz did not differ. The data revealed that low sampling rate can severely distort the estimation of correlation dimension. The optimal sampling rate for analyzing resting EEG on normal subjects is 512 Hz. Limitation and aliasing phenomenon are discussed in the paper.

An estimation of the first positive Lyapunov exponent of the EEG in patients with schizophrenia

We studied the complexity of the electroencephalogram (EEG) in schizophrenic patients by estimating the first Lyapunov exponent (L1), which might serve as an indicator of the specific brain function in schizophrenia. We recorded the EEG from 25 schizophrenic patients (12 male, 13 female; age=25.1+/-7.0 years) fulfilling DSM-IV criteria and 15 healthy controls (9 male, 6 female; age=27. 8+/-4.2 years) at 16 electrodes, different from previous studies which recorded the EEGs at limited electrodes. We employed a method with an optimal embedding dimension to calculate the L1s. For limited noisy data, this algorithm was strikingly faster and more accurate than previous ones. Our results showed that the schizophrenic patients had lower values of the L1 at the left inferior frontal and anterior temporal regions compared with normal controls. These results for L1 in non-linear analysis have some differences from those for power ratios in linear analysis. These suggest that the non-linear analysis of the EEGs such as the estimation of the L1 might be a useful tool in analyzing EEG data to explore the neurodynamics of the brains of schizophrenic patients.

Towards a quantitative characterisation of functional states of the brain: from the non-linear methodology to the global linear description

The paper traces the development of a global approach to the electric activity of the brain, from its roots in non-linear dynamical approach to the current state of art. The rationale of a three-dimensional system of global multichannel EEG descriptors (sigma, phi and omega) is provided and results obtained by means of the global descriptors in various application areas are summarised. Finally, arguments in favour of a global, 'holistic' assessment of brain functional states are presented. Definitions and properties of the global EEG descriptors are summarised in the Appendix.

Single-dose piracetam effects on global complexity measures of human spontaneous multichannel EEG

Global complexity of 47-channel resting electroencephalogram (EEG) of healthy young volunteers was studied after intake of a single dose of a nootropic drug (piracetam, Nootropil UCB Pharma) in 12 healthy volunteers. Four treatment levels were used: 2.4, 4.8, 9.6 g piracetam and placebo. Brain electric activity was assessed through Global Dimensional Complexity and Global Omega-Complexity as quantitative measures of the complexity of the trajectory of multichannel EEG in state space. After oral ingestion (1-1.5 h), both measures showed significant decreases from placebo to 2.4 g piracetam. In addition, Global Dimensional Complexity showed a significant return to placebo values at 9.6 g piracetam. The results indicate that a single dose of piracetam dose-dependently affects the spontaneous EEG in normal volunteers, showing effects at the lowest treatment level. The decreased EEG complexity is interpreted as increased cooperativity of brain functional processes.

Test for low-dimensional determinism in electroencephalograms

We tested low-dimensional determinism in an electroencephalogram (EEG), based on the fact that smoothness (continuity) on an embedded phase space is enough to imply determinism within time series. A modified version of the method developed by Salvino and Cawley [Phys. Rev. Lett. 73, 1091 (1994)] was used. In our method, we chose a box randomly and then estimated the mean directional element in the box containing the d+1 data points, where d is the embedding dimension. The global average for the mean local directional elements over the boxes, W, is a measure for smoothness. The nonlinear noise reduction method developed by Sauer [Physica D 58, 193 (1992)] is then applied to the EEG. We also compared the results for the EEG with those for its surrogate data. We found that the W values for the noise-reduced EEG had stable values around 0.35, which means that the EEG is not a low-dimensional deterministic signal. However, this method may not be applicable to the time series generated from high-dimensional deterministic systems. We cannot exclude the possibility that the determinism in the EEG may be too high-dimensional to be detected with current methods.

Spatiotemporal EEG analysis and distributed source estimation in presurgical epilepsy evaluation

In the attempts to localize electric sources in the brain on the basis of multichannel EEG and/or MEG measurements, distributed source estimation procedures have become of increasing interest. Several commercial software packages offer such localization programs and results using these methods are seen more and more frequently in the literature. It is crucial that the users understand the similarities and differences of these methods and that they become aware of the advantages and limitations that are inherent to each approach. This review provides this information from a theoretical as well as from a practical point of view. The theoretical part gives the algorithmic basis of the electromagnetic inverse problem and shows how the different a priori assumptions are formally integrated in these equations. The authors restrict this formalism to the linear inverse solutions i.e., those solutions in which the inversion procedure can be represented as a matrix applied to the data. It will be shown that their properties can be best characterized by their resolution kernels and that methods with optimal resolution matrices can be designed. The authors also discuss the important problem of regularization strategies that are used to minimize the influence of noise. Finally, a new kind of inverse solution, termed ELECTRA (for ELECTRical Analysis), is presented that is based on constraining the source model on the basis of the currents that can actually be measured by the scalp recorded EEG. The practical part of the review illustrates the localization procedures with different clinical data sets. Three aspects become important when working with real data: 1) Clinical data is usually far from ideal (limited number of electrodes, noise, etc.). The behavior of inverse procedures in such unfortunate situations has to be evaluated. 2) The selection of the time points or time periods of interest is crucial, especially in the analysis of spontaneous EEG. 3) Additional information coming from other modalities is usually available and can be incorporated. The authors are illustrating these important points in the case of interictal and ictal epileptiform activity. Spike averaging, frequency domain source localization, and temporal segmentation based on electric field topographies will be discussed. Finally, the technique of EEG-triggered functional magnetic resonance imaging (fMRI) will be illustrated, where EEG is recorded in the magnet and is used to synchronize fMRI acquisition with interictal events. The analysis of both functional data, i.e. the EEG in terms of three-dimensional source localization and the EEG-triggered fMRI, combines the advantages of the two techniques: the temporal resolution of the EEG and the spatial resolution of the fMRI.

Global, regional, and local measures of complexity of multichannel electroencephalography in acute, neuroleptic-naive, first-break schizophrenics

BACKGROUND

Schizophrenic symptoms commonly are felt to indicate a loosened coordination, i.e. a decreased connectivity of brain processes.

METHODS

To address this hypothesis directly, global and regional multichannel electroencephalographic (EEG) complexities (omega complexity and dimensional complexity) and single channel EEG dimensional complexities were calculated from 19-channel EEG data from 9 neuroleptic-naive, first-break, acute schizophrenics and 9 age- and sex-matched controls. Twenty artifact-free 2 second EEG epochs during resting with closed eyes were analyzed (2-30 Hz bandpass, average reference for global and regional complexities, local EEG gradient time series for single channels).

RESULTS

Anterior regional Omega-Complexity was significantly increased in schizophrenics compared with controls (p < 0.001) and anterior regional Dimensional Complexity showed a trend for increase. Single channel Dimensional Complexity of local gradient waveshapes was prominently increased in the schizophrenics at the right precentral location (p = 0.003).

CONCLUSIONS

The results indicate a loosened cooperativity or coordination (vice versa: an increased independence) of the active brain processes in the anterior brain regions of the schizophrenics.

Neuronal complexity loss in temporal lobe epilepsy: effects of carbamazepine on the dynamics of the epileptogenic focus

Analysis methods derived from the theory of non-linear dynamics have been shown to provide new information about the complex spatio-temporal behaviour of neuronal networks involved in temporal lobe epilepsy. To test whether day to day alterations in neuronal complexity are influenced by changes in serum level of carbamazepine (CBZ), a moving-window correlation dimension analysis was applied to electrocorticographic and stereoelectroencephalographic recordings of 10 patients with unilateral temporal lobe epilepsy. Data sets (n = 78) were obtained from interictal states at subsequent days during the presurgical evaluation with strongly variant CBZ serum levels. The so-called neuronal complexity loss L* was used to quantify the change of dimensionality in brain electrical activity recorded under different levels of medication. We found a significant inverse relationship between L* and CBZ serum level spatially restricted to the primary epileptogenic area. This finding can be assumed to reflect the mechanism of action of CBZ attributed to an inhibition of sustained high-frequency firing of bursting neurons.

Multichannel EEG fields during and without visual input: frequency domain model source locations and dimensional complexities

27-Channel EEG potential map series were recorded from 12 normals with closed and open eyes. Intracerebral dipole model source locations in the frequency domain were computed. Eye opening (visual input) caused centralization (convergence and elevation) of the source locations of the seven frequency bands, indicative of generalized activity; especially, there was clear anteriorization of alpha-2 (10.5-12 Hz) and beta-2 (18.5-21 Hz) sources (alpha-2 also to the left). Complexity of the map series' trajectories in state space (assessed by Global Dimensional Complexity and Global OMEGA Complexity) increased significantly with eye opening, indicative of more independent, parallel, active processes. Contrary to PET and fMRI, these results suggest that brain activity is more distributed and independent during visual input than after eye closing (when it is more localized and more posterior).

The evolution of complexity in human brain development: an EEG study

Analysis of the EEG as a signal from a deterministic non-linear system should, in principle, allow insights into the complexity of underlying brain activity. We examined the capability of this method to analyse the marked changes in brain activity during normal brain development. Resting EEGs of 54 healthy children (newborns to 14 years old) and of 12 normal adults were recorded digitally. The following parameters were calculated: correlation dimension, a measure of the complexity of the underlying system, and the first Lyapunov coefficient, indicating the system's 'unpredictability'. Analysis of variance (ANOVA) was performed with probands grouped by age. The subgroups of children older than 1 year was further examined by regression analysis. In all analysed epochs, Lyapunov coefficients were significantly positive (P < 0.0001. t-test). The presence of non-linear dynamics was asserted statistically in 64-76% of examined epochs. A highly significant increase in correlation dimension with age was found in all examined leads (P < 0.0001, ANOVA). In all age groups, marked differences in correlation dimension in different brain regions became evident (P < 0.01-0.0001, ANOVA). Evidence for the presence of non-linearity can be found even in newborns. Brain maturation was reflected in a marked and highly significant increase in correlation dimension (complexity). Our work indicates that non-linear dynamics analysis is suitable for measuring complexity of brain activity during maturation and provides age-dependent normal values as a basis for further study.

On the validity of estimating EEG correlation dimension from a spatial embedding

We demonstrate by using simulations that spatial embedding of single-variable time series data does not reliably reconstruct state-space dynamics. Instead, correlation dimension estimated from spatially embedded data is largely a measure of linear cross-correlation in the data set. For actual electroencephalographic (EEG) data, we demonstrate a high negative correlation between spatial correlation dimension and the average amount of lag-zero cross-correlation between "nearest-neighbor" embedding channels (the greater the cross-correlation, the lower the dimension). We also show that the essential results obtained from spatially embedding EEG data are also obtained when one spatially embeds across a set of highly cross-correlated stochastic (second-order autoregressive) processes. Although, with appropriate surrogate data, correlation dimension estimated from spatially embedded data detects nonlinearity, its use is not recommended because correlation dimension estimated from temporally embedded data both reconstructs state-space dynamics and, with appropriate surrogate data, detects nonlinearity as well.

Age increases brain complexity

This study investigated age-related changes in the human brain function using both traditional EEG analysis (power spectra) and the correlational dimension, a measure reflecting the complexity of EEG dynamics and, probably, the complexity of neurophysiological processes generating the EEG. Assuming that the accumulation of individual experience is determined by the formation of functionally related groups of neurons showing a repetitive synchronous activation (cell assemblies), an increase in the number of such independently oscillating cortical cell assemblies can be expected, despite a decline of some metabolic and memory functions with normal ageing. Thus, the "wisdom of old age' may find its neurophysiological basis in greater complexity of brain dynamics compared to young ages. The experimental hypothesis was that EEG dimension steadily increases with age. In order to test this hypothesis the resting EEGs of 5 age groups from 7 to 60 were analysed. The results confirm the hypothesis: after a jump in the brain dynamics complexity during puberty a linear increase with age is observed. During maturation (7-25 years), the maximum gain in complexity occurs over the frontal associative cortex.

Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram

We have re-examined single channel EEG data obtained from normal human subjects. In the original analysis, calculation of the correlation dimension with the Grassberger-Procaccia algorithm produced results consistent with and interpretation of low-dimensional behavior. The re-examination suggests that the previous indication of low-dimensional structure was an artifact of autocorrelation in the oversampled signal. Calculations with a variant of the Grassberger-Procaccia algorithm modified to be less sensitive to autocorrelations, and comparison with linear gaussian surrogate data, indicate that these data may be more appropriately modeled by linearly filtered noise. Discriminant analysis further indicates that the correlation dimension is a poor discriminator for distinguishing between EEGs recorded at rest and during periods of cognitive activity. It remains possible that the application of other nonlinear measures or the examination of multichannel EEG data may resolve structures not found in these calculations.

Frequency domain source localization shows state-dependent diazepam effects in 47-channel EEG

The topic of this study was to evaluate state-dependent effects of diazepam on the frequency characteristics of 47-channel spontaneous EEG maps. A novel method, the FFT-Dipole-Approximation (Lehmann and Michel, 1990), was used to study effects on the strength and the topography of the maps in the different frequency bands. Map topography was characterized by the 3-dimensional location of the equivalent dipole source and map strength was defined as the spatial standard deviation (the Global Field Power) of the maps of each frequency point. The Global Field Power can be considered as a measure of the amount of energy produced by the system, while the source location gives an estimate of the center of gravity of all sources in the brain that were active at a certain frequency. State-dependency was studied by evaluating the drug effects before and after a continuous performance task of 25 min duration. Clear interactions between drug (diazepam vs. placebo) and time after drug intake (before and after the task) were found, especially in the inferior-superior location of the dipole sources. It supports the hypothesis that diazepam, like other drugs, has different effects on brain functions depending on the momentary functional state of the brain. In addition to the drug effects, clearly different source locations and Global Field Power were found for the different frequency bands, replicating earlier reports (Michel et al., 1992).

Non-linear dynamical analysis of multichannel EEG: clinical applications in dementia and Parkinson's disease

The irregular, aperiodic character of the EEG is usually explained by a stochastic model. In this view the EEG is linearly filtered noise. According to chaos theory such irregular signals can also result from low dimensional deterministic chaos. In this case the underlying dynamics is nonlinear, and has only few effective degrees of freedom. In contrast, stochastic models are less efficient, because they require in principle infinite degrees of freedom. Chaotic dynamics in the EEG can be studied by calculating the correlation dimension (D2). Although it has become clear that D2 calculations alone cannot prove chaos, the D2 has potential value as an EEG diagnostic. In this study we investigated whether D2 could be used to discriminate EEGs from normal controls, demented patients and Parkinson patients. We have analyzed epochs (20 channels; 2.5 s) from 52 EEGs (20 controls; 15 patients with dementia; 17 patients with Parkinson's disease). Controls had a mean D2 of 6.5 (0.9); demented patients of 4.4 (1.5), and Parkinson patients of 5.3 (0.9). Both groups were significantly different from controls (p < 0.001). There was a significant positive correlation between D2 and relative power in the beta band (r = 0.81) and a significant negative correlation between D2 and power in the delta (r = -0.60) and theta band (r = -0.37). These results suggest the possible usefulness of multichannel D2 estimation in a clinical setting.

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.

EEG-based, neural-net predictive classification of Alzheimer's disease versus control subjects is augmented by non-linear EEG measures

Attempts to classify Alzheimer's disease (AD) subjects versus controls using spectral-band measures of electroencephalographic (EEG) data typically achieve around 80% success. This study assessed the ability of adding non-linear EEG measures and using a neural-net classification procedure to improve this performance level. The non-linear EEG measures were estimated correlation dimension ("dimensional complexity," or DCx) and saturation (degree of leveling-off of DCx with increasing embedding dimension). In a sample of 39 subjects (14 ADs, 25 controls), it was found that (a) the addition of non-linear EEG measures improved the classification accuracy of the AD/control status of subjects, and (b) a back-percolation neural net predictively classified the subjects much better than the standard linear techniques of multivariate discriminant analysis or nearest-neighbor discriminant analysis.

Dimensionality alterations of the hippocampal electroencephalographic activity following the induction of long-term potentiation in rats

In the present in vivo experimental study the complexity alterations of the hippocampal electroencephalographic (EEG) activity were investigated prior and during the maintenance phase of long-term potentiation (LTP), using analytical methods based on the recent concepts of deterministic chaos. LTP was induced in the hippocampal dentate hilus after stimulation of the medial perforant path of the rat's brain. During the experimental procedure hippocampal EEG epochs were recorded prior and after the induction of LTP. Dimensionality computations performed on these epochs showed a maintained relative reduction in the correlation dimension during the maintenance phase of LTP. This result might suggest that different functional states of the brain are governed by different degrees of complexity and that the altered efficacy in the information process, as it is achieved by the induction of LTP, modifies the spontaneous EEG activity of the potentiated hippocampal area in a plastic manner.

Space-oriented EEG segmentation reveals changes in brain electric field maps under the influence of a nootropic drug

Map landscape-based segmentation of the sequences of momentary potential distribution maps (42-channel recordings) into brain microstates during spontaneous brain activity was used to study brain electric field spatial effects of single doses of piracetam (2.9, 4.8, and 9.6 g Nootropil UCB and placebo) in a double-blind study of five normal young volunteers. Four 15-second epochs were analyzed from each subject and drug condition. The most prominent class of microstates (covering 49% of the time) consisted of potential maps with a generally anterior-posterior field orientation. The map orientation of this microstate class showed an increasing clockwise deviation from the placebo condition with increasing drug doses (Fisher's probability product, p < 0.014). The results of this study suggest the use of microstate segmentation analysis for the assessment of central effects of medication in spontaneous multi-channel electroencephalographic data, as a complementary approach to frequency-domain analysis.