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

Exploring the complexity of EEG patterns in Parkinson's disease

Parkinson's disease (PD) is a progressive neurodegenerative disorder primarily associated with motor dysfunctions. By the time of definitive diagnosis, about 60% of dopaminergic neurons have already been lost; moreover, even if dopaminergic drugs are highly effective in symptoms control, they only help maintaining a near-healthy condition when started as soon as possible. Therefore, interest in identifying early biomarkers of PD has grown in recent years, especially using neurophysiological techniques such as electroencephalography (EEG). This study aims to investigate brain complexity differences in PD patients compared to healthy controls, focusing on the beta band using approximate entropy (ApEn) analysis of resting-state EEG recordings. Sixty participants were recruited, including 25 PD patients and 35 healthy elderly subjects, matched for age and gender. EEG were recorded for each participant and ApEn values were computed in the beta 1 (13-20 Hz) and beta 2 (20-30 Hz) frequency bands for each EEG-channel and for ROIs. PD patients showed statistically lower ApEn values compared to controls in both beta 1 and beta 2 bands. Regarding electrodes analysis, beta 1 band alterations were found in frontocentral areas, while beta 2 band alterations were observed in centroparietal and frontocentral areas. Considering ROIs, statistically lower ApEn values for PD patients has been reported in central and parietal ROIs in the beta 2 band. Complexity reduction in these areas may underlie beta oscillatory activity dysfunction, reflecting impaired cortical mechanisms associated with motor dysfunction in PD. The results suggest that ApEn analysis of resting EEG activity may serve as a potential tool for early PD detection. Further studies are necessary to validate this approach in PD diagnosis and rehabilitation planning.

Heterogeneous correlate and potential diagnostic biomarker of tinnitus based on nonlinear dynamics of resting-state EEG recordings

Tinnitus is a heterogeneous condition of hearing a rattling sound when there is no auditory stimulus. This rattling sound is associated with abnormal synchronous oscillations in auditory and non-auditory cortical areas. Since tinnitus is a highly heterogeneous condition with no objective detection criteria, it is necessary to search for indicators that can be compared between and within participants for diagnostic purposes. This study introduces heterogeneous though comparable indicators of tinnitus through investigation of spontaneous fluctuations in resting-state brain dynamics. The proposed approach uses nonlinear measures of chaos theory, to detect tinnitus and cross correlation patterns to reflect many of the previously reported neural correlates of tinnitus. These indicators may serve as effective measures of tinnitus risk even at early ages before any symptom is reported. The approach quantifies differences in oscillatory brain dynamics of tinnitus and normal subjects. It demonstrates that the left temporal areas of subjects with tinnitus exhibit larger lyapunov exponent indicating irregularity of brain dynamics in these regions. More complex dynamics is further recognized in tinnitus cases through entropy. We use this evidence to distinguish tinnitus patients from normal participants. Besides, we illustrate that certain anticorrelation patterns appear in these nonlinear measures across temporal and frontal areas in the brain perhaps corresponding to increased/decreased connectivity in certain brain networks and a shift in the balance of excitation and inhibition in tinnitus. Additionally, the main correlations are lost in tinnitus participants compared to control group suggesting involvement of distinct neural mechanisms in generation and persistence of tinnitus.

Oscillatory vs. non-oscillatory subthalamic beta activity in Parkinson's disease

Parkinson's disease is characterized by exaggerated beta activity (13-35 Hz) in cortico-basal ganglia motor loops. Beta activity includes both periodic fluctuations (i.e. oscillatory activity) and aperiodic fluctuations reflecting spiking activity and excitation/inhibition balance (i.e. non-oscillatory activity). However, the relative contribution, dopamine dependency and clinical correlations of oscillatory vs. non-oscillatory beta activity remain unclear. We recorded, modelled and analysed subthalamic local field potentials in parkinsonian patients at rest while off or on medication. Autoregressive modelling with additive 1/f noise clarified the relationships between measures of beta activity in the time domain (i.e. amplitude and duration of beta bursts) or in the frequency domain (i.e. power and sharpness of the spectral peak) and oscillatory vs. non-oscillatory activity: burst duration and spectral sharpness are specifically sensitive to oscillatory activity, whereas burst amplitude and spectral power are ambiguously sensitive to both oscillatory and non-oscillatory activity. Our experimental data confirmed the model predictions and assumptions. We subsequently analysed the effect of levodopa, obtaining strong-to-extreme Bayesian evidence that oscillatory beta activity is reduced in patients on vs. off medication, with moderate evidence for absence of modulation of the non-oscillatory component. Finally, specifically the oscillatory component of beta activity correlated with the rate of motor progression of the disease. Methodologically, these results provide an integrative understanding of beta-based biomarkers relevant for adaptive deep brain stimulation. Biologically, they suggest that primarily the oscillatory component of subthalamic beta activity is dopamine dependent and may play a role not only in the pathophysiology but also in the progression of Parkinson's disease. KEY POINTS: Beta activity in Parkinson's disease includes both true periodic fluctuations (i.e. oscillatory activity) and aperiodic fluctuations reflecting spiking activity and synaptic balance (i.e. non-oscillatory activity). The relative contribution, dopamine dependency and clinical correlations of oscillatory vs. non-oscillatory beta activity remain unclear. Burst duration and spectral sharpness are specifically sensitive to oscillatory activity, while burst amplitude and spectral power are ambiguously sensitive to both oscillatory and non-oscillatory activity. Only the oscillatory component of subthalamic beta activity is dopamine-dependent. Stronger beta oscillatory activity correlates with faster motor progression of the disease.

NoLiTiA: An Open-Source Toolbox for Non-linear Time Series Analysis

In many scientific fields including neuroscience, climatology or physics, complex relationships can be described most parsimoniously by non-linear mechanics. Despite their relevance, many neuroscientists still apply linear estimates in order to evaluate complex interactions. This is partially due to the lack of a comprehensive compilation of non-linear methods. Available packages mostly specialize in only one aspect of non-linear time-series analysis and most often require some coding proficiency to use. Here, we introduce NoLiTiA, a free open-source MATLAB toolbox for non-linear time series analysis. In comparison to other currently available non-linear packages, NoLiTiA offers (1) an implementation of a broad range of classic and recently developed methods, (2) an implementation of newly proposed spatially and time-resolved recurrence amplitude analysis and (3) an intuitive environment accessible even to users with little coding experience due to a graphical user interface and batch-editor. The core methodology derives from three distinct fields of complex systems theory, including dynamical systems theory, recurrence quantification analysis and information theory. Besides established methodology including estimation of dynamic invariants like Lyapunov exponents and entropy-based measures, such as active information storage, we include recent developments of quantifying time-resolved aperiodic oscillations. In general, the toolbox will make non-linear methods accessible to the broad neuroscientific community engaged in time series processing.

Effective Connectivity During Rest and Music Listening: An EEG Study on Parkinson's Disease

Music-based interventions seem to enhance motor, sensory and cognitive functions in Parkinson’s disease (PD), but the underlying action mechanisms are still largely unknown. This electroencephalography (EEG) study aimed to investigate the effective connectivity patterns characterizing PD in the resting state and during music listening. EEG recordings were obtained from fourteen non-demented PD patients and 12 healthy controls, at rest and while listening to three music tracks. Theta- and alpha-band power spectral density and multivariate partial directed coherence were computed. Power and connectivity measures were compared between patients and controls in the four conditions and in music vs. rest. Compared to controls, patients showed enhanced theta-band power and slightly enhanced alpha-band power, but markedly reduced theta- and alpha-band interactions among EEG channels, especially concerning the information received by the right central channel. EEG power differences were partially reduced by music listening, which induced power increases in controls but not in patients. Connectivity differences were slightly compensated by music, whose effects largely depended on the track. In PD, music enhanced the frontotemporal inter-hemispheric communication. Our findings suggest that PD is characterized by enhanced activity but reduced information flow within the EEG network, being only partially normalized by music. Nevertheless, music capability to facilitate inter-hemispheric communication might underlie its beneficial effects on PD pathophysiology and should be further investigated.

Using Nonlinear Dynamics and Multivariate Statistics to Analyze EEG Signals of Insomniacs with the Intervention of Superficial Acupuncture

Objective

As a noninvasive and nonpharmacological therapeutic approach, superficial acupuncture (SA) is a special method of acupuncture. In this study, using nonlinear dynamics and multivariate statistics, we studied the electroencephalography (EEG) of primary insomnia under SA intervention to investigate how brain regions change.

Method

This study included 30 adults with primary insomnia. They underwent superficial acupuncture at the Shangen acupoint. The EEG signals were collected for 10 minutes at each state, including the resting state, the intervention state, and the postintervention state. The data were conducted using nonlinear dynamics (including approximate entropy (ApEn) and correlation dimension (CD)) and multivariate statistics.

Result

The repeated-measures ANOVA results showed that both ApEn and CD values were not significantly different at the three states (p > 0.05). The paired t-test results showed that the ApEn values of electrodes O2 (the right occipital lobe) at the postintervention state have decreased, compared with the resting state (p < 0.05), and no difference was detected in CD (p > 0.05). The cluster analysis results of ApEn showed that patients' EEG has changed from the right prefrontal lobe (electrode Fp2) to the right posterior temporal lobe (electrode T6) and finally to the right occipital lobe (electrode O2), before, during, and after the SA intervention. In addition, the factor analysis results of CD revealed that patients' EEG of all brain regions except for the occipital lobes has changed to the frontal lobes and anterior temporal and frontal lobes from pre- to postintervention.

Conclusion

SA activated the corresponding brain regions and reduced the complexity of the brain involved. It is feasible to use nonlinear dynamics analysis and multivariate statistics to examine the effects of SA on the human brain.

Complexity Analysis of EEG, MEG, and fMRI in Mild Cognitive Impairment and Alzheimer's Disease: A Review

Alzheimer's disease (AD) is a degenerative brain disease with a high and irreversible incidence. In recent years, because brain signals have complex nonlinear dynamics, there has been growing interest in studying complex changes in the time series of brain signals in patients with AD. We reviewed studies of complexity analyses of single-channel time series from electroencephalogram (EEG), magnetoencephalogram (MEG), and functional magnetic resonance imaging (fMRI) in AD and determined future research directions. A systematic literature search for 2000-2019 was performed in the Web of Science and PubMed databases, resulting in 126 identified studies. Compared to healthy individuals, the signals from AD patients have less complexity and more predictable oscillations, which are found mainly in the left parietal, occipital, right frontal, and temporal regions. This complexity is considered a potential biomarker for accurately responding to the functional lesion in AD. The current review helps to reveal the patterns of dysfunction in the brains of patients with AD and to investigate whether signal complexity can be used as a biomarker to accurately respond to the functional lesion in AD. We proposed further studies in the signal complexities of AD patients, including investigating the reliability of complexity algorithms and the spatial patterns of signal complexity. In conclusion, the current review helps to better understand the complexity of abnormalities in the AD brain and provide useful information for AD diagnosis.

Complexity of resting-state EEG activity in the patients with early-stage Parkinson's disease

To investigate the abnormal brain activities in the early stage of Parkinson's disease (PD), the electroencephalogram (EEG) signals were recorded with 20 channels from non-dementia PD patients (18 patients, 8 females) and age matched healthy controls (18 subjects, 8 females) during the resting state. Two methods based on the ordinal patterns of the recorded series, i.e., permutation entropy (PE) and order index (OI), were introduced to characterize the complexity of the cortical activities for two groups. It was observed that the resting-state EEG of PD patients showed lower PE and higher OI than healthy controls, which indicated that the early-stage PD caused the reduced complexity of EEG. We further applied two methods to determine the complexity of EEG rhythms in five sub-bands. The results showed that the gamma, beta and alpha rhythms of PD patients were characterized by lower PE and higher OI, i.e., reduced complexity, than healthy subjects. No significant differences were observed in theta or delta rhythms between two groups. The findings suggested that PE and OI were promising methods to detect the abnormal changes in the dynamics of EEG signals associated with early-stage PD. Further, such changes in EEG complexity may be the early markers of the cortical or subcortical dysfunction caused by PD.

Structure and Topology Dynamics of Hyper-Frequency Networks during Rest and Auditory Oddball Performance

Resting-state and task-related recordings are characterized by oscillatory brain activity and widely distributed networks of synchronized oscillatory circuits. Electroencephalographic recordings (EEG) were used to assess network structure and network dynamics during resting state with eyes open and closed, and auditory oddball performance through phase synchronization between EEG channels. For this assessment, we constructed a hyper-frequency network (HFN) based on within- and cross-frequency coupling (WFC and CFC, respectively) at 10 oscillation frequencies ranging between 2 and 20 Hz. We found that CFC generally differentiates between task conditions better than WFC. CFC was the highest during resting state with eyes open. Using a graph-theoretical approach (GTA), we found that HFNs possess small-world network (SWN) topology with a slight tendency to random network characteristics. Moreover, analysis of the temporal fluctuations of HFNs revealed specific network topology dynamics (NTD), i.e., temporal changes of different graph-theoretical measures such as strength, clustering coefficient, characteristic path length (CPL), local, and global efficiency determined for HFNs at different time windows. The different topology metrics showed significant differences between conditions in the mean and standard deviation of these metrics both across time and nodes. In addition, using an artificial neural network approach, we found stimulus-related dynamics that varied across the different network topology metrics. We conclude that functional connectivity dynamics (FCD), or NTD, which was found using the HFN approach during rest and stimulus processing, reflects temporal and topological changes in the functional organization and reorganization of neuronal cell assemblies.

A Novel Application of Multiscale Entropy in Electroencephalography to Predict the Efficacy of Acetylcholinesterase Inhibitor in Alzheimer's Disease

Alzheimer's disease (AD) is the most common form of dementia. According to one hypothesis, AD is caused by the reduced synthesis of the neurotransmitter acetylcholine. Therefore, acetylcholinesterase (AChE) inhibitors are considered to be an effective therapy. For clinicians, however, AChE inhibitors are not a predictable treatment for individual patients. We aimed to disclose the difference by biosignal processing. In this study, we used multiscale entropy (MSE) analysis, which can disclose the embedded information in different time scales, in electroencephalography (EEG), in an attempt to predict the efficacy of AChE inhibitors. Seventeen newly diagnosed AD patients were enrolled, with an initial minimental state examination (MMSE) score of 18.8 ± 4.5. After 12 months of AChE inhibitor therapy, 7 patients were responsive and 10 patients were nonresponsive. The major difference between these two groups is Slope 2 (MSE6 to 20). The area below the receiver operating characteristic (ROC) curve of Slope 2 is 0.871 (95% CI = 0.69–1). The sensitivity is 85.7% and the specificity is 60%, whereas the cut-off value of Slope 2 is −0.024. Therefore, MSE analysis of EEG signals, especially Slope 2, provides a potential tool for predicting the efficacy of AChE inhibitors prior to therapy.

Role of EEG as biomarker in the early detection and classification of dementia

The early detection and classification of dementia are important clinical support tasks for medical practitioners in customizing patient treatment programs to better manage the development and progression of these diseases. Efforts are being made to diagnose these neurodegenerative disorders in the early stages. Indeed, early diagnosis helps patients to obtain the maximum treatment benefit before significant mental decline occurs. The use of electroencephalogram as a tool for the detection of changes in brain activities and clinical diagnosis is becoming increasingly popular for its capabilities in quantifying changes in brain degeneration in dementia. This paper reviews the role of electroencephalogram as a biomarker based on signal processing to detect dementia in early stages and classify its severity. The review starts with a discussion of dementia types and cognitive spectrum followed by the presentation of the effective preprocessing denoising to eliminate possible artifacts. It continues with a description of feature extraction by using linear and nonlinear techniques, and it ends with a brief explanation of vast variety of separation techniques to classify EEG signals. This paper also provides an idea from the most popular studies that may help in diagnosing dementia in early stages and classifying through electroencephalogram signal processing and analysis.

Non-linear dynamical analysis of EEG time series distinguishes patients with Parkinson's disease from healthy individuals

The pathophysiology of Parkinson’s disease (PD) is known to involve altered patterns of neuronal firing and synchronization in cortical-basal ganglia circuits. One window into the nature of the aberrant temporal dynamics in the cerebral cortex of PD patients can come from analysis of the patients electroencephalography (EEG). Rather than using spectral-based methods, we used data models based on delay differential equations (DDE) as non-linear time-domain classification tools to analyze EEG recordings from PD patients on and off dopaminergic therapy and healthy individuals. Two sets of 50 1-s segments of 64-channel EEG activity were recorded from nine PD patients on and off medication and nine age-matched controls. The 64 EEG channels were grouped into 10 clusters covering frontal, central, parietal, and occipital brain regions for analysis. DDE models were fitted to individual trials, and model coefficients and error were used as features for classification. The best models were selected using repeated random sub-sampling validation and classification performance was measured using the area under the ROC curve A′. In a companion paper, we show that DDEs can uncover hidden dynamical structure from short segments of simulated time series of known dynamical systems in high noise regimes. Using the same method for finding the best models, we found here that even short segments of EEG data in PD patients and controls contained dynamical structure, and moreover, that PD patients exhibited a greater dynamic range than controls. DDE model output on the means from one set of 50 trials provided nearly complete separation of PD patients off medication from controls: across brain regions, the area under the receiver-operating characteristic curves, A′, varied from 0.95 to 1.0. For distinguishing PD patients on vs. off medication, classification performance A′ ranged from 0.86 to 1.0 across brain regions. Moreover, the generalizability of the model to the second set of 50 trials was excellent, with A′ ranging from 0.81 to 0.94 across brain regions for controls vs. PD off medication, and from 0.62 to 0.82 for PD on medication vs. off. Finally, model features significantly predicted individual patients’ motor severity, as assessed with standard clinical rating scales.

Cortical information flow in Parkinson's disease: a composite network/field model

The basal ganglia play a crucial role in the execution of movements, as demonstrated by the severe motor deficits that accompany Parkinson's disease (PD). Since motor commands originate in the cortex, an important question is how the basal ganglia influence cortical information flow, and how this influence becomes pathological in PD. To explore this, we developed a composite neuronal network/neural field model. The network model consisted of 4950 spiking neurons, divided into 15 excitatory and inhibitory cell populations in the thalamus and cortex. The field model consisted of the cortex, thalamus, striatum, subthalamic nucleus, and globus pallidus. Both models have been separately validated in previous work. Three field models were used: one with basal ganglia parameters based on data from healthy individuals, one based on data from individuals with PD, and one purely thalamocortical model. Spikes generated by these field models were then used to drive the network model. Compared to the network driven by the healthy model, the PD-driven network had lower firing rates, a shift in spectral power toward lower frequencies, and higher probability of bursting; each of these findings is consistent with empirical data on PD. In the healthy model, we found strong Granger causality between cortical layers in the beta and low gamma frequency bands, but this causality was largely absent in the PD model. In particular, the reduction in Granger causality from the main “input” layer of the cortex (layer 4) to the main “output” layer (layer 5) was pronounced. This may account for symptoms of PD that seem to reflect deficits in information flow, such as bradykinesia. In general, these results demonstrate that the brain's large-scale oscillatory environment, represented here by the field model, strongly influences the information processing that occurs within its subnetworks. Hence, it may be preferable to drive spiking network models with physiologically realistic inputs rather than pure white noise.

Effects of memantine on event-related potential, oscillations, and complexity in individuals with and without family histories of alcoholism

OBJECTIVE

Enhanced N-methyl-D-aspartate (NMDA) receptor function associated with a positive family history of alcoholism (FHP) has been hypothesized to contribute to the heritable risk for alcoholism. The objective of this study was to evaluate the relationship of alcoholism family history, NMDA receptor function, and cortical information processing by testing acute effects of the NMDA receptor antagonist memantine on event-related potential (ERP).

METHOD

Twenty-two healthy FHP and 20 healthy family history-negative (FHN; no alcoholic relatives) subjects were administered placebo or 40 mg of memantine under double-blind counterbalanced conditions on two separate occasions. Electroencephalogram data were collected from eight channels with eyes open during an auditory oddball discrimination task. We evaluated P3b amplitude, total theta, alpha activity, and fractal dimension from ERP trials.

RESULTS

FHP and FHN subjects did not differ in P3b amplitude. A significant Group × Drug interaction was observed in theta, alpha activity, and fractal dimension at the parietal and occipital sites. FHP individuals exhibited significantly higher fractal dimension and lower theta and alpha activity after placebo relative to FHN subjects. Following memantine administration, theta activity decreased in both groups but more markedly for FHN individuals. Alpha activity decreased for FHN subjects and increased for FHP individuals, whereas the fractal dimension decreased for FHP subjects and increased for FHN subjects after memantine.

CONCLUSIONS

A plausible interpretation of these results is that FHP individuals may have altered NMDA receptor function compared with FHN individuals. These findings provide additional evidence of differences in the regulation of NMDA receptor function between FHP and FHN individuals.

Investigation of EEG abnormalities in the early stage of Parkinson's disease

The objective of the present study was to investigate brain activity abnormalities in the early stage of Parkinson's disease (PD). To achieve this goal, eyes-closed resting state electroencephalography (EEG) signals were recorded from 15 early-stage PD patients and 15 age-matched healthy controls. The AR Burg method and the wavelet packet entropy (WPE) method were used to characterize EEG signals in different frequency bands between the groups, respectively. In the case of the AR Burg method, an increase of relative powers in the δ- and θ-band, and a decrease of relative powers in the α- and β-band were observed for patients compared with controls. For the WPE method, EEG signals from patients showed significant higher entropy over the global frequency domain. Furthermore, WPE in the γ-band of patients was higher than that of controls, while WPE in the δ-, θ-, α- and β-band were all lower. All of these changes in EEG dynamics may represent early signs of cortical dysfunction, which have potential use as biomarkers of PD in the early stage. Our findings may be further used for early intervention and early diagnosis of PD.

Lifespan differences in nonlinear dynamics during rest and auditory oddball performance

Electroencephalographic recordings (EEG) were used to assess age-associated differences in nonlinear brain dynamics during both rest and auditory oddball performance in children aged 9.0-12.8 years, younger adults, and older adults. We computed nonlinear coupling dynamics and dimensional complexity, and also determined spectral alpha power as an indicator of cortical reactivity. During rest, both nonlinear coupling and spectral alpha power decreased with age, whereas dimensional complexity increased. In contrast, when attending to the deviant stimulus, nonlinear coupling increased with age, and complexity decreased. Correlational analyses showed that nonlinear measures assessed during auditory oddball performance were reliably related to an independently assessed measure of perceptual speed. We conclude that cortical dynamics during rest and stimulus processing undergo substantial reorganization from childhood to old age, and propose that lifespan age differences in nonlinear dynamics during stimulus processing reflect lifespan changes in the functional organization of neuronal cell assemblies.

Empirical mode decomposition based detrended sample entropy in electroencephalography for Alzheimer's disease

Quantitative electroencephalographs (qEEG) provide a potential method to objectively quantify the cortical activations in Alzheimer's disease (AD), but they are too insensitive to probe the alteration of EEG in the early AD. The sample entropy (SaEn) attempts to quantify the complex information embedded in EEG non-linearly, which fits in that EEG originates from non-linear interactions. However, a technical issue which has been ignored by most researchers is that the signal should be stationary. In order to resolve the non-stationarity of SaEn in EEG to improve the sensitivity, an empirical mode decomposition (EMD) was applied for detrending in this study. Twenty-seven AD patients (9M/18F; mean age 74.0±1.5 years) were included. Their initial Minimal Mental Status Examination was 19.3±0.7. They received the first resting-awake 30-mine EEG before the therapy. Five of them received a follow-up examination within 6 months after the therapy. The 30-s EEG data without artifacts were selected and analyzed with a new proposed method, "EMD-based detrended-SaEn" to attenuate the influence of intrinsic non-stationarity. The correlation factors in 27 AD patients showed a moderate correlation (0.361-0.523, p<0.05) between MMSE and EMD-based detrended SaEn in Fp1, Fp2, F4 and T3. There was a high correlation (Correlation coefficient=0.975, p<0.05) between the changes of MMSE and the changes of EMD-based detrended-SaEn in F7 in 5 follow-up patients. The dynamic complexity of EEG fluctuations is degraded by pathological degeneration, and EMD-based detrended SaEn provides an objective, non-invasive and non-expensive tool for evaluating and following AD patients.

Nonlinear analysis of electroencephalogram at rest and during cognitive tasks in patients with schizophrenia

BACKGROUND

In spite of the large number of studies on schizophrenia, a full understanding of its core pathology still eludes us. The application of the nonlinear theory of electroencephalography (EEG) analysis provides an interesting tool to differentiate between physiologic conditions (e.g., resting state and mathematical task) and normal and pathologic brain activities. The aim of the present study was to investigate nonlinear EEG activity in patients with schizophrenia.

METHODS

We recorded 19-lead EEGs in patients with stable schizophrenia and healthy controls under 4 different conditions: eyes closed, eyes open, forward counting and backward counting. A nonlinear measure of complexity was calculated by means of correlation dimension (D2).

RESULTS

We included 17 patients and 17 controls in our analysis. Comparing the 2 populations, we observed greater D2 values in the patient group. In controls, increased D2 values were observed during active states (eyes open and the 2 cognitive tasks) compared with baseline conditions. This increase of brain complexity, which can be interpreted as an increase of information processing and integration, was not preserved in the patient population.

LIMITATIONS

Patients with schizophrenia were taking antipsychotic medications, so the presence of medication effects cannot be excluded.

CONCLUSION

Our results suggest that patients with schizophrenia present changes in brain activity compared with healthy controls, and this pathologic alteration can be successfully studied with nonlinear EEG analysis.

Nonlinear features of surface EEG showing systematic brain signal adaptations with muscle force and fatigue

Nonlinear dynamics has been introduced to the analysis of biological data and increasingly recognized to be functionally relevant. The purpose of this study was to examine chaotic properties of human scalp EEG signals associated with voluntary motor tasks using the largest Lyapunov exponent (L1). 64-channel scalp EEG data were recorded from eight healthy subjects in two tasks: (1) intermittent handgrip contractions at 20, 40, 60, and 80% of maximal voluntary contraction (MVC) with 20 trials at each level. No significant fatigue were induced; (2) intermittent handgrip MVCs (100 trials) that resulted in significant fatigue. The L1 values of all EEG channels were calculated in each trial first then averaged across the 20 trials at each force level (Task 1) or over each of the 5-trial blocks (Task 2) before the group means were obtained. A multivariate statistical model was used to examine the effect of force and fatigue on L1. L1 values were greater with higher force (Task 1), and decreased significantly with fatigue (Task 2). The L1 of the EEG signals changes systematically and correlates significantly with muscle force and fatigue. The results suggest that nonlinear chaotic index L1 may serve as a quantitative measure for motor control-related cortical signal adaptations.

Spectral and complexity features of the EEG changed by visual input in a case of subcortical stroke compared to healthy controls

OBJECTIVE

To compare spectral and complexity characteristics of the EEG in a unique case of subcortical infarct to those seen in healthy controls.

METHODS

Absolute and relative frequency spectra, theta/beta ratio, the brain symmetry index (BSI), Omega-complexity and synchronization likelihood were calculated of the EEG recorded in eyes closed and eyes open conditions.

RESULTS

Increased absolute delta, theta, and Omega-complexity in these frequency bands, higher theta/beta ratios, and decreased relative beta activity were found in the side of the infarct. The BSI localized the excess of slow, and decrease of fast frequency activity to the area of ischemia. Following eyes opening the increase of fast and decrease of slow frequencies, the increase of Omega-complexity in the alpha and beta bands, and the decrease of synchronization likelihood for the fast frequency bands were reduced in the side of the infarct.

CONCLUSIONS

The subcortical infarct caused ipsilaterally increased slow, and decreased fast frequency activity accompanied by decreased synchronization of slow, increased synchronization of fast frequencies. Reduced reactivity in the ischemic side was particularly apparent for complexity measures.

SIGNIFICANCE

Complexity indices of the EEG are sensitive complementary measures of electrophysiological changes caused by local lesions such as subcortical stroke.

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.

A method for detection of Alzheimer's disease using ICA-enhanced EEG measurements

OBJECTIVE

Many researchers have studied automatic EEG classification and recently a lot of work has been done on artefact-removal from EEG data using independent component analyses (ICA). However, demonstrating that a ICA-processed multichannel EEG measurement becomes more interpretable compared to the raw data (as is usually done in work on ICA-processing of EEG data) does not yet prove that detection of (incipient) anomalies is also better possible after ICA-processing. The objective of this study is to show that ICA-preprocessing is useful when constructing a detection system for Alzheimer's disease.

METHODS AND MATERIAL

The paper describes a method for detection of EEG patterns indicative of Alzheimer's disease using automatic pattern recognition techniques. Our method incorporates an artefact removal stage based on ICA prior to automatic classification. The method is evaluated on measurements of a length of 8s from two groups of patients, where one group is in an initial stage of the disease (28 patients), whereas the other group is in a more progressed stage (15 patients). Both setups include a control group that should be classified as normal (10 and 21, respectively).

RESULTS

Our final classification results for the group with severe Alzheimer's disease are comparable to the best results from literature. We show that ICA-based reduction of artefacts improves classification results for patients in an initial stage.

CONCLUSION

We conclude that a more robust detection of Alzheimer's disease related EEG patterns may be obtained by employing ICA as ICA based pre-processing of EEG data can improve classification results for patients in an initial stage of Alzheimer's disease.

The influence of auditory background stimulation (Mozart's sonata K. 448) on visual brain activity

Twenty individuals solved a visual oddball task in two response conditions: while listening to the Mozart's sonata K. 448, and while listening to nothing. The recorded event-related potentials (ERP) were analyzed in the time and frequency domains. In the music response condition the ERP peak latencies on the left hemisphere increased, whereas on the right hemisphere a decrease of peak latencies as compared with the silence response condition was observed. In the theta, lower-1 alpha and gamma band increases in induced event-related coherences were observed while respondents solved the oddball task and listened to music, whereas a decoupling of brain areas in the gamma band was observed in the silence response condition. It is suggested that auditory background stimulation can influence visual brain activity, even if both stimuli are unrelated.

EEG dynamics in patients with Alzheimer's disease

Alzheimer's disease (AD) is the most common neurodegenerative disorder characterized by cognitive and intellectual deficits and behavior disturbance. The electroencephalogram (EEG) has been used as a tool for diagnosing AD for several decades. The hallmark of EEG abnormalities in AD patients is a shift of the power spectrum to lower frequencies and a decrease in coherence of fast rhythms. These abnormalities are thought to be associated with functional disconnections among cortical areas resulting from death of cortical neurons, axonal pathology, cholinergic deficits, etc. This article reviews main findings of EEG abnormalities in AD patients obtained from conventional spectral analysis and nonlinear dynamical methods. In particular, nonlinear alterations in the EEG of AD patients, i.e. a decreased complexity of EEG patterns and reduced information transmission among cortical areas, and their clinical implications are discussed. For future studies, improvement of the accuracy of differential diagnosis and early detection of AD based on multimodal approaches, longitudinal studies on nonlinear dynamics of the EEG, drug effects on the EEG dynamics, and linear and nonlinear functional connectivity among cortical regions in AD are proposed to be investigated. EEG abnormalities of AD patients are characterized by slowed mean frequency, less complex activity, and reduced coherences among cortical regions. These abnormalities suggest that the EEG has utility as a valuable tool for differential and early diagnosis of AD.

Dimensional complexity of the EEG in patients with posttraumatic stress disorder

Recent electrophysiological studies have reported evidence of information processing abnormalities in patients with posttraumatic stress disorder (PTSD). The aim of this study is to examine dynamical complexity of the EEG in PTSD patients, which is thought to reflect information processing of the brain. Resting EEG recordings (32,800 data points acquired continuously from 82 s of an EEG record) were obtained in 16 channels of 27 patients with PTSD from a mixed civilian trauma population and 14 healthy subjects. The correlation dimension (D2) of the EEG was used to quantify the complexity of the cortical dynamics underlying the EEG signal. The PTSD patients were found to have lower D2 values than those of the healthy subjects in most channels (Fp1, F8, C4, P4, T3, T4, T5, T6, and O1), indicating that PTSD patients have globally reduced complexity in their EEG waveforms. This study supports the hypotheses that PTSD patients exhibit disturbed cortical information processing, and that non-linear dynamical analysis of the EEG can be a tool for detecting changes in neurodynamics of the brain in PTSD.

A neural complexity measure applied to MEG data in Alzheimer's disease

OBJECTIVE

A measure of neural complexity (C(N)) (Proc. Natl Acad. Sci. USA 91 (1994) 5033) was applied to magnetoencephalography (MEG) data to test the hypothesis that C(N) decreases when information processing in the brain is impaired, as is the case in patients with Alzheimer's Disease (AD).

METHODS

One hundred and fifty-one channel MEGs were recorded in 20 AD patients and 20 healthy age-matched controls in a resting condition with eyes open (EO) and eyes closed (EC). Artifact-free epochs of 117 channels were selected for analysis. C(N) and D(2) were computed in different frequency bands, and correlated with the MMSE.

RESULTS

The Group x Frequency band interaction was significant for both C(N) and D(2). C(N) was higher in AD, as compared with controls, in the 2-4 and 4-8Hz bands, and D(2) was higher in AD patients in the 14-20 and 20-30Hz bands. The C(N) was higher in the EC condition compared to the EO condition, whereas the D(2) was higher in the EO condition.

CONCLUSIONS

The hypothesis of Tononi et al. (Proc. Natl Acad. Sci. USA 91 (1994) 5033) that the neural complexity decreases in AD patients has to be rejected. However, both neural complexity and the correlation dimension did show differences between controls and AD patients which depended on frequency band.

Chaos and schizophrenia: does the method fit the madness?

Over the past 30 years, investigators have used nonlinear and so-called chaos theory-based techniques to examine a wide range of phenomena ranging from electroencephalogram and cardiac rate and rhythm analyses to stock market and weather predictions. Psychiatric neuroscientists are now beginning to apply nonlinear methods to mental disorders such as schizophrenia. These applications are relevant from the level of complex genetic architecture and calcium channel dynamics to the symptomatic, behavioral, and functional outcome of schizophrenia. The key point of this surge of interest is distinguishing complex, nonlinear but lawfully mediated systems from truly random systems. The application of these methods to studies in schizophrenia has yielded findings that are consistent with the general hypothesis that an altered sequential or temporal architecture is a key feature of this disorder. Specifically, we propose that the temporal architecture of schizophrenia is characterized by bursts of complex, nonlinear phenomena alternating with truly random events. Analyzing these patterns of molecular (e.g., calcium channel activity) to molar (e.g., symptom level) phenomena via nonlinear systems methods can provide new approaches to understanding complex temporal and sequential shifts in neural substrate activity, pathophysiology, and the course and treatment and outcome of schizophrenia.

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.

Recurrent neural network-based approach for early recognition of Alzheimer's disease in EEG

OBJECTIVE

We explored the ability of specifically designed and trained recurrent neural networks (RNNs), combined with wavelet preprocessing, to discriminate between the electroencephalograms (EEGs) of patients with mild Alzheimer's disease (AD) and their age-matched control subjects.

METHODS

Twomin recordings of resting eyes-closed continuous EEGs (as well as their wavelet-filtered subbands) obtained from parieto-occipital channels of 10 early AD patients and 10 healthy controls were input into RNNs for training and testing purposes. The RNNs were chosen because they can implement extremely non-linear decision boundaries and possess memory of the state, which is crucial for the considered task.

RESULTS

The best training/testing results were achieved using a 3-layer RNN on left parietal channel level 4 high-pass wavelet subbands. When trained on 3 AD and 3 control recordings, the resulting RNN tested well on all remaining controls and 5 out of 7 AD patients. This represented a significantly better than chance performance of about 80% sensitivity at 100% specificity.

CONCLUSION

The suggested combined wavelet/RNN approach may be useful in analyzing long-term continuous EEGs for early recognition of AD. This approach should be extended on larger patient populations before its clinical diagnostic value can be established. Further lines of investigation might also require that EEGs be recorded from patients engaged in certain mental (cognitive) activities.

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.

Nonlinear dynamics and chaos theory: concepts and applications relevant to pharmacodynamics

The theory of nonlinear dynamical systems (chaos theory), which deals with deterministic systems that exhibit a complicated, apparently random-looking behavior, has formed an interdisciplinary area of research and has affected almost every field of science in the last 20 years. Life sciences are one of the most applicable areas for the ideas of chaos because of the complexity of biological systems. It is widely appreciated that chaotic behavior dominates physiological systems. This is suggested by experimental studies and has also been encouraged by very successful modeling. Pharmacodynamics are very tightly associated with complex physiological processes, and the implications of this relation demand that the new approach of nonlinear dynamics should be adopted in greater extent in pharmacodynamic studies. This is necessary not only for the sake of more detailed study, but mainly because nonlinear dynamics suggest a whole new rationale, fundamentally different from the classic approach. In this work the basic principles of dynamical systems are presented and applications of nonlinear dynamics in topics relevant to drug research and especially to pharmacodynamics are reviewed. Special attention is focused on three major fields of physiological systems with great importance in pharmacotherapy, namely cardiovascular, central nervous, and endocrine systems, where tools and concepts from nonlinear dynamics have been applied.

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.

Correlations between ERP parameters and intelligence: a reconsideration

The present study investigated differences in ERP parameters related to intelligence. For that purpose 74 individuals (Intelligence: M=107; S.D.=12; range 73-135), of average creativity passively listened to two tones and performed two auditory, and two visual oddball tasks while their EEG was recorded. The approximate entropy parameters, peak latencies and amplitudes were determined. The correlation coefficients indicated that in the attended conditions, the more intelligent individuals showed more regular ERP waveforms than less intelligent individuals. It was further found that less intelligent individuals showed increased P300 latencies and reduced amplitudes. The differences were explained with a more specific engagement of neural networks in more intelligent individuals.

On Variability and Stability in Human Movement

Current research in biology and physiology has unequivocally demonstrated the significance of variability for the optimal functioning of healthy and adaptable systems. Different pathologies are characterized by reductions in complexity of organization, often signified by loss of variability and adaptability. It is argued that the traditional perspective on biology in general and movement science in particular that tended to associate noise and variability with performance decrements and pathology is no longer tenable. Tools and methodologies that have emerged from the dynamical systems perspective to coordination and control are discussed in the context of postural control and transitions in interlimb coordination and locomotion. First, it is shown that variability can play a functional role in the detection and exploration of stability boundaries during balance control. Second, pattern transitions are characterized by increased variability in movement coordination dynamics. Under conditions of movement pathologies, such as in Parkinson’s disease, reductions in variability in coordination dynamics clearly identify movement coordination and transition problems so characteristic for these patients. It is concluded that the relation between variability and stability is complex and that variability cannot be equated with instability without knowledge of the underlying movement dynamics.

Nonlinear EEG analysis and its potential role in epileptology

Deterministic chaos offers a striking explanation for apparently irregular behavior of the brain that is evidenced in the EEG. Recent developments in the physical-mathematical framework of the theory of nonlinear dynamics (colloquially often termed chaos theory) provide new concepts and powerful algorithms to analyze such time series. Because of its high versatility, nonlinear time series analysis has already gone beyond the physical sciences and, at present, is being successfully applied in a variety of disciplines, including cardiology, neurology, psychiatry, and epileptology. However, it is well known that different influencing factors limit the use of nonlinear measures to characterize EEG dynamics in a strict sense. Nevertheless, when interpreted with care, relative estimates of, e.g., the correlation dimension or the Lyapunov exponents, can reliably characterize different states of normal and pathologic brain function. In epileptology, extraction of nonlinear measures from the intracranially recorded EEG promises to be important for clinical practice. In addition to an immense reduction of information content of long-lasting EEG recordings, previous studies have shown that these measures enable (a) localization of the primary epileptogenic area in different cerebral regions during the interictal state, (b) investigations of antiepileptic drug effects, (c) analyses of spatio-temporal interactions between the epileptogenic zone and other brain areas, and (d) detection of features predictive of imminent seizure activity. Nonlinear time series analysis provides new and supplementary information about the epileptogenic process and thus contributes to an improvement in presurgical evaluation.

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.

Nonlinear EEG analysis in early Alzheimer's disease

Nonlinear EEG analysis attempts to characterize the dynamics of neural networks in the brain. Abnormalities in nonlinear EEG measures have been found repeatedly in Alzheimer's disease (AD). The present study was undertaken to investigate whether these abnormalities could already be found in the early stage of AD. In a representative sample of 49 community-dwelling elderly, Alzheimer's disease was diagnosed in 7 subjects. Correlation dimension (D2) and nonlinear prediction were measured at 16 electrodes and in two different activational states. Also, 10 surrogate data sets were generated for each EEG epoch in order to investigate the presence of nonlinear dynamics. Differences between nonlinear statistics derived from original and from surrogate data sets were expressed as Z-scores. We found lower D2 and higher predictability in the demented subjects compared to the normal subjects. The results obtained with the Z-scores pointed to changed nonlinear dynamics in frontal and temporal areas in demented subjects. However, the major differences between demented and healthy subjects are not due to nonlinearity. From this it appears that linear dynamics change first in the course of AD, followed by changes in nonlinear dynamics.

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.

Working memory load and EEG-dynamics as revealed by point correlation dimension analysis

The results of the present study showed a decreased dimensional complexity during working-memory load, which was induced by the Corsi-Bock-Tapping task as compared to a baseline task. This baseline task was similar to the Corsi-Block-Tapping with respect to both the required processes of perception and the motor performance. A load-specific change of brain dynamics was observed, which was most pronounced over frontal cortical areas. This finding is in agreement with the literature and encourages further research on the ongoing EEG, especially with clinical tests, where little is known about their psychophysiological correlates. From a methodological point of view, the point correlation dimension, which deals with non-stationary data, was applied to EEG-time series that were a concatenation of several EEG-subepochs of the same experimental conditions. From the results it is proposed that this procedure might offer an approach for EEG analysis, where the EEG-epochs are of short duration and non-stationary data are to be expected.

Decrease of non-linear structure in the EEG of Alzheimer patients compared to healthy controls

OBJECTIVE

Non-linear EEG analysis can provide information about the functioning of neural networks that cannot be obtained with linear analysis. The correlation dimension (D2) is considered to be a reflection of the complexity of the cortical dynamics underlying the EEG signal. The presence of non-linear dynamics can be determined by comparing the D2 calculated from original EEG data with the D2 from phase-randomized surrogate data.

METHODS

In a prospective study, we used this method in order to investigate non-linear structure in the EEG of Alzheimer patients and controls. Twenty-four patients (mean age 75.6 years) with 'probable Alzheimer's disease' (NINCDS-ADRDA criteria) and 22 controls (mean age 70.3 years) were examined. D2 was calculated from original and surrogate data at 16 electrodes and in three conditions: with eyes open, eyes closed and during mental arithmetic.

RESULTS

D2 was significantly lower in the Alzheimer patients compared to controls (P = 0.023). The difference between original and surrogate data was significant in both groups, implicating that non-linear dynamics play a role in the D2 value. Moreover, this difference between original and surrogate data was smaller in the patient group. D2 increased with activation, but not significantly more in controls than in patients.

CONCLUSIONS

In conclusion, we found decreased dimensional complexity in the EEG of Alzheimer patients. This decrease seems to be attributable at least partially to different non-linear EEG dynamics. Because of this, non-linear EEG analysis could be a useful tool to increase our insight into brain dysfunction in Alzheimer's disease.

Nonlinear analysis of the EEG of schizophrenics with optimal embedding dimension

We estimated the correlation dimensions of EEGs in patients with schizophrenia to investigate the dynamical properties underlying the EEG. We employed a new method, proposed by Kennel et al. (Kennel MB, Brown R, Abarbanel HDI. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 1992;45:3403-11), to calculate the correlation dimension D2. That method determined the proper minimum embedding dimension by looking at the behaviour of nearest neighbours under a change in the embedding dimension d from d to d + 1. We demonstrated that for limited noisy data, our algorithm was strikingly faster and more accurate than previous ones. We estimated the D2 of EEGs from 16 channels in patients with schizophrenia according to DSM-IV whereas previous studies, which estimated chaoticity of EEG in schizophrenia, recorded EEG only in a limited number of channels. Schizophrenic patients had a lower correlation dimension in the left inferior frontal and anterior temporal regions compared with controls. Our finding of decreased left frontal and temporal chaotic activity in schizophrenics is in line with the findings of a hypofrontality and hypotemporality reported in previous clinical studies such as EEG, blood flow, brain MRI and positron emission tomography studies in schizophrenia. This result suggests that chaos analysis may be a useful tool in analysing EEG data to explore the brain mechanism of schizophrenia.

Nonlinear dynamical analysis of periodic lateralized epileptiform discharges

Nonlinear time series analysis can be used to investigate the dynamics underlying the generation of EEG signal. In the present study we used this approach to study the pathophysiology of PLEDs. We calculated the correlation dimension D2 of an EEG with typical PLEDs, and compared the results with those obtained for surrogate data. These surrogate data have the same power spectrum and amplitude distribution as the original EEG data, but are otherwise random. By construction, such surrogate data can be described by a linear model. Our results showed that D2 estimations for PLEDs were low, on the order of one, and that the results for EEG and the surrogate data were clearly different, indicating that the EEG with PLEDs reflects nonlinear dynamics of the underlying neural networks.