0000000000061957
AUTHOR
Jürgen Fell
Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep
Under selected conditions, nonlinear dynamical systems, which can be described by deterministic models, are able to generate so-called deterministic chaos. In this case the dynamics show a sensitive dependence on initial conditions, which means that different states of a system, being arbitrarily close initially, will become macroscopically separated for sufficiently long times. In this sense, the unpredictability of the EEG might be a basic phenomenon of its chaotic character. Recent investigations of the dimensionality of EEG attractors in phase space have led to the assumption that the EEG can be regarded as a deterministic process which should not be mistaken for simple noise. The calcu…
Time course of human 40 Hz EEG activity accompanying P3 responses in an auditory oddball paradigm
In order to quantify the time course of auditory P3-related gamma activity, root mean square (RMS) values were calculated from band-filtered (30-45 Hz) target and non-target responses in an auditory oddball experiment. Evoked (phase locked) gamma activity was evaluated from the time domain averages, whereas induced (not necessarily phase locked) activity was analyzed on the basis of single trials. Gamma RMS values were integrated across different time windows, namely the prestimulus, N50/P50, N100, pre P3, P3 and post P3 window. The single trial P3 window hereby was defined by a maximum amplitude criterion. In accordance with other studies, we found a pronounced increase of evoked gamma act…
Alterations of Continuous MEG Measures during Mental Activities
In a pilot study, we investigated the topography of 11 continuous MEG measures for the eyes-opened and eyes-closed condition together with three simple mental tasks (mental arithmetic, visual imagery, word generation). One-minute recordings for each condition from 16 right-handed subjects were analyzed. The electrophysiological measures consisted of 6 spectral band measures together with spectral edge frequency and spectral entropy, plus the time-domain-based entropy of amplitudes (ENA) and the nonlinear measures correlation dimension D2 and Lyapunov exponent L1. In summary, our results indicate a pronounced task-dependent difference between the anterior and the posterior region, but no lat…
Spectral analysis of P300 generation in depression and schizophrenia.
In the past it was reported in several studies that both depressive and schizophrenic patients exhibit reduced P300 amplitudes compared to healthy controls. In order to elucidate the underlying mechanisms of spectral P300 generation, we analysed P300 responses in depression and schizophrenia by a frequency based approach. Herefore, the amplification (poststimulus/prestimulus) of spectral power in different frequency bands was evaluated for non-target and target epochs. Generally, we found that P300 responses are accompanied by a pronounced frequency amplification in the delta and theta range. For the depressive patients we detected only under target condition a statistically significant red…
Surrogate data analysis of sleep electroencephalograms reveals evidence for nonlinearity
We tested the hypothesis of whether sleep electroencephalographic (EEG) signals of different time windows (164 s, 82 s, 41 s and 20.5 s) are in accordance with linear stochastic models. For this purpose we analyzed the all-night sleep electroencephalogram of a healthy subject and corresponding Gaussian-rescaled phase randomized surrogates with a battery of five non-linear measures. The following nonlinear measures were implemented: largest Lyapunov exponent L1, correlation dimension D2, and the Green-Savit measures delta 2, delta 4 and delta 6. The hypothesis of linear stochastic data was rejected with high statistical significance. L1 and D2 yielded the most pronounced effects, while the G…
An approach to single trial analysis of event-related potentials based on signal detection theory.
Abstract The aim of the present paper was to introduce a single trial analysis to event-related potential measurement in order to illuminate the mechanisms behind an impaired P300 amplitude occurring under certain experimental conditions. For this purpose we applied tools from linear system theory and signal detection theory to single trials in an oddball paradigm in order to estimate the amplitude of the positive deflection around the P300 latency following target and nontarget stimuli. According to the density functions of these amplitude distributions we operationally defined ‘P300 absent in target’ (P300 amplitude smaller than an individual threshold under target conditions) as well as …
Macrostructural EEG characterization based on nonparametric change point segmentation: application to sleep analysis
In the present investigation a new methodology for macrostructural EEG characterization based on automatic segmentation has been applied to sleep analysis. A nonparametric statistical approach for EEG segmentation was chosen, because it minimizes the need for a priori information about a signal. The method provides the detection of change-points i.e. boundaries between quasi-stationary EEG segments based on the EEG characteristics within four fundamental frequency bands (delta, theta, alpha and beta). Polysomnographic data of 18 healthy subjects were analyzed. Our findings show that nonparametric change-point segmentation in combination with cluster analysis enables us to obtain a clear pic…
The calculation of the first positive Lyapunov exponent in sleep EEG data
To help determine if the EEG is quasiperiodic or chaotic we performed a new analysis by calculating the first positive Lyapunov exponent L1 from sleep EEG data. Lyapunov exponents measure the mean exponential expansion or contraction of a flow in phase space. L1 is zero for periodic as well as quasiperiodic processes, but positive in case of chaotic processes expressing the sensitive dependence on initial conditions. We calculated L1 for sleep EEG segments of 15 healthy male subjects corresponding to sleep stages I, II, III, IV and REM (according to Rechtschaffen and Kales). Our investigations support the assumption that EEG signals are neither quasiperiodic waves nor simple noise. Moreover…
Sequential analysis of the brain's transfer properties during consecutive REM episodes
Abstract Classical analysis of the spontaneous sleep EEG has revealed alterations of REM sleep in psychiatric diseases and under the influence of drugs. In order to elucidate possible functional differences between different REM episodes even in healthy subjects we investigated in 10 volunteers the transfer properties of the brain by measuring auditory (AEP) and visual evoked potentials (VEP) from scalp positions Fz, Cz and Pz during the night. According to linear system theory we computed the so-called amplitude-frequency characteristics (AFC) from averaged AEPs and VEPs during the first and each of the following 3 REM episodes. These functions describe the relationship between the input a…
Brief Communication HUMAN SCALP RECORDED SIGMA ACTIVITY IS MODULATED BY SLOW EEG OSCILLATIONS DURING DEEP SLEEP
The EEG during deep sleep exhibits a distinct cortically generated slow oscillation of around and below 1 Hz which can be distinguished from other delta (0.5-3.5 Hz) activity. Intracranial studies showed that this slow oscillation triggers and groups cortical network firing. In the present study, we examined whether the phases of the slow oscillation during sleep stage 4 are correlated with the magnitude of sigma (12-16 Hz) and gamma (> 20 Hz) scalp activity. For this purpose, 10-min segments of uninterrupted stage 4 sleep EEG from 9 subjects were analyzed by applying wavelet techniques. We found that scalp recorded sigma, but not gamma, activity is modulated by the phases of the slow oscil…
Differential pathophysiological mechanisms of reduced P300 amplitude in schizophrenia and depression: a single trial analysis
In order to address basic mechanisms behind a reduced averaged P300 wave in schizophrenia and depression, 17 unmedicated schizophrenic and 11 unmedicated depressive subjects were tested in an 'oddball paradigm' against healthy controls matched for gender and age. The amplitude distributions of single trials' maximum positive deflections after stimulation (P300) for both target and nontarget stimuli were determined, which served as a basis for calculating the discrimination index d'. This index characterizes differences in the electrophysiological responses to target and nontarget stimuli of a subject being engaged in a discrimination task. As a main result d' was significantly lower for sch…
Nonlinear analysis of continuous ECG during sleep I. Reconstruction.
In recent years evidence has accumulated that ECG signals are of a nonlinear nature. It has been recognized that strictly periodic cardiac rhythms are not accompanied by healthy conditions but, on the contrary, by pathological states. Therefore, the application of methods from nonlinear system theory for the analysis of ECG signals has gained increasing interest. Crucial for the application of nonlinear methods is the reconstruction (embedding) of the time series in a phase space with appropriate dimension. In this study continuous ECG signals of 12 healthy subjects recorded during different sleep stages were analysed. Proper embedding dimension was determined by application of two techniqu…
Linear inverse filtering improves spatial separation of nonlinear brain dynamics: a simulation study.
We examined topographic variations in nonlinear measures based on scalp voltages, which were generated by two simulated current dipoles each placed in a different hemisphere of a spherical volume conductor (three-shell model). Dipole dynamics were that of a three-torus and the x-component of the Lorenz-system and scalp voltage were calculated for a configuration of 29 electrode positions. Although estimates for correlation dimension D2 and Lyapunov exponent L1 were close to the theoretical values for the original time series, the simulated scalp voltage data showed almost no topographic resolution of dipole positions. In order to enhance topographic differentiation, we constructed linear in…
Human Sleep EEG under the Influence of Pulsed Radio Frequency Electromagnetic Fields
Former exploratory investigations of sleep alterations due to global system for mobile communications (GSM) signals have shown a hypnotic and REM-suppressive effect under field exposure. This effect was observed in a first study using a power flux density of 0.5 W/m<sup>2</sup>, and the same trend occurred in a second study with a power flux density of 0.2 W/m<sup>2</sup>. For the present study, we applied a submaximal power flux density of 50 W/m<sup>2</sup>. To investigate putative effects of radio frequency electromagnetic fields (EMFs) of cellular GSM phones on human sleep EEG pattern, all-night polysomnographies of 20 healthy male subjects both with …
Neural net classification of REM sleep based on spectral measures as compared to nonlinear measures
In various studies the implementation of nonlinear and nonconventional measures has significantly improved EEG (electroencephalogram) analyses as compared to using conventional parameters alone. A neural network algorithm well approved in our laboratory for the automatic recognition of rapid eye movement (REM) sleep was investigated in this regard. Originally based on a broad range of spectral power inputs, we additionally supplied the nonlinear measures of the largest Lyapunov exponent and correlation dimension as well as the nonconventional stochastic measures of spectral entropy and entropy of amplitudes. No improvement in the detection of REM sleep could be achieved by the inclusion of …
Non-linear dynamics of alpha and theta rhythm: correlation dimensions and Lyapunov exponents from healthy subject's spontaneous EEG.
The aim of the present paper was to analyze some non-linear dynamic properties of the resting EEG from healthy subjects under eyes closed conditions. For this purpose we digitally filtered the spontaneous EEG in the theta (3-8 Hz) and alpha frequency range (8-13 Hz) and considered these independent rhythms as signals from a deterministic system. Under certain conditions non-linear dynamic systems are able to generate deterministic chaos, which means that similar causes do not produce similar effects. This phenomenon is called sensitive dependence on initial conditions. From different lead positions (F3, F4, Cz, P3, P4, O1 and O2) we calculated the so-called correlation dimension D2, which i…
Nonlinear analysis of sleep EEG data in schizophrenia: calculation of the principal Lyapunov exponent
The generating mechanism of the electroencephalogram (EEG) points to the hypothesis that EEG signals derive from a nonlinear dynamic system. Hence, the unpredictability of the EEG might be considered as a phenomenon exhibiting its chaotic character. The essential property of chaotic dynamics is the so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's first positive Lyapunov exponent, L1. We calculated L1 for sleep EEG segments of 13 schizophrenic patients and 13 control subjects that corresponded to sleep stages I, II, III, IV and REM (rapid eye movement), as defined by Rechtschaffen and Kales, for the lead positions Cz and Pz. Du…
Covariation of spectral and nonlinear EEG measures with alpha biofeedback.
Item does not contain fulltext This study investigated how different spectral and nonlinear EEG measures covaried with alpha power during auditory alpha biofeedback training, performed by 13 healthy subjects. We found a significant positive correlation of alpha power with the largest Lyapunov-exponent, pointing to an increased dynamical instability of the EEG accompanying alpha enhancement. Alpha power amplification, moreover, was significantly correlated with a decrease of spectral entropy within the alpha range. This outcome reflects a sharpening of the alpha peak during biofeedback training. The fact that the sharpening effect clearly preceded the increase of alpha amplitude could be exp…
Is the nonREM–REM sleep cycle reset by forced awakenings from REM sleep?
In selective REM sleep deprivation (SRSD), the occurrence of stage REM is repeatedly interrupted by short awakenings. Typically, the interventions aggregate in clusters resembling the REM episodes in undisturbed sleep. This salient phenomenon can easily be explained if the nonREM–REM sleep process is continued during the periods of forced wakefulness. However, earlier studies have alternatively suggested that awakenings from sleep might rather discontinue and reset the ultradian process. Theoretically, the two explanations predict a different distribution of REM episode duration. We evaluated 117 SRSD treatment nights recorded from 14 depressive inpatients receiving low dosages of Trimipram…
Nonlinear analysis of continuous ECG during sleep II. Dynamical measures
The hypothesis that cardiac rhythms are associated with chaotic dynamics implicating a healthy flexibility has motivated the investigation of continuous ECG with methods of nonlinear system theory. Sleep is known to be associated with modulations of the sympathetic and parasympathetic control of cardiac dynamics. Thus, the differentiation of ECG signals recorded during different sleep stages can serve to determine the usefulness of nonlinear measures in discriminating ECG states in general. For this purpose the following six nonlinear measures were implemented: correlation dimension D2, Lyapunov exponent L1. Kolmogorov entropy K2, as well as three measures derived from the analysis of unsta…