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Quantitative measure of complexity of EEG signal dynamics

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Klonowski W., Jernajczyk W., Niedzielska K., Rydz A., Stepien R.
Acta Neurobiologiae Experimentalis
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1999
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vol. 59
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issue 4
315-321
EN
Since electroencephalographic (EEG) signal may be considered chaotic, Nonlinear Dynamics and Deterministic Chaos Theory may supply effective quantitative descriptors of EEG dynamics and of underlying chaos in the brain. We have used Karhunen-Loeve decomposition of the covariance matrix of the EEG signal to analyse EEG signals of 4 healthy subjects, under drug-free condition and under the influence of Diazepam. We found that what we call KL-complexity of the signal differs profoundly for the signals registered in different EEG channels, from about 5-8 for signals in frontal channels up to 40 and more in occipital ones. But no consistency in the influence of Diazepam administration on KL-complexity is observed. We also estimated the embedding dimension of the EEG signals of the same subjects, which turned to be between 7 and 11, so endorsing the presumption about existence of low-dimensional chaotic attractor. We are sure that nonlinear time series analysis can be used to investigate the dynamics underlying the generation of EEG signal. This approach does not seem practical yet, but deserves further study.
2
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Deterministic brain oscillations in the magnetoencephalogram

100%
Kowalik Z. J., Witte O. W.
Acta Neurobiologiae Experimentalis
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2000
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vol. 60
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issue 2
195-202
EN
Determinism is a special property of some systems and is defined by its state-space behavior in which the trajectories in time never intersect. Whether or not determinism exists in brain activities is a question that may be resolved by analysis of the dynamical properties of the electroencephalogram (EEG) or magnetoencephalogram (MEG). We will show that even though there are strong nonstationarities in most brain behaviors, small epochs of deterministic dynamics can still be observed. We will also show that the local Lyapunov exponents are measures that can demonstrate smooth transitions into these deterministic states.
3
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EEG analysis with nonlinear deterministic and stochastic methods: a combined strategy

100%
Fell J., Kaplan A., Darkhovsky B., Roschke J.
Acta Neurobiologiae Experimentalis
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2000
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vol. 60
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issue 1
87-108
EN
We describe nonlinear deterministic versus stochastic methodology, their applications to EEG research and the neurophysiological background underlying both approaches. Nonlinear methods are based on the concept of attractors in phase space. This concept on the one hand incorporates the idea of an autonomous (stationary) system, on the other hand implicates the investigation of a long time evolution. It is an unresolved problem in nonlinear EEG research that nonlinear methods per se give no feedback about the stationarity aspect. Hence, we introduce a combined strategy utilizing both stochastic and nonlinear deterministic methods. We propose, in a first step to segment the EEG time series into piecewise quasi-stationary epochs by means of nonparametric change point analysis. Subsequently, nonlinear measures can be estimated with higher confidence for the segmented epochs fullfilling the stationarity condition.
4
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The role of the thalamic reticular neurons in alpha- and gamma-oscillations in neocortex: a mechanism for selective perception and stimulus binding

100%
Skinner J. E., Molnar M., Kowalik Z. J.
Acta Neurobiologiae Experimentalis
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2000
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vol. 60
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issue 1
123-142
EN
The long-term objective is to understand how large masses of neurons in the brain process information during various learning and memory paradigms. Both time- and space-dependent processes have been identified in animals through computer-based analytic quantifications of event-related extracellular potentials. New nonlinear analyses have been introduced that presume that the fine-grain variation in the signal is determined and patterned in phase-space. Some neurons in the primary visual cortex manifest gamma-band oscillations. These cells show both a nonspecific phase-alignment (response synchrony) and a specific tuning (orientation tuning) when stimuli are presented to their receptive fields. This dual regulation of the sensory cells is proposed to underlie stimulus binding, a theoretical mechanism for 'object' perception. Nonlinear analytic results from gamma-activities in a simple model neuropil (olfactory bulb) suggest that neuroplasticity may arise through self-organization, a process in which a nonlinear change in the dynamics of the oscillatory field potentials is the hallmark. This self-organization may follow simple dynamical laws in which global cooperativity among the neurons is transiently brought about that, over trials, results in enduring changes in the nonlinear dynamics of some neurons. In conclusion, the sculpturing of the synaptic throughput in the sensory cortex (stimulus binding) may be associated with the irregular phases of the gamma-activities and may result from both specific and nonspecific systems operating together in a nonlinear self-organizing manner.
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