Non-linear behaviour of human EEG: fractal exponent versus correlation dimension in awake and sleep stages

Pereda, Ernesto; Gamundı́, Antoni; Rial, Rubén V.; González, José M.

doi:10.1016/s0304-3940(98)00435-2

Cited by 176 publications

(119 citation statements)

References 18 publications

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“…It is often applied to anatomical structures such as dendrites, in which branchlets far from the cell body have the same appearance as branches close in. The spectra of EEG signals often show the 1/f power-law distribution across frequencies , which is an example of selfsimilarity (Pereda et al, 1998;Watters, 2000;Hwa and Ferree, 2002). The self-similarity of events in a scale-free network offers a key to understanding how cortical gamma synchronization can be reinitialized by a phase transition over much of a human cerebral hemisphere (Cover Illustration, Fig.…”

Section: Sudden Changes In Eeg Occur Simultaneously Over Large Distanmentioning

confidence: 99%

“…The records of the movements of sand appear chaotic and give temporal and spatial spectra with 1/f α forms. Likewise the EEG gives records that appear chaotic, with temporal and spatial spectra that are 1/f α , where the exponent α has been estimated 1 < α < 3 (Pereda et al, 1998;. In both systems the appearance of "noise" is illusory.…”

Section: Eeg Phase Data and The Concept Of Self-organized Criticalitymentioning

confidence: 99%

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Origin, structure, and role of background EEG activity. Part 2. Analytic phase

Freeman

2004

Clinical Neurophysiology

172

200

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Objective: To explain spontaneous EEG through measurements of spatiotemporal patterns of phase among beta-gamma oscillations.Methods: High-density 8x8 intracranial arrays were fixed over sensory cortices of rabbits. EEGs were spatially low pass filtered, temporally band pass filtered and segmented in overlapping windows stepped at 2 ms. Phase was measured with the cosine as the temporal basis function, using both Fourier and Hilbert transforms to compensate for their respective limitations. Spatial patterns in 2-D phase surfaces were measured with the geometric form of the cone as the spatial basis function.Results: Two fundamental state variables were measured at each digitizing step in the 64 EEGs: the rate of change in phase with time (frequency) and the rate of change in phase with distance (gradient). The parameters of location, diameter, duration, and phase velocity of the cone of phase were derived from these two state variables. Parameter distributions including recurrence intervals extending into the low theta range were fractal; the mean values varied with window duration and interelectrode distance. Conclusions:The formation of spatial amplitude patterns began with phase transitions that were documented by phase discontinuities and phase cones. The multiplicity of overlapping cones indicated that sensory neocortices maintained a scale-free state of self-organized criticality (SOC) in each hemisphere as the basis for its rapid integration of sensory input with prior learning stored in cortical synaptic webs. Further evidence came from the fractal properties of the phase parameters and the self-similarity of phase patterns in the ms/mm to m/s ranges.Significance: These EEG data suggest that neocortical dynamics is analogous to the dynamics of self-stabilizing systems, such as a sand pile that maintains its critical angle by avalanches, and a pan of boiling water that maintains its critical temperature by bubbles that release heat. Betagamma oscillations stem from the ability of neocortex to maintain its stability under continuous sensory bombardment. Modeling implies that the critical parameter of neocortex (analogous to angle of repose or temperature) is the mean firing rates of neurons that are homeostatically regulated by refractory periods everywhere at all times in cortex. The advantage of SOC in perception may be the ability it gives neocortex to generate instantaneous global phase transitions (avalanches, bubbles) large enough to include the multiple sensory areas that are necessary to form Gestalts (multisensory percepts).Background EEG analytic phase 3Walter J Freeman

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Section: Sudden Changes In Eeg Occur Simultaneously Over Large Distanmentioning

confidence: 99%

Section: Eeg Phase Data and The Concept Of Self-organized Criticalitymentioning

confidence: 99%

Origin, structure, and role of background EEG activity. Part 2. Analytic phase

Freeman

2004

Clinical Neurophysiology

172

200

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“…In certain cases it might be possible to transform a linear model with time dependent parameters into a stationary nonlinear model by increasing the model order m. For time series of human sleep EEG, the surrogate data analysis revealed evidences for a rejection of the null hypothesis of a linear stochastic process (see e.g. [2,4,6]). These analyzes were performed on segments with a length larger than 10s (16 s in [4] and 20.5, 41, 82 and 164 s in [2]).…”

Section: Introductionmentioning

confidence: 99%

“…[2,4,6]). These analyzes were performed on segments with a length larger than 10s (16 s in [4] and 20.5, 41, 82 and 164 s in [2]). Because the null hypothesis includes also stationarity, its rejection can be both due to nonlinearity and nonstationarity and the test cannot distinguish between these two possibilities.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of human sleep EEG

2003

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Several investigators of EEG time series reported a rejection of the null hypothesis of linear stochastic dynamics for epochs longer than 10 s. We examine whether this rejection is related to nonlinearity or to nonstationarity. Our approach is a combination of autoregressive modeling and surrogate data testing. It is shown that the fraction of subsegments, for which the null hypothesis has to be rejected increases with the length of the subsegments and can be related to fluctuations of the AR-coefficients on time scales in the range from 2-30 s.

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“…Many studies have characterized the fractal properties of local aspects of EEG temporal dynamics, namely of amplitude modulations at single electrodes (37)(38)(39)(40); these properties have been linked to cognitive tasks (41), sleep (42)(43)(44), and clinical conditions such as epilepsy (45,46), Alzheimer's disease (47,48), mania (49), dementia (50), and schizophrenia (51). Whereas these studies indicate that the fractal characterization of electric potential time series can be a useful measure of local brain activity, they cannot be related to the temporal properties of global brain networks.…”

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confidence: 99%

EEG microstate sequences in healthy humans at rest reveal scale-free dynamics

Ville

Britz

Michel

2010

Proc. Natl. Acad. Sci. U.S.A.

513

422

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Recent findings identified electroencephalography (EEG) microstates as the electrophysiological correlates of fMRI resting-state networks. Microstates are defined as short periods (100 ms) during which the EEG scalp topography remains quasi-stable; that is, the global topography is fixed but strength might vary and polarity invert. Microstates represent the subsecond coherent activation within global functional brain networks. Surprisingly, these rapidly changing EEG microstates correlate significantly with activity in fMRI resting-state networks after convolution with the hemodynamic response function that constitutes a strong temporal smoothing filter. We postulate here that microstate sequences should reveal scale-free, self-similar dynamics to explain this remarkable effect and thus that microstate time series show dependencies over long time ranges. To that aim, we deploy wavelet-based fractal analysis that allows determining scale-free behavior. We find strong statistical evidence that microstate sequences are scale free over six dyadic scales covering the 256-ms to 16-s range. The degree of long-range dependency is maintained when shuffling the local microstate labels but becomes indistinguishable from white noise when equalizing microstate durations, which indicates that temporal dynamics are their key characteristic. These results advance the understanding of temporal dynamics of brain-scale neuronal network models such as the global workspace model. Whereas microstates can be considered the "atoms of thoughts," the shortest constituting elements of cognition, they carry a dynamic signature that is reminiscent at characteristic timescales up to multiple seconds. The scale-free dynamics of the microstates might be the basis for the rapid reorganization and adaptation of the functional networks of the brain.critical state | microstates | resting-state networks | self-similar processes | wavelet fractal analysis T he human brain is intrinsically organized into interconnected neuronal clusters that form large-scale neurocognitive networks (1, 2). These networks have to dynamically and rapidly reorganize and coordinate on subsecond temporal scales to allow the execution of mental processes in a timely fashion (3, 4). Precise timing is crucial for the government of the continuous information flow from multiple sources to ensure perception, cognition, and action and ultimately consciousness. The anatomical architecture of several large-scale networks is well known and has been studied with different methods ranging from tracer studies to resting-state fMRI (5, 6). However, much less is known about their underlying temporal dynamics.Multichannel electroencephalography (EEG) is a key method to access real-time information about the function of large-scale neuronal networks with high temporal resolution. Traditionally, spontaneous EEG analysis relies mainly on the power variation in different frequency bands at a subset of electrodes; however, observing this variation inherently sacrifices temporal accuracy due t...

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Non-linear behaviour of human EEG: fractal exponent versus correlation dimension in awake and sleep stages

Cited by 176 publications

References 18 publications

Origin, structure, and role of background EEG activity. Part 2. Analytic phase

Origin, structure, and role of background EEG activity. Part 2. Analytic phase

Dynamics of human sleep EEG

EEG microstate sequences in healthy humans at rest reveal scale-free dynamics

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