Evidence of chaotic dynamics of brain activity during the sleep cycle

Babloyantz, Agnessa; Salazar, Michael R.; Nicolis, C.

doi:10.1016/0375-9601(85)90444-x

Cited by 567 publications

(158 citation statements)

References 1 publication

Supporting

Mentioning

143

Contrasting

Unclassified

Order By: Relevance

“…One records from all electrodes simultaneously in the absence of sensory cues. The field potentials could then be analyzed by several techniques of nonlinear time series analysis (1)(2)(3)(4). The values of dynamical parameters such as entropies and Lyapunov exponents and dimensions characterize the dynamics of the signal.…”

Section: Discussionmentioning

confidence: 99%

Computation with chaos: a paradigm for cortical activity.

Babloyantz

Lourenço

1994

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

View full text Add to dashboard Cite

A device comprising two interconnected networks of osciliators exhibiting spatiotemporal chaos is considered. An external cue stabilizes input specific unstable periodic orbits of the first network, thus creating an "attentive" state. Only in this state is the device able to perform pattern discrimination and motion detection. We discuss the relevance of the procedure to the information processing of the brain.Electrical activity of cerebral cortex can be measured noninvasively from the scalp. The electroencephalograms (EEGs) thus obtained are local averaged activity of millions of cells. According to the behavioral states of the brain, the EEG shows well-defined ethology. Some pathologies such as, for example, the "petit-mal" epilepsy or CreutzfeldJackob coma generate very characteristic waves. Thus, before the advent of more sophisticated medical imagery techniques the EEG was a diagnostic tool for assessing neurological diseases. It still is a common tool for assessing sleep disorders.In the past decade the techniques of nonlinear time series analysis were applied by Babloyantz and her colleagues to the human EEG (1-4). They could show that in several behavioral states as well as in petit-mal epilepsy and Creutzfeld-Jackob coma the EEG may be described by deterministic chaotic dynamics. Several groups have confirmed the existence of chaotic dynamics in the human cortex (see refs. 5 and 6 and references therein).Drawing on these findings a model of cerebral cortex was recently constructed (7). In this model, the various behavioral states of the cortex are seen as spatiotemporal chaotic cortical activity of increasing coherence generated by the nature of the input from the thalamus. The space average of network activity over an area of the cortex provides EEGlike signals, which are akin to behavioral states of human brain activity. Such models led to the concept that the dynamics of cerebral cortex is of spatiotemporal chaotic nature. Thus, it seems that information processing in the brain is performed at a global network level. The information processing capacity of neuronal networks was demonstrated recently by measuring the active neuronal population in the Aplysia abdominal ganglion network during spontaneous and evoked behaviors using multineuronal optical measurements (8). It was found that a distributed organization involving a large number of neurons ofthe network may generate the two behaviors. These functional behaviors stem from altered activities of a large ensemble of neurons and thus they are a network property. This assumption raises the following question: If brain dynamics is of a chaotic nature then how does such a system process information?The importance of providing an answer to this question is 2-fold. First, it may give a clue for the understanding of brain processes. Second, the relevant concepts could be integrated into artificial neural networks in order to produce a more efficient computational device by mimicking more closely brain dynamics and its awesome capacity for storag...

show abstract

Section: Discussionmentioning

confidence: 99%

Computation with chaos: a paradigm for cortical activity.

Babloyantz

Lourenço

1994

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

View full text Add to dashboard Cite

show abstract

“…The EEG data recorded from the human brain during sleep cycles were also analyzed according to the procedure cited above (7). Chaotic attractors were identified for stage two and stage four of deep sleep.…”

Section: Normal Brain Activitymentioning

confidence: 99%

“…Recent progress in the theory of nonlinear dynamical systems has provided new methods for the study of time series in such fields as hydrodynamics (1), chemistry (2), climatic variability (3,4), biochemistry (5,6), and human brain activity (7). The study of such complex systems may be performed by analyzing experimental data recorded as a series of measurements in time of a pertinent and easily accessible variable of the system.…”

mentioning

confidence: 99%

Low-dimensional chaos in an instance of epilepsy.

Babloyantz¹,

Destexhe²

1986

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

654

223

View full text Add to dashboard Cite

Using a time series obtained from the electroencephalogram recording of a human epileptic seizure, we show the existence of a chaotic attractor, the latter being the direct consequence of the deterministic nature of brain activity. This result is compared with other attractors seen in normal human brain dynamics. A sudden jump is observed between the dimensionalities of these brain attractors (4.05 ± 0.05 for deep sleep) and the very low dimensionality of the epileptic state (2.05 ± 0.09). The evaluation of the autocorrelation function and of the largest Lyapunov exponent allows us to sharpen further the main features of underlying dynamics. Possible implications in biological and medical research are briefly discussed.Recent progress in the theory of nonlinear dynamical systems has provided new methods for the study of time series in such fields as hydrodynamics (1), chemistry (2), climatic variability (3, 4), biochemistry (5, 6), and human brain activity (7). The study of such complex systems may be performed by analyzing experimental data recorded as a series of measurements in time of a pertinent and easily accessible variable of the system. In most cases, such variables describe a global or averaged property of the system. For example, a time series may be obtained by recording at regular time intervals the mean electrical activity of a portion of the mammalian cortex. Although it may seem that such data offer only a one-dimensional view of the activity of the brain, this is not the case: it can be shown that a time series may provide information about a large number ofpertinent variables, which may subsequently be used to explore and characterize the system's dynamics (8).More specifically, by using a time series one can determine the possibility of constructing an attractor and thereby establishing the deterministic character of the dynamics of the underlying system. This topological entity portrays the essential features of the system's dynamics and may be characterized by the numerical value of its Hausdorff dimension D. A steady state is represented by a point attractor D = 0 and a time periodic regime exhibits a line attractor with D = 1. In general, ifD is a noninteger-that is, a fractal dimension-we may be in the presence of a chaotic attractor. The main feature of chaotic attractors is their sensitivity to the initial conditions. After a lapse of time, it is increasingly difficult to predict the future evolution of the system from a given initial state.In this paper, we analyze the electrical activity of the human cortex by means of the electroencephalogram (EEG) recorded from an epileptic human patient and also from normal persons during sleep cycles. First, on the basis of analyses of the time series of EEG data, we show the existence of an epileptic attractor and determine its correlation dimension I, which is easily accessible from experimental data. Then, we analyze other dynamical properties of the time series, such as Lyapunov exponents and time autocorrelation function. The next sec...

show abstract

“…Aperiodic oscillations are found at various levels of biological complexity, namely, in a single cell unit such as the giant axon of squids [4][5][6][7][8][9] ; in a more complex element such as in an aggregate of chicken embryo heart cells 10 ; and in highly complex systems such as human brain 11 . In almost all cases the oscillations are related to the membrane potential.…”

Section: Introductionmentioning

confidence: 99%

Chaotic oscillations in a lipid doped membrane

Delgado¹,

Medina²

2001

J. Braz. Chem. Soc.

View full text Add to dashboard Cite

O potencial elétrico de uma membrana dopada com trioleína e colocada entre duas soluções aquosas de cloretos de sódio e potássio foi analisada para verificar a ocorrência de caos determinístico, usando métodos padrão de teoria de sistemas dinâmicos não lineares. Os resultados fornecem evidências sólidas de que este sistema apresenta dinâmica caótica, e não é apenas um exemplo de ruído experimental.The electric potential of a membrane doped with triolein, placed between aqueous solutions of sodium chloride and potassium chloride, was analyzed for the existence of deterministic chaos using standard methods of nonlinear dynamics system theory. The results provide solid evidence that the system shows a chaotic dynamics and not just an example of experimental noise in the data.

show abstract

Evidence of chaotic dynamics of brain activity during the sleep cycle

Cited by 567 publications

References 1 publication

Computation with chaos: a paradigm for cortical activity.

Computation with chaos: a paradigm for cortical activity.

Low-dimensional chaos in an instance of epilepsy.

Chaotic oscillations in a lipid doped membrane

Contact Info

Product

Resources

About