Deterministic brain oscillations in the magnetoencephalogram.

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.

[1]  Christopher Essex,et al.  Chaotic time series analyses of epileptic seizures , 1990 .

[2]  Z J Kowalik,et al.  Changes of chaoticness in spontaneous EEG/MEG , 1994, Integrative physiological and behavioral science : the official journal of the Pavlovian Society.

[3]  Alfonso M Albano,et al.  Phase-randomized surrogates can produce spurious identifications of non-random structure , 1994 .

[4]  D. T. Kaplan,et al.  Direct test for determinism in a time series. , 1992, Physical review letters.

[5]  James Theiler,et al.  On the evidence for how-dimensional chaos in an epileptic electroencephalogram , 1995 .

[6]  Z J Kowalik,et al.  Testing the determinism of EEG and MEG , 1994, Integrative physiological and behavioral science : the official journal of the Pavlovian Society.

[7]  P. Rapp,et al.  Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram. , 1996, Electroencephalography and clinical neurophysiology.

[8]  Matthias M. Müller,et al.  Dynamical aspects of the EEG in different psychopathological states in an interview situation: a pilot study , 1997, Schizophrenia Research.

[9]  Andrzej Wróbel,et al.  Why does the human brain need to be a nonlinear system? , 1996, Behavioral and Brain Sciences.

[10]  L D Iasemidis,et al.  Non-linearity in invasive EEG recordings from patients with temporal lobe epilepsy. , 1997, Electroencephalography and clinical neurophysiology.

[11]  Rodney C. Wolff,et al.  Local Lyapunov Exponents: Looking Closely at Chaos , 1992 .

[12]  W. Pritchard,et al.  Dimensional analysis of resting human EEG. II: Surrogate-data testing indicates nonlinearity but not low-dimensional chaos. , 1995, Psychophysiology.

[13]  J. E. Skinner,et al.  Chaos and physiology: deterministic chaos in excitable cell assemblies. , 1994, Physiological reviews.

[14]  A. Babloyantz,et al.  Low-dimensional chaos in an instance of epilepsy. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[15]  C. Elger,et al.  Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss. , 1995, Electroencephalography and clinical neurophysiology.

[16]  Larry E. Roberts,et al.  Relativity of Dynamical Measures in Study of the Human Brain , 1998 .

[17]  C. Stam,et al.  Nonlinearity in human resting, eyes-closed EEG: an in-depth case study. , 2000, Acta neurobiologiae experimentalis.