On the evidence for how-dimensional chaos in an epileptic electroencephalogram

A variant of the method of surrogate data is applied to a single time series from an electroencephalogram (EEG) recording of a patient undergoing an epileptic seizure. The time series is a nearly periodic pattern of spike-and-wave complexes. The surrogate data sets are generated by shuffling the individual spike-and-wave cycles, and correspond to a null hypothesis that there is no deterministic structure in the cycle-to-cycle variability of the original data. Using estimates of autocorrelation, correlation dimension, and Lyapunov exponent as discriminating statistics, the evidence for dynamical correlations between successive spikeand-wave patterns is evaluated both formally and informally.

[1]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[2]  Dimension calculations in a minimal embedding space: Low-dimensional attractors for human electroencephalograms , 1987 .

[3]  Sawada,et al.  Measurement of the Lyapunov spectrum from a chaotic time series. , 1985, Physical review letters.

[4]  F. H. Lopes da Silva,et al.  Chaos or noise in EEG signals; dependence on state and brain site. , 1991, Electroencephalography and clinical neurophysiology.

[5]  N Xu,et al.  The fractal dimension of EEG as a physical measure of conscious human brain activities. , 1988, Bulletin of mathematical biology.

[6]  I. Dvor̂ak,et al.  On some problems encountered in the estimation of the correlation dimension of the EEG , 1986 .

[7]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[8]  Floris Takens,et al.  On the numerical determination of the dimension of an attractor , 1985 .

[9]  W. Pritchard,et al.  Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis. , 1992, The International journal of neuroscience.

[10]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[11]  G. Yule.  On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers , 1927 .

[12]  André Longtin,et al.  NONLINEAR FORECASTING OF SPIKE TRAINS FROM SENSORY NEURONS , 1993 .

[13]  B. LeBaron,et al.  Nonlinear Dynamics and Stock Returns , 2021, Cycles and Chaos in Economic Equilibrium.

[14]  G. Mayer-Kress,et al.  Analysis of the human electroencephalogram with methods from nonlinear dynamics , 1987 .

[15]  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.

[16]  A. Babloyantz,et al.  Strange Attractors in the Human Cortex , 1987 .

[17]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.

[18]  James Theiler,et al.  Statistical error in a chord estimator of correlation dimension: The rule of five'' , 1993 .

[19]  Agnessa Babloyantz,et al.  A comparative study of the experimental quantification of deterministic chaos , 1988 .

[20]  P. E. Rapp,et al.  9. Oscillations and chaos in cellular metabolism and physiological systems , 1986 .

[21]  P. Rapp,et al.  The algorithmic complexity of neural spike trains increases during focal seizures , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[22]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[23]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[24]  Theodore R. Bashore,et al.  Experimental Studies of Chaotic Neural Behavior: Cellular Activity and Electroencephalographic Signals , 1986 .

[25]  A. Babloyantz,et al.  The Creutzfeld-Jakob Disease in the Hierarchy of Chaotic Attractors , 1988 .

[26]  F. Yates,et al.  Dimensional analysis of nonlinear oscillations in brain, heart, and muscle , 1988 .

[27]  USING COARSE-GRAINED MEASURES TO CHARACTERIZE ELECTROMYOGRAPHIC SIGNALS , 1993 .

[28]  Xu Nan,et al.  The fractal dimension of EEG as a physical measure of conscious human brain activities. , 1988 .

[29]  M. Mackey,et al.  Temporal Disorder in Human Oscillatory Systems , 1987 .

[30]  Agnessa Babloyantz,et al.  Lyapunov exponents for nonuniform attractors , 1991 .