Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings

SummaryPurpose: An understanding of the principles governing the behavior of complex neuronal networks, in particular their capability of generating epileptic seizures implies the characterization of the conditions under which a transition from the interictal to the ictal state takes place. Signal analysis methods derived from the theory of nonlinear dynamics provide new tools to characterize the behavior of such networks, and are particularly relevant for the analysis of epileptiform activity.Methods: We calculated the correlation dimension, tested for irreversibility, and made recurrence plots of EEG signals recorded intracranially both during interictal and ictal states in temporal lobe epilepsy patients who were surgical candidates.Results: Epileptic seizure activity often, but not always, emerges as a low-dimensional oscillation. In general, the seizure behaves as a nonstationary phenomenon during which both phases of low and high complexity may occur. Nevertheless a low dimension may be found mainly in the zone of ictal onset and nearby structures. Both the zone of ictal onset and the pattern of propagation of seizure activity in the brain could be identified using this type of analysis. Furthermore, the results obtained were in close agreement with visual inspection of the EEG records.Conclusions: Application of these mathematical tools provides novel insights into the spatio-temporal dynamics of “epileptic brain states”. In this way it may be of practical use in the localization of an epileptogenic region in the brain, and thus be of assistance in the presurgical evaluation of patients with localization-related epilepsy.

[1]  Cranio-cerebral topometry in man: A. Delmas and B. Pertuiset Charles C. Thomas, Springfield (Ill.), 1959, 436 pp., $ 38.50 , 1961 .

[2]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[3]  J. Gotman.  Automatic recognition of epileptic seizures in the EEG. , 1982, Electroencephalography and clinical neurophysiology.

[4]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[5]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[6]  A. Provenzale,et al.  A search for chaotic behavior in large and mesoscale motions in the Pacific Ocean , 1986 .

[7]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[8]  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.

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

[10]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[11]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[12]  Schwartz,et al.  Singular-value decomposition and the Grassberger-Procaccia algorithm. , 1988, Physical review. A, General physics.

[13]  J. Havstad,et al.  Attractor dimension of nonstationary dynamical systems from small data sets. , 1989, Physical review. A, General physics.

[14]  A. Provenzale,et al.  Finite correlation dimension for stochastic systems with power-law spectra , 1989 .

[15]  J. Gotman.  Automatic seizure detection: improvements and evaluation. , 1990, Electroencephalography and clinical neurophysiology.

[16]  Stephen M. Hammel,et al.  A noise reduction method for chaotic systems , 1990 .

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

[18]  C D Binnie,et al.  Combined use of subdural and intracerebral electrodes in preoperative evaluation of epilepsy. , 1990, Neurosurgery.

[19]  Demetrios N. Velis,et al.  Combined use of subdural and intracerebral electrodes in preoperative evaluation of epilepsy. , 1990 .

[20]  F. H. Lopes da Silva,et al.  Anatomic organization and physiology of the limbic cortex. , 1990, Physiological reviews.

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

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

[23]  Jerome Engel,et al.  Role of the Frontal Lobes in the Propagation of Mesial Temporal Lobe Seizures , 1991, Epilepsia.

[24]  W. Kamphuis,et al.  Current source density of sustained potential shifts associated with electrographic seizures and with spreading depression in rat hippocampus , 1992, Brain Research.

[25]  Martin Casdagli,et al.  Nonlinear Modeling And Forecasting , 1992 .

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

[27]  Leonard A. Smith,et al.  Distinguishing between low-dimensional dynamics and randomness in measured time series , 1992 .

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

[29]  N Pradhan,et al.  A nonlinear perspective in understanding the neurodynamics of EEG. , 1993, Computers in biology and medicine.

[30]  Floris Takens,et al.  DETECTING NONLINEARITIES IN STATIONARY TIME SERIES , 1993 .

[31]  Albano,et al.  Filtered noise can mimic low-dimensional chaotic attractors. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  R. Cerf,et al.  Wave-separation in complex systems. Application to brain-signals , 1993 .

[33]  M. Kaboudan.  A complexity test based on the correlation integral , 1993 .

[34]  P. Grassberger,et al.  On noise reduction methods for chaotic data. , 1993, Chaos.

[35]  Theiler,et al.  Generating surrogate data for time series with several simultaneously measured variables. , 1994, Physical review letters.

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

[37]  P E Rapp,et al.  A guide to dynamical analysis , 1994, Integrative physiological and behavioral science : the official journal of the Pavlovian Society.

[38]  A A Borbély,et al.  All-night sleep EEG and artificial stochastic control signals have similar correlation dimensions. , 1994, Electroencephalography and clinical neurophysiology.

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

[40]  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.

[41]  R Biscay,et al.  EEG predictability: adequacy of non-linear forecasting methods. , 1995, International journal of bio-medical computing.

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

[43]  Hatsuo Hayashi,et al.  Chaotic responses of the hippocampal CA3 region to a mossy fiber stimulation in vitro , 1995, Brain Research.

[44]  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.

[45]  W. Freeman.  Societies of Brains: A Study in the Neuroscience of Love and Hate. By W. J. Freeman. Erlbaum: Hillsdale, NJ. 1994. , 1997, Psychological Medicine.

[46]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[47]  H. Kantz,et al.  Dimension estimates and physiological data. , 1995, Chaos.

[48]  Cees Diks,et al.  Reversibility as a criterion for discriminating time series , 1995 .

[49]  Demetrios N. Velis,et al.  Mesial temporal versus neocortical temporal lobe seizures: Demonstration of different electroencephalographic spreading patterns by combined use of subdural and intracerebral electrodes , 1995 .

[50]  C. J. Stam,et al.  Investigation of nonlinear structure in multichannel EEG , 1995 .

[51]  D. N Velis,et al.  Time reversibility of intracranial human EEG recordings in mesial temporal lobe epilepsy , 1996 .

[52]  Francisco J. Varela,et al.  Entropy quantification of human brain spatio-temporal dynamics , 1996 .

[53]  Francisco J. Varela,et al.  Detecting non-linearities in neuro-electrical signals: a study of synchronous local field potentials , 1996 .

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

[55]  Demetrios N. Velis,et al.  Signal processing of EEG: evidence for chaos or noise. An application to seizure activity in epilepsy , 1996 .

[56]  Hatsuo Hayashi,et al.  Chaotic and phase-locked responses of the somatosensory cortex to a periodic medial lemniscus stimulation in the anesthetized rat , 1996, Brain Research.

[57]  F. H. Lopes da Silva,et al.  Alpha rhythms: noise, dynamics and models. , 1997, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[58]  F. H. Lopes da Silva,et al.  Spatio-temporal models in biological and artificial systems , 1997 .

[59]  Fernando H. Lopes da Silva,et al.  Epilepsy: network models of generation , 1998 .

[60]  A. Soong,et al.  Evidence of chaotic dynamics underlying the human alpha-rhythm electroencephalogram , 1989, Biological Cybernetics.

[61]  Steven J. Schiff,et al.  Differentiation of linearly correlated noise from chaos in a biologic system using surrogate data , 1992, Biological Cybernetics.

[62]  Katarzyna J. Blinowska,et al.  Non-linear and linear forecasting of the EEG time series , 1991, Biological Cybernetics.

[63]  W. J. Williams,et al.  Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures , 2005, Brain Topography.