Brain Topography

, Volume 9, Issue 4, pp 249–270 | Cite as

Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings

  • Jan Pieter M. Pijn
  • Demetrios N. Velis
  • Marcel J. van der Heyden
  • Jaap DeGoede
  • Cees W. M. van Veelen
  • Fernando H. Lopes da Silva


Purpose: 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.

Key words

Chaos Nonlinear dynamics Intracranial EEG Temporal lobe epilepsy Ictal propagation 

List of abbreviations

In the text


analog to digital converter


complex partial seizure


electro corticogram




finite impulse response (filter)


linear Gaussian random process


logarithm with base 10


mesial temporal lobe epilepsy


pulse code modulation


subchonic electro corticogram




temporal lobe epilepsy


quantitative EEG (analysis)



anterior temporal left,-right


mid temporal left,-right


posterior temporal left,-right


amygdala left,-right


hippocampus left,-right


input amplifiers common reference electrode


current-source electrode for compensating potential changes of G1








Mathematical symbols


correlation integral


correlation dimension


Heaviside or step function


distance between two vectors (maximum norm)


largest delay


correlation entropy


logarithm with base 10


embedding dimension


number of (reconstructed) vectors in phase space


sampling frequency


time-window for the ‘Theiler correction’


radius of a sphere in phase space

\(\vec V_m (i)\)

(reconstructed) vector in m-dimensional phase space


number of samples and time span of the window for the “Theiler correction”


samplei of the time series

Duffing equation



x,\(\dot x, \ddot x\)

position, velocity and acceleration of the beam


friction coefficient


amplitude of the driving force


angular frequency of the driving force


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Copyright information

© Human Sciences Press, Inc 1997

Authors and Affiliations

  • Jan Pieter M. Pijn
    • 1
  • Demetrios N. Velis
    • 1
  • Marcel J. van der Heyden
    • 2
  • Jaap DeGoede
    • 2
  • Cees W. M. van Veelen
    • 3
  • Fernando H. Lopes da Silva
    • 1
    • 4
  1. 1.“Meer en Bosch”/“De Cruquiushoeve”Instituut voor EpilepsiebestrijdingSW HeemstedeThe Netherlands
  2. 2.Department of PhysiologyState University LeidenLeidenThe Netherlands
  3. 3.Department of NeurosurgeryUniversity Hospital UtrechtUtrechtThe Netherlands
  4. 4.Graduate School of Neurosciences, Institute of Neurobiology, Faculty of BiologyUniversity of AmsterdamAmsterdamThe Netherlands

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