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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
Article

Summary

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

ADC

analog to digital converter

CPS

complex partial seizure

ECoG

electro corticogram

EEG

electroencephalogram

FIR

finite impulse response (filter)

LGRP

linear Gaussian random process

log

logarithm with base 10

MTLE

mesial temporal lobe epilepsy

PCM

pulse code modulation

SCECoG

subchonic electro corticogram

SEEG

stereoelectroencephalogram

TLE

temporal lobe epilepsy

QEEG

quantitative EEG (analysis)

Electrodes

ATL, ATR

anterior temporal left,-right

MTL, MTR

mid temporal left,-right

PTL, PTR

posterior temporal left,-right

AML, AMR

amygdala left,-right

HCL, HCR

hippocampus left,-right

G1

input amplifiers common reference electrode

G2

current-source electrode for compensating potential changes of G1

Epochs

i

interictal

P

pre-ictal

S

seizure

Mathematical symbols

C(r,m)

correlation integral

D2

correlation dimension

h

Heaviside or step function

d

distance between two vectors (maximum norm)

k

largest delay

K2

correlation entropy

log

logarithm with base 10

m

embedding dimension

N

number of (reconstructed) vectors in phase space

ν

sampling frequency

T

time-window for the ‘Theiler correction’

r

radius of a sphere in phase space

\(\vec V_m (i)\)

(reconstructed) vector in m-dimensional phase space

W,T

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

xi

samplei of the time series

Duffing equation

t

time

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

position, velocity and acceleration of the beam

δ

friction coefficient

γ

amplitude of the driving force

ω

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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