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Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings

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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.

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Abbreviations

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)

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

i:

interictal

P:

pre-ictal

S:

seizure

C(r,m) :

correlation integral

D2 :

correlation dimension

h :

Heaviside or step function

d :

distance between two vectors (maximum norm)

k :

largest delay

K 2 :

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”

x i :

samplei of the time series

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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Authors and Affiliations

  1. “Meer en Bosch”/“De Cruquiushoeve”, Instituut voor Epilepsiebestrijding, Achterweg 5, 2103, SW Heemstede, The Netherlands

    Jan Pieter M. Pijn, Demetrios N. Velis & Fernando H. Lopes da Silva

  2. Department of Physiology, State University Leiden, Leiden, The Netherlands

    Marcel J. van der Heyden & Jaap DeGoede

  3. Department of Neurosurgery, University Hospital Utrecht, Utrecht, The Netherlands

    Cees W. M. van Veelen

  4. Graduate School of Neurosciences, Institute of Neurobiology, Faculty of Biology, University of Amsterdam, Amsterdam, The Netherlands

    Fernando H. Lopes da Silva

Authors
  1. Jan Pieter M. Pijn
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  2. Demetrios N. Velis
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  3. Marcel J. van der Heyden
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  4. Jaap DeGoede
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  5. Cees W. M. van Veelen
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  6. Fernando H. Lopes da Silva
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Correspondence to Jan Pieter M. Pijn.

Additional information

We thank Tjeerd olde Scheper for his help in doing the analyses and Wouter Blanes for his continuous support in producing code for our computer as well as text for this manuscript. This work was subsidized in part by CLEO (Dutch Commission for research in Epilepsy), grants A71 and A88, by the NEF (Dutch Epilepsy Foundation), grant 95-01 and by NWO (Netherlands Organization for Scientific Research), grant 629-61-270.

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Pijn, J.P.M., Velis, D.N., van der Heyden, M.J. et al. Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings. Brain Topogr 9, 249–270 (1997). https://doi.org/10.1007/BF01464480

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