Controlled test for predictive power of Lyapunov exponents: Their inability to predict epileptic seizures

Ying-Cheng Lai, Mary Ann F Harrison, Mark G. Frei, Ivan Osorio

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

Lyapunov exponents are a set of fundamental dynamical invariants characterizing a system's sensitive dependence on initial conditions. For more than a decade, it has been claimed that the exponents computed from electroencephalogram (EEG) or electrocorticogram (ECoG) signals can be used for prediction of epileptic seizures minutes or even tens of minutes in advance. The purpose of this paper is to examine the predictive power of Lyapunov exponents. Three approaches are employed. (1) We present qualitative arguments suggesting that the Lyapunov exponents generally are not useful for seizure prediction. (2) We construct a two-dimensional, nonstationary chaotic map with a parameter slowly varying in a range containing a crisis, and test whether this critical event can be predicted by monitoring the evolution of finite-time Lyapunov exponents. This can thus be regarded as a "control test" for the claimed predictive power of the exponents for seizure. We find that two major obstacles arise in this application: statistical fluctuations of the Lyapunov exponents due to finite time computation and noise from the time series. We show that increasing the amount of data in a moving window will not improve the exponents' detective power for characteristic system changes, and that the presence of small noise can ruin completely the predictive power of the exponents. (3) We report negative results obtained from ECoG signals recorded from patients with epilepsy. All these indicate firmly that, the use of Lyapunov exponents for seizure prediction is practically impossible as the brain dynamical system generating the ECoG signals is more complicated than low-dimensional chaotic systems, and is noisy.

Original languageEnglish (US)
Pages (from-to)630-642
Number of pages13
JournalChaos
Volume14
Issue number3
DOIs
StatePublished - Sep 2004

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seizures
Lyapunov Exponent
exponents
Predict
Exponent
Chaotic systems
Electroencephalography
Time series
Prediction
Brain
Dynamical systems
Epilepsy
Chaotic Map
Monitoring
Chaotic System
predictions
epilepsy
Initial conditions
Dynamical system
electroencephalography

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Controlled test for predictive power of Lyapunov exponents : Their inability to predict epileptic seizures. / Lai, Ying-Cheng; Harrison, Mary Ann F; Frei, Mark G.; Osorio, Ivan.

In: Chaos, Vol. 14, No. 3, 09.2004, p. 630-642.

Research output: Contribution to journalArticle

Lai, Ying-Cheng ; Harrison, Mary Ann F ; Frei, Mark G. ; Osorio, Ivan. / Controlled test for predictive power of Lyapunov exponents : Their inability to predict epileptic seizures. In: Chaos. 2004 ; Vol. 14, No. 3. pp. 630-642.
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