### 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. (C) 2004 American Institute of Physics.

Original language | English |
---|---|

Pages (from-to) | 630-642 |

Number of pages | 13 |

Journal | Chaos |

Volume | 14 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 2004 |

### Keywords

- chaotic time series
- brain electrical activity
- human electroencephalogram
- correlation integrals
- ring cavity
- system
- dimension
- attractors
- dynamics
- spectrum

### Cite this

*Chaos*,

*14*(3), 630-642. https://doi.org/10.1063/1.1777831

**Controlled test for predictive power of Lyapunov exponents : their inability to predict epileptic seizures.** / Lai, Ying-Cheng; Harrison, M A F ; Frei, M G ; Osorio, Ivan.

Research output: Contribution to journal › Article

*Chaos*, vol. 14, no. 3, pp. 630-642. https://doi.org/10.1063/1.1777831

}

TY - JOUR

T1 - Controlled test for predictive power of Lyapunov exponents

T2 - their inability to predict epileptic seizures

AU - Lai, Ying-Cheng

AU - Harrison, M A F

AU - Frei, M G

AU - Osorio, Ivan

PY - 2004/9

Y1 - 2004/9

N2 - 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. (C) 2004 American Institute of Physics.

AB - 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. (C) 2004 American Institute of Physics.

KW - chaotic time series

KW - brain electrical activity

KW - human electroencephalogram

KW - correlation integrals

KW - ring cavity

KW - system

KW - dimension

KW - attractors

KW - dynamics

KW - spectrum

U2 - 10.1063/1.1777831

DO - 10.1063/1.1777831

M3 - Article

VL - 14

SP - 630

EP - 642

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 3

ER -