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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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Epileptic seizures show a certain degree of rhythmicity, a feature of heuristic and practical interest. In this paper, we introduce a simple model of this type of behavior, and suggest a measure for detecting and quantifying it. To evaluate our method, we develop a set of test segments that incorporate rhythmicity features, and present results from the application of this measure to test segments. We then analyze electrocorticogram segments containing seizures, and present two examples. Finally, we discuss the similarity of our method to techniques for detecting unstable periodic orbits in chaotic time series., ((c) 2008 American Institute of Physics.)

Reports in the literature have indicated potential value of the correlation integral and dimension for prediction of epileptic seizures up to several minutes before electrographic onset. We apply these measures to over 2000 total hours of continuous electrocortiogram, taken from 20 patients with epilepsy, examine their sensitivity to quantifiable properties such as the signal amplitude and autocorrelation, and investigate the influence of embedding and filtering strategies on their performance. The results are compared against those obtained from surrogate time series. Our conclusion is that neither the correlation dimension nor the correlation integral has predictive power for seizures.