Quantitative analysis of EEG signals: Time-frequency methods and ...

sites minutes before the starting of the seizure, with a progressive phase entrainment of
the nonfocal ones. They propose this phase-locking as a method for assigning degrees
of participation of each focal site and for classifying their importance in the developing
of the seizure. Krystal and Weiner (1991), using the same algorithm, obtained similar
results in electroconvulsive therapy seizures.
Sleep
Some groups also had success in evaluating Lyapunov exponents during dierent
sleep stages. Babloyantz (1988) reported positive Lyapunov exponents during deep
sleep, obtaining a value of = 0:4 ; 0:8 for stage II and a value of = 0:3 ; 0:6 for
stage IV.
Principe and Lo (1991) reported a greater value of = 2:1 for sleep stage II, but
they remark that an accurate value is impossible to obtain because of the complexity of
the signal, its time varying nature and the sensibility of the results with the election of
the parameters for the calculations.
Roschke et al. (1993), following the modication of the Wolf algorithm proposed by
Frank et al. (1990) calculated the Lyapunov exponent of recordings from 15 healthy
male subjects in sleep stages I, II, III, IV and REM. They found in all cases positive
values, thus stating that EEG signals are neither quasiperiodic waves, nor simple noise.
They also report a decrement in the Lyapunov exponents as sleep becomes slower.
Roschke et al. (1994) studied dierences in Correlation Dimension and Lyapunov
exponents in sleep recordings of depressive and schizophrenic patients compared with
healthy controls. They mainly found alterations during slow sleep in depression, and
during REM sleep in schizophrenia.
Other studies
Gallez and Babloyantz (1991) analyzed the complete Lyapunov spectrum in awake
\eyes closed" state (alpha waves), deep sleep (stage IV) and Creutzfeld-Jakob coma.
They found in all cases studied at least two positive Lyapunov exponents, increasing
this numberuptothreeinthecaseofalphawaves, implying that alpha waves correspond
to a more complex system than the one present during sleep.
Stam et al. (1995) studied 13 Parkinson and 9 demented patients against 9 healthy
subjects by using the Correlation Dimension, the Lyapunov Exponents and the Kolmogorov
entropy calculated from a spatial reconstruction of the embedding vectors
(multichanneling). They report a value of = 6:17 for the control subjects, a similar
value of =6:12 (but with lower Correlation Dimension) for Parkinson patients and a
signicant lower value of =4:84 for demented patients.
Wallenstein and Nash (1991) implemented the Wolf algorithm with avarying prop-
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