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

EEG segment D e (min) D 2 1
0 ; 8 sec 0:0195 8 4:30 4:6
21 ; 29 sec 0:0156 13 2:60 4:0
29 ; 37 sec 0:0156 10 2:50 4:0
37 ; 44 sec 0:0156 11 2:05 3:5
44 ; 52 sec 0:0156 13 2:15 3:0
Table 5: Optimal value of time lag (insec ), minimum embedding dimension D (min)
e ,
Correlation Dimension (D 2 ), and maximum Lyapunov exponent ( 1 ) for the stationary
EEG segments (Data-set size: N = 2048 see text).
showed in table 5, it can be concluded that the dynamical behavior was more regular
during the seizure.
Summarizing, we found a good evidence that during the epileptic seizure there is
a transition from a complex to a simple dynamical behavior. Furthermore, this result
yields insights with respect to the theory of how epileptic seizures occur (i.e.
synchronization of the disordered background EEG activity).
as a
5.7 Conclusion
Deterministic chaos theory gives an alternative new type of analysis compared with
the ones given by the traditional methods. However, the application of chaos methods,
should be done with care in order to avoid misleading results. In this way a right election
of parameters required for the calculations is critical.
Chaos analysis has several prerequisites, some of them making impossible its application
to the study of EEG signals. One of these prerequisites is the availability of
long data recordings but on the other hand, data must be stationary. Consequently,
chaos analysis cannot be applied in nonstationary short data recordings as in the case of
event-related potentials. In these types of series, the dynamics of the system is changing
completely in fractions of a second due to the eect of the stimulus and therefore, it has
no sense to dene an attractor and to calculate any metric invariant from it.
Since methods for calculation of D 2 and 1 were developed for ideal signals (i.e.
innite, noise-free and stationary), then, due to the complex structure of the EEGs,
results should be considered of relative relevance and, as suggested by Pritchard and
Duke (1992), is more realistic to talk about Dimensionality instead of Correlation Dimension.
By using this view, several groups reported changes in D 2 and 1 values in
dierent brain states and pathologies. Nevertheless, these measures seem not to be suit-
84