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

Summary
Since the rsts recordings in humans performed in 1929, the EEG has become one of
the most important diagnostic tools in clinical neurophysiology, but up to now, EEG
analysis still relies mostly on its visual inspection. Due to the fact that visual inspection
is very subjective and hardly allows any statistical analysis or standardization, several
methods were proposed in order to quantify the information of the EEG. Among these,
the Fourier Transform emerged as a very powerful tool capable of characterizing the
frequency components of EEG signals, even reaching diagnostical importance. However,
Fourier Transform has some disadvantages that limit its applicability and therefore,
other methods for extracting \hidden" information from the EEG are necessary.
In this work, I described, extended and compared methods of analysis of dierent
types of EEG signals, namely time-frequency methods (Gabor Transform and Wavelet
Transform) and Chaos methods (attractor reconstruction, Correlation dimension, Lyapunov
exponents, etc.).
Time-frequency methods provided new information about sources and dynamics of
Grand Mal (Tonic-clonic) seizures, something very dicult to obtain with conventional
methods. Grand Mal seizures were rst dominated by alpha (7:5 ; 12:5Hz) and theta
(3:5;7:5Hz)rhythms, these rhythms later becoming slower in correlation with the starting
of the clonic phase. The dynamics of the frequency patterns during these seizures
was very interesting in relation to processes of neuronal fatigue, neurotransmitter disbalance,
similarity with animal experiments and computer simulations. The analysis
with Chaos theory showed a decrease in parameters as the Correlation Dimension or
the maximum Lyapunov exponent, parameters that characterize the complexity and
\chaoticity" of the signal. These results showed a transition to a more simple system
during epileptic seizures.
In order to study basic features of brain oscillations, I analyzed event-related responses
(i.e. alterations of the ongoing EEG due to an external or internal stimuli) with
recent methods of time-frequency analysis. In this context, the study of event-related
alpha oscillations (i.e. event-related responses in the alpha range) showed that these
responses were distributed along the scalp with signicant dierences in their delays
between anterior and posterior electrodes. This result implied that several sources were
involved in the origin of the event-related alpha oscillations. Furthermore, their independence
on the performance of a cognitive task, the best denition in occipital locations
and the short latency of the responses pointed towards a relation between event-related
alpha oscillations and primary sensory processing.
The study of the responses upon bimodal stimulation (simultaneous visual and audi-
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