Quantitative analysis of EEG signals:
Time-Frequency methods and
Chaos Theory.
Rodrigo Quian Quiroga
Directors:
Prof. T. Aach1 and Prof. E. Basar2
1Institute of Signal Processing and 2Institute of Physiology
Medical University of Lübeck - Germany
Date: 4.12.98
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Summary
Since the firsts 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 different 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 difficult to obtain with
conventional methods. Grand Mal seizures were first dominated by alpha
($7.5-12.5Hz$) and theta ($3.5-7.5 Hz$) 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 significant differences 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 definition 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 auditory stimulation) showed a significant increase of amplitude in comparison with the unimodal ones. Then, it was possible to conjecture a relation between gamma ($30-60 Hz$) oscillations and a process responsible of carrying the information that two sensory perceptions of bimodal stimulation correspond in fact to the same stimulus.
In particular, this thesis is the first work where the novel method
``Wavelet entropy", a measure of the distribution of the signal in the
frequency domain, was adjusted and applied to the analysis of event-related
responses. In event-related potentials, significant decreases in the wavelet
entropy correlated with the P300 cognitive
response showed that this response was associated with an ordering of the
spontaneous EEG oscillations.