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

Preface
In this work, I will describe and extend two new approaches that started to be applied
to physiological signals: 1) the time-frequency methods, and 2) the methods based on
Chaos theory. I will discuss their applicability and usefulness mainly in two types of
brain signals: a) EEG recordings from \Grand Mal" epileptic seizures, and b) Eventrelated
potentials. Moreover, I will compare all these new methods, comparison which
was not performed so far, stressing their advantages over conventional approaches in the
analysis of EEG signals. Furthermore, the results obtained will be closely linked with
physiological interpretations. In particular, this thesis is the rst work where the novel
method \Wavelet entropy" is adjusted and applied to the analysis of evoked responses.
The structure is as follows:
The rst part of the thesis consists in an introduction to basic concepts of electroencephalography
and a review of previous approaches to its quantitative analysis.
In particular, chapter x1 gives a brief description of the necessary background
of neurophysiology focusing on the concepts needed for understanding the basics
of brain signals, and chapter x2 describes the traditional Fourier analysis and its
main applications to EEGs.
Chapters x3 to x6 are the main part of the thesis, each chapter referring to one of
the new quantitative methods. They all have the same internal structure: 1) they
start with an introduction in which the goal of the method is described, 2) then,
a theoretical background is given, 3) their application to dierent types of EEG
is shown and nally, 4) a physiological interpretation of the results is given and
advantages of the methods are discussed in comparison with other approaches.
More specically, chapter x3 presents the Gabor Transform, a time-frequency
method that solves some of the disadvantages of the Fourier Transform. Furthermore,
since in many cases a more detailed information is required, as I will
show with the study of Grand Mal seizures, I will introduce new denitions that
will allow a better quantitative analysisoftheEEG.
Chapter x4 describes the theoretical background of the Wavelet Transform. Studies
where the Wavelet Transform is applied to Tonic-Clonic seizures and to eventrelated
potentials will show the advantages of this new method in the analysis of
EEG signals.
Chapter x5 presents the approach based on the Non-linear Dynamics (Chaos)
theory. I will show its application to dierenttype of seizure recordings, correlating
ix