Étude méthodologique de l'électroencéphalographie quantitative. Application a quelques exemples

Abstract : SUMMARY This methodological study of quantitative electroencephalography starts with the history of EEG methods of analysis and of their applications. This thesis is basically focused on a comparative study of the most important methods of analysis. In the presentation of methods I first present the analysis of the instantaneous amplitude histograms of EEGs which is dependent upon the sampling frequency. Considering now the Fourier spectral analysis this method implies to take quite a number of precautions before being properly applied to EEG. For instance, it is necessary to compute enough measures to allow later on the statistical validation of a power spectrum analysis G(f). Then, I propose the example of spectral multiple EEG channels analysis, which is based on the method of spectral regression. This method of analysis gives more precisely the relations of causality at specific frequencies by finding their sources across EEG channels and determining if those sources are based on real signals source or random noise. I have later specified the mathematical relations between the integrative method of Drohocki and spectral analysis. The mean value l of n measures of successive epochs of an EEG signal, which is rectified and integrated: l is proportional to the root­mean­square (rms) value of the analyzed signal and also to its standard error. The coefficient of variation CV(l) of the integrated measures is proportional to the spectral coefficient of variation CV(k), which for a first approximation is equal to k/√T, with T being the time epoch of analysis and k a “coefficient of spectral regression” that I have defined by the formula (k2 = ∑G2/(∑G)2) in reference to Blackman and Tuckey. This presentation of methods is achieved with the period analysis and its relations to spectral analysis, followed by a brief survey of new heuristic methods, which are mimicking the electroencephalographist practitioner in his way and are applying methods of linear prediction. My results are divided into three chapters. In the first chapter I present first Applications of quantitative EEG recorded in rat. Then I give three examples of applying the integrative method of Drohocki. First by computing the ratio of integrated values of ECoG/EMG for quantifying the phases of wakefulness and sleep. When this ratio is above or below an experimentally first computed predetermined threshold, this ratio can well determine the state of wakefulness or sleep. I have applied this technique to the study of the hypovariability of the ECoG and of the neck muscles EMG recorded in rats before and after administration of neuroleptics. The ECoG/EMG ratio provides the time­course of the electro­pharmacokinetic effect through hours of the neuroleptic treatment. Secondly I have studied the statistical decomposition of the observed polymodal composite distributions of values of integrated ECoG signals computed over successive periods of one­hour time span. Such an analysis provides a decomposition of these polymodal distributions into a sum of elementary Gaussian distributions. Each elementary Gaussian distribution being specific of a homogeneous state of vigilance. Thirdly, this chapter is mainly concerned with the comparative study between the three different tracings of occipital ECoG in the rat for quantifying homogeneous phases of wakefulness, slow wave sleep and REM sleep (paradoxical sleep). The four principal methods of EEG analysis previously compared theoretically, have then been now compared experimentally, based on the three different states of vigilance. I have first verified the precedent mathematical relationships established between the integrative method and spectral analysis. By correlation analysis and multi­linear regression, I have been able to obtain pertinent information which has been reduced to 5 independent parameters. Step-by­step discriminant analysis has shown that the mean frequency of the spectral peak and the mean integrated amplitude are sufficient for a good discrimination between the three analyzed states of vigilance. The second chapter of results is based on EEG recordings in man. in order to give Applications of quantitative EEG recorded in man. I describe a program of statistical spectral analysis, which works in real time based on four EEG channels simultaneously recorded with a double rejection of artifacts and a pre­treatment of the sampled EEGs. After longitudinal studies of different quantified recordings I have computed a four factor variance analysis on a transversal study sample of EEG recordings for a group of 7 subjects receiving two different treatments (placebo at the beginning of the night before and nitrazépam 5mg, p.o. the day after), 2 sequences (eyes open followed by eyes closed EEG recordings), 4 posterior EEG channels, and computed characteristic spectral parameters. Results of variance analysis reveal that only sequences and parameters appear to be statistically different. Later further 3 factor variance analyses over the 32 computed spectral parameters have found, which parameters are the best discriminant parameters between EEG sequences : the spectral peak, the coefficient of resonance and of complexity, the fast mean frequencies. etc. These factorial analyses have allowed me to compare spectral differences between two mean power spectra by applying Student t tests in different conditions : between treatments, sequences, EEG channels and between subjects. Finally, in the third chapter of results, I have presented a first modulation analysis of EEG by applying Hilbert transform to EEG. Starting from an EEG signal x(t) we can evaluate a signal y(t), which is characterized by a Gaussian random narrow band process, from an analysis of modulation y(t) = m(t) cos(ω0t + φ(t)), with m(t) being the amplitude modulation and φ(t) the frequency modulation around a broadcasting frequency ω0 = 2πfo. This modulation analysis is based on the Hilbert transform ˆx(t) obtained from the Fourier transform X(f) of x(t), by a multiplication by (­j.sign(f)) followed by inverse transformation. This gives directly the computation of the “envelope” m(t) of x(t), in the radioelectric sense of the word envelope. The frequency modulation is obtained directly by derivation of the phase modulation. I have applied this analysis to the precedent three tracings of states of vigilance in rat. I have found that the hippocampal theta rhythm is characteristic of a specific amplitude modulation during the REM state of sleep in rat together with a frequency modulation, which is not present in the two other states of wakefulness and of slow wave sleep in rat. This last method can be applied in case of non­stationary EEG tracings and it keeps all the signal information. The amplitude and frequency modulations are specific respectively of the instantaneous amplitude and frequency and we know the difficulty to obtain directly this last instantaneous frequency. This is why I have attempted to apply the techniques of statistical radioelectricity in quantitative electroencephalography. In this thesis, which is based on 15 articles, I have wanted to illustrate the theory of analysis of electrobiological signal by some various examples of applications in animal and in man. I have wished to show also how new methods of analyses may lead and drive to new applications.
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Pierre Etevenon. Étude méthodologique de l'électroencéphalographie quantitative. Application a quelques exemples. Imagerie médicale. Paris 6, 1977. Français. ⟨tel-01170957⟩

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