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

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aect the whole spectrum and for this reason, in order to avoid spurious eects in the Fourier spectrum, signals must be stationary. This is particularly important in the case of EEG signals due to the presence of artifacts. Artifacts are alterations (usually of high amplitude) of the ongoing EEG due to causes not related with the brain activity (e.g. blinking, head movements, etc.) and they give spurious eects in the Fourier spectrum that can lead to misinterpretations. In the case of analyzing background EEGs, this is partially resolved by selecting small \artifact free" segments of data, later averaging the spectrum of the selected segments. However, this widely used procedure is very subjective because it requires the decision of what should be considered an appropriate segment to be analyzed (i.e. which segments are representative of the whole EEG?). An easy and intuitive way to obtain a time evolution of the frequency patterns is by making the Fourier spectrum of successive segments (\windows") of data, then plotting them as a function of time. This procedure is called the Short Time Fourier Transform or Gabor Transform and the plots obtained are called spectograms. The problem of stationarity ispartially resolved by taking short windows. Spectograms give an elegant representation of the signal and they are suitable for visualizing large scale frequency variations (i.e. of the order of minutes or hours) as for example for studying sleep stages. However, as I showed in section x3, they are not suitable for analyzing epileptic seizures, in which the frequency patterns change in the order of seconds. In this context, the introduction of the band relative intensity ratio (RIR) and the mean and maximum band frequencies, allowed a more detailed study of the frequency behavior during Grand Mal epileptic seizures, as already summarized in section x7.1.1. Furthermore, with these quantitative parameters it was possible to make a statistical analysis of the frequency behavior in several scalp recorded seizures. Other interesting point to mention is that although in scalp recordings of Grand Mal seizures muscle activity obscures completely the EEG, it was possible to study the frequency patterns by leaving aside the high frequency components related with muscle artifacts, thus obtaining a very interesting quantitative frequency pattern that keeps \hidden" with the traditional analysis of EEG recordings. 7.2.2 Gabor Transform vs. Wavelet Transform Gabor Transform gives an optimal representation of the EEG in the time-frequency domain. However, one critical limitation arises when choosing the size of the window to be applied due to the Uncertainty Principle. If the window is too narrow, the frequency resolution will be poor, and if the window is too wide, the time localization will be not so precise. In fact, frequencies can not be resolved instantaneously. Then, for slow processes a wide window will be necessary and for data involving fast processes, a narrow 105
window will be more suitable. Due to its xed window size, Gabor Transform is not optimal for analyzing signals having dierent ranges of frequencies. The main advantage of the Wavelet Transform is that the size of the window isvariable, being wide when studying low frequencies and narrow when studying the high ones. Then, the time-frequency resolution is automatically adapted (see appendix xA.3), thus being an optimal method for analyzing signals involving dierent ranges of frequencies. Furthermore, due to their adapted window size, wavelets lacks of the requirement of stationarity. Wavelet Transform consists in making a correlation between the original signal and scaled versions of the same \mother function". This mother function can be chosen between a wide range of options each one having dierent characteristics that can be more or less appropriate depending on the signal to be analyzed. At this respect, B- Spline functions were very suitable for analyzing EEG signals due to their compact support and smoothness. Successive correlations of the signal to be studied with scaled versions of the wavelet function (and their complementary function) can be arranged in a hierarchical scheme allowing the decomposition of the signal in dierent scales (frequency bands). This method, the multiresolution decomposition, allowed the study of the alpha responses to visual event-related potentials and the study of the gamma responses upon bimodal stimulation. The time-frequency resolution of wavelets was crucial for making physiological interpretations of the event-related responses (see section x7.1.2) because these results were based in statistically signicant dierences in the amplitudes and time delays of the responses, dierences that in the latter case were in the order of 100 ms and would have been very dicult to resolve with other methods like the Gabor Transform. Furthermore, the access to discrete coecients in the case of the Wavelet Transform allows a very easy implementation of statistical tests. As showed with alpha and gamma responses to ERPs, with the Wavelet Transform frequency behaviors can be resolved up to fractions of a second. On the other hand, with the election of an adequate window, Gabor Transform is more suitable for the analysis of signals with a more limited frequency content as shown with Grand Mal seizures, in which the interesting activity was limited to the lower frequencies of the EEG (up to 12:5Hz see section x3.4). Although with Gabor Transform the general characteristics of the frequency dynamics during the Grand Mal seizures was already visible (see section x7.1.1), by using an alternative decomposition of the signal based on the Wavelet Transform, the Wavelet Packets, it was possible to study with a better resolution the evolution of the frequency 106
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Quantitative analysis of EEG signal
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1. Berichterstatter: Prof. Dr.-Ing.
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an okzipitalen Positionen und (c) d
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To my family: Mama, Consuelo, Hugui
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Preface In this work, I will descri
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I would certainly like to remember
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Contents Zusammenfassung Preface Ac
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5.2.6 Calculating Lyapunov Exponent
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Summary Since the rsts recordings i
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1 Outline of Neurophysiology: Brain
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Figure 2: Normal 20 channels (10-20
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1.1.2 EEG in Epilepsy One important
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Figure 3: Scalp EEG of 18 channels
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Figure 4: Averaged responses upon N
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2 Fourier Transform 2.1 Introductio
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I xx (k) =jX(k)j 2 = X(k) X (k) (
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17 Figure 5: Topographical mapping
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1987) is that coherence gives the c
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3 Gabor Transform (Short Time Fouri
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where k g D k= R 1 ;1 jg D(t 0 )j 2
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and the band maximum peak frequency
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Figure 7: Intracraneal seizure reco
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Figure 10: Mean (soft line) and max
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EEG as the one with least amount of
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Figure 11: Scalp EEG of the right c
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3.5 Conclusion In this chapter I de
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Original signal FOURIER TRANSFORM G
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4.2.3 Multiresolution Analysis Cont
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Original signal -15 0 15 -1sec 0 1s
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4.2.5 Wavelet Packets In the approa
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marked decrease in computational ti
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ain activity during an epileptic se
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3 2 3 3 3 3.2 Hz 3.6 Hz 4.0 Hz 4.4
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Silva et al.,1973a,1973b Lopes da S
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sweep #1 sweep #2 sweep #3 sweep #4
Page 72 and 73: VEP non-target target F3 F4 F3 F4 F
Page 74 and 75: VEP non-target target F3 F4 F3 F4 F
Page 76 and 77: Electrode F3 F4 Cz P3 P4 O1 O2 Dela
Page 78 and 79: In conclusion, our results point to
Page 80 and 81: 63 Figure 22: Gamma responses for a
Page 82 and 83: Figure 24: T-test comparison of the
Page 84 and 85: wavelet coecients allowed an easy d
Page 86 and 87: the position vs. the linear momentu
Page 88 and 89: unknown topology it is necessary to
Page 90 and 91: the sum of the positive exponents (
Page 92 and 93: performed. On one hand, must be lar
Page 94 and 95: Duke (1992) and Elbert et al. (1994
Page 96 and 97: agation time. They applied this pro
Page 98 and 99: Figure 28: Histogram for the EEG da
Page 100 and 101: Figure 29: Attractors corresponding
Page 102 and 103: able for automatic detection proces
Page 104 and 105: ENTROPY Thermodynamics Signal analy
Page 106 and 107: 6.3 Application to visual event-rel
Page 108 and 109: VEP Non Target Target F3 -20 -10 0
Page 110 and 111: 1 VEP NON-TARGET TARGET 1 1 F3 F3 0
Page 112 and 113: 1 VEP NON-TARGET TARGET 1 1 F3 F3 0
Page 114 and 115: and the Lorenz equations (a model o
Page 116 and 117: P300 deection. Due to the relation
Page 118 and 119: 7 General Discussion In this chapte
Page 120 and 121: Wavelet analysis was also applied t
Page 124 and 125: peaks. 7.2.3 Wavelet Transform vs.
Page 126 and 127: the ones having wide peaks (being t
Page 128 and 129: A Time-frequency resolution and the
Page 130 and 131: Z 1 ;1 tx(t) d dt x(t) dt = 1 2 Z 1
Page 132 and 133: Figure 37: Time-frequency resolutio
Page 134 and 135: References Abarbanel HDI, Brown R,
Page 136 and 137: Berger, H. Uber das Elektrenkephalo
Page 138 and 139: Gastaut H and Broughton R. Epilepti
Page 140 and 141: Lopes da Silva FH, van Lierop THMT,
Page 142 and 143: Pradhan N, Sadasivan P, Chatterji S
Page 144 and 145: Serrano E, Ph.D. Thesis, Department
Page 146: Biographical sketch 21.03.1967 born
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