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

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P300 deection. Due to the relation between the P300 and the decreases in the entropy, it can be tentatively assumed that the cognitive (P300) response involves a higher degree of order than the one related with the ongoing EEG and the one related with the P100 response. From this, we can postulate that the cognitive response is possibly related with a tuning of the EEG oscillations, thus giving a narrower frequency response reected in a low entropy value. However, this conjecture should be veried with more subjects and with dierent experiments. Furthermore, since in this case the WS was dened from the mean wavelet coecients (after averaging the coecients of the single trials) we can not discard the possibility of other oscillations being present in a non phase-locked way (therefore their contribution being cancelled when averaging). The importance of delta oscillations in the generation of the P300 was reported in several previous works. Basar-Eroglu et al. (1992) by using an auditory oddball paradigm in 10 subjects, pointed out the importance of delta oscillators in the generation of the P300, suggesting that they are related mainly with decision making and matching. Schurmann et al. (1995), also remarked the importance of delta oscillations in the generation of the P300, nding also delta enhancement uponTARGET responses in the single trials. Furthermore, they obtain better averaged responses by selectively averaging single trials with an enhanced delta response. A similar result was recently reported by Demiralp et al. (1999), who after applying a wavelet multirresolution decomposition to evoked responses, used the delta coecients as discriminators between good and bad single trials. 6.4 Conclusions Wavelet-entropy proved to be a very useful tool for characterizing the event-related responses. With this method a new approach to the measure of order/noise of a system can be achieved 8 . Up to now, this type of descriptions were merely based on Chaos analysis. However, these methods have several prerequisites, some of them making their application to the study of EEG signals impossible. One of these prerequisites is the data length. Chaos analysis cannot be applied to short data recordings as in the case of event-related potentials. In this type of signals, the dynamics of the system is changing completely in fractions of a second duetotheeectof the stimulus, and then it has no sense to dene an attractor and to calculate parameters as the Correlation Dimension, 8 We should remark that high WS values does not necesarily mean noise since for example chaotic deterministic systems also have a broadband spectra. However, analysis of how the EEG gets tuned in frequency after stimulation is directly related with the question of the deterministic/random nature of it as it will be further discussed in sec.7.1.3. 99
Lyapunov Exponent or Kolmogorov Entropy from them. Previous methods for measuring the spectral entropy from the Fourier Transform are also not suitable for the analysis of ERPs. This is because the Fourier Transform requires stationarity of the signal, and can not describe the time evolution of the frequencies. In this context, the denition of a time-varying entropy allowed the study of the time evolution of the \ordering" of the ongoing EEG due to stimulation, thus making possible the correlation between changes in entropy of the signal and sensory/cognitive processes of the ERPs. The information obtained with the Wavelet-Entropy turned out not to be trivially related with the energy. This means that with this method, new information can be accessed with a dierent approach than the one obtained by making the traditional analysis of amplitude of the evoked responses. WS appears as a natural measure of order in EEG signals. This is very interesting in order to study synchronizations upon dierent stimuli as in the case of ERPs. Taking into account the resonance theory, WS can measure the degree of synchronicity of the cell groups involved in the dierent responses. Further implementations of the method are in progress in order to optimize the results by having more frequency bands. This would allow a more accurate denition of the entropy and moreover will allow the denition of the entropy for dierent frequency bands. However, we would like to remark that in the case of ERPs this is not so easy to achieve since a high time resolution is needed, thus limiting the frequency resolution due to the uncertainty principle. 100
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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
Page 66 and 67: 3 2 3 3 3 3.2 Hz 3.6 Hz 4.0 Hz 4.4
Page 68 and 69: Silva et al.,1973a,1973b Lopes da S
Page 70 and 71: 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 118 and 119: 7 General Discussion In this chapte
Page 120 and 121: Wavelet analysis was also applied t
Page 122 and 123: aect the whole spectrum and for thi
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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