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

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and the Lorenz equations (a model of Rayleigh-Benard convection). By changing the control parameters of the models, they showed increases of the spectral entropy upon the disordering of the systems in their route to chaoticity. Inouye and coworkers (1991, 1993) introduced the spectral entropy to the analysis of EEG signals. From the spectral entropy they dened an irregularity indexand they reported in rest EEGs, more irregularityinanterior than in occipital areas. Furthermore, they reported a greater degree of EEG desynchronization during mental arithmetic in comparison with rest EEG. Stam and coworkers (Stam et al., 1993) instead, dened an accelaration spectrum entropy from the second derivative of the signal and they reported dierences of this measure in dementia, Parkinson disease (Jelles et al., 1995) and during mental activation (Thomeer et al., 1994). Blanco et al. (1998a) proposed a further improvement by dening the entropy from the Wavelet Transform due to its advantages over the Fourier transform. Among these, the most important one is that the time evolution of the entropy can be followed. Since the entropy is dened from the time-frequency representation of the signal, the nearly optimal time-frequency resolution of the Wavelet Transform is crucial for having an accurate measure. This is particularly important in the case of event-related potentials, in which the relevant response is limited to a fraction of a second. Furthermore, Wavelet Transform lacks of the requirement of stationarity. I showed the application of the Wavelet-entropy (WS) to the study of ERPs. WS proved to be a very useful tool for characterizing the event-related responses, furthermore, the information obtained with the WS probed not to be trivially related with the energy and consequently with the amplitude of the signal. This means that with this method, new information can be accessed with an approach dierent from the traditional analysis of amplitude and delays of the event-related responses. WS as a measure of resonance in the brain Following the resonance theory, the ERP can be seen as an evoked synchronization, frequency stabilization, frequency selective enhancement and/or phase reordering of the ongoing EEG, and it should not be interpreted as an additive component to a noisy background EEG (see sec. x1.3). WS appears as an ideal tool for measuring the synchronization of the EEG oscillations upon stimulation. In this context, synchronization means that the group of cells involved in the generation of the response react to the stimulation tuned in frequency. That means, they produce a narrow band in the frequency domain and consequently they are correlated with a decrease in the entropy. Basar (1980) already mentioned the importance of the entropy for understanding the relation between the pre-stimulus ongoing EEG and the event-related responses by making an analogy with the concept 97
of magnetization in physics. WS is a natural measure of the resonance phenomena (see section x1.3). Resonance is related with a decrease of entropy, since only some of the spontaneous oscillations of the ongoing EEG will be enhanced, thus giving a more ordered frequency distribution than the broadband spectrum of the EEG. This relation was showed with the simulations described in table 1, in whose noisy (broadband) signals had higher entropy than the ones corresponding to ordered (narrowband) behaviors. Study of the P100-N200 complex In agreement with previous ndings (overview in Regan, 1989), the P100 peak was best dened in occipital locations. Furthermore, its task independence (at least the one related with the TARGET stimuli) points towards a relation between this response and primary sensory rocessing. According to the resonance theory, it is very interesting to analyze the frequency characteristics of the dierent evoked peaks in order to understand the response mechanisms involved in its generation. The distribution of energy in the frequency domain showed that the P100-N200 responses corresponded to a wide range of frequencies mostly in the alpha and theta bands. These responses did not produce any signicant decreases of entropy compared with the one of the normal ongoing EEG due to its wide-band frequency distribution of the involved generators. The involvement of alpha and theta oscillation in the generation of these peaks was already described by Stampfer and Basar (1985), who obtain a similar result by digitally ltering auditory evoked potential in humans. Study of the P300 response According to previous evidence (Regan, 1989 Polich and Kok, 1995 Basar-Eroglu et al., 1992), the P300 positive deection was observed upon TARGET stimuli, best dened in parietal and occipital electrodes at about 500-600 ms. These responses, traditionally related with a cognitive process, showed a signicant decrease in the WS since they involved only delta generators. Although the correlation between the P300 and the entropy decreases was clear due to their common appearance only upon TARGET stimuli and their posterior localization, a dierence of about 100-200 ms was observed between them. This is because after the P300 there is a positive slow rebound in the delta range (see g. 3). Consequently, although the minimum of the P300 is at about 400-500 ms, the P300 complex can be viewed as a delta wave extending up to larger latencies. A similar observation was made by Stampfer and Basar (1985), who after ltering in the delta band the TARGET stimuli of an oddball paradigm in auditory ERP, described the presence of a negative deection at about 600 ms as a continuation of the positive 98
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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
Page 64 and 65: 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 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 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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