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

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1 VEP NON-TARGET TARGET 1 1 F3 F3 0 1 -1.0 -0.5 0.0 0.5 1.0 0 1 -1.0 -0.5 0.0 0.5 1.0 0 1 -1.0 -0.5 0.0 0.5 1.0 Cz Cz 0 0 0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 93 1 1 1 P3 P3 0 -1.0 -0.5 0.0 0.5 1.0 0 -1.0 -0.5 0.0 0.5 1.0 0 -1.0 -0.5 0.0 0.5 1.0 1 1 1 O1 O1 0 -1.0 -0.5 0.0 0.5 1.0 0 -1.0 -0.5 0.0 0.5 1.0 0 -1.0 -0.5 0.0 0.5 1.0 Figure 33: Wavelet Entropy corresponding to the same recording.
correlated with the denition of the P300 response. There are no decreases of entropy correlated with the P100 response. This is consistent with the distribution of energy described in g. 32, since the P100 peaks have a wide-band frequency composition corresponding to alpha and theta oscillations. On the other hand, the P300 response corresponded only to delta oscillations, thus having a lower entropy. It is very interesting to note that the results of the entropy are not directly related with the ones of the energy. This can be clearly seen, for example, by analyzing the TARGET response of electrode O1, where there is a high energy increase at about 200ms without signicant changes in the entropy for this time. Considering the whole group of subjects, the grand average of the WS is shown in gure 34. As pointed out with the typical subject, posterior decreases are observable upon TARGET stimulation at about 600 ms, these decreases being clearly correlated with the denition of the P300 response. On the contrary, P100 peaks produced no relevant decreases in the entropy since they corresponded to a wider range of frequencies. In order to verify statistically the decreases of entropy correlated with the P300 responses, pre- and post-stimulus mean entropy values were compared by using t-tests. As shown in gure 35, entropies are signicantly decreased in posterior electrodes upon TARGET stimulation. Then, entropy decreases respond to a dynamical process related with the stimulation, rather than to random uctuations. 6.3.3 Discussion Results of the calculation of the WS in dierent digitally generated signals conrmed the expected correlation between the WS and the complexity of them, being high for the random signal and low for the sinusoidal one. This shows that WS could be used as a measure for describing the behavior of EEG signals, since a noisy activity will have a broadband spectrum and consequently a high entropy, and on the other side, more ordered activity as a sinusoidal signal will have lower entropy. Then, WS gives a new approach to the measure and quantication of the order of a system, its physiological interpretation being very interesting due to its relation with tuning of cell groups involved in the generation of the EEG signal. Entropy in signal analysis The concept of entropy emerged last century as a useful state function applied to the study of the thermodynamic of gases (Feynman, 1964). Furthermore, entropy was related with the order of a system and its applications rapidly expanded to several disciplines due to its very interesting meanings. One important milestone was the introduction of the theory of communication (Shannon, 1948 see also Feynman, 1996) relating 94
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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
Page 60 and 61: 4.2.5 Wavelet Packets In the approa
Page 62 and 63: 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 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 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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