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

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6.3 Application to visual event-related potentials 6.3.1 Methods and Materials In 9 voluntary healthy subjects (no neurological decits, no medication known to aect the EEG) two types of experiments were performed: 1. No-task visual evoked potential (VEP): subjects were watching a checkerboard pattern (sidelength of the checks: 50'), the stimulus being achecker reversal. 2. Oddball paradigm (NON-TARGET/TARGET stimuli): subjects were watching the same pattern as above. Two dierent stimuli were presented in a pseudorandom order. NON-TARGET stimuli (75%) were pattern reversal, and TARGET stimuli (25%) consisted in a pattern reversal with horizontal and vertical displacement of one-half of the square side length. Subjects were instructed to pay attention to the appearance of the target stimuli. In both cases, 200 stimuli were presented and the duration of each stimulus was 1 second. Recordings were made following the international 10 ; 20 system in seven dierent electrodes (F3, F4, Cz, P3, P4, O1, O2) referenced to linked earlobes. Data were amplied with a time constant of 1:5sec: and a low-pass lter at 70Hz. For each single sweep, 1sec: pre- and post-stimulus EEG were digitized with a sampling rate of 250Hz and stored in a hard disk. After visual inspection of the data, 30 sweeps free of artifacts were randomly selected for each type of stimuli (VEP, NON-TARGET and TARGET) for future analysis. A Wavelet Transform was applied to each single sweep using a quadratic B-Spline function as mother wavelet. The multiresolution decomposition method (Mallat, 1989) was used for separating the signal in frequency bands, dened in agreement with the traditional frequency bands used in physiological EEG analysis. After a ve octave wavelet decomposition, the components of the following bands were obtained: 62 ; 125Hz,31; 62Hz (gamma), 16 ; 31Hz (beta), 8 ; 16Hz (alpha), 4 ; 8Hz (theta) and the residues in the 0:5 ; 4Hz band (delta). For each subject the results of the wavelet decomposition of the 30 single sweeps were averaged, obtaining the mean components (C ij ). Finally, from this coecients the Wavelet-entropy was calculated as described in the previous section. In this case, since the WS is calculated from the averaged wavelet coecients, only phase-locked oscillations will contribute to it, the others being cancelled (for the same data, an analysis of phase-locking in the alpha band was done in Quian Quiroga et.al., 1999d). 89
Signal WS X 1 0:15 X 2 0:36 X 3 0:53 Table 6: Wavelet entropy for a sinusoidal signal (X 1 ), for a random signal (X 3 ) and for a sinusoidal signal with noise (X 2 = 1 (X 2 1 + X 3 )). Statistical analysis Statistical analysis was performed by computing the mean entropy values in the second pre- and post-stimulus. Signicance of entropy decreases were calculated for each electrode and stimuli type by comparing minimum pre- and post-stimulation with t-test comparisons. 6.3.2 Results The Wavelet entropy (WS) was tested with 3 dierent time series. A: a pure sinusoidal signal with a frequency of 12 Hz (X 1 ) B: a random signal (X 3 ) and C: a signal composed of the sum of the two previous ones (X 2 ). The random signal was obtained from a white noise generator. Table 6 shows the results of the WS for the three signals. As expected, the WS is higher for the noisy signal (broad-band spectrum) and minimum for the sinusoidal one (narrow-band spectrum). The event-related responses of one typical subject are shown in gure 31. Only the central and left electrodes are shown, having the right ones similar behavior. Left side of the gure corresponds to VEP, center to NON-TARGET and right sidetoTARGET stimuli. The P100 response is clearly visible upon all stimuli types at about 100 ms, best dened in occipital locations. In the case of TARGET stimulation, a marked positive peak appears between 400 and 500 ms, according to the expected cognitive P300 response. Figure 32 shows the results of the band and total energies for the same subject. Only the lower frequency bands are plotted since the higher ones showed no relevant contribution to the total energy. All stimuli types show alpha and theta band increases in occipital locations at 100-200 ms, correlated with the P100-N200 complex. Only upon TARGET stimulation an increase in the posterior locations is visualized in the delta band at 500-600 ms, this increase being related with the cognitive response(P300). Results of the WS for the same subject are shown in gure 33. Decreases in the entropy are more signicant in posterior sites upon TARGET stimulation, strongly 90
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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
Page 56 and 57: 4.2.3 Multiresolution Analysis Cont
Page 58 and 59: 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 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 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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