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

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Figure 28: Histogram for the EEG data N1 in the selected zone (see text). EEG N 0 N d D e D 2 1 N1 34000 15000 13 5:5 ; 6:0 0:26 N2 32000 13000 13 5:0 ; 6:0 0:23 N3 35000 14000 13 4:5 ; 5:5 0:25 A1 35000 15000 13 4:5 ; 5:5 0:28 A2 34000 14000 13 5:0 ; 5:5 0:26 A3 36000 15000 13 4:5 ; 5:0 0:27 Table 4: Correlation Dimension (D 2 ) and maximum Lyapunov exponent ( 1 ) for the dierent EEG signals (N means normal recordings and A abnormal ones). N 0 is the total length of the EEG recordings, N d the length employed for the calculations and D e the embedding dimension. 81
criterion (see sec. x5.2.4). D 2 varied between 4:5 ; 6 without a clear dierence between normal and pathological EEG recordings. Maximum Lyapunov exponents were positive in all the cases giving an evidence of chaotic activity (in the case of signals having a deterministic origin). 5.6 Application to intracranially recorded tonic-clonic seizures 5.6.1 Material and Methods The subject and data analyzed was described in sec. x3.3. The EEG corresponds to a 9-hour intracranial recording from a 21 years old patient with tonic-clonic seizures. 5.6.2 Results and Discussion Figure 7 shows the EEG signal corresponding to a segment of 64 sec from one depth electrode in the left hippocampus. As seen in the gure, the epileptic seizure starts about second 10 and nishes about second 54. In order to study changes in the EEG behavior the signal was divided in intervals of 8 sec as follows: ( i ) pre-seizure (0 ; 8sec) ( ii ) starting of the seizure (10 ; 18sec) ( iii ) full development of the seizure (21 ; 29sec) and (29 ; 37sec) ( iv ) ending of the seizure (37 ; 44sec) and (44 ; 52sec). For these intervals, stationaritywas tested following the criterion described in sec. x5.3. The length of the bins used was of 512 data. In the second interval (10 ; 18sec) the criterion of stationarity was not satised due to the fast changes in the EEG morphology. The time delay and the minimum embedding dimension were estimated with the geometrical method introduced by Rosestein and the False Nearest Neighbor method, respectively (see sect. x5.2.4). Fig. 29 displays the two dimensional projection of the phase portraits for the selected intervals. Each EEG segment was characterized by its Correlation Dimensions and maximum Lyapunov exponents. Table 5 shows the stationary zones, optimal time lags , minimum embedding dimensions, Correlation Dimension and maximum Lyapunov exponent for the dierent EEG intervals. These last two parameters were obtained as an average among the corresponding values obtained for all the considered embedding dimensions. These values are in good agreement with those given in the literature in background activity and in epileptic seizures (see sec. x5.4). The seizure is characterized by a drop in the value of the maximum Lyapunov exponent. A similar situation is observed for the Correlation Dimension. From the values 82
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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
Page 48 and 49: EEG as the one with least amount of
Page 50 and 51: Figure 11: Scalp EEG of the right c
Page 52 and 53: 3.5 Conclusion In this chapter I de
Page 54 and 55: 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 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 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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