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

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Figure 29: Attractors corresponding to the selected zones (see text) during a Grand Mal seizure. 83
EEG segment D e (min) D 2 1 0 ; 8 sec 0:0195 8 4:30 4:6 21 ; 29 sec 0:0156 13 2:60 4:0 29 ; 37 sec 0:0156 10 2:50 4:0 37 ; 44 sec 0:0156 11 2:05 3:5 44 ; 52 sec 0:0156 13 2:15 3:0 Table 5: Optimal value of time lag (insec ), minimum embedding dimension D (min) e , Correlation Dimension (D 2 ), and maximum Lyapunov exponent ( 1 ) for the stationary EEG segments (Data-set size: N = 2048 see text). showed in table 5, it can be concluded that the dynamical behavior was more regular during the seizure. Summarizing, we found a good evidence that during the epileptic seizure there is a transition from a complex to a simple dynamical behavior. Furthermore, this result yields insights with respect to the theory of how epileptic seizures occur (i.e. synchronization of the disordered background EEG activity). as a 5.7 Conclusion Deterministic chaos theory gives an alternative new type of analysis compared with the ones given by the traditional methods. However, the application of chaos methods, should be done with care in order to avoid misleading results. In this way a right election of parameters required for the calculations is critical. Chaos analysis has several prerequisites, some of them making impossible its application to the study of EEG signals. One of these prerequisites is the availability of long data recordings but on the other hand, data must be stationary. Consequently, chaos analysis cannot be applied in nonstationary short data recordings as in the case of event-related potentials. In these types of series, the dynamics of the system is changing completely in fractions of a second due to the eect of the stimulus and therefore, it has no sense to dene an attractor and to calculate any metric invariant from it. Since methods for calculation of D 2 and 1 were developed for ideal signals (i.e. innite, noise-free and stationary), then, due to the complex structure of the EEGs, results should be considered of relative relevance and, as suggested by Pritchard and Duke (1992), is more realistic to talk about Dimensionality instead of Correlation Dimension. By using this view, several groups reported changes in D 2 and 1 values in dierent brain states and pathologies. Nevertheless, these measures seem not to be suit- 84
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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
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 98 and 99: Figure 28: Histogram for the EEG da
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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