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

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Silva et al.,1973a,1973b Lopes da Silva and Storn van Leewen, 1977 Basar et al., 1997). Moreover, many studies were performed in order to understand their functional meanings. These studies showed that alpha rhythms could be correlated even to sensory or cognitive processes depending on the task performed and generators involved, therefore not having an unique and specic function (for a review, see Basar et al., 1997). 4.5.2 Material and Methods In 10 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 a checker reversal (N = 100 stimuli). 2. Oddball paradigm: subjects were watching the same pattern as above. Two different 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 (N = 200 stimuli). The inter-stimulus interval varied pseudo-randomly between 2.5 and 3.5 s. After each pattern reversal, the reverted pattern was shown for one second, then the pattern was re-reverted. 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 of1:5sec: and a low-pass lter at 70Hz. With each stimulus, a single sweep of EEG data was recorded, i.e.: 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, components corresponding to the alpha band (8 ; 16Hz) were analyzed. For each subject the alpha components of the 30 single sweeps were averaged. Finally, results for each subject were averaged to obtain a \grand average". The temporal reso- 51
lution of the scale corresponding to the alpha band was of 64 ms 5 . However it should be remarked that the \real" resolution will depend on the characteristics of the signal and the mother function (i.e. how the mother function matches the signal see section 4.2.4). In this respect, the optimal resolution of B-Splines was shown with numerical computations (Unser et al., 1992). It is also interesting to note that non-redundancy is important for increasing the computational speed. Statistical analysis The wavelet coecients processed were the ones obtained after averaging the responses of the 30 single trials for each electrode and subject. Then, wavelet coecients were rectied and the maximum coecients and their time delay with respect to the stimulus occurrence were computed in the rst 500 ms post-stimulation. The analysis was limited to the rst 500 ms owing to the fact that no subject showed meaningful alpha responses after this time. Comparison between modalities and electrodes were done by using a multiple factor ANOVA test. Comparison between wavelets and conventional digital ltering Figure 18 gives some examples of single-trial evoked potentials, showing the comparison of results obtained with Wavelet Transform and with digital ltering. In addition, the gure shows the relation between the wavelet coecients (used for all statistical analyses) and the waveforms reconstructed from the wavelet coecients for a specic level (which will be shown in the gures). I would like to remark that the sweeps selected do not necessary show a clear event-related response, but they are suitable for showing the better resolution achieved with the multiresolution decomposition based on the Wavelet Transform in comparison with conventional digital ltering. The digital lter used was an ideal lter (i.e. a digital lter based on band pass ltering in the Fourier domain as used in several earlier papers, Basar, 1980) with the lter limits set in agreement with the limits obtained with the multiresolution decomposition for the alpha band. As a general remark it can be stated that with the wavelet coecients a better resolution and localization of the features of the signal is achieved. In between the vertical dashed lines in sweep #1 three oscillations in the alpha range are shown, having the last oscillation a larger amplitude as observed in the original sweep. This is well resolved with the wavelet coecients and also in the reconstructed form. However, this ne structure of this train of alpha oscillations is not resolved by digital ltering i.e. reading a maximum from this curve is imprecise. In sweep #2, in between the dashed 5 From sec. 4.2.2 the time steps b jk are 2 j data points, and since the alpha band corresponds to j = 4 and the sampling rate was of 250Hz we have t =2 4 =250Hz =64ms 52
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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
Page 18 and 19: Summary Since the rsts recordings i
Page 20 and 21: 1 Outline of Neurophysiology: Brain
Page 22 and 23: Figure 2: Normal 20 channels (10-20
Page 24 and 25: 1.1.2 EEG in Epilepsy One important
Page 26 and 27: Figure 3: Scalp EEG of 18 channels
Page 28 and 29: Figure 4: Averaged responses upon N
Page 30 and 31: 2 Fourier Transform 2.1 Introductio
Page 32 and 33: I xx (k) =jX(k)j 2 = X(k) X (k) (
Page 34 and 35: 17 Figure 5: Topographical mapping
Page 36 and 37: 1987) is that coherence gives the c
Page 38 and 39: 3 Gabor Transform (Short Time Fouri
Page 40 and 41: where k g D k= R 1 ;1 jg D(t 0 )j 2
Page 42 and 43: and the band maximum peak frequency
Page 44 and 45: Figure 7: Intracraneal seizure reco
Page 46 and 47: 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 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 114 and 115: and the Lorenz equations (a model o
Page 116 and 117: P300 deection. Due to the relation
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7 General Discussion In this chapte
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Wavelet analysis was also applied t
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aect the whole spectrum and for thi
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peaks. 7.2.3 Wavelet Transform vs.
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the ones having wide peaks (being t
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A Time-frequency resolution and the
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Z 1 ;1 tx(t) d dt x(t) dt = 1 2 Z 1
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Figure 37: Time-frequency resolutio
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References Abarbanel HDI, Brown R,
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Berger, H. Uber das Elektrenkephalo
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Gastaut H and Broughton R. Epilepti
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Lopes da Silva FH, van Lierop THMT,
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Pradhan N, Sadasivan P, Chatterji S
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Serrano E, Ph.D. Thesis, Department
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Biographical sketch 21.03.1967 born
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