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

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Wavelet analysis was also applied to study the gamma responses to bimodal stimulation (simultaneous auditory and visual stimulation). This analysis showed a signicant enhancement of the responses upon bimodal stimulus in comparison with unimodal ones (auditory and visual separately). Then, it was possible to conjecture a relation between gamma oscillations and a fast process responsible of carrying the information that the two sensory perceptions of a bimodal stimulation correspond in fact to the same stimulus. Finally, a very interesting analysis of the event-related responses was accessed by the Wavelet-entropy. By seeing the ERP as a synchronization or selective enhancement of some of the ongoing EEG oscillations, the WS appears as a natural method for obtaining a quantitative measure of the ordering of the EEG spontaneous oscillations due to stimulation. Following this view, the P300 response, traditionally related with cognitive processes, seems to be related with a \tuned" response of EEG oscillations. On the other hand, P100 responses were related with oscillations not \tuned" in frequency, thus having a wider frequency composition. 7.1.3 Are EEG signals chaos or noise? First reports of Chaos analysis on EEG signals showed convergence of the Correlation Dimension (D 2 ) to small values, thus claiming that EEG dynamics correspond to low dimensional deterministic chaos. After the nding that ltered noise can also have convergent low dimensional D 2 values, other works stressed the necessity of validation of the metric estimates by means of surrogates tests. In this direction, it was stated that the nature of EEG signals is indistinguishable from noise. In order to deal with this dispute, in the following I will discuss about noise as an inherent property of the system under study, and not about noise produced by the surrounding or by limitations of the measuring systems (ampliers, etc.). In principle we can state that a system is random when we cannot predict its outcome, but in fact the concept of noise is an idealization since it depends on our ability for analyzing the system (I am excluding in this discussion problems related with quantum mechanics and the uncertainty principle). For example, if from the spin, the initial impulse, the mechanical laws, etc., we can calculate the evolution of a coin ipped in the air, then its outcome will not be random. In the past, the dynamics of air convections of the atmosphere, for example, was considered random, until Lorenz (1969) showed that it can be modeled by three dierential equations, thus being deterministic. Chaos theory has grown very fast, developing new methods that showed how many systems, in former times considered noise, have in fact a deterministic chaotic nature. One of the most used methods for distinguishing deter- 103
ministic chaos and noise is the D 2 . However, this method was in principle developed for stationary, noise-free and long data sets. Several eorts were made in order to adapt EEG signals to these requirements with dierent results, among them, singular value decomposition, alternative phase space reconstructions (multichanneling), ltering, etc. But, if it is impossible to distinguish EEG signals from noise with \chaos methods", is it because the EEG corresponds to a noisy phenomenon, or is it because the available methods are not suitable for analyzing the nature of the EEGs? It is like the question of the ipped coin. Is this phenomenon random, or is it that we don't have the ability, or a suitable method to study it? Probably neurophysiological evidence could give more straightforward evidence to resolve this dispute. In fact, EEG alpha oscillations are blockade with eyes opening external or internal stimulation lead to evoked responses that are reproducible upon similar conditions pre-stimulus EEG inuences evoked responses (Basar, 1980) EEG activity can be synchronized in sleep or in pathologies as epilepsy. In summary, EEG patterns have reproducible clear changes upon dierent conditions. Since all these experiments point towards a deterministic origin of the EEG, then, in my opinion, the question about a noisy origin of EEGs based on results obtained with methods as the D 2 should be restricted to a discussion of the possibilities of these methods and not to a discussion about the nature of the signal. 7.2 Comparison of the methods In principle, there is not a \best method" for quantitative analysis of EEG signals. The selection of the adequate method will depend on the type of signal to be studied and on the questions expected to be answered. 7.2.1 Fourier Transform vs. Gabor Transform Fourier Transform gives a representation in the frequency domain. This allows the visualization of periodicities that would be dicult to observe from the EEG, especially when several rhythms occur simultaneously. Frequencies are grouped in bands, their total or relative power and their topographical distribution constituting the main quantitative method of analysis of the EEG. This procedure was adapted to several commercial systems and has been used as a diagnostical tool in medical centers. It is important to remark that the grouping in frequency bands is not arbitrary because it was shown that these bands can be related to dierent functions, sources and pathologies. However, Fourier Transform gives no information about the time of occurrence of the frequency patterns. Moreover, transients localized in time in the original signal will 104
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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
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4.2.5 Wavelet Packets In the approa
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marked decrease in computational ti
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ain activity during an epileptic se
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3 2 3 3 3 3.2 Hz 3.6 Hz 4.0 Hz 4.4
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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 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 122 and 123: aect the whole spectrum and for thi
Page 124 and 125: peaks. 7.2.3 Wavelet Transform vs.
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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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