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

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the ones having wide peaks (being the limit case a wide band spectrum corresponding to noise or to a chaotic system). Then, the concept of entropy isvery interesting due to the fact that it can be associated to frequency tuning of the neuronal groups. Although in principle the entropy of the signal can be visualized from the Fourier spectrum (i.e. just by looking how narrow or wide are the peaks), the WS allows the following of its time evolution and furthermore, gives a reliable way of quantication. Moreover, the advantage of dening the measure of entropy from the wavelet coecients and not from other alternative time-frequency distribution as the Gabor Transform is that the resolution of the Wavelet Transform is crucial for analyzing the evolution of fast varying signals as in the case of event-related potentials. 7.2.6 Wavelet-Entropy vs. Chaos analysis As stated in several parts of this thesis, ERPs can be considered as a selective enhancement, synchronization or in another words, an ordering of the spontaneous EEG oscillations. In this context, Wavelet Entropy appears as a natural and optimal method for measuring this evoked ordering of the EEG signals. Although using a completely dierent approach, and applied to dierenttypeofEEG signals, Chaos analysis was in principle used for answering similar type of questions. Parameters such asD 2 or 1 give a measure of the complexity, chaoticity, and by extension give an idea of the order of the signal. In this context, converging low values of D 2 for example, were used as a proof of a low dimensional, deterministic, ordered dynamic of the EEG signals in several situations. However as I already mentioned, chaos methods are very dicult to apply to EEG signals and furthermore, in many cases lead to pitfalls and wrong results. As discussed in section x7.1.3, it is very dicult to resolve disputes about the nature of EEG signals by using these methods and it is more reasonable to consider other physiological evidence as for example the response of the EEG to stimulation (ERP). However, Chaos methods are limited to the analysis of long and stationary EEG recordings, being impossible to implement them to the analysis of fast varying nonstationary signals as ERPs. On the other hand, WS is applicable to ERPs and appears as an ideal parameter for obtaining quantitative answers to these type of questions. In particular, I showed in section x6.3.2 that decreases of entropy after stimulation were correlated with an ordering of the brain rhythms involved in a cognitive process. 109
Conclusion In this thesis I showed the application of several methods to the analysis of dierent type of EEG signals. Due to the high complexity of EEGs, these methods needed to be adapted or extended. Furthermore, it was possible to compare their abilities in reaching results that allow interesting physiological interpretations. The methods described complement the information obtained by the visual inspection of the EEG carried by trained electroencephalographers and furthermore, they give aquantication that allows the performance of statistical analysis. Moreover they can give an alternative way of visualization and in the best case the access to information that keeps \hidden" in the visual inspection of the EEG. In this context, I showed a dynamics of the frequency patterns during Grand Mal seizures. Seizures were dominated by alpha and theta rhythms, later becoming slower with the starting of the clonic phase. Moreover, Chaos analysis showed a transition to a simpler system during the seizures. I also showed a distributed origin of event-related alpha oscillations, this ones being related with primary sensory processing. It was possible to conjecture a relation between gamma oscillations and a process responsible of carrying out the information that two sensory perceptions of a bimodal stimulation correspond in fact to the same stimulus. Responses to unexpected (TARGET) stimulation, traditionally related with cognitive processing, showed a \tuning" in their frequency composition in comparison with the ongoing EEG. All these results give a valuable contribution in understanding the brain dynamics. However, despite all the advances due to the development of new techniques and experiments, is still very little what we know about this topic. The attempts to understand the dynamics of the brain by analyzing the EEG is like trying to understand the conversations occurring in a building by analyzing a sound recorded from far away. Dierent stages and apartments are making dierent tasks, and we are not able to get inside and see what is going on. The EEG, the sound recorded from far away, is still one of our main tools to access to one of the most unknown and complex systems in nature, one of the still elusive \treasures" of science. In this context, we must design clever experiments and we are obliged to develop a great variety of methods and improve them up to the limits of their abilities in order to learn more about the behavior of the brain. And that is what makes the study of the brain so fascinating! 110
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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
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sweep #1 sweep #2 sweep #3 sweep #4
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VEP non-target target F3 F4 F3 F4 F
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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 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 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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