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

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performed. On one hand, must be large enough in order to give a reliable statistic and on the other hand if it is too large, it will not be possible to observe fast changes. 2. The mean and variance for each bin were calculated, and zones in which their values do not have signicant changes (e.g. less than 20%) were selected. 3. Finally, the corresponding histogram for this zone was constructed, and the normality of the obtained distribution was veried. I would like to remark that although the above criterion is arbitrary and does not prove stationarity 7 , it was very useful as a rst approximation in order to select EEG data segments to work with, or to reject others with clear non stationary behavior. However, I would like to stress that in general elaborated statistical criteria can be hardly fullled by EEG signals. For a more complete discussion about stationarity related with the application of Chaos methods, see for example Schreiber (1997). Eckman et al. (1987) presented another approach to the problem of stationarity by using the so called recurrence plots. Recurrence plots are based on distance calculations in the phase space. After a phase space reconstruction, the Euclidean distance between the embedding vectors (lets say N in total) is calculated. Then, an NxN plot is performed in the following way: for each pair of embedding vectors (i j) (i represented in the horizontal axis and j in the vertical axis) a point is plotted if its distance is less than a certain value r. Stationary signals will be characterized by homogeneous plots and non-stationary signals will show inhomogeneities due to varying features of the embedding vectors in the phase space. As an example, Fig. 25 shows the recurrence plot of an stationary one minute EEG signal (see Blanco et al., 1995a). Recurrence plots give an elegant representation of the stationarity of the signal, but in many occasions their interpretation is subjective and further analysis is required. 5.4 Short review of Chaos analysis of EEG signals 5.4.1 Correlation Dimension Since the pioneering work of Babloyantz and coworkers (Babloyantz, 1985), several groups started to study the dynamics of the brain activity by reconstructing the trajectory of the system in the phase space and by calculating parameters as the Correlation Dimension (D 2 ). Low D 2 values correspond to simple systems and high D 2 values to 7 Autocorrelation function is not checked, and the choice of what is considered as stable mean and variances is in fact arbitrary. 75
Figure 25: Recurrence Plot of a stationary EEG signal. Horizontal axis (i) andvertical axis (j) represent the 3200 embedding vectors obtained from the signal after phase space reconstruction. A point is plotted in the position (i j) if the distance between vectors i and j is less than a certain value r. more complex ones this value tending to innity, in theory, in the case of noise. D 2 proved to be very useful for characterizing the brain dynamics in dierent sleep states. It was found that D 2 decreases in deep sleep stages, thus reecting a synchronization of the EEG (Babloyantz, 1986, Roschke and Aldenho, 1991 Achermann et al., 1994a,b Pradhan et al., 1995). D 2 was also used for characterizing the brain dynamics doing mental tasks (Lutzenberger et al., 1995 Molle et al., 1996). Furthermore, D 2 was compared between normal subjects and patients with dierent pathologies, with the general result that decreases in D 2 are related with abnormal synchronizations of the EEG, as demonstrated in epilepsy (Blanco et al., 1996a Babloyantz and Destexhe, 1986 Pijn et al., 1991 Iasemidis et al., 1990 Lehnertz and Elger, 1995, 1998) and other pathologies as Alzheimer, dementia, Parkinson, depression, schizophrenia or Creutzfeld-Jakob coma. (Pritchard et al., 1994, Besthorn et al., 1995 Stam et al., 1995, Roschke et al., 1994 Gallez and Babloyantz, 1991). For a more detailed review of dierent application of chaos analysis in brain signals I suggest the works of Basar (1989), Pritchard and 76
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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
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 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 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 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,
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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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