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

More documents

Recommendations

Info

wavelet coecients allowed an easy design and implementation of statistical tests. In this context, the resolution achieved with Wavelet Transform was very important for obtaining signicance of the results. The frequency dynamics during the seizures was already described with Gabor Transform (sec. x3.4). However, with wavelets packets it was possible to follow with better accuracy the time evolution of the frequency peaks. Further advantages can be obtained when comparing frequency patterns of dierent channels in order to obtain information about the sources of the seizures. In this case, the time resolution of wavelets can be crucial due to the fact that the seizure spread, from the focus to other locations, can take place in a few milliseconds. Wavelet Transform, due to its varying window size, is more suitable for analyzing signals involving dierent ranges of frequencies. In fact, as showed with alpha and gamma responses to ERPs, frequency behaviors can be resolved up to fractions of a second. On the other hand, with the election of a adequate window, Gabor Transform is more suitable for the analysis of signals with a more limited frequency content as shown in the previous chapter with Grand Mal seizures, in which the interesting activity was limited to the lower frequencies of the EEG (up to 12:5Hz). 67
5 Deterministic Chaos 5.1 Introduction In the previous chapters I described the application of several time-frequency methods to the analysis of brain signals. Since these methods are linear, a completely dierent approach canbeachieved by applying the concepts of non-linear dynamics, also known as Deterministic Chaos theory. Chaotic systems have an apparently noisy behavior but are in fact ruled by deterministic laws. They are characterized by their sensibility on initial conditions. That means, similar initial conditions give completely dierent outcomes after some time. Since chaotic signals look like noise and furthermore, since they also have a broadband frequency spectrum, linear approaches as the ones described in the previous sections are sometimes not suitable for their study. Several methods were developed in order to calculate the degree of determinism (or random nature), complexity, chaoticity, etc. of these signals. Among these, the Correlation Dimension, Lyapunov Exponents and Kolmogorov Entropy have been the most popular. In this chapter I will give a mathematical background of these methods and then I will describe their application to the study of EEG signals. The chapter is organized as follows. After a brief denition of the basic concepts related with chaos, the mathematical background for the calculation of the Correlation Dimension and Lyapunov Exponents will be described. In section x5.2.4, I will remark some problems in the selection of computational parameters. One of these problems is the stationarity of the signal to be studied. In Section x5.3, I will describe a criterion based on weak stationarity (Blanco et al., 1995a). In section x5.4, I will give a brief review of previous results of chaos analysis of EEG signals. In sections x5.5 and x5.6, I will show the application of Chaos methods to scalp normal EEG recordings and to intracranially recorded Grand Mal seizures (Blanco et al., 1995a,b, 1996a). Finally in section x5.7, I will discuss about the applicability andresults of chaos analysis to EEG signals. 5.2 Theoretical Background 5.2.1 Basic concepts Phase space: It is a common practice in physics to represent the evolution of a system in phase spaces. For example, in mechanics,itisvery useful to represent the movement of a system as a pendulum by plotting the position vs. the velocity or more generally, 68
Page 1 and 2:
Quantitative analysis of EEG signal
Page 3 and 4:
1. Berichterstatter: Prof. Dr.-Ing.
Page 5 and 6:
an okzipitalen Positionen und (c) d
Page 8 and 9:
To my family: Mama, Consuelo, Hugui
Page 10 and 11:
Preface In this work, I will descri
Page 12 and 13:
I would certainly like to remember
Page 14 and 15:
Contents Zusammenfassung Preface Ac
Page 16 and 17:
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 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 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 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
show all

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

Create successful ePaper yourself

Delete template?

Save as template?