1. EEG analysis during hypnagogium Petr Svoboda Laboratory of System Reliability Faculty of Transportation Czech Technical University e-mail: svobodap@spel.cz

2. Presented methods Traditional methods Fourier transform Parametrical methods Autoregressive estimator Nonlinear methods - Chaos theory Delay-time embedding, Correlation dimension, Takens estimator, State Space dimension, Lyapunov exponents

3. EEG activity electric potential of brain‘s neural activity registered on the skelet four basic frequencies

4. Traditional methods Signal‘s stationarity frequency resolution leakage of frequency spectra quality of the spectral estimate phase of the signal is lost Potencial problems Estimate of a periodogram using the Fourier transform

5. Parametric model Autoregressive (AR) model: Approximation of an EEG signal by adequate parametric model Approximation of an EEG signal by linear time invariant filter with transfer function H(z)=1/A(z) Whitening of signal by AR filter:

6. Analyzed signal Pole placementAutocovariance function Spectral estimate

7. Comparison of traditional and parametric methods Parametric methods: + frequency resolution + parametric description of analyzed signal - estimate of AR model order - high noise sensitivity Traditional methods: + low noise sensitivity - frequency resolution

8. Microsleep classification + Alpha, deltha and theta activity of spectral estimate Traditional methods Parametrical methods + Alpha, deltha and theta activity of spectral estimate - estimate of AR model order - placement of poles in a complex plane

9. Classification by spectral estimate Classification into 2 states RELAXATION DROWSINESS Classification based on neural network (back propagation) Classical methods: accuracy of about 87% Parametrical methods: accuracy of about 90%

10. Relaxation Drowsiness

12. Chaos theory analysis of dynamic deterministic systems high sensitivity on initial conditions known dynamics and phase of the system detecting nonlinearity by surrogate data testing delay-time embedding state-space dimension estimate estimate of delay time estimate of fractal dimension D 2 Takens estimator for D 2 dimension largest Lyapunov exponents

13. Delay-time embedding S i =[x(i),x(i+L),… x(i+(m-1)L)] L… time delay S i … state-space vector m… state dimension x… analyzed signal

14. Selection of Delay Time L Time delay should be set so, x(i),x(i+L),… are independent autocorrelation method method of Mutual Information (MI)

15. Fractal dimension & Takens estimator Fractal dimension is a measure of complexity of the analyzed signal D 2 = log C(r) / log r Where C(r) is correlation integral D 2 computed by maximum likelihood estimator is known as Takens estimator

16. Microsleep classification + matematical description of state-space trajectory reconstruction nonlinearity detection - correlation dimension D 2 estimate + Takens estimator + largest Lyapunov exponents Chaos theory

18. Largest Lyapunov Exponents Sensitive dependence on initial conditions