EEG analysis during hypnagogium

Petr SvobodaLaboratory of System ReliabilityFaculty of TransportationCzech Technical University

e-mail: svobodap@spel.cz

Presented methods

Traditional methodsFourier transform

Parametrical methodsAutoregressive estimator

Nonlinear methods - Chaos theoryDelay-time embedding, Correlation dimension, Takens estimator, State Space dimension, Lyapunov exponents

EEG activity

Name Freq. [Hz]

Deltha 0,5-4Theta 4-8Alpha 8-15Beta 15-35

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

Traditional methods

Signal‘s stationarity frequency resolution leakage of frequency spectraquality of the spectral estimatephase of the signal is lost

Potencial problems

Estimate of a periodogram using the Fourier transform

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:

Analyzed signal

Pole placement

Autocovariance function

Spectral estimate

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

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

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%

Relaxation

Drowsiness

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 D2

Takens estimator for D2 dimension largest Lyapunov exponents

Delay-time embedding

Si=[x(i),x(i+L),… x(i+(m-1)L)]

L… time delaySi… state-space vectorm… state dimensionx… analyzed signal

Selection of Delay Time L

Time delay should be set so, x(i),x(i+L),… are independent

autocorrelation methodmethod of Mutual Information (MI)

Fractal dimension & Takens estimator

Fractal dimension is a measure of complexity of the analyzed signal

D2 = log C(r) / log r

Where C(r) is correlation integral

D2 computed by maximum likelihood estimator is known as Takens estimator

Microsleep classification

+ matematical description of state-space trajectory reconstructionnonlinearity detection

- correlation dimension D2 estimate

+ Takens estimator+ largest Lyapunov exponents

Chaos theory

Largest Lyapunov Exponents

Sensitive dependence on initial conditions