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EEG and fMRI Analysis of Sleep Stages using Fuzzy C-Means Clustering and Wavelet Phase Synchronization

This lesson discusses the different stages of sleep, their characteristics in EEG signals, and their classification using fuzzy c-means clustering. It also explores the concept of phase synchronization in sleep EEG signals using wavelet analysis.

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EEG and fMRI Analysis of Sleep Stages using Fuzzy C-Means Clustering and Wavelet Phase Synchronization

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  1. M.Tech. (CS), Semester III, Course B50 Functional Brain Signal Processing: EEG & fMRILesson 6 Kaushik Majumdar Indian Statistical Institute Bangalore Center kmajumdar@isibang.ac.in

  2. Sleep • Non-rapid eye movement (NREM) sleep – stage 1. • NREM sleep – stage 2. • NREM sleep – stage 3. • NREM sleep – stage 4. • Rapid eye movement sleep (REM).

  3. Carskadon and Dement, 2011 EEG at NREM Arrow indicates K-complex and underlines indicate sleep spindles.

  4. NREM Stage 1 Sleep • This is a stage between sleep and wakefulness and has a duration of 1 – 7 minutes. The muscles are active, and the eyes roll slowly, opening and closing moderately. It has low arousal threshold. Percentage of this stage gets prolonged in total sleep duration in a severely disrupted sleep.

  5. NREM Stage 2 Sleep • Duration 10 – 25 minutes. EEG contains sleep spindles and K-complexes. Mild stimulus that can awaken during stage 1 NREM sleep may produce only K-complexes in the EEG, but no arousal may occur.

  6. NREM Stage 3 Sleep • Slow wave sleep (SWS) starts. EEG contains delta activity with amplitude (at least 75 microvolt) concentration in the band 2 - 3.5 Hz. Delta activity spans 20 – 50% of the duration of EEG. This stage lasts only for a few minutes.

  7. NREM Stage 4 Sleep • High voltage (at least 75 micro volts) slow wave activity occupies more than 50% of the EEG. Duration of this stage is 20 – 40 minutes in the first cycle. • Stage 3 and stage 4 sleep together called slow wave sleep (SWS), delta sleep or deep sleep.

  8. REM Sleep • During REM sleep muscles become completely inactive. REM sleep stage is entered about 100 minutes after the stage 1 NREM sleep. EEG during REM sleep is similar to awake state EEG, although the person is hardest to awaken at this stage compared to any other sleep stage. • N1→N2→N3→N4→N2→REM

  9. Sleep Stage Classification in EEG • There are continuous transitions between sleep stages. EEG is not well separated. • There is wide inter-subject variability in spectral features associated with sleep EEG. • Even for one particular individual features vary substantially from cycle to cycle. • Number of sleep stages may vary from subject to subject depending on age and pathological conditions.

  10. Fuzzy C-Means (or K-Means) Clustering • I. Gath and A. V. Geva, “Unsupervised optimal fuzzy clustering,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11(7), p. 773 – 781, July 1989.

  11. Phase ϕ is the phase here s(t) Ψ(t) is instantaneous phase at time t. H() is Hilbert transformation.

  12. Hilbert Transform • H(s(t)) and s(t) are mutually orthogonal. That is absolute value of difference of instantaneous phases of H(s(t)) and s(t) is π/2. • Show that H(sin(t)) = -cos(t). It is known that and Solution:

  13. H(sin(t)) = -cos(t) (cont.) H(s(t)) Similarly it can be shown that H(cos(t)) = sin(t) Ψ(t) S(t)

  14. Phase Synchronization

  15. Phase Synchronization (cont.) Strict m:n phase syn-chronization in [t1, t2] m:n phase syn-chronization in [t1, t2] Because the phase difference will have to lie between 0 and 2π. Also circular statistics are to be taken into consideration. In most practical applications m = n = 1 is assumed.

  16. Phase Synchronization (cont.) n γ(t) 1 pk = # values in the kth bin/total number of values.

  17. Statistical Significance on Surrogate Signals • Shifted surrogate signal generation (at least 100 pairs). • Fixing the confidence level (usually 95% or more).

  18. Prasad et al., Clin. EEG Neurosci., 44(1): 16 – 24, 2013 Hilbert Phase Synchronization in Epilepsy Phase is always associated with a narrow frequency band. So before measuring phase synchronization signals must be band-pass filtered. Here the band is 30 – 40 Hz. The red line in the bottom is level of statistical significance.

  19. Polikar, 1996 Wavelet Analysis A signal in which frequency is varying with respect to time and therefore nonstationary.

  20. http://en.wikipedia.org/wiki/Wavelet Wavelet Analysis (cont.) Meyer wavelet Morlet or Gabor wavelet Mexican hat wavelet Shift and scale operation, where ψ(t) is the mother wavelet. Morelet or Gabor wavelet

  21. van Quyen et al., 2001 Wavelet Phase Synchronization Wavelet phase synchronization measure between signals x(t) and y(t) at the time point and frequency f. This is the frequency band for which the synchronization measure is valid.

  22. References • M. A. Carskadon and W. C. Dement, Chapter 2 – Normal human sleep: an overview, in Monitoring and Staging of Human Sleep, in M. H. Kryger, T. Roth and W. C. Dement (eds), Principles and Practice of Sleep Medicine, 5e, Elsevier Saunders, St. Louis, 2011. • Wikipedia article on sleep at http://en.wikipedia.org/wiki/Sleep

  23. References (cont.) • R. Polikar, The engineer’s ultimate guide to wavelet analysis: the wavelet tutorial, 1996, freely downloadable from http://person.hst.aau.dk/enk/ST8/wavelet_tutotial.pdf • M. L. van Quyen et al., Comparison of Hilbert transform and wavelet methods for the analysis of neural synchrony, J. Neurosci. Meth., 111: 83 – 98, 2001.

  24. THANK YOUThis lecture is available at http://www.isibang.ac.in/~kaushik

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