Functional Brain Signal Processing: EEG & fMRI

Lesson 6

Kaushik Majumdar

Indian Statistical Institute Bangalore Center

kmajumdar@isibang.ac.in

M.Tech. (CS), Semester III, Course B50

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).

EEG at NREM

Carskadon and Dement, 2011

Arrow indicates K-complex and underlines indicate sleep spindles.

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.

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.

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.

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.

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

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.

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.

Phase

sin(2 )nt ϕ is the phase here

50 100 150 200 250 300 350 400 450 500

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

0 0

1 ( )( ( )) . .

( ) ( ) ( ). . lim lim

t

t

sH s t p v d

t

s s sp v d d d

t t t

1 ( ( ))( ) tan

( )

H s tt

s t

Ψ(t) is instantaneous phase at time t. H() is Hilbert transformation.

s(t)

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 thatsin( )x

dxx

cos( )

0xdx

x

and

1 sin( ) 1 sin( )(sin( )) ,

x t zH t dx dz t x z dx dz

t x z

Solution:

H(sin(t)) = -cos(t) (cont.)

1 sin( )cos( ) cos( )sin( )t z t zdz

z

1 cos( ) 1 sin( )sin( ) cos( )

z zt dz t dz

z z

cos( )t

Similarly it can be shown that H(cos(t)) = sin(t)

H(s(t))

S(t)

Ψ(t)

Phase Synchronization

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8-20

-15

-10

-5

0

5

10

15

20

time

ampl

itude

Phase Synchronization (cont.)

1 2( ) ( ) , [ , ]m t n t C t t t Strict m:n phase syn-chronization in [t1, t2]

1 2( ) ( ) , [ , ]m t n t C t t t m:n phase syn-chronization in [t1, t2]

1 2( ) ( ) 2 , [ , ]m t n t C t t t

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.

Phase Synchronization (cont.)

( ) ( ) ( ) 2t t t γ(t)

1

log( )n

k kk

S p p

1

n

pk = # values in the kth bin/total number of values.

max

max

S S

S

Statistical Significance on Surrogate Signals

Shifted surrogate signal generation (at least 100 pairs).

Fixing the confidence level (usually 95% or more).

Hilbert Phase Synchronization in Epilepsy

Prasad et al., Clin. EEG Neurosci., 44(1): 16 – 24, 2013

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.

Wavelet Analysis

A signal in which frequency is varying with respect to time and therefore nonstationary.

Polikar, 1996

Wavelet Analysis (cont.)

Meyer wavelet Morlet or Gabor wavelet Mexican hat wavelet

http://en.wikipedia.org/wiki/Wavelet

,

1( )a b

t bt

aa

Shift and scale operation, where ψ(t) is the mother wavelet.

2, 2( ) exp( 2 ( )) exp

2f

tt f j f t

Morelet or Gabor wavelet

Wavelet Phase Synchronization

*,( , ) ( ) ( )x fW f x t W t dt

van Quyen et al., 2001

*( , ) ( , )exp( ( ( , ) ( , )))

( , ) ( , )x y

y x

x y

W f W fj f f

W f W f

Wavelet phase synchronization measure between signals x(t) and y(t) at the time point and frequency f.

4 4,

f ff fnco nco

This is the frequency band for which the synchronization measure is valid. 6nco f

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

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.

THANK YOU

This lecture is available at http://www.isibang.ac.in/~kaushik