CLASSIFICATION OF MICROSTRUCTURE OF HUMAN SLEEP USING EEG MODELLING José M Allen Lima, Agostinho C da Rosa Institute for Systems and Robotics Instituto Superior Técnico Av Rovisco Pais, 1 Torre Norte 6.21 1000 Lisbon Portugal tel:+351.1.8418277 fax: +351.1.8418291 Email:
[email protected],
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ABSTRACT This paper presents an automatic classifier for a sleep paradigm. This classification, Cyclic Alternating Pattern Sequence (CAPS) is based on the microstructure of sleep. The classifier is based on one Electroencephalogram, EEG, model to estimate its rhythmic activities. It was tested on 4 normal subjects and achieved better agreement with a visual reference than human-human agreement.
1. INTRODUCTION One of the most common sleep scoring criteria is known as the Rechtshaffen and Kales (R&K) criteria [6]. It scores sleep in four stages of slow sleep, 1NREM~4NREM and one stage of paradoxical sleep, REM1. The classification is made in pages. It is called a classification of macrostructure of sleep. More recently Terzano et al. presented a new scoring method for the microstructure of human sleep [9], the Cyclic Alternating Pattern Sequences (CAPS). The microstructure is based on short time transient events. Most of these events are ignored in the R&K criteria. According to [17], sleep is composed by the interaction of two distinct homeostatic processes. Predictive homeostasis assures the natural development of sleep. Reactive homeostasis appears as a response to internal and external disturbances. This process can be observed in the EEG signal as short non-stationary transients known as Arousal Related Phasic Events (ARPE) [17]. One way to estimate the sleep stability using CAPS is with the CAPS Rate ( CAPSTime NREMTime ). Modifications of the CAPS Rate are present in several diseases [10,12,14,15,16,18]. Deviations from the normal CAPS Rate can also be observed in presence of acoustic noise in the sleep of normal subjects [11,13].
1
REM stands for Rapid Eye Movement.
2. CAPS SCORING METHOD The CAPS is a hierarchical classification of sleep EEG. It uses only one EEG channel and the classification is made second by second. Sleep is scored in two main stages: The cyclic alternating pattern sequence (CAPS) and non CAPS (NCAPS). The CAPS stage is composed by, at least, two cycle alternating pattern (CAP) sub-stages. On the other hand, each CAP is composed by a phase A followed by a phase B. A summarised version of the A, B scoring criteria presented in [17] is shown below: Phase A: is characterised by: intermittent alpha rhythm in stage 1NREM, K-complexes or delta bursts. Slow high voltage waves and desynchronised EEG patterns. Desynchronised EEG patterns alone. This phase is related to the presence of ARPE. Phase B: is characterised by: Continuous stationary EEG with rare, isolated arousal related phasic events. Both phases have a minimum duration of 2 seconds and a maximum of 60 seconds.
3. EEG MODELLING The EEG is commonly decomposed in several rhythmic activities. Each one is defined as a band in the frequency spectrum. The most used activities in the EEG analysis are: delta (0.25~4Hz [8]), theta (4~8Hz [2]), alpha (8~13Hz [8]) and sigma (12.25~15Hz [2]). The estimation of these activities is made using an estimator based on a EEG model (see [7]). The estimator is shown on Figure 1. The first filter is a cortical EEG estimator. It is an approximation of the inverse filter cause by signal transmission from the cerebral cortex to scalp [3,5]. In the feedback loops, there are resonant filters tuned for each rhythmic activity. These filters are time-invariant and their shape is based on histological works [1,2,9].
The feedback gains are time-variant and are estimated for each moment. Because of this, the model is time-variant. e( n )
1 H p ( e jω )
ε ( n)
c( n ) H1 ( e jω ) H 2 ( e jω ) HV ( e jω )
φ1 φ2 φV
x1 ( n )
k1
x2 ( n)
k2
⋅
2
y1 ( n )
⋅
2
y2 ( n )
⋅
2
yV ( n )
c( n) xV ( n )
kV
Figure 1: Block diagram of the model based Estimator 3.1 Estimation of feedback gains The estimation of the feedback gains is carried using Linear Mean Squares (LMS) approximation. From Figure 1 it is clear that c( n) behaves like an approximation of
c( n) . On the other hand, c( n) is a linear combination of the filter outputs. Using LMS and Finite Impulse Response (FIR) filters the estimated gains are given by:
(
)
H is the
If c( n) is a non-stationary process, then ℜ will be time dependent and the gains have to be estimated for all time instants (see [19] for further details).
3.2 Detection of Phasic Events The detection is carried by testing changes of the squared signal of each band. The decision is made with a jump of mean statistical test (JMST). Because the band signal, xi ( n) = k i ⋅ φi ( n) , is assumed to have a zero mean gaussian distribution,
yi (n) = xi ( n) , will have a particular gamma 2
distribution. For a N point segment the multivariable distribution is given by: 1
( 2π )
1 2
CX
2
1 y (1) y (2)
y( N )
e
−
1 [ SQRT (Y )]T C X−1 [ SQRT (Y )] 2
Where C X is the covariance matrix of the original signal. The phasic event is modelled with a change of the distribution. This change affects only the mean of the process. The framework of maximum likelihood (ML) binary hypothesis test is used as a start for the JMST. Let the two hypotheses be:
2
The superscript H on the transpose (hermitian matrix).
To perform the ML test one has to estimate C X , compute the inverse matrix and do a vector-matrixvector multiplication. Because of these computational difficulties, a sub-optimal JMST is here presented. This test behaves like a ML test for white noise. It differs from the ML when noise is correlated, which is the actual case. Let c=
1 N
N
∑ E[r (i )] i =1
The sub-optimal JMST is defined as: Λ′ = −
1 β − 1 1 N N ln( β ) + ∑ y (i ) 2 2 β c i =1
E[Λ ′| H1 ] ≥ 0
Where ℜ is the signal correlation matrix, matrix of the impulse response of all filters2 and T I 1 = [1 0 0] ( M × 1) .
N
1≤ n ≤ N 1≤ n ≤ N
This test verify the following properties:
Hℜ H H K = H ∗ ℜ T I 1
f Y (Y ) =
H 0 : y ( n) = r (n) H1 : y ( n ) = β r ( n )
H stands for conjugate
E[Λ ′| H 0 ] ≤ 0
Equality stands if, and only if,
β = 1 . For a study on
test variance see [19]. This test has only to compute a sum of the last signal samples. This computational advantage makes it more efficient than the ML test. The EEG signal of one night sleep here processed has about 3 × 10 samples. The computational efficiency is, therefore, an important advantage. 6
4. CAPS RULES VALIDATION After detecting the phasic events, a finite state machine (FSM) is used to validate the phasic events into CAPS phase A. As it was stated before, to be a CAPS cycle it has to have, at least, two cycles AB. Both phases must have duration between 2 and 60 seconds, otherwise it is considered NCAP.
5. CAPS EXAMPLES This section provides a few examples of the CAPS scoring criteria of the EEG signal. The phase A is underscored. The segments are 30 second length. Figures 2 and 3 are CAPS examples, while figure 4 and 5 are NCAP examples.
The next figure shows an example of the whole night CAPS classifications (8 hours) and, on top, the hypnogram (macrostructure classification).
2000 0 -2000 0
5
10
15 seg
20
25
30 W 1 2 3 4
Figure 2: CAPS in sleep stage 1NREM 2000
REM
1
2
3
1
2
3
1
2
4 Hypnogram
5
6
7h
4 5 Visual Capsnogram
6
7h
3 4 5 Automatic Capsnogram
6
7h
0 A
-2000 0
5
10
15 seg
20
25
30
B NCAP
Figure 3: CAPS in sleep stage 4NREM 2000
A
0 B
-2000 0
5
10
15 seg
20
25
30
Figure 4: NCAP with an isolated ARPE
NCAP
Figure 8: Example of an 8 hours recording
2000 0 -2000 0
5
10
15 seg
20
25
30
Table 1 resumes the classification results of the 4 records. Individual Correctness (%) CAPS Rate Error (%)
Figure 5: NCAP in sleep stage REM
6. RESULTS The CAPS classifier was tested on 4 sleep records of young normal adults. The visual scoring was made by one of the most trained specialists in the field. Two examples of manual and automatic classification of CAPS are shown in the next figures. The length of these signal segments is 60 seconds.
1 86.0
2 89.1
3 87.4
4 91.3
3.0
-5.9
-9.0
-1.3
Table 1: Performance indexes Correctness is defined as the percentage of seconds that automatic and visual classifications agree. The CAPS Rate Error is defined by: VisualCAPSRate − AutoCAPSRate × 100 VisualCAPSRate
EEG -A -B -NCAP
Auto
-A -B -NCAP
Visual
Figure 6: Beginning of a CAPS sequence
EEG -A -B -NCAP
Auto
-A -B -NCAP
Visual
Figure 7: End of a CAPS sequence
7. DISCUSSION This work presented an automatic classifier for the microstructure paradigm of human sleep, the Cyclic Alternating Pattern Sequence. Manual classification is a long and tedious process and with low agreement between human scorer. It can take about 20 hours to classify a record. On the other hand the agreement between human scorers is below 80% [20]. The agreement between automatic and a visual reference was higher than between human specialists. This paper introduced a new way of estimating the feedback gains and the rhythmic activities of the EEG. A sub-optimal statistical test was also introduced to overcome the computational limitations of the ML test. A more detailed study of the statistical properties
of this test will be presented in the final version of this paper.
8. ACKNOWLEDGEMENTS This work was partly supported by the Hypnos Project of the Portuguese Scientific Investigation Institute (JNICT) included in the PRAXIS XXI programme.
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