1 Introduction TIrE STUDY of sleep disorders, from humble beginnings, has grown into a major science, built on expertise from both the clinical and physical sciences. Despite this, the human sleep process is still far from being understood. Early attempts to develop a method for quantifying the sleep process led to a set of rules for the visual scoring of sleep (from the electro-encephalogram (EEG), eye movements--~lectro-oculograms (EOGs) and muscle tone--electro-myogram (EMG)) and culminated in the publication of a manual of standardised sleep scoring in 1968 (RECHTSHAFFENand KALES, 1968). These rules viewed sleep as being composed of six main stages (wake, REM or dreaming sleep and sleep stages 1, 2, 3 and 4 representing progressively deeper sleep) on a time scale of 20 or 30 s. This set of rules is still in regular use for the human scoring of sleep (requiring some 2-5 h of expert time per 8 h recording) and the majority of automatic sleep staging systems are based on the software implementation of these rules. It is known that the rules break down when applied to abnormal sleep patterns, and furthermore they rely explicitly on measurements of the absolute amplitude and frequency of the EEG. Amplitude, however, is not a true sleep-related variable, as it is dependent on such factors as age, electrode placement and skull morphology (KEMP et al., 1987; WEBB and DREBELOW, 1982). It is clear from simple electromagnetic modelling of the EEG potential (ROBERTS, 1990) that the EEG is representatively only of the bulk action of cortical neurones; our hypothesis is that methods of analysis based on state changes in the EEG offer the possibility of a less subjective means of quantification of the sleep process.

Correspondence should be addressed to Dr S. Roberts. First received 4th February and in final form 23rd July 1991

~) IFMBE: 1992

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2 Materials

Data consisted of nine whole night sleep recordings from a control group (total sleep time = 71 h, mean age of subjects = 27.4 years, age range = 21-36 years, all female). Recordings were made using the 8-channel Medilog recorders (Oxford Medical Ltd) and consisted of the standard four channels of EEG (C4-A1), two EOGs and a mental (chin) EMG. No analogue prefiltering was employed, the recorder having a passband of 0.5-40Hz, with roll-offs at 20dB decade -1. Digitisation with 8-bit accuracy was performed, off-line, at 40 times real speed by the Medilog 9200 replay system, giving an equivalent real time sample rate of 128 Hz. The EEG data was then digitally low-pass filtered (30 Hz cut-off using a linear phase filter) prior to further processing as described below. 3 Methods

The observation we make of the state of the cortex during sleep, in the form of an EEG recording, is that of a highly complex, nonstationary time series (BODENSTEINand PRAETORIUS, 1975; COHEN and SANCES, 1977; JANSENet al., 1981; GATH and BAR-ON, 1980; BARLOW,1985). On a time scale of the order of 10s or less (COHEN and SANCES, 1977; BARLOW, 1985), however, the EEG can be considered to be quasistationary, although changes between states occur with unpredictable timing and direction (KEMP et al., 1987). The aim of our study was the reliable identification and separation of these states throughout a sleep record. The approach we have developed relies primarily on two different techniques; a Kalman filter algorithm, for the parameterisation of the EEG, and a self-organising (neural) network, for clustering in high-dimensional space. These techniques will now be described in detail. 3.1 K a l m a n filter The possibility that linear prediction, as normally applied to stationary signals, could be modified for use

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with nonstationary signals was first advanced by KALMAN (1960) and KALMAN and B u c v 0961). BOHLIN (1971) was the first to use a Kalman-Bucy filter to obtain a running spectral estimate of the E E G and such a filter has been employed for E E G analysis by several researchers since (HASMAN et al., 1978; JANSEN et al., 1981; JANSEN et al., 1979). The filter is an extension of the stationary autoregressive (AR) model of the form P

x, = Y

Oix,-i + ~,

(1)

i=l

where et is a white noise process with uniform variance and p is the order of the model. The set of coefficients {0} are time dependent parameters, which are updated with every sample according to the error between that sample and the corresponding prediction 2~. The coefficients can be later averaged over any time window, depending on the temporal resolution desired. The algorithm for computing these coefficients has been described in detail elsewhere (SKAGEN, 1988; Box and JENKINS,1976; PAPOULIS,1984).

number of clusters and their statistics to be estimated a priori after which supervised clustering can be performed. Self-organising networks, of the type originally proposed by KOHONEN (1982), do not require such a priori information. Kohonen's network converges to an ordered output mapping which maximally separates dissimilar input vectors. Kohonen has shown, for cases when a priori knowledge of the statistics of different clusters of input vectors was available, that the decision boundary between input classes formed in output-space was close to the optimal (Bayesian) decision boundary (KoHONEN, 1990). Consider a mapping 4): A-~ B where B represents an array of output units labelled by the indices [j, k] 82and A an input-sPace with inputs represented by the vector set {x}. Let each output unit have a weight vector associated with it, say mjk(t), whose dimension is the same as that of the input vectors. To obtain the mapping ~, the weight vectors mjk are initially given random values and the input data set {x} is then presented, repeatedly and in random order, to the network. At each presentation of an input vector x(t) we compute for each output unit the Euclidean distance r/jk, in input-space, between mik(t ) and xt (i.e. ~/jk= IIx(t) --m~k(t)ll) and select the unit, [j, k]* with the minimum qjk. A neighbourhood X around l-j, k]* is then defined such that, within X , weight vectors are adapted according to the following rule:

mjk(t + 1) = mjk(t ) + r

-- mjk(t)]

(2)

where ~(t) is an adaption parameter, 0 ~ ~ 1. w Mirrored by a c'orr~sponding increase in the mean value of ~PR

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(HASAN, 1983). F o r this reason, a visual scorer will use information from eye movements (EOGs) or muscle tone (EMG) to make the distinction. In our study, we derive a R E M probability, based on ' E M G observations', which can then be employed to separate areas of R E M from those of light sleep. As proposed by KEMP et al. (1987) we use a simple model of muscle tone in which low activity (during muscle inhibition in R E M sleep) and high activity (during n o n R E M sleep and wakefulness) are viewed as two modes in a double Gaussian distribution. For any value of muscle tone, a corresponding R E M probability Pe,,a can thus be assigned. The time course of this probability is also shown in Fig. 10; note the correlation between this and the L#n trace. Areas for which both are high correspond to R E M sleep, areas where ~ R is high but P~m0 is low correspond to light sleep, and this is seen mainly at the onset of sleep.

6 A u t o m a t i c sleep staging To show that it is possible, if desirable, to use this method to produce an automatic system which replicates h u m a n sleep staging, we also constructed a classifier for 30 s sections of the EEG. We chose the h u m a n scoring convention where the sleep stage is a member of the set {W, R, 1, 2, 3, 4} (RECHTSHAFFENand KALES,1968). F r o m our training data we calculated the mean for 5e w, 5eR, ~ s and Pemg for each of the six h u m a n scored sleep stages (again, only nonartefactual sections were used) as tabulated below. Note the increase and decrease of likelihood with sleep stage and that Pemo essentially acts as a Boolean discriminator for the R E M stage. The average standard deviation was 0-2. Stage W R 1 2 3 4

"~w 0-8 0"2 0.5 0.1 0-1 0"1

.Le• 0-1 0.6 0-4 0.2 0.0 -0-1

~s 0.1 0-2 0.1 0-7 0.9 1.0

Pemg 0-0 0.8 0-2 0.1 0.1 0.0

During classification of a sleep record we can calculate a Euclidean distance measurement between the current likelihood values and the mean values shown in the table. A corresponding probability of association can thus be calculated for each h u m a n scored sleep stage from this set of distance measurement. We could make a classification at this point by picking the sleep stage with the minimum distance measurement and hence the highest probability, but this reliance on a priori probabilities does not reject unclear or artefactual information before a decision is made. The use of Bayesian smoothing, however, provides a set of a posteriori probabilities, such that unclear information from the present E E G segment (characterised by &e(t) falling far from any sleep stage means and hence uniformly low probability values) can be suppressed in favour of clear information from past or future (K~MP et al., 1987). Such smoothing, however, is optimised with respect to a particular model of the system (here a model of the transitions from one sleep stage to the next). At present, we have assumed a M a r k o v chain model, in accordance with our own findings and those of other authors (KEMP et al., 1987; LARSON and SCHUBERT, 1979). Results for two test subjects, X and Y, are shown in Fig. 11, and are presented with a resolution of 30s together with the corresponding h u m a n scored hypnograms. It is clear that the gross structure of sleep is well

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represented by our a u t o m a t e d system based on conventional h u m a n scoring. Although we have demonstrated that an automated h y p n o g r a m can be derived from our method of analysis, we believe that it is not the best format for detailed investigations of the sleep process, because of the p o o r temporal resolution and the limitation imposed by having discrete stages.

7 Conclusions In this paper we have proposed a model of the E E G as a continuous process with eight halting states, in a 100dimensional space. The model is based on the parameterisation of consecutive i s E E G segments in terms of K a l m a n filter coefficients. These coefficients are then used as inputs to a self-organising network for the m a x i m u m separation of the different types of signal activity in a highdimensional output-space. This clustering technique required no a priori assumptions or rules, and was performed in an unsupervised manner. We also argued that the eight halting states obtained with our model are representative of a set of three competing processes which describe the macro-structure of sleep. The brain state during sleep (based on an observation of its electrical activity) can then be described as a time-varying superposition of these three processes, namely ug(t) = ~s(t)Ugs + s

+

~w(t)Ugw

where &o are likelihood values and the functions qJ~ are representative of the dynamics of each of the unmixed states. The brain state characterised by WR is itself separable into two states on the basis of E M G observations; one occurring during R E M sleep when central inhibition of muscle tone is present, and the other during light sleep when this inhibition is not seen. The halting state model and the above likelihood values arise as a result of the analysis of real EEGs, with no prior rules concerning features, amplitude or frequency characteristics. We have also shown this set of likelihoods can be used to classify segments according to criteria such as those employed in visual scoring. It is known, however, that the latter inevitably produces suboptimal decisions (KEMP et al., 1987) and we believe that our method will help make quantification of the sleep process more objective, especially in cases where the rules of visual scoring break down, such as with patterns of disturbed sleep and with the elderly. Acknowledgments--The authors would like to thank the UK Science and Engineering Research Council for their support of one of the authors and Dr W. L. Davies of Oxford Medical Ltd for loan of some of the equipment used in this study. Thanks should also go to Dr J. Stradling of the Churchill Hospital, Oxford, for valuable discussions and comments.

References

BARLOW,J. S. (1985) Methods of analysis of nonstationary EEGs, with emphasis on segmentation techniques: a comparative review. J. Clin. Neurophysiol., 2, (3), 267-304. BODENSTEIN,G. and PgAETOgiUS, H. M. (1975) Pattern recognition of the EEG by adaptive segmentation. Part 1: segmentation and feature extraction. Proc. of the 2nd Symp. of the Study Group for EEG methodology, 449-459. BOnLIN, T. (1971) Analysis of EEG signals with changing spectra. Technical Report 18.212, IBM Nordic Lab, Sweden. Box, G. E. P. and JENKINS, G. M. (1976) Time series analysis: forecasting and control. Holden-Day. BROOMHEAD,D. S., LOWE, D. and WEBB, A. R. (1989) A sum rule

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satisfied by optimised feed-forward layered networks. RSRE Memo. 4341, Malvern, 1989. COHEN, B. A. and SANCES, A. (1977) Stationarity of the human electroencephalogram. Med. & Biol. Eng. & Comp., 15, 513518. COHEN, B. A. (1986) Biomedical signal processing. CRC Press, Boca Raton, Florida, USA. GATH, I. and BAR-ON, E. (1980) Computerized method for scoring of polygraphic sleep recordings. Comp. Prog. Biomed, 11, 217-223. HASAN, J. (1983) Differentiation of normal and disturbed sleep by automatic analysis. Acta Physiol. Scand, supplementum 1983, 526, 1-103. HASMAN, A., JANSEN, B. H., LAND~WEERD, G. H. and voN BLOKLAND-VOGEL-SANG,A. W. (1978) Demonstration of segmentation techniques for EEG records. Int. J. Biomed. Comput., 9, 311-321. JANSEN, B. H., HASMAN,A., LENTEN, R. and VISSER,S. L. (1979) A study of inter- and intraindividual variability of the EEG of 16 normal subjects by means of segmentation. Amsterdam, 2nd European congress on EEG and Neurophysiology, Elsevier, 617-628. JANSEN, B. H. (1979) EEG segmentation and classification: an explorative study. PhD thesis, Free University of Amsterdam. JANSEN, B. H., BOURNE, J. R. and WARD, J. W. (1981) Autoregressive estimation of short segment spectra for computerized EEG analysis. IEEE Trans., BME-28, 630-638. KALMAN, R. E., (1960) A new approach to linear filtering and prediction problems. Trans. of Am. Soc. Mech. Eng. (Series D), 82, 35-34. KALMAN, R. E. and BucY, R. S. (1961) New results in linear filtering and prediction theory. Trans. of Am. Soc. Mech. Eng. (Series D), 83, 95-108. KEMP, B., GRONEVELD, E. W., JANSSEN, A. J. M. and FRANZEN, J. M. (1987) A model based monitor of human sleep stages. Biol. Cybern., 57, 365-378. KOnONEN, T. (1982) Self-organized formation of topographically correct feature maps. Biological Cybernetics, 43, 59-69. KOHONEN, T. (1990) The self-organizing map. Proc. IEEE, 78, (9), 1464-1480. LARSON,M. J. and SCHUBERT,B. O. (1979) Probabilistic models in engineering sciences II. Wiley, New York, Chichester, Brisbane, Toronto. LIPPMANN, R. P. (1987) An introduction to computing with neural nets. IEEE ASSP Magazine, 5-22. LOWE, D. and WEBS, A. R. (1990) Exploiting prior knowledge in

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network optimization: an illustration from medical prognosis. Network: Computation in Neural Systems, 1, (3), 299-323. PAPOULIS, A. (1984) Probability, random variables, and stochastic processes. McGraw-Hill. RECHTSCI-tArFEN, A. and KALES, A. (1968) A manual of standardized terminology, techniques and scoring system for sleep stages of human subjects. Technical report, UCLA, Los Angeles, USA. ROBERTS, S. (1990) Analysis and interpretation of the human sleep EEG. Internal Research Report, Medical Engineering Unit, University of Oxford. SKAGEN, D. W. (1988) Estimation of running frequency spectra using a Kalman filter algorithm. J. of Biomed. Eng., 10, 275279. WEga, W. B. and D~aELOW, L. M. (1982) A modified method for scoring slow wave sleep of older subjects. Sleep, 5 : 195-199. WIDROW, B. and STEARNS,S. D. (1985) Adaptive signal processing. Prentice-Hall, New Jersey. ZADEn, L. A. (1965) Fuzzy sets. Information and Control, 8, 338353.

Authors" biographies Stephen Roberts graduated with a degree in Physics from Oxford University. He worked for two years in the research department of Oxford Medical Ltd and since 1989 he has been engaged in research towards the degree of D.Phil. within the Medical Engineering Unit of Oxford University. His research interests include biomedical signal processing, artificial neural networks, brain function during sleep and nonlinear dynamics. Lionel Tarassenko graduated from Oxford with a degree in Engineering Science and then worked in an industrial research laboratory on the new digital signal processing techniques. He returned to Oxford to undertake research in medical electronics and physiology and, since being appointed a University Lecturer in 1988, he has continued to work on the application of electronics to medicine. However, his main research interest has been the development of neural network techniques and their application to a wide range of problems.

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New method of automated sleep quantification.

Since its discovery some 50 years ago, the electro-encephalogram (EEG) has formed the basis for classification of sleep into several stages, either la...
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