1.8.3.02

Sleep Dynamics and Sleep Disorders: a SyntacticApproach to Hypnogram Classification

Ana L. N. Fred* T. Paiva*** Instituto de TelecomunicaEöes, DEEC, Instituto Superior Tdcnico

IST - Torre Norte, Av. Rovisco Pais, 1096 Lisboa Codex PORTUGAL** Centro de Estudos Egas Moniz, Hospital de Santa Maria, Lisboa PORTUGAL

ABSTRACT: This paper addresses the problem of au-

tomatic classification of sleep macrostmcture, as given bythe hypnogram. The proposed approach is based on themodeling of sleep dynamics in terms of stochastic context-free grammars, automatically inferred from the existinghypnogram data. These grammars are then applied in thediscrimination between a control group and six patholog-ical populations. A global performance of 84Vo of correctclassifications is achieved.

INTRODUCTIONSleep macrostructure is composed of patterns in

physiological variables. These patterns are usu-

ally classified into sleep stages, according to the

Rechtschaffen and Kales (R&K) criteria tl] Thehypnogram is the graphical representation of the evo-

lution of sleep stages along the night. The existenceof a typical organization of sleep stages is well known.Some authors have characterized it in terms of statis-tics of transitions between stages, latencies and du-rations. Markovian models have been applied to de-

scribe the transition mechanisms [2]. Concerning the

assessment of sleep quality, tests are usually based onsleep efficiency parameters (global statistics) derived

from the hypnogram.Our perspective is to view the hypnogram as expres-

sion of a language, modeled and analysed in termsof stochastic grammars. We have shown, in previ-ous work [3, 4], the adequacy of syntactic modelingin automatic sleep analysis. Reference [3] concerns

the application of this approach to the comparison ofa population of normals with a population of psychi-

atric (dysthymic) patients. From the structural pointof view, grammars proved to be a natural way of representation, being able to describe the tendencies ofsleep cyclicity and having higher discriminating capac-

ity than statistical tests based on sleep efficiency pa-

rameters. This methodology has been further refinedby the introduction of a priori information in the pro'cess of grammar inference [5] and by modeling stage

duration in terms of attributed grammars [4]. This ad-

Medical & Biological Engineering & Computing Vol. 34, Supplement 1, Part 1, 1996The 1Oth Nordic-Baltic Conference on Biomedical Engineering, June 9-13, 1996, Tampere, Finland

ditional information has been useful in the classifica-

tion of borderline situations, leading to reduced errorprobability. In this paper stochastic grammars are ap-

plied in the discrimination between seven populations:normal; dysthymia; sleep apnea; generalized anxiety;fibromyalgia; panic disorder; Parkinson disease.

METHODFigure 1 describes schematically the methodology

used.Hypnogram data are translated into string descrip-

tion by selecting as symbols of the language the set

{W, 1,2,3,4, R}, in correspondence with the sleep

stages: wakefulness, stage I,2,3, and 4 non-REM, and

stage REM - Rapid Eyes Movements. Seven popula-

tions were used: normals (39 samples), dysthymic (22

samples), apnea (53 samples), anxiety (21), fibromyal-gia (29), panic (12) and parkinson (20 samples).

For each population, a stochastic context-free gram-mar was inferred using Crespi-Reghizzi's method [6].The estimation of rules probabilities was based on the

method of stochastic presentation. Arbitrary samples

r were then classified using Bayes decision rule:

Decide r€ Population;if Pr(G;lt) > Pr(G1lr), i *i

with

Pr(G ;l') = P r(xl9;) P'r(G i)

Pr(r)

where Pr(xlGt) is the probability of r according tothe rules in the grammar representing population i,and Pr(G;) is the a priori probability of population i'

RESULTSTable 1 shows the results of classifications obtained.

The value in row f , column j represent the percentage

of elements of population i classified as 7. The last

column gives the total error rate for the population ofthe corresponding row.

395

Hlpnograns

'w12w123234313131 ...

Stochaslic Grammarc

Figure 1: Methodology in hypnogram analysis andclassification.

Results show clear differences in the temporal or-ganization of sleep stages for the several populationsunder study, as error rates for each population pairare lower than 13%. When considering the discrimi-nation between the seven populations simultaneously,the highest error rate is obtained for the normal pop-ulation (28.2%\, which corresponds to false alarms.

CONCLUSIONS

A fully automatic approach for the modeling andclassification of sleep macrostructure, as given by thehypnogram, was described and applied in the clas-sification of six pathological populations and a con-trol group. According to the proposed methodology,sleep dynamics were modeled by stochastic context-free grammars, inferred from the hypnogram data byan automatic procedure. No a priori informationwas introduced. Using a Bayesian decision criterion,hypnograms from the several populations were classi-fied by determining the probability of being generatedby each of the candidate grammars representing theseveral groups. The inferred grammars showed cleardifferences between the populations under study, be-ing able to discriminate between them.

References

[1] A. Rechtschaffen and A. Kales. A Manual ofStandardized Terminology, Techniques and Scor-ing System for Sleep Stages of Human Subjects.U. S. Government Printing Office, WashingtonDC. 1968.

[2] B Kemp and H. A. Kamphuisen. Simulation ofhuman hypnograms using a markov chain model.Sleep, 9:405-414, 1986.

[3] A. L. N. Fred and J. M. N. Leitäo. Use of stochas-tic grammars for hypnogram analysis. In Proc, ofthe 1lth IAPR Int'l Conference on Pcttern Recog-nition, pages 242-245, August L992.

[4] A. L. N. Fred and J. M. N. Leitåo. AttriburtedGrammars in Hypnogram Analysis. ln Proc, ofthe Int'l Conference on Systems, Man and Cyber-netics, Vancouver, October 1995.

[5] A. L. N. Fred and J. M. N. Leitäo. Solomonoffcoding as a means of introducing prior informa-tion in syntactic pattern recognition. In Proc, ofthe 12th IAPR Int'l Conference on Pattern Recog-nition, Jerusalem, October 1994.

[6] K. S. Fu and T. L. Booth. Grammatical inference:Introduction and survey. IEEE Trans. Sgstems,Man and Cybernetics, SMC-5, January 1975.

Medical & Biological Engineering & Computing Vol. 34, Supplement 1, Part 1, 1996The 1Oth Nordic-Baltic Conference'on Biomedical Engineering, June 9-13, 1996, Tampere, Finland

Classif ication Probability

Norm. Lryst. Apn. Anx. .F'rbr. I,an. Park. .tirr.N ormalDysthymiaApneaAnxietyFibromyalgiaPanic disorderParkinson

/ I.ö4.5D./4.86.90

10.0

81.8J./4.83.48.35.0

62. 5.10

86.80

10.30

10.0

10.39.11.9

90.53.40

5.0

12.80

D./0

86.20

5.0

2.60000

9t.75.0

2.60

1.9000

85.0

28.213.6L3.29.513.88.315.0

Table 1: Classification results (in percentage).

396