J . Sleep Rex (1992) 1, 128-131

The duration of REM sleep episodes in normal sleep

A N D R E W J . B E L Y A V I N * Royal Air Force, Institute of Aviation Medicine, Farnborough. Hampshire, UK

Accepted in revised form 31 January 1992; received 28 December 1991

SUMMARY The distributions of the durations of the first 3 REM sleep episodes have been analysed using a total of 134 overnight sleep recordings from 10 subjects. From investigation of the length of uninterrupted episodes of stage REM, it is shown that arousals t o stage 0/1 could play an important part in the process of REM exit, and that by the middle of the sleep period, these arousals probably occur according to a Poisson process. During the first and second REM episodes a more complex process appears t o be at work, which could reflect increased pressure for slow wave sleep. These findings suggest that the duration of a REM episode is determined by a process that has a large stochastic element, which is not necessarily tied to REM entry.

KEYWORDS arousals. duration of REM episodes, REM sleep

INTRODUCTION

The cyclic alternation between REM and non-REM sleep has been long recognized. The way in which this cycle is regulated, however, is not well understood. McCarley and Massaquoi (1986) describe a possible oscillatory control mechanism which would mediate both entry into and exit from the REM state. Since the mechanism is expressed as the solution to a set of differential equations, the times of REM entry and REM exit are precisely prescribed, unless the mechanism is modified through the introduction of a stochastic element, such as that proposed by Massaquoi and McCarley (1990). Achermann et al. (1990) propose a mechanism for REM entry and exit as part of a more general model of the sleep process. The mechanism for REM entry and exit is prescribed as an external trigger. In addition the REM sleep episode is based on a threshold for a noisy slow wave activity signal, and therefore corresponds to a simple form of stochastic model.

Empirical studies of REM sleep (e.g. Belyavin and Nicholson 1987; Nicholson et al. 1989) suggest that while the REM cycle is clearly reproducible, there is a substantial stochastic element determining both onset and duration of REM sleep. The bimodality of the distribution of the latency to REM under some circumstances, combined with the general cyclical appearance of REM episodes, supports the idea that a regular trigger is at least partially responsible for REM entry. The aim of the present study is to characterize the duration of REM sleep episodes, and thus describe the relationship between REM entry and REM exit. * Correspondence: Dr A. J. Belyavin, Royal Air Force Institute of Aviation Medicine, Farnborough, Hants, GU14 6S2, UK.

METHODS

The analysis was based on the sleep recordings from 10 subjects for placebo nights from the series of drug studies described in Nicholson et al. (1989). The subjects were selected as those for whom 10 or more such nights were available.

The subjects were healthy male volunteers aged between 18 and 29 years at the time of the recordings, and they were familiar with the laboratory and recording techniques. They were not taking any medication, and were required to refrain from napping and undue exercise, and to abstain from alcohol the day before and during each experimental day; beverages containing caffeine were avoided from midday until after the overnight sleep. Each sleep recording was separated by at least 1 week.

The individual bedrooms were lightproofed and sound attenuated, and the temperature and humidity were controlled. At least two channels of electroencephalographic activity were recorded (C4-A1 and 01-A2 or ozPz-03), together with bilateral electro-oculograms and the submen- tal electromyogram, on a Grass 8-10 EEG machine in an adjoining room. Each sleep record was scored independ- ently into 30-s epochs by two analysts according to conventional criteria (Rechtschaffen and Kales 1968). The onset of sleep (stage 2) was defined as the appearance of the first sleep spindle or K complex, and the latency to REM sleep as the interval from sleep onset to the first REM period.

The analysis was restricted to those sleeps for which the first REM event occurred before 102.5 min after sleep onset, corresponding to those without a missed first REM sleep episode according to the definition in Belyavin and

128

The duration of REM episodes in normal sleep 129

Nicholson (1987). A total of 134 sleeps remained after application of this criterion.

The duration of the first three REM sleep episodes was calculated for each sleep, where interruptions to REM of less than 10min duration were treated as part of the episode. The number of sequences of half minutes allocated exclusively to stage REM for each of the sleep episodes was then counted, and the length of the first uninterrupted sequence determined.

RESULTS

The distribution of the durations and number of interruptions, including the last for the three R E M episodes was calculated and summary statistics are displayed in Table 1.

The durations of the REM episodes were investigated using Analysis of Variance (ANOVA), identifying subjects as a source of variation. It was found that the mean durations of the first two R E M episodes differed with subject ( F = 3.46, d.f. = 9, 124, P < 0.001, and F = 3.74, d.f. = 9, 124, P < 0.001, respectively) while the third duration did not. Comparison between the durations of the three REM episodes indicated that the mean duration of the second REM episode was longer than the first ( P < 0.001), while the third and the second did not differ. As an extension to the ANOVA, the number of interruptions was included as a covariate, to test for an association with duration. It was found that the number of interruptions and duration were positively associated for all three REM episodes (P < 0.001 in all cases).

The duration of the first uninterrupted sequence was investigated in a similar manner. It was found that the length was dependent on subject for the first two REM episodes (P<O.Ol in both cases), but was not for the third. If the duration were determined by a stochastic process which yielded a uniform probability of terminating with time, duration would be distributed in the geometric form. The distributions of duration were tested for this form, despite the inhomogeneity implied by the results of the ANOVA. A x2 goodness of fit test was applied by dividing the distribution into 5 bins. The results of the fit are displayed in Table 2. The distributions are not a good fit for

Table 1 (n = 134 nights)

Number of interruptions and durations of REM cpisodes

Number Interruptions Durarion (min) REM .___

Episode Mean s . d . Min. Max. Mean s . d . Min. Max.

1 2.11 1.22 1 6 12.93 7.68 0.5 37.5

3 3.68 2.08 I 13 30.50 15.86 1,s 89.0 2 3.34 1.65 1 10 26.35 11.97 5.5 67.0

Note: Interruptions includc the exit from the REM cpisodc

Table 2 REM

Distribution o f duration of first uninterrupted episode of

R E M E P l REMEPZ R E M E P 3

Range (min)

0-1.1 1.1-3.1 3.1-6.1 6.1-10.1

>10.1 Mean s .d.

_ _ ~ ~

Obs. EXQ.

~~

36 22.3 20 34.1 31 32.6 20 23.3 27 21.7

5.75 5.57

Range (mln 1

~~

0-1.6 1.6-4.6 4.6-8.6 8.6- 12.6

>12.6

Obs. Exp.

- ~~

27 24.0 25 35.9 27 30.3 32 17.9 23 25.9

7.85 6.18

~ _ _ _ Obs. Exp.

16 24.6 37 36.5 38 30.4 22 17.8 22 24.7

7.65 7.13

Obs. = Observed count in the range. Exp. = Expected count for a geometric distribution

REM episodes 1 and 2 with chi-squared values of 16.09 (d . f .=4 , P<0.01) and 15.48 ( d . f . = 4 , P<0.01) , respec- tively. However, the fit is adequate for REM episode 3, x2 = 5.78, suggesting that the interruptions to REM episodes have a uniform probability of occurring in time, at least for the third R E M episode.

If the episode were composed of a series of sequences of uninterrupted REM, distributed in the geometric form, and the interruptions were short, the duration of the whole episode would be approximately distributed in the Gamma form with parameter equal to the number of interruptions. The observed distributions of duration of the three REM episodes are displayed in Fig. 1. For none of the three REM events is the number of interuptions constant and there is evidence for variation of the parameters over the population. Although all three distributions resemble the Gamma form, any fit is unlikely to be completely satisfactory.

After examining the number of interruptions in each of the three REM episodes, it was decided to test whether the duration of the first REM episode could be distributed in the Gamma form with parameter 2, the second with parameter 3 and the third with parameter 4. The scale parameter was estimated in each case from the distribution mean and the assumed Gamma parameter. The range was divided into 6 intervals and a x’ test with 5 degrees of freedom was used to assess goodness of fit. The values found were 10.3, 13.1 and 7.4 for the three REM events respectively, rejecting an adequate fit for period 2

Finally the nature of the interruptions to REM episodes was considered by counting the number of transitions from stage REM to stage non-REM, stage REM to stage 0/1, and stage 0/1 after REM to stage non-REM (2, 3 or 4). For the first 100min of sleep, 54.9% of interruptions to REM were stage 0/1, while during the third 100 min, 87.8% were of the same kind. Similarly, for the first 100 min, the proportion of final exits from the REM state to the non-REM state which were direct was 56.9%, while during the third 100min the

( P < 0.05).

130 A . J . Belyavin

fraction was 33.2%. These figures d o not add up to 100% because the latter figures for exit are included in the count of interruptions.

DISCUSSION

The variability of the durations of all three R E M episodes strongly suggests that R E M is not under any form of rigid control, such that once the R E M state has been entered, the time of exit from R E M is prescribed. Equally, if termination of the complete REM episode were determined by a uniform probability with time, e.g. by a noisy signal exceeding a fixed threshold value, the shape of the distributions of REM duration would be even more long-tailed and nearer the exponential form than those exhibited in Fig. 1.

Examination of the length of the first uninterrupted period of stage REM suggests that for the third R E M episode at least, interruptions to REM occur as a Poisson process to a first approximation. The data on transitions indicate that the majority of these interruptions are to stage 0/1. Given that exits from REM to non-REM are more frequently through stage 0/1 in the third 100 min of sleep, it is possible that such arousals play a part in the transition from REM to non-REM. The evidence on the distribution of REM duration provides some support for this hypothesis; if interruptions were the motor of REM exit, the duration of a REM episode would be distributed in the Gamma form with parameters dependent on the number of interruptions to REM sleep, and would depend on the number of interruptions, as observed. While the overall distribution would be a mixture of Gamma distributions with different but similar parameters, it is likely that it would not deviate strongly in shape from a distribution of the same form with parameters close to the mean, as observed for the third REM episode.

If the probability of exit from an interruption to non-REM sleep was uniform with time through the R E M period, the number of interruptions would be distributed in the geometric form, which is not consistent with the means and standard disributions given in Table 1. The observed distribution is consistent with a probability which changes as the REM episode proceeds, and it is possible that this reflects a homeostatic process controlling R E M sleep, such as that indicated by Belyavin and Nicholson (1987). Such a structure would be better described by a form of semi-Markov process, rather than the solution to a differential equation.

The argument over the mechanisms for R E M exit in the earlier REM episodes is not as easy to develop, due to the inhomogeneities between the subjects. Clearly both the first REM episode and the first uninterrupted R E M sequence in that event is shorter, and other mechanisms are probably at work. The most plausible candidate is the higher pressure for slow-wave sleep at this period of the night.

Overall the structure of the third R E M episode suggests

In

al

In

n - r 0

0 10 20 30 40 50 60 70 80 90

Figure 1. Histograms of the durations of the first three REM episodes in minutes. N = 134 nights. (a) REM episode 1, (b) REM episode 2, (c) REM episode 3.

that by the time that pressure for slow-wave sleep has been reduced, exit from REM sleep is at least partially mediated through arousal to stage 0/1. The distribution of the durations of REM episodes rules out both precise control of REM duration, based on a n exit trigger tightly related to an entry trigger, and a simplistic stochastic model of R E M exit based on a uniform probability with time through the episode. The intervention of a homeostatic control mechanism cannot be ruled out.

REFERENCES

Achermann, P., Beersma, D. G. M., Borbtly, A. A. Thc two-process model: ultradian dynamics of sleep. In: J . A . Horne (Ed.) Sleep '90. Pontenagel Press, Bochum, 1990: 296-300.

Belyavin, A.J . and Nicholson, A. N . Rapid eye movement sleep in man: Modulation by benzodiazepines. Neuroyharmacology, 19x7,

McCarley, R. W. and Massaquoi, S. G. A limit cycle mathematical model of the REM sleep oscillator system. Am. J . fhysiol., 1986,

26: 485-491'.

25 1 : R 101 1 -R1029.

The duration of REM episodes in normal sleep 131

Massaquoi, S. G. and McCarley, R . W. Resetting the R E M sleep oscillator. In: J.A. Horne (Ed.) Sleep '90. Pontenagel Press, Bochum, 1990: 301-305.

Nicholson, A. N. , Belyavin, A. J . and Pascoe, P. A . Modulation of rapid eye movement sleep in humans by drugs that modify monoaminergic and purinergic transmission. Neuropsycho- pharmacology, 1989. 2: 131-143.

Rechtschaffen, A. and Kales, A . A manual of standardised methodology, techniques and scoring system for sleep stages of human subjects. United States Department of Health, Education and Welfare, Public Health Service, Bethesda, 1968.