Journal of Biological Rhythms, Vol. 4, No. 2 , 1989, pp. 149-160

Sleep Initiation and Initial Sleep Intensity: Interactions of Womeostatie and Circadian ~echanisms'

Alexander A. Borbkly, Peter Achermann, Lorenz Trachsel, and Zrene Tobler P Institute of Pharmacology, University of Zürich, CH-8006 Zürich, Switzerland

Abstract Sleep initiation and sleep intensity in humans show a dissimilar time course. The i

propensity of sleep initiation (PSI), as measured by the multiple sleep latency test, remains at a relatively constant level throughout the habitual period of waking or exhibits a midafternoon peak. When waking is extended into the sleep period, PSI rises rapidly within a few hours. In contrast, sleep intensity, as measured by electroencephalographic slow-wave activity during naps, shows a gradual increase during the period of habitual waking. In the two-process model of sleep regulation, it corresponds to the rising limb of the homeostatic Process S. We propose that PSI is determined by the difference between Frocess S and the threshold N defining sleep onset, which is modulated by the circadian process C. In contrast to a previous version of the model, the parameters of H (amplitude, phase, skewness) differ from those of threshold L, which defines sleep termination. The present model is able to simulate the time course of PSI under baseline conditions as well as following recovery sleep after extended sleep deprivation. The simulations suggest that during the regular period of waking, a circadian process coun- teracts the increasing sleep propensity induced by a homeostatic process. Data obtained in the rat indicate that during the circadian period of predominant waking, a circadian process prevents a major intrusion of sleep.

Sleep in humans typically occurs during a specific portion of the 24-hr cycle. In the absence of time cues, the rest-activity rhythm persists with a period that usually deviates from 24 hr (Aschoff, 1965). It has been clearly recognized that "[a] s leep wake cycle is not a prerequisite for the rhythmicity of many functions within the human body, and those rhythms are in most cases not rigidly bound to sleep"

I (Aschoff el al., 1975, p. 53). The internal desynchronization of the sleepwaking cycle from other rhythms (e.g., body temperature) suggests that separate self-sustaining oscillators are involved in the temporal organization of physiological processes.

Models to account for the circadian rest-activity rhythm were proposed in early papers. Thus Aschoff and Wever (1962) advanced the hypothesis that the circadian activity and rest periods, and their changes under experimental conditions, can be simulated by applying a threshold to a sinusoidal process. Depending on the thresh- old level and the amplitude of the oscillation, different activity-rest ratios are ob- tained. Twenty years later, Kronauer et al. (1982) proposed a similar concept in the

1 . This paper is dedicated to Professor Jürgen Aschoff on the occasion of his 75th birthday.

framework of their two-oscillator model. The values of an oscillatory function ex- ceeding a threshold were defined as waking, the subthreshold values as sleep. Al- though these models were useful for analyzing circadian aspects of sleep and rest regulation, their major limitations was that they did not address the homeostatic aspect.

At the Ringberg Symposium on Vertebrate Circadian Systems (Aschoff et al., 1982), a new model was presented in which the combined action of a circadian and a homeostatic process determines sleep propensity (Borbely, 1982a). This two- process model was initially developed for rat sleep, and was then more explicitly formulated for human sleep (Borbely, 1982b). The characteristics of the homeostatic process (Process S) were derived from physiological data. One of the main param- eters is slow-wave activity of the sleep electroencephalogram (EEG), which was shown to be a function of the duration of pnor sleep and waking. Slow-wave activity declines exponentially in the Course of the sleep period, and thus may reflect the progressive decrease in sleep intensity (Borbely et al., 1981). When sleep follows upon an extended waking period, the initial level of slow-wave activity is increased. This observation suggests that Process S increases gradually during waking. Recent experiments have confirmed this hypothesis (Beersma et al., 1987; Dijk et al., 1987a; Knowles et al., 1987). Naps occurring at progressively later times during the day show an increasing trend in slow-wave activity. The rise can be closely approxi- mated by a saturating exponential function (Fig. 1).

Daan and collaborators proposed a quantitative version of the two-process model (Daan and Beersma, 1984; Daan et al., 1984). They determined the time constants of Process S on the basis of the sleep EEG, and defined the characteristics of the sleep termination threshold L, which is modulated by a circadian process. Based on sleep duration data from a study in which sleep had been initiated at various phases of the 24-hr cycle (Akerstedt and Gillberg, 1982), L was specified as a skewed sinusoidal function with a steeply rising and a slowly declining part (Daan et aE., 1984). To specify also the time of sleep onset, a second threshold H, delimiting the rising portion of S, was introduced into the model. Since H could not be derived from experimental data, its amplitude and skewness were assumed to be identical to those of L. The homeostatic parameter S now oscillated between the thresholds N and L. Varying the amplitude of the circadian moduiation and the distance between H and L permitted a circadian, a circabidian, or a polyphasic sleep-waking pattern to be obtained (Daan et al., 1984). Adjusting the parameters and superimposing a noise component upon the thresholds made it possible to simulate internal desyn- chronization, which occurs occasionally under conditions devoid of time cues (Aschoff, 1965). In contrast to other models (Wever, 1979; Kronauer et al., 1982), not more than a single self-sustained circadian pacemaker was required.

In the present study, we attempt to specify the upper threshold W in more detail. Our approach is based on the assumption that the propensity of sleep initiation (PSI) is determined by the interval (S - H) between the upper threshold and Process S. Although this assumption was already implicit in the previous formulation of the model (Daan et al., 1984; Fig. 61, no attempt was made at that time to simulate the

SLEEP INITIATION AND SLEEP INTENSITY

LEEP DEPRIVATION

TIME OF DAY (HOURS)

FIGURE 1. Dissimdanty between the time Course of the sleep intensity parameter (Process S) and that of the propensity of sleep initiation (PSI). Process S rises during waking and declines during sleep. The rise and decay rates (hr-') of the exponential functions have been derived from the changes of EEG slow-wave activity. PSI has been determined by the multiple sleep latency test administered at 2-hr intervals between 7 and 17 hr of the baseline day, and between 5 and 17 hr after a night without sleep. The 24-hr value comesponds to the sleep latency of the baseiine sleep period. The curve (thin continuous line) connects mean values (n = 6-43). Note thai sleep latency is plotted from top to bottom. To facilitate cornparison with Process S, the baseline values (7-17 hr) are replotted on the right side of the figure (thin intempted line). Process S is shown for the regular waking period and for sleep deprivation (heavy continuous line), as well as for a regular sleep period (24-7 hr) and the subsequent waking period (heavy intempted line). Vertical lines dehmit sleep and waking.

PSI. In the present study, gross estimates of the parameters of M have been obtained from empirical data.

TME MULTIPLE SLEEP LATENCY TEST AS A MEASURE OF PSI

The multiple sleep latency test (MSLT) is a procedure widely used to assess the PSI W during the day. The test was developed by Carskadon and Dement (1979) and has

been recently reviewed (Carskadon and Dement, 1987). In the lest situation, the subject typically lies down in a darkened room and dtempts to fall asleep. W e n sleep sets in, the subject is awakened, and the test is repeated at 2-hr intervals throughout the day. Sleep latency is used as an objective measure of the PSI.

The MSLT has been shown to be a sensitive indicator of long-term sleep ho- meostasis. Sleep restriction during several nights induced a progressive reduction of sleep latency, whereas sleep extension had the opposite effect (Carskadon and De- ment, 1982). Total sleep loss reduced the Scores to very low values (Carskadon and Dement, 1979, 1982).

Examination of the time course during the day in various studies shows that a midafternoon trough was conspicuous in some cases (e.g., Carskadon and Dement, 1979, Fig. 4, B-1, R-2; Richardson et al., 1982; Dijk et al., 1987a), but not in all (e.g. Carskadon and Dement, 1979, Fig. 4, B-2; Borbely et al., 1985). When waking was extended beyond the habitual bedtime, sleep latency showed a rapid decline within a few hours (Carskadon and Dement, 1979; Richardson et al., 1982; Borbely et al., 1985) and remained at a low level (see Fig. 1).

DISSIMILAR TIME COURSE OF PROCESS S AND PSI

The time course of Process S and of PSI is shown in Figure 1 for a regular and an extended waking period. The S curve is based on the time constants of the model, which are in close correspondence with experimental data (Borbely et al., 1981; Beersma et al., 1987). For the PSI curve, the sleep latency values obtained by the MSLT and the recording of the baseline night (bedtime at 24 hr) have been used (Borbely et al., 1985). Note that in the figure, sleep latency has been plotted so that the values decrease from bottom to top in order to represent in both curves a higher sleep pressure by higher values. The two curves show a dissimilar time course. Whereas Process S increases progressively throughout the waking period, PSI re- mains at a fairly constant level. Extension of waking beyond the habitual bedtime induces a sharp rise in PSI from 24 hr to 5 hr. The curve is at a ceding level (i.e., sleep latency is at a minimum) throughout the remaining part of the day.

SIMULATION OF PSI

Figure 2 shows the simulation of PSI by the two-process model. The parameters of S and L con-espond to those in the original version (Daan et aE., 1984). The S curve differs from that in the previous model in that it does not attain the upper threshold H at sleep onset, since under everyday life conditions bedtime is determined by clock time, personal habits, social conventions, anticipated wake-up time, and so on, rather than exclusively by a physiological process. PSI is represented by the differ- ence between S and H. The amplitude and skewness of H have been adjusted in order to generate a uniform level of S - N during most of the waking period (Fig. 2, lower panel). When waking is extended beyond the regular bedtime, the S - H curve rises steeply to its ceiling level, which corresponds to the minimum duration of sleep latency. Thus the time course of S - N is similar to that of sleep latency shown in Figure 1. A comment is wan-anted for the initial part of the curve (7-10 hr) that follows upon a regular sleep period. The rising trend in this section does not correspond to the data. Wowever, PSI in the first 2-3 hr after sleep termination may be elevated as a consequence of prior sleep (see, e.g., Borbely et al., 1985,4-hr sleep schedule). "Sleep inertia" as a further factor influencing vigilante during the first 2-3 hr &er sleep termination has been recently incorporated into the two-process model by Folkard and Akerstedt (1987). Its effect is indicated by a dotted line in the lower panel of Figure 2 to suggest that it may cornpensate the rising trend of S - H.

In the simulation shown in Figure 3, H is represented by a sine function. This

SLEEP INITIATION AND SLEEP INTENSITU

U = 0 0 0.0

t- > s SLEEP DEPRIVATION L I- "'5 z - / - -

W a a g % Q ,:

- 0.5 7 13 19 1 7 13

TIME OF DAY (HOURS)

FIGURE 2. Simulation of PSI during a regular waking period and during sleep deprivation. The sleepwaking schedule corresponds to that shown in Figure 1. Top panel: Process S rises during waking and declines during sleep according to exponential functions. The regular sleep period starts at 24 hr and is terminated at 7 hr when S intersects the threshold L. The thresholds of sleep onset (H) and of sleep termination (L) are modulated by a ckcadian process (C). However, the amplitude, skewness, and phase of N and L differ. Bottom panel: The propensity of sleep initiation is assumed to correspond to S - H. The curve rernains at a fairly constant level during the waking period and rises rapidly to the ceiling level (corre- sponding to zero; thin horizontal line) dunng sleep deprivation. To facilitate the comparison

& of the curves, the baseline values (7-17 hr) are replotted on the right side. The dotted line connects the values at the beginning and the end of the sleep penod. A decaying sleep inertia is assumed to prevail during the first hours of waking (lef side, dotted curve) offsetting the initial rising part of S - H.

modification results in a prominent rise of the S - H curve in the afternoon, and thus is able to simulate the rnidday peak of PSI that has been obseßred in various studies.

Subjects living under conditions without time cues are known to delay their bedtime so that it comesponds to the minimum of their body temperature rhythm (Aschoff et al., 1967). In the context of the present simulations, "physiological bedtime" is defined by the intersection of Process S with the upper threshold H. It

BORBELY ET AL.

1 0

SLEEP DEP

7 13 19 1 7 13

TIME OF DAY (HOURS)

FIGURE 3. Simulation of PSI duning a regular waking period and during sleep deprivation. The sleepwaking schedule corresponds to that shown in Figure 1. The figure corresponds to Figure 2 with the exception of H, whish here is represented by a sine function. Note the rise in the S - H curve in midafternoon, corresponding to the daytime trough in sleep latency.

is evident from Figures 2 an$ 3 that this time point is a few hours later than the habitual bedtime and thus may account for its phase delay observed under conditions of free mn. In addition, the rnodel predicts a marked shortening of sleep latency. Zulley (1979) reported a significant reduction of the latency to stage 1 in three of five subjects as the zeitgeber was removed. Mthough these observations are consistent with the prediction, rnore detailed data are needed for its confirmation.

PSI AFTER RECOVERY SLEEP FOLLOWING PROLONGED SLEEP DEPRIVATION

Carskadon and Dernent (1979) applied the MSLT to investigate the effect of two nights of sleep loss on the PSI. It was a puzzling observation that after the first recovery sleep period, sleep latency initiagy remained at a low level, and then showed a progressively increasing trend. Commenting on these observations the

SLEEP INITIATION AND SLEEP INTENSITY

authors speculated "that both a night's sleep and an extended period of wakefulness are necessary to complete the recuperation process" (Carskadon and Dement, 1979, p. 504).

In Figure 4, we have simulated this result by using the model presented in Figure 2. It is assumed that due to the preceding extensive sleep deprivation period, Process S is still at a somewhat elevated level after recovery sleep in comparison to its level after the baseline sleep period (in the simulation, the initial level of S has arbitrarily been Set at 0.41 units). The close proximity of S to H results in a low S - H parameter (corresponding to a short sleep latency) during the first 6 hr of waking (sleep inertia is assumed to offset the initial rising trend). Due to the different rise rates of S and H, the differente S - H becomes more negative in the second two-thirds of the day

SLEEP IN THE RAT: DISSIMILAR TIME COURSE OF PROCESS S AND SLOW-WAVE ACTIVITY

Figure 5 shows the time Course of an EEG parameter (see Trachsel et al., 1988, for the methods) and of the simulated Process S in the rat. The curve connecting the

TIME OF DAY (HOURS)

FIGURE 4. Simulation of PSI after a recovery night following prolonged sleep deprivation. The curves are plotted as in Figure 2. Due to the raised initial level of S, PSI shows a gradual decline between 11 and 21 hr.

BORBEL Y ET AL.

125

0.60

>-

I-> -0I- 100 :00 .. 0« 0.450...... Sm

w UJ> UJ« 75S ..

:Cf)

SC-O

0.30z -~-l -;UJ 50 ~0 ww

0.15

24186o25

12

HOURS

FIGURE 5. EEG slow-wave activity and Process S in the rat. The EEG curve connects mean(n = 8) hourly non-REM sleep values of relative spectral power density in the 0.75-4.0 Hzband. The values are expressed as percentage of the mean level in the first light hour(= 100%). The procedure for computing the time course of Process S is specified in the text.The dotted curve connects the mean hourly values. The horizontal bars at the top and theverticallines delimit the 12-hr dark and light period.

hourly values of EEG slow-wave activity in non-REM sleep is at a fairly uniformlevel during the first 11 hr of the dark period, when the animal is predominantlyawake. Then the curve rises steeply and reaches a maximum in the second hour ofthe light period. A progressive decline folIows, which reaches a minimum at hour 11of the light period. The time course of Process S was computed from the sequenceof waking and sleep episodes in individual animals. It was assumed that S risesaccording to a saturating exponential function during waking episodes, and declinesin proportion to the cumulated EEG slow-wave activity within non-REM sleep ep­isodes. It was further assumed that S remains unchanged during REM sleep epi­sodes. Esimates from previous data (Tobler and Borbely, 1986) yielded a time con­stant of approximately 8 hr for the saturating exponential function that correspondsto the rising limb of S. This parameter is equivalent to the reciprocal value of the riserate rr (see Appendix). The declining part of Process S shows a good correspondenceto the decline of EEG slow-wave activity (Fig. 5). In contrast, the rising parts of thetwo curves are dissimilar, since the progressive increase of S is not paralleled by theEEG parameter.

The results lend themselves to at least two different interpretations. One couldsurmise that the buildup and decline of S in rats, unlike the same factors in humans,are not independent of the circadian phase. Thus, in order to account for the data,one has to assurne that during the first 11 hr of the dark period, S rises more slowlywithin waking episodes or declines more rapidly within non-REM sleep episodesthan during the rest of the 24-hr cycle. These arguments imply that one of the basic

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SLEEP INITIATION AND SLEEP INTENSITY

tenets of the two-process model, the independence of Process S from circadianphase, is not supported. As an alternative and more attractive interpretation, weassurne that the computed S curve does indeed faithfully represent Process S asdefined by the two-process model. As has been assumed for all simulations, EEGslow-wave activity within non-REM sleep episodes also retlects the change of S inthe dark period. However, due to a circadian "disturbing factor" that is present inthe dark period, slow-wave activity does not correspond to the level of S. Thisassumption is supported by arecent human study, in which EEG slow-wave activitywas experimentally reduced in the initial 3 hr of the sleep period by means ofacoustic stimulation (Dijk et al., 1987b). The remaining low level of slow-waveactivity corresponded to the change of Process S, whereas the rebound in the sub­sequent undisturbed part of sleep corresponded to both the change and the level ofS. The hypothetical circadian disturbance may exert an effect on rat sleep similar tothat ofthe slow-wave suppressing acoustic stimuli on human sleep. Moreover, in therat, the high-frequency EEG activity (10-25 Hz) in non-REM sleep whose level iselevated during a large part of the dark period (Trachsel et al., 1988) may be aphysiological index of the circadian "disturbing factor."

The similar time course of PSI in humans (Fig. 1) and EEG slow-wave activityin rats (Fig. 5) may be more than a coincidence. In the rat, non-REM sleep episodesdo not last longer than a few minutes (Trachsel et al., 1988), whereas in humans theirduration ranges from 60 to 90 min (Achermann and Borbely, 1987). It is thereforemore likely in rats than in humans that the manifestation of slow-wave activity isintluenced by processes affecting sleep initiation. Thus the dissimilar time course ofProcess Sand PSI in humans, and of Process Sand EEG in rats, may both begenerated by a circadian "disturbing factor" that in humans is retlected by themodulation of threshold H.

COMMENT

The present study showed that PSI can be simulated in the two-process model by thedifference between Process Sand the upper threshold H. It was evident, however,that the previous version of the model (Daan et al., 1984), in which the parametersof H corresponded to those of the lower threshold L, was inadequate for the presentpurpose; neither the sudden rise of PSI during extended waking nor its midafternoonpeak could be simulated. In the present version of the model, the amplitude, skew­ness, and phase have therefore been independently specified. These modificationsdo not contradict the original assumption that Hand L are modulated by a singlecircadian pacemaker, since differences in phase and shape are known to be presentfor the rhythms of other parameters as weIl (e.g., body temperature, plasma cortisol,plasma melatonin). However, it remains to be demonstrated that phenomena simu­lated by the previous, quantitative version of the model (i.e., internal desynchroni­zation, polyphasic sleep during continuous bed rest) can still be accounted for.

For simulating the time course of the PSI, we have used two sets of parameters.A sinusoidal function skewed in the opposite direction to threshold L yielded arelatively uniform level of S - H during most of the waking period (Fig. 2), whereas

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BORBEL Y ET AL.

a phase-delayed sine function aIlowed us to simulate the midafternoon peak (Fig. 3).The variability of the results reported in the literature make it difficult at present todefine H in detail and to establish a quantitative relations hip to actual sleep latencydata. Nevertheless, with both parameter sets used in the simulations, we were ableto account for the steep rise during the initial part of sleep deprivation. Moreover,the puzzling increasing trend of sleep latency that was observed after the recoverynight foIlowing prolonged sleep deprivation is easily explained by the unequal riserates of Sand H (Fig. 4).

Whereas the EEG slow-wave activity during daytime naps increased monoton­icaIly as a function of the duration of prior waking, sleep latency showed a midaf­ternoon trough (Dijk et al., 1987a). As shown in Figure 4, it is possible to simulatethe main aspects of this result by appropriately defining the parameters of H. Alter­natively, it may weil be that the threshold H has abimodal time course with a localminimum in midafternoon, and that the trough in sleep latency is the result of thecharacteristics of H (Dijk et al., 1987a). Further experiments are needed to discrim­inate between the two possibilities.

In previous versions of the two-process model, we have shown that the timingof sleep and waking can be accounted for by the interaction between a homeostaticand a circadian process. The present study was focused on the propensity of sleepinitiation. We propose that during the circadian episode of predominant waking, acircadian process counteracts the progressively increasing sleep tendency, andthereby enables the organism to maintain the waking state at a uniform, high level.However, when waking is extended beyond its "circadian limit," the propensity ofsleep initiation rises dramatically as a result of the synergistic action of the homeo­static and circadian sleep-regulating processes.

APPENDIX

The following equations and parameter values were used in the simulations:Process S, rising limb (waking):

Process S, falling Iimb (sleep):

S(t) = Sf' exp( -t . rf)

Sn Sf: initial level of S at the onset of waking or sleep

rr: : rise rate, 0.055 . hr-Irf: : fall rate, 0.238 . hr-I

Thresholds:

L: L(t) = AL' skew(t - TJ + LH: H(t) = AH' skew(t - TH) + H

(Figs. 2, 4)

46 I 158

SLEEP INITIATION AND SLEEP INTENSITY

H(t) = AH . sin[w(t - TH)] + H(Fig. 3)

skew(t) = 0.97 . sin[w(t - T)] + 0.22 . sin[2w(t - T)] + 0.07 . sin[3w(t - T)]+ 0.03, sin[4w(t - T)]+ 0.001 . sin[5w(t - T)]

Amplitudes of threshold oscillations (units):

0.12

- 0.22 (Figs. 2, 4)- 0.20 (Fig. 3)

Phase of threshold oscillations at 0 hr:

TL = 8.6 hrTH = 3.6 hr (Figs. 2,4)

6.6 hr (Fig. 3)

Mean value of thresholds (units):

[ = 0.17

H = 0.67 (Figs. 2, 4)0.69 (Fig. 3)

Angular frequency of oscillation: w = 2 1T/24hr

ACKNOWLEDGMENTS

This study was supported by the Swiss National Foundation, Grant No. 3.234-0.85, and by the Stiftungfür Wissenschaftliche Forschung an der Universität Zürich. We thank Dr. D. J. Dijk for comments andMs. Karin Jaggi for drawing the figures.

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