1 In previous studies we have demonstrated that train drivers and truck drivers exhibit pronounced subjective and behavioral sleepiness towards particularly the early morning. (Kecklund and Akerstedt, 1993 ; Torsvall and Âkerstedt, 1987). The physiological changes include increased alpha and theta power density and slow rolling eye movements. The same phenomenon may be observed in process operators in the industry (fig.l), although here sleepiness frequently develops into full-blown sleep episodes (Torsvall et al, 1989). Interestingly, in this study the sleep episodes during work were not recognized by the subject, although the experience of sleepiness was.

Figure 1. Hypnogram from 24h ambulatory recording of a three-shift worker. R = REM sleep. The subject falls asleep three times during work

I – The three-process model of alertness

2The inspiration for the development of the alertness model was the « two-process model of sleep regulation » which had shown that sleep length and slow wave activity could be described by a combination of a homeostatic and a circadian influence (Borbély, 1982). This model was based on the amount of EEG slow wave activity during sleep but it seemed likely that a similar approach could be used to model and predict alertness variations.

3To construct the model we used published data from experiments with life on a 22. Oh day (Folkard étal, 1985), sleep deprivation (Folkard and Akerstedt, 1991 ; Fröberg et al, 1975 ; Fröberg et al, 1975 ; Fröberg, 1977) and other studies. It should be emphasized that these studies are completely independent of those used for the Borbély model and also use a completely different parameter : subjective sleepiness. We found that subjective sleepiness (or alertness) was, indeed, predictable using three processes : S, C, and W. Space does not permit a discussion of the derivation of the model but the reader is referred to Folkard and Akerstedt (1991). Here will be described the main traits of the model.

Figure 2. Parameters of the three-process model of alertness regulation. S = homeostatic component during waking. S’ = homeostatic component during sleep. C = circadian component. W = wake up component. S+C = the alertness prediction (excluding W). « 7 » = level of risk

4Process C represents sleepiness due to circadian influences and has the general sinusoidal form indicated in fig. 2. Our attempts to model empirical data suggest that the phase estimate may have to be delayed by up to four hours in students, shift workers or other groups in which evening type preferences dominate.

5Process S is an exponential function of the time since awakening. Maximum alertness is reached upon awakening and alertness initially falls rapidly but levels out and gradually approaches an asymptote. The rate of decrease of the exponential function corresponds to 3.5 % of the previous value per hour. At sleep onset process S is reversed and called S’ and recovery occurs as an exponential function that initially increases at a very rapid rate but subsequently levels off towards an upper asymptote. The rate of increase of the exponential function is 28.7 % per hour, i.e. much steeper than the decay during the day. It is of interest to note that the exponential functions arrived at are very similar to those demonstrated by Borbély et al. (1982).

6The final component is the wakeup process W, or sleep inertia, after forced awakenings. This function is also exponential but with an even steeper initial decrease – the rate of decrease is 62.7 % per hour, i.e. already after the first hour most of the inertia has dissipated. W is subtracted from the S+C level. Spontaneous awakenings constitute a special problem since the exact time of awakening often is not available, and since the time between the first formal awakening and the time of finally rising might be considerable. Tentatively, we assume that such a process might take approximately 1 hour.

7The estimated alertness (or sleepiness) is then expressed as the arithmetic sum of the three functions above (S+C in figure 2). It should be emphasized that the homeostatic function involves, not only prior time awake, but also the amount of prior sleep. It also recognizes that recuperation is more rapid in the initials hours of sleep and that loss of alertness is more rapid during the initial hours of wakefulness. Furthermore, the recuperative process (S’) increases in speed with increasing sleep loss and the loss of alertness is less rapid if initial alertness is low. Incidentally, the S’ function has recently been demonstrated to predict slow wave activity (Åkerstedt et al, 1992) and total sleep length (Kecklund et al., 1992).

II – Prediction of involuntary sleep

8Using the three-process model we have found it possible to predict with high accuracy the variation of subjective sleepiness under conditions of sleep deprivation and various experimental or naturally occurring alternations of sleep/wake behavior (Folkard and Âkerstedt, 1991). In these validation studies it was also found that level 7 of predicted alertness corresponded to a point when slow eye movements (SEM) started to occur during waking polysomnography under conditions of five minutes of open eyes. This has been taken to indicate a level of sleep onset risk. This is admittedly arbitrary but contains considerable face value.

9To continue the validation work we have tried to predict alpha power density (after spectral analysis of the CzPz derivation) in two field studies with ambulatory EEG recordings. The first derives from 15 truck drivers during a night drive (Kecklund and Âkerstedt, 1993). On the whole, alpha power density rises as predicted alertness falls (figure 3). The right part of the figure illustrâtes the close relation between the alpha power density and predicted alertness. Baseline levels (100 %) coincide with predicted levels of 10 and above and characterized daytime driving (not in the figure). This means that the relation between predicted alertness and alpha (and thêta) intrusions is in effect curvilinear – the point of inflection appears around the level of 7-8. This is very close to the earlier observation that SEM (as well as alpha and thêta intrusions) are completely absent for high to medium levels of alertness (14-9) but start to appear around 7 together with perceptions of « fighting sleep » (Folkard and Âkerstedt, 1991).

Figure 3. Left : Mean alpha power density and predicted alertness plotted against time of day for truck drivers working at night. Right : Mean alpha power density plotted against predicted alertness for the same group. 100 % = baseline (daytime values). N = 15 subjects at each point

10Figure 4 shows a similar analysis carried out with 15 train drivers during night work (Torsvall and Åkerstedt, 1987). Here, the covariation between predicted alertness and alpha power density during the night drive is even higher than for the truck drivers. Again, daytime driving is associated with an absence of alpha or theta activity beyond baseline, and with high-to-medium levels of predicted alertness. Thus the true relationship is curvilinear between predicted alertness and sleep intrusions into the waking EEG, and the first increase above base line occurs around the level 7-8 of predicted alertness.

Figure 4. Left : Mean alpha power density and predicted alertness plotted against time of day for train drivers with night work. Right : Alpha power density plotted against predicted alertness. 100 % = baseline (day). N = 13 in each point

11The percentage increase in train and truck drivers differs considerably. This difference is not possible to interpret, however, since many factors may have influenced the calculation of the relative values – the subjects were different in age and occupation and the studies were carried out with different techniques many years apart.

12In order to further test the prediction of the model we used a 64 hour sleep deprivation study (Gillberg and Åkerstedt, 1981) in which EEG measures were obtained in connection with performance tests. The study involved 12 male subjects living on a semi-constant routine. The latter included isolation from environmental time cues and a three-hourly control of activity and intake of food and fluid. In each three-hour module ratings of sleepiness were carried out and a 32 minute monotonous vigilance test was used.

13Figure 5 shows the time elapsed before the first miss due to sleep (scored visually), plotted against time, together with predicted alertness from the model (the acrophase was set to 2048h). The data in the left panel show a very pronounced fall across time awake, together with a superimposition of a circadian pattern. The right panel shows that the amount of variance accounted for by the model prediction is considerable. The number of minutes without a miss increases by 2.5 for each level of the scale (above the intercept). Performance without misses appears to require a level of 13, whereas a rapid onset (<10 min.) of misses occurs at around 3. There appears to exist no obvious « critical point » in these data, but the probability of missing due to sleep is linearly related to predicted alertness.

Figure 5. Left : Mean latency to first miss due to sleep and predicted alertness, plotted against time awake across 64 hours in three-hour intervals. N = 12. Right : Latency to miss plotted against predicted alertness

14Taken together, the data suggest that the alertness model may be used to define levels of critical sleepiness but that the outcome will be influenced by the activity of the subject and the environmental setting. At level 3 and below occurrences of sleep seem highly likely almost regardless of the situation. Between 3 and 7 the probability of sleep intrusions are high, at least for average sedentary activity. Between 7 and 10 the risk of sleep intrusions is reduced but very definitely present for situations of monotony. Above 10 sleep is unlikely unless the situation is highly conducive to it.