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When these mathematical models are compared to emerging experimental
data on performance relative to sleep-wake dynamics, they often reveal new
to continually improve the predictions of the two-process model can be
found in a mathematical modeling paper by McCauley and colleagues,
31
who showed that the two-process model belongs to a broader class of models
formulated in terms of coupled nonhomogeneous first-order ordinary dif-
ferential equations. Their new model includes an additional component
modulating the homeostatic process across days and weeks, and better
reflects the neurobehavioral changes observed under both acute total and
chronic partial sleep loss than the original two-process model. The authors
speculate that adenosine receptor upregulation (wakefulness) and down-
regulation (sleep) constitute the underlying neurobiological mechanism.
Importantly, the model predicts a critical amount of daily wake duration
(corresponding to a total sleep time of 3.8-8.2 h), the model, over a period
of weeks, converges to an asymptotically stable equilibrium (i.e., perfor-
mance deficits will stabilize at a certain level). If daily wake duration is above
20.2 h, the model diverges and, similar to acute total sleep deprivation, per-
et al.
also
Figure 7.1 Circadian variation across a 40-h period of wakefulness in measures of sub-
jective sleepiness as assessed by visual analogue scale (VAS, note reversed scale direc-
tion); in cognitive performance speed as assessed by the digit symbol substitution task
(DSST); in psychomotor speed as reflected in the 10% fastest reaction times (RT)
assessed by the Psychomotor Vigilance Test (PVT); and in core body temperature
(CBT) as assessed by a rectal thermistor. Data shown are the mean values from five sub-
jects who remained awake in dim light, in bed, in a constant routine protocol, for 36 h
consecutively (a distance-weighted least-squares function was fitted to each variable).
The circadian trough is evident in each variable (marked by vertical broken lines).
A phase difference is also apparent such that all three neurobehavioral variables had
their average minimum between 3.0 and 4.5 h after the time of the body temperature
minimum. This phase delay in neurobehavioral functions relative to CBT has been con-
sistently observed. Although body temperature reflects predominantly the endogenous
circadian clock, neurobehavioral functions are also affected by the homeostatic pres-
sure for sleep, which escalates with time awake and which may contribute to the phase
delay through interaction with the circadian clock. Neurobehavioral functions usually
show a circadian decline at night as is observed in CBT, but they continue their decline
after CBT begins to rise, making the subsequent 2-6 h period (clock time approximately
0600-1000 h) a zone of maximum vulnerability to loss of alertness and to performance
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