Proving the Carry-over Effect of Slow-Wave Sleep by Mathematical Models
Toshinori Kobayashi, Yoichi Tsuji, Yoshinobu Iguchi
Psychiatric Research Institute of Tokyo
In order to study the psychophysiological function of “slow wave sleep (SWS), we are trying to identify the control mechanism of SWS. It is well known that the amount of SWS found in a sleep episode depends upon the length of wakefulness prior to the sleep episode. But Karakan et al. (1970) and Miyashita et al (1978) reported that SWS of a sleep episode was also influenced by SWS of the preceding sleep episode. So, we examined the hypothesis that SWS of a sleep episode depended not only on prior wakefulness to the sleep episode but also on SWS of the preceding sleep episode by the use of mathematical models and the experiment. Two models were prepared to examine the hypothesis: one is MODEL (CO), in which SWS of a sleep episode depends upon both prior wakefulness and SWS carried over from the preceding sleep episode, the other is MODEL (nCO), in which SWS of a sleep episode depends on only prior wakefulness to the sleep episode. Four pairs of night sleep and dayti,me naps were recorded in the experiment for eight healthy university students (aged 18 to 25) as follows: (1) Morning nap (0900-1300) was recorded after the mid night sleep (23000300) or early morning sleep (0300-0700), and (2) evening nap (1700-2100) after mid night sleep or early morning sleep. We compared SWS of night sleep and daytime naps estimated by two models with those obtained by the experiment. There was close agreement between SWS estimated by MODEL (CO) and that obtained by the experiment. This result indicates that there is carry over of SWS from night sleep to daytime nap. So, SWS of a sleep episode depends on both prior wakefulness to the sleep episode and SWS carried over from the preceding sleep episode. SWS is accumulated in proportion to the length of wakefulness prior to a sleep episode during waking and is released according to sleep progression during sleep. When SWS is relatively large compared with the length of sleep episode, all SWS is not completely released in the sleep episode. A part of SWS remains in the brain. The remainder of SWS is carried over to the following sleep episode. When SWS is considered as an index of a kind of fatigue in the brain, it is accumulated during waking and is restored during sleep. When the fatigue is not fully restored in a sleep episode, it carries over into the following sleep episode.