Sleep timing is based on the interactions between circadian and homeostatic processes. However, sleep deprivation perturbs the time of sleep onset, and the timing and duration of the following recovery sleep may differ from that of baseline sleep. Here we show that the responses to 0–24 h of sleep deprivation can be approximated by a one-dimensional, discontinuous map computed from a physiologically-based ordinary differential equation model for human sleep-wake regulation. The map relates the circadian phase of sleep onset to the circadian phase of the previous sleep onset and reproduces sleep patterns seen in experimental data for the timing and duration of recovery sleep when sleep onset occurs 8 or 20 h after the usual sleep onset. In addition, the durations of recovery sleep predicted by the map for sleep deprivations of 0 to 24 h are consistent with numerical simulations of recovery sleep using the full (nonautonomous, 8-dimensional) model. Our results demonstrate that the circadian phase of sleep onset affects the duration of recovery sleep more strongly than the homeostatic sleep drive for most durations of sleep deprivation. In addition, the map establishes a lower bound for the length of recovery sleep. As a result, the map provides a computationally-efficient way of incorporating sleep dynamics into new technologies that allow users to predict the effects of sleep deprivation and identify optimal sleep schedules.

睡眠时间基于昼夜节律和稳态过程之间的相互作用。但是，睡眠剥夺会扰乱睡眠开始的时间，随后恢复睡眠的时间和持续时间可能与基准睡眠不同。在这里，我们表明，对0-24小时的睡眠剥夺的反应可以通过一维不连续的图来近似，该图是从基于生理学的常微分方程模型中计算出来的，用于人类的睡眠-唤醒调节。该图将睡眠发作的昼夜节律阶段与先前睡眠发作的昼夜节律阶段相关联，并再现了在实验数据中看到的睡眠模式，以了解当睡眠发作发生在通常的睡眠发作后8或20小时时恢复睡眠的时间和持续时间。此外，该图预测的0至24小时睡眠剥夺的恢复睡眠持续时间与使用完整（非自治，8维）模型的恢复睡眠的数值模拟一致。我们的结果表明，对于大多数睡眠剥夺的持续时间，睡眠的昼夜节律对恢复睡眠的持续时间的影响比体内稳态睡眠驱动的影响更大。此外，该图确定了恢复睡眠时间的下限。结果，该图提供了一种将睡眠动力学纳入新技术的计算有效方式，从而使用户能够预测睡眠剥夺的影响并确定最佳的睡眠时间表。我们的结果表明，对于大多数睡眠剥夺的持续时间，睡眠的昼夜节律对恢复睡眠的持续时间的影响比体内稳态睡眠驱动的影响更大。此外，该图确定了恢复睡眠时间的下限。结果，该图提供了一种将睡眠动力学纳入新技术的计算有效方式，从而使用户能够预测睡眠剥夺的影响并确定最佳的睡眠时间表。我们的结果表明，对于大多数睡眠剥夺的持续时间，睡眠的昼夜节律对恢复睡眠的持续时间的影响比体内稳态睡眠驱动的影响更大。此外，该图确定了恢复睡眠时间的下限。结果，该图提供了一种将睡眠动力学纳入新技术的计算有效方式，从而使用户能够预测睡眠剥夺的影响并确定最佳的睡眠时间表。