Mathematical model of the human circadian system with two interacting oscillators

Abstract

Human subjects during extended isolation from environmental time cues show complex variations in timing and duration of sleep with a progressive pattern, which eventually results in rest-activity and body temperature rhythms having different average periods. We present a model where temperature and rest-activity are each governed by an oscillator of the van der Pol type, denoted x and y, respectively. The oscillators affect one another through "velocity" type coupling, the effect of x on y being about four times greater than y on x. Periodic zeitgeber, z, is modeled as forcing only on y. We find that the entire pattern sequence can be realistically reproduced by causing only the intrinsic period of the y oscillator to increase while that of x remains stable. Desynchronization between x and y is the result of the intrinsic periods of the two oscillators becoming so disparate that the coupling is no longer able to enforce synchrony. Prior to desynchronization both human subjects and our model exhibit "phase trapping" wherein the relative phase of x and y is slowly modulated although the average x and y periods match. The model phase relations between temperature and both the timing and duration of sleep are, throughout, in good agreement with entrained and free-running human data. Most importantly, the model shows that the dramatic change in the length of the rest-activity cycle when desynchronization occurs is actually due to a relatively small variation in the governing variable, y.

A Parallelism between Human Body Temperature and Performance Independent of the Endogenous Circadian Pacemaker

“…Because the present study never determined whether the observed rhythms at T were indeed endogenous-capable of continuing, even when activity, meals, light, and so on were homogenized at all phases of T-we do not know whether the process underlying them can truly be referred to as a biological oscillator. Previous models of the circadian system did indeed regard human sleep/wake processes as having a separate circadian oscillator (Wever et al, 1975;Kronauer et al, 1982). These models posited two mutually interactive oscillators (or groups of oscillators) to underlie the human circadian system.…”

Influence of cedar essence on spontaneous activity and sleep of rats and human daytime nap

“…The polysomnograms (EEG, EMG, EOG, ECG and respiration) were monitored to score sleep stages by the manual of Rechtschaffen and Kales. 4 We measured sleep latency to N R E M sleep stages 1 (Sl) and 2 (S2) according to the guidelines5 of the multiple sleep latency test (MSLT) twice a day on two consecutive days during the morning (O5):3O-l1:30 h) and the afternoon (13:30-14:30 h). For CE odor exposure, we used a small electrically operated apparatus with a built-in plastic bottle for emitting the odor in the bedroom and placed it under the footboard of the bed.…”

Rapid Eye Movement (REM) sleep: cholinergic mechanisms

“…Circadian rhythms for muscarinic receptors have been described in autopsy material from human cortex (Perry et al 1977) and from rat brain (Kafka et al 1981). Moreover, Kronauer et al (1982) propose the existence of a' strong oscillator', termed the' X oscillator', which regulates the circadian organization of REM sleep, temperature, and cortisol. Since cholinergic agonists lower body temperature and stimulate cortisol secretion, one wonders whether acetylcholine acts upon or through the 'X oscillator'.…”