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Sleep-Wake Cycle Modeling

By Karthika Swamy Cohen 

Does temperature affect sleep patterns? Studies have shown that factors such as room temperature, as well as core body and distal skin temperatures, can have a significant impact on the length and frequency of REM bouts during sleep. 

 At the “Advances in Modeling Sleep-wake Behavior and Circadian Rhythms” minisymposium on Wednesday at the SIAM Conference on the Life Sciences, Pamela Pyzza (Ohio Wesleyan University) described mathematical modeling of influence of temperature on human sleep patterns.

Neuroanatomy of sleep. Image credit: Pamela Pyzza, LS16 presentation.
Pyzza and her collaborators started with a model of human sleep wake patterns, and then incorporated temperature into the model. They’re trying to answer the question: What role does temperature play in shaping the structure of sleep? 

Thermoregulation is the process by which our body maintains its core internal temperature. When at a cold location, our body temperature tends to slowly move towards the ambient temperature. The body cools down or heats up to maintain a nice middle ground. Thermoreguation is at play at certain times during sleep. It occurs during non-REM (NREM) sleep but not during REM sleep. 

The body tries to raise its internal temperature during sleep by awakening, changing positions, blood vessel contraction and vasodilation, and by increasing NREM sleep (when it can be thermoregulated). Pyzza and her group modeled the homeostatic process along with the circadian process in order to factor in the influence of temperature. 

The sleep-wake model incorporates details of both ambient and body temperatures. Morris-Lecar equations are used to describe the mean activity of each neuron population involved in the sleep wake cycle. Neurons in the preoptic anterior hypothalamus (POAH) are active in sleep and those in the midbrain reticular formation (MRF) are active during wake times. The model follows eight hours of sleep followed by a 16-hour wake cycle. There are 4-5 REM and NREM cycles per night, the formed being smaller than the latter. The model falls asleep into NREM and wakes up from REM.

Temperature effects play a role in two places during the cycle, and these are described mathematically by differential equations. In REM sleep, we don't thermoregulate, so we just tend to ambient temperature: this results in a smaller differential equation. Humans can maintain a steady temperature within a range in which our body can thermoregulate. If it’s drastically cold or drastically warm (outside of this range), the body just tends toward ambient temperature. 

Sleep-wake cycle. Image credit: Pamela Pyzza, LS16 presentation.
The model shows that the body is comfortable when awake and during NREM. During REM however, since we don't thermoregulate, we tend to wake ourselves up. It follows the same patter when the body is forced to a temperature outside of the range where we thermoregulate. 

When away from a comfortable ambient or thermoneutral temperature (about 29 degrees centigrade), the model shows that it doesn’t take a significant amount of time to fall asleep, there is an increased amount of wakefulness. This trend in sleep behavior is consistent with experimental work for sleep at drastic ambient temperatures. 

The group also used the model for jet lag simulation. Here, they found that forcing the system to fall asleep five hours later—as in, after a long flight—instigates long REM latency and higher REM homeostat. This clearly indicates a shorter night sleep during the first night. It shows a longer REM latency period at the start of the following night and a greater amount of REM by the end of the night. 

At a related minisymposium on Tuesday, “Dynamical Systems with Applications to Biology and Medicine,” Selenne Bañuelos (California State University) discussed a mathematical model that studies the effects of temperature on REM/nonREM dynamics.  The human sleep–wake regulation model she described, which is based on previously developed models of sleep dynamics and thermoregulation, simulates increased duration and number of REM bouts through the night and appearance of awakenings resulting from digressions in thermoneutrality in the body. The model demonstrates the importance of temperature to sleep regulation. 

Karthika Swamy Cohen is the managing editor of SIAM News.