Development of a Personalized Mathematical Model of the Annual Variation in Bedroom Temperature and Sleep Efficiency

Abstract

High sleep quality is essential for people’s health. Numerous studies have investigated the relationship between indoor environmental quality and sleep quality, and the thermal environment, in particular, has been shown to have a significant effect on sleep quality. However, most of these studies measured the thermal environment of the bedroom for only short periods of time. Although seasonal variations and individual differences in sleep quality have been reported, most studies on the thermal environment and sleep quality have not adequately taken these factors into account. Therefore, the present study measured bedroom temperature and sleep quality objectively without intervention for 1 year and mathematically modeled the annual variation in bedroom temperature and sleep efficiency using a simplified sine function. This mathematical model was able to quantitatively characterize individual differences in the annual variation of bedroom temperature and sleep efficiency. The amplitude and phase of the sine function indicate the annual variation range of sleep efficiency and the degree to which sleep efficiency decreases in summer or winter. The mathematical model was also able to identify bedroom temperatures that optimize sleep efficiency. Analysis of each participant’s annual bedroom temperature and sleep efficiency revealed that sleep efficiency was high in the spring and fall when temperatures were moderate for all participants, while sleep efficiency decreased during the summer and winter and that there were individual differences in terms of whether sleep efficiency decreased more during the summer or winter. Furthermore, there were differences in the bedroom temperature that optimized sleep efficiency for each individual, and the vulnerability of sleep efficiency to fluctuations in bedroom temperature also differed for each individual. By utilizing the developed mathematical model, the bedroom temperature could be individually controlled to enhance sleep efficiency, thereby impacting health and performance.