A Mathematical Method for Studying the Endogenous Component of the Circadian Temperature Rhythm and the Effect of Aging

Abstract

A mathematical model was developed in order to study the endogenous component of the circadian rhythm in body temperature. The model describes the fluctuations in body temperature as a function of a cosine-shaped endogenous rhythm plus an exogenous component which is linearly correlated with the time spent in active wakefulness. The model was evaluated in 4 young and 4 old rats. In 7 out of 8 rats there was a significant lack of fit when the traditional cosinor method was used, as compared with only 1 out of 8 when using our model. In all 8 rats the regression was highly significant and also useful as defined by the ? m criterion. The results from the model were in agreement with literature regarding constant routine studies in humans. The mean amplitude of the endogenous rhythm was 0.24°C in young rats and 0.19°C in old rats, whereas the amplitudes of the overt rhythm were 0.38 and 0.26°C, respectively. The age-related differences in the amplitude of the overt circadian temperature rhythm could to a large extent be attributed to age-related differences in activity-induced heat production. Finally, the acrophase of the endogenous rhythm occurred 18.7 minutes later than that of the overt rhythm. If applicable to human, the proposed method may form a valuable extension to existing constant routine protocols for studying the endogenous circadian rhythm in body temperature.