A mathematical method for studying the endogenous component of the circadian temperature rhythm and the effect of aging

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 gamma(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 degrees C in young rats and 0.19 degrees C in old rats, whereas the amplitudes of the overt rhythm were 0.38 and 0.26 degrees 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.