Serial section analysis of circadian rhythms by best-fitting periods

Many human circadian rhythms are asymmetric, displaying a longer proportion of the envelope above the mesor than below it. Asymmetry reduces the percentage of variability (%R) accounted for by a fitted symmetric sine curve calculated with the aid of a fixed 24-hr period chosen because of the basic 24-hr rhythmicity of the investigated parameter. A higher %R would be expected when substituting the best-fitting period (BFT) for the fixed one. A dense serial section analysis of circadian temperature oscillations by 1-hr shifts of a 24-hr window showed that BFT length, calculated separately for each window, cyclically varied through successive sections between tau greater than 24 hr and tau less than 24 hr. Since only the sequence (starting point of the window) of the same temperature readings differed from one window to the other, the varying BFT length and %R were determined by the shape of the envelope in the particular 24-hr section. Thus, BFT is not an unambiguous term in the analysis of asymmetric circadian rhythms. However, a "true" BFT for calculation of sine curve complying best with the shape of the envelope of such a rhythm can be arrived at by selecting the BFT that acquired the highest %R in the course of the serial section analysis. Both single amplitudes should be considered for BFT phase estimation in asymmetric rhythms. The upward-directed single amplitude points out the phase of the peak of the rhythm while the downward-directed single amplitude, postponed by one half of the respective BFT, indicates the phase of the trough, usually with a higher %R than that for the peak amplitude. A program for this specific type of serial section analysis has been written in PASCAL.