THE BASE-LINE COSINUS FUNCTION - A PERIODIC REGRESSION-MODEL FOR BIOLOGICAL RHYTHMS

A periodic regression model, named the Baseline Cosinus Function (BCF) , was designed to fit biological rhythms that show temporal deviations (peaks) above or below an otherwise relatively stable baseline. The B CF model has four parameters only, namely, baseline, peak-height, acro phase, and peak-width. BCF-regressions to daily rhythms in urinary 6-s ulphatoxymelatonin (aMT6s), hypothalamic glutamate concentration, and body temperature of hamsters are compared to fits of single (SCF) and complex cosine functions (CCF; using the fundamental and the first har monic). Goodness of fit statistics show that BCF-regressions to aMT6s- profiles of 36 hamsters resulted in lower residual errors than both SC F and CCF regressions, in particular when rhythms were determined unde r long photoperiod (n = 18) with relatively short nocturnal peaks (chi (2) = 316.6, 142.7 and 74.5 for SCF, CCF and BCE respectively). For aM T6s rhythms obtained from hamsters in short photoperiod (n = 18) with prolonged nocturnal peaks, goodness of fit was equivalent in CCF and B CF regressions (chi(2) = 326.3, 107.0 and 101.4, for SCF, CCF, BCF, re spectively), while BCF requires one parameter less than CCF. BCF-fits to daily patterns of hypothalamic glutamate and body temperature demon strate that this model may be applied to various data types and has pa rticular advantages when rhythms are sharply peaked, and when an indep endent estimate of peak-width, i.e., the total duration of a rise abov e the baseline, is desired.