Fitting Sine Curves to 24 h Urinary Data

Abstract

IN studies of biological rhythms it is often desirable to obtain an objective estimate of the phase and amplitude of a suspected rhythm from observation recorded over a single cycle, such as a single period of 24 h. The usual technique is to attempt to fit the observations to a sine curve. Most techniques of fitting a sine curve are applicable only to a series of points and, for conventional methods, the points must be uniformly spaced in time. Many biological data, especially of renal excretion but also of respiratory or heat exchange, represent the average value of the variables since the previous sampling. The sampling intervals are often irregular and are correctly represented graphically by a histogram, though in published work they are often presented as points at the midpoint of the collection period. This does not cause much distortion if the time intervals are short and equal, but a gross distortion of the actual behaviour is introduced when, for example, there are long collection periods of urine as in a night's sleep.