Measures of location and dispersion of sleep state distributions within the circular frame of a 12:12 light: Dark schedule in the rat

Distributions within a 12:12 light:dark schedule of wakefulness (W), active sleep (AS), quiet sleep (QS) and of QS rich in delta (QSD) and in spindle (QSS) activities were evaluated for 52 days from 15 rats. Angular statistics were applied for each state by equating their hourly incidence to data distributed around a circle. Measures of location (mean angle, median angle, mode angle, maximum semicircle), dispersion (mean vector, standard deviation, quartile deviation), skewness and kurtosis were computed and their intra- and interindividual variabilities were compared. Mean angles (in hours and after lights-on) averaged 5.5 for QS, 8.6 for AS, 18.4 for W, 1.9 for QSD and 10.6 for QSS. Length of vectors, representing concentration around the mean angle, averaged 0.22 for QS, 0.36 for AS, 0.22 for W, 0.38 for QSD and 0.23 for QSS. Distributions of QS and W were closely related to the light- dark step function. QSD had a leptokurtic distribution, sharply rising at the beginning of the sleep-predominant phase, whereas AS and QSS had smoother distributions reaching maxima in its second half. In rodents as in humans, QSS and AS have opposite distributions to QSD. QSS may contribute to maintain sleep through the resting phase of the light-dark schedule after restorative function associated with delta activity has been fulfilled.