Gaillard J M
Electroencephalogr Clin Neurophysiol. 1977 Jun;42(6):754-60. doi: 10.1016/0013-4694(77)90228-0.
By fitting orthogonal polynomials to the cumulated occurrences of sleep stages, it is possible to describe in a simple form their general trend, i.e. their temporal evolution, in the absence of cyclic ultradian variations. Thus, stages 1, 2 and 3 can be described by a cubic function, REM stage by a parabolic one, while total sleep itself is linear. The fittings can be performed on a general average or on individual data, allowing completion of the subject's clinical description. The first derivative of the general trends gives the instantaneous trend, which has the form of a probability, that of the occurrence of a given stage at a given moment of the night. The study of normal sleep with this technique reveals new aspects of its evolution as a function of time, and makes it possible to propose and test hypotheses on the reciprocal relations between stages.
