Analysis of variability in length of sleep state bouts reveals memory-free sleep subcomponents consistent among primary insomnia patients

Abstract

The statistical distributions of bout lengths for the different (macro) sleep states (wake, N1, N2, N3, and REM sleep) are essential to understanding whether any memory-free subcomponent (“micro state”) is involved in the organization of sleep. Micro state detection can be prevented by the fusion of data including various sources of variability, in particular by the differences in sleep architecture between individuals, along sleep time (or nighttime), or between different nights. In this analysis, a mathematical model of sleep was adopted to disentangle these features and advance the understanding of the dynamics and mechanisms of sleep and its states. The analysis involved 116 primary insomnia patients taking placebo before going to bed and undergoing polysomnography for one night. The individual sequences of macro sleep states had been previously modeled with a mixed-effect nonhomogeneous modified Markov chain model, from which individual conditional probability distributions for the bout durations were derived in this analysis as functions of sleep time. The probability distributions, affected by neither subject, night-time, nor multiple-night pooling, substantially changed at ¼ and ¾ sleep time, had modified exponential shape, and were best described as the sum of one to four exponentials, depending on the sleep state. The time constants and proportions of bouts contributing to each exponential were similar in the different subjects, changing over sleep time. Variability in bout durations thus indicated the presence of multiple memory-free sleep subcomponents whose mean residence times and access probabilities could be identified and shown to be consistent among the studied subjects. NEW & NOTEWORTHY We present a new methodology for deriving, from polysomnography data, the individual conditional probability for the duration of the bouts of wake, N1, N2, N3, and REM sleep. We evaluated the variability of this probability within and between primary insomnia patients and along sleep time. The multiexponential shapes of the probability distributions within the individuals revealed memory-free mechanisms and sleep subcomponents with consistent features in the studied population.