• adult;
  • biological rhythms;
  • computational model;
  • human;
  • sleep disorders


Sleep fragmentation of any cause is disruptive to the rejuvenating value of sleep. However, methods to quantify sleep architecture remain limited. We have previously shown that human sleep–wake stage distributions exhibit multi-exponential dynamics, which are fragmented by obstructive sleep apnea (OSA), suggesting that Markov models may be a useful method to quantify architecture in health and disease. Sleep stage data were obtained from two subsets of the Sleep Heart Health Study database: control subjects with no medications, no OSA, no medical co-morbidities and no sleepiness (n = 374); and subjects with severe OSA (n = 338). Sleep architecture was simplified into three stages: wake after sleep onset (WASO); non-rapid eye movement (NREM) sleep; and rapid eye movement (REM) sleep. The connectivity and transition rates among eight ‘generator’ states of a first-order continuous-time Markov model were inferred from the observed (‘phenotypic’) distributions: three exponentials each of NREM sleep and WASO; and two exponentials of REM sleep. Ultradian REM cycling was accomplished by imposing time-variation to REM state entry rates. Fragmentation in subjects with severe OSA involved faster transition probabilities as well as additional state transition paths within the model. The Markov models exhibit two important features of human sleep architecture: multi-exponential stage dynamics (accounting for observed bout distributions); and probabilistic transitions (an inherent source of variability). In addition, the model quantifies the fragmentation associated with severe OSA. Markov sleep models may prove important for quantifying sleep disruption to provide objective metrics to correlate with endpoints ranging from sleepiness to cardiovascular morbidity.