Probabilistic sleep architecture models in patients with and without sleep apnea

Abstract

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.

Figure 1

Variability in human sleep architecture. Single-night hypnogram data from seven control subjects from the SHHS database are shown with the five AASM-defined stages (a). The number of rapid eye movement (REM) sleep bouts is plotted epoch-by-epoch below the aligned hypnograms (b). Note the REM ultradian rhythm, in comparison to the more evenly distributed wake after sleep onset (WASO) (c).

Figure 2

Inferring generator states from the distribution of phenotypic stage bout durations. (a) A simple two-state model of sleep (S) and wake (W), which yields distributions of each stage that are mono-exponential (gray dashed lines, displaced for clarity). (b) A second sleep state (S2) linked to the wake state, with a faster exit rate; the exit rate constants of the wake state add to 0.1 per min (as in a). W bouts are unchanged, but stage S is now bi-exponential (gray line: best mono-exponential fit for visual comparison). Example hypnograms are given below each model.

Figure 3

Eight-state Markov model of sleep–wake activity in control subjects. The connectivity was inferred by adjacent-stage analysis (see text; see Table 1 for fitting data). Note that all transitions are reversible except W2 to R2. (a) Matrix of rate constants for each transition. Gray shading indicates transitions that were either not considered (transitions within a phenotypic class, such as NR1 to NR2), or not observed in the adjacent-state analysis (such as NR3 to R1).

Figure 4

Simulated hypnograms from the Markov model of control SHHS subjects. (a) Randomly chosen simulated hypnograms, showing wake (W), REM (R) and NREM (N) sleep stages. The time legend shown in (d) applies here. (b) The number of observed REM sleep bouts over time shows the imposed probabilistic ultradian rhythm [for the seven hypnograms in (a) (solid line)], and for n = 30 simulations (dashed line). (c) Counts of WASO were more evenly distributed throughout the night, for n = 7 (solid line) and n = 30 (dashed line) simulations. Because all simulated nights began in stage W1, the first epoch count = 30 (not shown in this limited Y-axis range). (d) The same seven hypnograms of SHHS subjects shown in Fig. 1a are re-plotted with concatenated NREM substages, to reflect the simplified staging used in our analysis and modeling. (e) The number of observed REM epochs is plotted for n = 7 (solid line) and n = 30 (dashed line) control subjects from the SHHS. (f) The number of observed wake epochs is plotted for n = 7 (solid line) and n = 30 (dashed line) control SHHS subjects (same subjects analysed in e). REM, rapid eye movement; WASO, wake after sleep onset.

Figure 5

Distribution of bout durations from the Markov model. Frequency–duration histograms (1-epoch bins) were constructed for bouts of wake after sleep onset (WASO) (a), non-rapid eye movement (NREM) sleep (b) and rapid eye movement (REM) sleep (c). The best mono-exponential fit (gray dashed line) is overlaid on the simulated data to illustrate the need for multi-exponential fitting of these distributions.

Figure 6

Markov model of SHHS subjects with severe OSA. (a) Eight generator states defined the sleep apnea Markov model, the connectivity was inferred by adjacent-state analysis (see text; see Table 2 for fitting data). The gray shading indicates transitions observed in the OSA group but not in the control group (compare with Fig. 3). (b) The matrix contains rate constants for each transition in the model. Gray shading indicates transitions that were either not considered (transitions within a class, such as NR1 to NR2), or not found in the adjacent-state analysis (such as NR3 to W3).

Figure 7

Simulated hypnograms from the Markov model of obstructive sleep apnea (OSA). (a) Randomly chosen simulated hypnograms from the severe OSA model, with wake (W), REM (R) and NREM (N) sleep stages. The time legend applies to (d) as well. (b) The number of observed REM sleep bouts plotted below the hypnograms shows the imposed probabilistic REM sleep ultradian rhythm. Counts of REM sleep are shown for n = 7 (solid line) and n = 30 (dashed line) simulated hypnograms. (c) Counts of wake across the night, for n = 7 (solid line) and n = 30 (dashed line) simulated patients were more evenly distributed. (d) Single-night hypnogram data are aligned from seven SHHS subjects with severe OSA. Staging, as in prior figures, is simplified to WASO, NREM and REM sleep. The time legend in (a) applies. (e) Counts of REM sleep are plotted, as in (b), for n = 7 (solid line) and n = 30 (dashed line) subjects. (f) Counts of WASO are plotted, as in (c), for n = 7 (solid line) and n = 30 (dashed line) subjects. REM, rapid eye movement; WASO, wake after sleep onset.