The Use of a Semi-Markov Model for Describing Sleep Patterns

Yang, Mark C. K.; Hursch, Carolyn J.

doi:10.2307/2529133

Cited by 38 publications

(28 citation statements)

References 4 publications

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“…From the standpoint of future sleep architecture “fingerprinting”, there is potential for use of Markov chain models[23], [32], [33], the parameters of which could be extracted from sleep architecture information. For example, disease states (or lesion sites) could be associated with changes in the number of exponential functions describing a given stage distribution, which stage transitions are possible, and the probabilities governing each transition.…”

Section: Discussionmentioning

confidence: 99%

Obstructive Sleep Apnea Alters Sleep Stage Transition Dynamics

et al. 2010

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IntroductionEnhanced characterization of sleep architecture, compared with routine polysomnographic metrics such as stage percentages and sleep efficiency, may improve the predictive phenotyping of fragmented sleep. One approach involves using stage transition analysis to characterize sleep continuity.Methods and Principal FindingsWe analyzed hypnograms from Sleep Heart Health Study (SHHS) participants using the following stage designations: wake after sleep onset (WASO), non-rapid eye movement (NREM) sleep, and REM sleep. We show that individual patient hypnograms contain insufficient number of bouts to adequately describe the transition kinetics, necessitating pooling of data. We compared a control group of individuals free of medications, obstructive sleep apnea (OSA), medical co-morbidities, or sleepiness (n = 374) with mild (n = 496) or severe OSA (n = 338). WASO, REM sleep, and NREM sleep bout durations exhibited multi-exponential temporal dynamics. The presence of OSA accelerated the “decay” rate of NREM and REM sleep bouts, resulting in instability manifesting as shorter bouts and increased number of stage transitions. For WASO bouts, previously attributed to a power law process, a multi-exponential decay described the data well. Simulations demonstrated that a multi-exponential process can mimic a power law distribution.Conclusion and SignificanceOSA alters sleep architecture dynamics by decreasing the temporal stability of NREM and REM sleep bouts. Multi-exponential fitting is superior to routine mono-exponential fitting, and may thus provide improved predictive metrics of sleep continuity. However, because a single night of sleep contains insufficient transitions to characterize these dynamics, extended monitoring of sleep, probably at home, would be necessary for individualized clinical application.

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Section: Discussionmentioning

confidence: 99%

Obstructive Sleep Apnea Alters Sleep Stage Transition Dynamics

et al. 2010

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“…Because of the possible relevance of the longest (stable) and shortest (fragmentary) duration sleep or wake bouts to the restorative properties of sleep, we suggest that the entire distribution of state durations should be represented by modeling methods. Although some have postulated time-varying or semi-Markov models for sleep-wake architecture, a simple first order time invariant Markov model might also account for the complexity of empiric sleep-wake distributions [18], [19], [20]. It is also interesting to consider that a system of exponential generators could interact in a manner that would produce power law-like dynamics [21].…”

Section: Discussionmentioning

confidence: 99%

Power Law versus Exponential State Transition Dynamics: Application to Sleep-Wake Architecture

2010

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BackgroundDespite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot.Methodology/Principal FindingsTo characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the “incorrect” model over a range of parameters. The “zone of mimicry” of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions.Conclusions/SignificanceRecognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.

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“…[26][27][28][29] Approaches ranged from simply calculating average transition probabilities over constant periods of the night 29 to complex mixed effects models. 26 Yassouridis and others 30 (Figure 2A), transition probabilities to wake, S2, and REM are higher and transition probabilities to S1, S3, and S4 are lower.…”

Section: Discussionmentioning

confidence: 99%