Abstract
Obstructive sleep Apnea (OSA) is a form of sleep disordered breathing characterized by frequent episodes of upper airway collapse during sleep. Pediatric OSA occurs in 1–5% of children and can be related to other serious health conditions such as high blood pressure, behavioral issues, or altered growth. OSA is often diagnosed by studying the patient’s sleep cycle, the pattern with which they progress through various sleep states such as wakefulness, rapid eye-movement, and non-rapid eye-movement. The sleep state data is obtained using an overnight polysomnography test that the patient undergoes at a hospital or sleep clinic, where a technician manually labels each 30 second time interval with the current sleep state. This process is laborious and prone to human error. We seek an automatic method of classifying the sleep state, as well as a method to analyze the sleep cycles. This article is a pilot study in sleep state classification using two approaches: first, we’ll use methods from the field of topological data analysis to classify the sleep state and second, we’ll model sleep states as a Markov chain and visually analyze the sleep patterns. In the future, we will continue to build on this work to improve our methods.
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Acknowledgements
This work was started at the second Women in Data Science and Mathematics workshop (WiSDM 2) in summer 2019, at The Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University. We thank ICERM for the support. The authors would like to thank their fellow group members, Brenda Praggastis, Melissa Stockman, Kaisa Taipale, Marilyn Vazquez, Sunny Wang, and Emily Winn. We’d especially like to thank Brenda Praggastis for her help preprocessing the time series data and setting up some of the code for the persistent homology analysis. We also thank Mathieu Chalifour for discussion of polysomnography time series. ST was partially funded by NSF grants DMS1800446 and CMMI-1800466. KS was partially funded by NSF grant DMS 1547357. GH would like to thank the National Sciences and Engineering Research Council of Canada (NSERC DG 2016-05167), Seed grant from Women and Children’s Health Research Institute, Biomedical Research Award from American Association of Orthodontists Foundation, and the McIntyre Memorial fund from the School of Dentistry at the University of Alberta.
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Appendix
Appendix
This section contains tables and figures referred to in the main article (Tables 4, 5, 6, 7, 8, 9, 10, 11, 12 and Figs. 17, 18, 19, 20, 21).
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Tymochko, S., Singhal, K., Heo, G. (2021). Classifying Sleep States Using Persistent Homology and Markov Chains: A Pilot Study. In: Demir, I., Lou, Y., Wang, X., Welker, K. (eds) Advances in Data Science. Association for Women in Mathematics Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-79891-8_11
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