  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 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, also called an "epoch", 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.
