Sleep Inertia in Children
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SLEEP INERTIA IN CHILDREN THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Mathematical Science in the Graduate School of the Ohio State University By Kelsy Kinderknecht, BS, BA Graduate Program in Mathematics The Ohio State University 2013 Thesis Committee: Dr. Janet Best, PhD, Advisor Dr. Mark Splaingard, MD Dr. Adriana Dawes, PhD c Copyright by Kelsy Kinderknecht 2013 ABSTRACT Sleep inertia is known to cause delayed reaction times and general performance deficits immediately after awakening, but specifics manifested in children are not well defined. This research aims to elucidate the effects of sleep inertia in children aged 5 to 12. Results were that younger children sustained slower reaction times than older children at baseline and upon awakening. All age groups had greater impairment after a second awakening, possibly due to a circadian effect and/or cumulative fatigue. All groups had improved reactions in the final 2 minutes of testing compared to the first 2 minutes after awakening (though reaction times were still slower than at baseline), suggesting partial recovery in sleep inertia with increased time. Recovery from sleep inertia may be due to wake-promoting neuromodulators; the increase in concentration may be responsible for improved performance with extended time awake. The current study constructs a model based on volume transmission of these neuromodulators. The model is capable of producing results similar to those observed in individuals with little variance in reaction time, but the model struggles to produce adequate replications of more variable data. Furthermore, the model cannot produce many of the dynamics found in the observed data, suggesting that the current model, if appropriate at all, requires many alterations. ii ACKNOWLEDGMENTS It has been an honor to work with my advisors, Dr. Janet Best and Dr. Mark Splaingard, on this project, and I cannot thank them enough for their support and encouragement. I would also like to thank my committee member, Dr. Adriana Dawes, for her time and participation in my thesis defense. iii VITA 1989 . Born in Hays, Kansas 2011 . B.Sc. in Mathematics, The University of Kansas 2011 . B.A. in French, The University of Kansas 2011-Present . Graduate Teaching Associate, The Ohio State University FIELDS OF STUDY Major Field: Mathematics Specialization: Mathematical Biology iv TABLE OF CONTENTS Abstract . ii Acknowledgments . iii Vita . iv List of Figures . vii List of Tables . viii CHAPTER PAGE 1 Introduction . 1 1.1 Time Course of Sleep Inertia . 2 1.2 Psychomotor Vigilance Task . 3 1.3 Comparison of Sleepiness and Sleep Inertia . 4 1.4 Current Study . 8 2 Methods . 10 2.1 Methods of Data Collection . 10 2.2 Initial Data Analysis . 11 2.3 Methods of Model Construction . 11 2.3.1 Concentration of Neuromodulator . 13 2.3.2 Response Times as a Function of Concentration . 15 2.4 Numerical Methods . 17 3 Results . 19 3.1 Statistical Analysis of Data . 19 3.2 Comparison of Numerical Results to Model Simulations . 21 3.2.1 Example of 11-12 Year-Old . 22 3.2.2 Example of 5-6 Year-Old . 24 4 Discussion . 28 4.1 Future Work . 28 v 4.2 Conclusion . 30 Bibliography . 32 vi LIST OF FIGURES FIGURE PAGE 1.1 PVT Data in Presence of Sleep Deprivation . 6 2.1 Examples of Two 11-12 Year-Olds . 12 2.2 Concentration of Neuromodulator{Single Release . 15 2.3 Concentration of Neuromodulator{Repeated Release . 15 2.4 Concentration of Neuromodulator - Varying Radius and Firing Rate 16 2.5 Simulated Reaction Time as a Function of Concentration . 16 2.6 Simulated Reaction Time as a Function of Time Elapsed . 17 3.1 PVT Data for Individual 4011 . 23 3.2 Simulation of PVT Data for an 11-12 Year-Old . 24 3.3 PVT Data for Individual 1023 . 25 3.4 Modified Reaction Time as a Function of Concentration . 26 3.5 Simulation of PVT Data for a 5-6 Year-Old . 27 vii LIST OF TABLES TABLE PAGE 2.1 Biological Parameters Used in Concentration Function . 14 3.1 Means and Standard Errors { Entire PVT . 20 3.2 Means and Standard Errors { First and Last 2 Minutes of PVT . 21 viii CHAPTER 1 INTRODUCTION Sleep inertia is the period of grogginess that occurs immediately after awakening and that causes delayed reaction times and general deficits in alertness and behavioral performance [7, 11]. Sleep inertia may affect a variety of abilities, such as spatial memory, logical reasoning, mental arithmetic, grip strength, and response times [2, 7, 9]. It should be noted that the sleep stage from which a person awakens may affect the severity of sleep inertia and that performance decrements may be worse or last longer after an individual awakens from slow-wave sleep [2, 7, 12, 11]. Furthermore, it is likely that a sleep-deprived individual will suffer more severe effects of sleep inertia than one who is fully rested [2, 7]. Another factor affecting sleep inertia is an individual's circadian clock, which affects body temperature. A subject awakened at a particularly low point of the circadian temperature cycle will likely suffer from more severe sleep inertia [2]. There are few methods that have been proven to lessen the effects of sleep inertia: some studies have found that bright lighting, snacks, and/or showering immediately after awakening do not seem to decrease the effects or time course of sleep inertia (as measured by subjective sleepiness and performance on an arithmetic task) [9], while others have found bright lighting to have some dissipating effect on sleep inertia [6]. However, caffeine may help to reduce the time course of sleep inertia (as measured by psychomotor vigilance task, discussed later) if taken immediately after awakening [6, 16], and constant low-dose caffeine administration 1 almost completely eliminates sleep inertia after 2-hour naps under conditions of sleep deprivation [16]. 1.1 Time Course of Sleep Inertia The time course of sleep inertia is not well-defined: In extreme cases, impairment may be present for several hours [9], but often individuals recover within a few min- utes. These varying time courses may be the result of the type of task used to measure sleep inertia, as the dynamics and time course are likely different for different tasks [7]. Several studies have been conducted to determine the length of time required to recover from sleep inertia effects, with somewhat conflicting findings. In one study that used both subjective sleepiness (using a visual analogue scale) and a 2-minute addition task to measure sleep inertia, it was found that performance on both of these tasks increases asymptotically and does not approach the asymptote until 2-4 hours after waking, even under normal sleeping patterns (without sleep deprivation) [9]. It should be noted that this study was conducted only in subjects awakening from Stage N1 or N2 or REM sleep, but, since awakening from slow-wave sleep has been hypothesized to amplify sleep inertia effects, it can be expected that sleep inertia will last at least as long when an individual is awakened from N3 (slow-wave) sleep. Other studies have confirmed that sleep inertia effects can last up to an hour or more, even in the absence of sleep deprivation [13, 11], while others still maintain that the effects dissipate within 20-30 minutes [13]. The current study will observe only the first 10-15 minutes after awakening, a time period during which most sources agree sleep inertia is still present. 2 1.2 Psychomotor Vigilance Task The current study used a 10-minute visual psychomotor vigilance task (PVT). During the PVT, subjects are given a hand-held device with an LED display window and are instructed to closely observe the window. Each stimulus appears in bright red in the window, with intervals between stimuli following a random uniform distribution between 2 to 10 seconds. The subject is instructed to press a button as soon as the stimulus appears; the stimulus will remain visible in the window until a button is pressed. When the stimulus appears, the PVT device begins a counter in milliseconds, which stops as soon as the subject presses the button, at which time the response time is displayed to the subject for 1 second. If a subject presses the wrong button, presses a button in the absence of a stimulus, holds the button down for too long, or does not respond for more than 65 seconds, an error message will be recorded instead of the response time [1]. Most often, adults taking a PVT have responses below 500 ms; thus, a response above 500 ms is unusual and is often referred to as a \lapse." However, there are inter-individual differences and some subjects with slower response times may have many responses above 500 ms. Furthermore, children have much slower responses than adults in general, and they often present reactions of longer than 500ms. For these reasons, some studies define lapses as response times greater than twice the mean response time, rather than simply those greater than 500 ms [3, 6]. Response times of greater than 30 seconds or less than 100 ms are very rare and likely the result of an error or a coincidental pressing of the button before a subject realized a stimulus was present; thus, we disregard such response times in our study. The PVT was developed specifically to analyze the dynamics of the interactions between an individual's circadian clock and homeostatic sleep drive. It was designed so that it has a minimal learning curve, the duration of the task is relatively short, 3 there are a large number of stimuli in that relatively short period, and it maintains inter-individual differences.