The sleep onset process (SOP) is a dynamic process correlated with a multitude of behavioral and physiological markers. A principled analysis of the SOP can serve as a foundation for answering questions of fundamental importance in basic neuroscience and sleep medicine. Unfortunately, current methods for analyzing the SOP fail to account for the overwhelming evidence that the wake/sleep transition is governed by continuous, dynamic physiological processes. Instead, current practices coarsely discretize sleep both in terms of state, where it is viewed as a binary (wake or sleep) process, and in time, where it is viewed as a single time point derived from subjectively scored stages in 30-second epochs, effectively eliminating SOP dynamics from the analysis. These methods also fail to integrate information from both behavioral and physiological data. It is thus imperative to resolve the mismatch between the physiological evidence and analysis methodologies. In this paper, we develop a statistically and physiologically principled dynamic framework and empirical SOP model, combining simultaneously-recorded physiological measurements with behavioral data from a novel breathing task requiring no arousing external sensory stimuli. We fit the model using data from healthy subjects, and estimate the instantaneous probability that a subject is awake during the SOP. The model successfully tracked physiological and behavioral dynamics for individual nights, and significantly outperformed the instantaneous transition models implicit in clinical definitions of sleep onset. Our framework also provides a principled means for cross-subject data alignment as a function of wake probability, allowing us to characterize and compare SOP dynamics across different populations. This analysis enabled us to quantitatively compare the EEG of subjects showing reduced alpha power with the remaining subjects at identical response probabilities. Thus, by incorporating both physiological and behavioral dynamics into our model framework, the dynamics of our analyses can finally match those observed during the SOP.

How can we tell when someone has fallen asleep? Understanding the way we fall asleep is an important problem in sleep medicine, since sleep disorders can disrupt the process of falling asleep. In the case of insomnia, subjects may fall asleep too slowly, whereas during sleep deprivation or narcolepsy, subjects fall asleep too quickly. Current methods for tracking the wake/sleep transition are time-consuming, subjective, and simplify the sleep onset process in a way that severely limits the accuracy, power, and scope of any resulting clinical metrics. In this paper, we describe a new physiologically principled method that dynamically combines information from brainwaves, muscle activity, and a novel minimally-disruptive behavioral task, to automatically create a continuous dynamic characterization of a person's state of wakefulness. We apply this method to a cohort of healthy subjects, successfully tracking the changes in wakefulness as the subjects fall asleep. This analysis reveals and statistically quantifies a subset of subjects who still respond to behavioral stimuli even though their brain would appear to be asleep by clinical measures. By developing an automated tool to precisely track the wake/sleep transition, we can better characterize and diagnose sleep disorders, and more precisely measure the effect of sleep medications.

Competing interests: MJP and PLP have patents pending on the monitoring of sleep and anesthesia. MTB has a patent pending for a sleep monitoring device, has consulting agreements with Sunovion on drug-development (<$2000 anticipated in 2014, the first year of the relationship) and is on the clinical advisory board for Foramis (<$2000 anticipated in 2014, the first year of the relationship). JME received an honorarium (<$1000) from presenting Grand Rounds. All other authors have declared that no competing interests exist.

Funding: Research supported by an NIH New Innovator Award DP2-OD006454, (PLP) http://commonfund.nih.gov/newinnovator/index . The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2014 Prerau et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Overall, current practice views the SOP in a binary semantic framework, and analyzes behavioral and physiological data independently. In this paper, we place the SOP within a physiologically and statistically principled model framework, which allows us to explicitly characterize the dynamic interaction of multiple physiological and behavioral experimental observations. Specifically, given the behavioral task and our experimental setup, we simultaneously acquired three modalities of observations related to sleep initiation: behavioral responses, EMG activity, and EEG spectral power. These observation types each contribute information across multiple time scales about different components of a subject's neural state. By combining the information from of all of these different types of observations, we can create a more robust and principled estimate of wakefulness during the process of sleep initiation that takes advantage of both behavioral and physiological data.

Ideally, any descriptor of sleep must account for the fact that it is a complex neural process consisting of multiple local [28] – [30] and spatiotemporally-evolving [23] , [31] – [35] factors. In practice, neural activity is characterized through through polysomnography (PSG)—the visual analysis of brain (EEG), muscle (EMG), muscle (ECG), cardiac (EOG), and respiration (PTAF/Airflow) data. In current clinical practice, sleep EEG is visually scored using the Rechtschaffen and Kales (R&K) system [24] , comprised of Wake, Stage 1–3 NREM sleep, and REM, defined in 30-second epochs. Researchers such as Chiappa [36] and Hori [37] found that the R&K system was too coarse to properly track the SOP dynamics, and consequently developed alternative scoring systems with many more stages, which were scored in much smaller epochs. Unfortunately, neither of these higher resolution frameworks enjoyed wide implementation, perhaps due to labor-intensive scoring rules. Additionally, existing scoring systems do not explicitly account for heterogeneity observed in normal patients as well as variability associated with age, medications, or neurological disorders [38] – [40] .

As sleep is a neural process, direct observation of brain activity has been the primary means of tracking the SOP. The most obvious changes to the EEG during the SOP are a progressive decrease in alpha (8–12 Hz) power, as well as a progressive increase in slow (<1 Hz), delta (.5–5 Hz), and theta (5–8 Hz) power [1] , [23] – [26] . Recent intracranial recording studies suggest that this progression of EEG activity relates to changes in thalamic activity that occur prior to changes in cortical activity, the timing of which has high variability between subjects [27] .

While both active and passive behavioral metrics show general correlation with features of the SOP dynamics, neither is without issue. Therefore, an important goal is to search for a behavioral task that features multiple highly-salient trials (as with the active metrics), yet minimizes arousing external stimuli (as with the passive metrics).

Passive behavioral methods for measuring the SOP include actigraphy [17] , [20] , [21] , continuous pressure (dead man's switch) systems [22] , or a finger tapping task [19] . Actigraphy is the most prevalent form of passive measurement, and has recently been brought to popular attention through home sleep tracking applications for mobile devices [17] , [21] . Since actigraphy works under the assumption that behavioral quiescence in the absence of a task indicates sleep, it cannot distinguish between wakeful motionlessness during the SOP and actual sleep, and thus is not precise enough to describe sleep onset [1] . Passive paradigms involving the use of a “dead man's switch” or finger tapping task compress all SOP dynamics into a single data point by defining sleep onset as the moment at which behavior ceases, and thus tend to underestimate sleep latency [1] .

Ogilvie divides behavioral metrics of sleep onset into categories of active and passive behavioral measurement. Active metrics involve tasks with repeated externally-generated probes for wakefulness, each of which prompts the subject for a physical response via button press or verbal response. Additionally, response via cued respiration has been used for experimental and interventional behavioral paradigms [7] , [8] . These active probes could include subjective queries [9] – [11] , or auditory [12] – [14] and vibratory [15] stimuli. Use of a psychomotor vigilance task (PVT) derived metric [16] has also been proposed. Active methods are useful, as repeated trials yield multiple measurements of wakefulness across the entire SOP, which can be used to characterize SOP dynamics. Moreover, multiple measurements provide statistical power for descriptive and comparative data analyses. These active measurement schemes, however, have all required the use of external stimuli that are potentially arousing and can disrupt sleep [17] – [19] . It has therefore been a question of balancing the trade-off between stimulus salience and the degree to which the SOP is perturbed.

There have been numerous ways in which scientists have attempted to measure behavioral and physiological dynamics during the SOP. For an in-depth look at the methods employed in the past, see Ogilvie's review paper [1] , which comprehensively details the many multimodal correlates of sleep onset and the experimental strategies employed in characterizing them.

While powerful techniques for statistical modeling of dynamic processes have been widely available for several decades [6] , they have yet to be adopted in sleep medicine, nor used to characterize the multimodal dynamics of sleep. The absence of appropriate statistical paradigms for analyzing sleep dynamics is a fundamental impediment to progress in sleep medicine. Development of such statistical methods could have tremendous scientific and clinical impact. In this paper, we propose a dynamic state-space model framework for the characterization of simultaneously observed behavioral and physiological dynamics during the SOP. In doing so, we create a robust quantitative representation of SOP dynamics that can be used to more accurately and more precisely track the gradual transition from wakefulness to sleep. We use a fully Bayesian framework that facilitates flexible and rigorous statistical inferences, including comparison of SOP in different patient populations. We apply this method to data from healthy subjects, demonstrating the features of the method and providing a point of comparison for future studies of sleep pathologies.

Additionally, current experimental analysis of the SOP does not consider behavioral dynamics in conjunction with the physiology, and clinical sleep medicine does not record behavior at all. A reason for this may be the fact that behavioral and physiological dynamics can evolve at different time scales, which would be difficult to characterize using traditional staging methods. It is therefore essential to employ techniques that can fully capture the dynamics of both the physiology and behavior in a principled and integrated manner.

Current SOP analysis discretizes the data even further by reducing the complex, dynamic interplay of neural systems and behavior to a single “point of sleep onset” using semantic criteria. Most notably, the American Academy of Sleep Medicine (AASM), defines sleep onset as the first appearance of any 30-second epoch that contains at least 15 seconds of sleep [5] . By defining a single point of sleep onset, these analyses impose a binary model on the SOP, in which in which the transition from wake to sleep occurs instantaneously at a particular moment in time. This non-physiological transition effectively removes all temporal dynamics, and thus severely limits the degree to which these methods can successfully characterize and diagnose pathologies of sleep onset. Therefore, no matter how sophisticated experimental exploration of the SOP becomes, it will always be limited by the coarse way in which dynamics are described in the analyses.

While the wake/sleep transition has been shown to be continuous and dynamic in every physiological and behavioral system studied thus far [1] , current clinical and research practices unfortunately employ methodologies that essentially ignore these dynamics. This is because these analyses still rely on time-consuming, subjective discretization of the sleep process, performed by technicians who visually score the sleep time-series data in 30-second epochs according to semantically-defined sleep stages [5] . These scoring standards grossly oversimplify sleep dynamics by discretizing the data in both time (by using fixed, non-overlapping epochs) and state (by using discrete sleep stages).

Scientists have long noted that the sleep onset process (SOP), the gradual transition between wakefulness and sleep, is marked by a dynamic continuum of behavioral and physiological changes [1] . Consequently, the ability to understand and provide a principled characterization of SOP dynamics in both healthy and pathological subjects is of fundamental importance for sleep medicine and basic neuroscience alike. In sleep disorders such as insomnia, which has been associated with increased morbidity and mortality [2] , the time course of the wake/sleep transition may be pathologically protracted, resulting in difficulty falling asleep. In disorders of excessive sleepiness, such as narcolepsy or sleep deprivation, the wake/sleep transition occurs too rapidly, resulting in difficulty staying awake, with implications for performance and safety. While there is increasing recognition of the importance of objective sleep testing, there currently exist no quantitative metrics for clinically diagnosing insomnia, which is currently defined exclusively by patient self-report [3] . Hypersomnia, in contrast, is typically defined using a multiple sleep latency test (MSLT) [4] , a labor-intensive diagnostic involving multiple nap periods, all of which must be visually scored by technicians. Given the importance of sleep onset dynamics, the ability to track the continuous dynamical properties of the SOP in a principled, automated manner could provide critical insight into the pathophysiology of these populations, aiding in both diagnosis and in treatment.

Results

A Novel Breathing-Based Behavioral Task to Track the Sleep Onset Process In order to track the course of sleep initiation, our goal is to create a continuous-valued metric of wakefulness that is based on simultaneously observed data from multiple modalities, and for which statistical confidence can be computed. To do so, we must create a task that consists of multiple objective behavioral observations related to wakefulness, which can be tracked across the sleep initiation process. Standard behavioral response tasks that have been used previously, involving external audio, visual, or tactile stimuli, are potentially arousing and may perturb sleep initiation [17]–[19], [41]. We therefore require a paradigm free of arousing external stimuli, yet with repeated trials that can persist throughout the sleep initiation process. To solve this problem, we designed a self-regulated behavioral task centering on breathing. Subjects were given a small, 2oz, gel-filled stress ball to hold in their dominant hand. They were instructed to breathe normally with eyes closed, and to gently squeeze the ball on each inhale and release on each exhale. Thus, each breath acts as a stimulus, and each corresponding squeeze (or lack thereof) is the corresponding response. A correct response is defined as squeeze centered on a respiratory inhale, and an incorrect response is either a lack of response or an incorrectly timed squeeze. Subjects were instructed to start the task as soon as the lights were turned out. An additional bipolar adhesive EMG sensor recorded activity of the flexor digitorum profundus (FDP) responsible for finger flexion. Subjects also were fit with a glove designed with a force sensitive resistor (FSR) embedded in the middle finger, to measure finger flexion during the behavioral task (Fig. 1a). Both the glove and FDP EMG sensors detect even gentle squeezes (on the order of the force required for a mouse click), thereby allowing subjects to perform the task with minimal effort or muscle fatigue. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 1. Tracking the sleep onset process with a behavioral task mediated by breathing. (A) In addition to a high-density EEG cap and standard PSG sensor array, subjects were fitted with a force-sensing glove, bipolar EMG electrodes on their flexor digitorum profundus (FDP), and a small gel-filled stress ball. Subjects were instructed to breathe normally with eyes closed as they fell asleep, and to gently squeeze the stress ball on each inhale, releasing it on each exhale. (B) Times at which a squeeze was aligned with a corresponding inhale were scored as correct trials (green regions). Times with an inhale and no squeeze (or a misaligned squeeze) were scored as incorrect trials. (C) By scoring this task across the sleep initiation period, we can track behavioral dynamics during the transition from wake to sleep, without using any external task stimuli that could produce arousal. (D) EMG amplitude during squeezes decays during the SOP. Over the course of the experiment, the FDP traces (top panel) were processed to extract the median amplitudes of each squeeze (bottom panel), which can be used as a correlate of wakefulness during the SOP. https://doi.org/10.1371/journal.pcbi.1003866.g001 The traces from the glove and FDP EMG were time-aligned with simultaneously recorded PSG respiratory metrics (PTAF, airflow, and abdominal belt) (Fig. 1b,c). These recordings were then visually scored in the following manner: The apex of each respiratory inhale was considered a trial. If a squeeze (visually scored using the EMG/glove activity) was present during an inhale (visually scored using the PTAF, airflow, and abdominal belt), the trial was scored as correct (Fig. 1b, green regions). If there was no visible response or a misaligned squeeze, the trial was scored as incorrect (Fig. 1b, red regions). Periods including motion artifacts, signal degradation due to temporary sensor disconnection, or any other uncertainties in the signal were left unscored and treated as missing data in subsequent analyses. Scoring was started at the first sequence of trials following lights out that began with at least 3 consecutive correct responses. Scoring was stopped 10 minutes following the last correct response. Some subjects reported difficulty performing the task while they adjusted to wearing the full EEG/EMG/PSG montage. After excluding data from four nights with poor task compliance due to difficulty habituating to the extensive sensor montage, the remaining 16 nights from 9 subjects were processed using our algorithm. A wake probability curve was generated for each night.

Simultaneous Observations Provide a Robust Framework for Tracking the Sleep Onset Process Along with each behavioral response, we simultaneously observed the EMG activity in the FDP muscle—including the amplitude of each squeeze accompanying a correct response (Fig. 1d). To measure the magnitude of the squeeze, we computed the amplitude envelope of the EMG using a Hilbert transform, then calculated the mean amplitude in a 1 second window centered around the trial time. In tracking EMG data over the course of the SOP, we see that, like a continuous measurement of the muscle activity during a dead man's switch paradigm [1] the EMG squeeze amplitudes decay until the correct responses stop entirely (Fig. 1d, bottom panel). Thus, the EMG squeeze amplitudes provide a continuous-valued metric of both muscle tone and of wakefulness. Paired with the behavioral task, we simultaneously recorded EEG data from each of the subjects. For our analysis, we chose to focus on the most straightforward, continuous correlates of sleep in the EEG: the power in delta, theta, and alpha bands. The power in these bands contributes information about different neurophysiological systems in play during the SOP. With all these sources of information, we can devise a method for integrating them into a single, statistically principled model of wakefulness during the SOP.

An Empirical Wake Probability Model of Sleep Onset Process Dynamics Our modeling approach centers on the idea that the EMG, EEG, and behavioral observations each provide information related to the activity of different physiological systems involved in different aspects of the SOP. By integrating the information across these systems, we can create a robust framework for tracking the dynamic changes in a subject's wakefulness as they fall asleep. In this section, we provide a non-technical summary of our modeling methodology and its rationale. We describe the mathematical formulation of our approach in detail in the Materials and Methods section, Formulation of the Wake Probability Model of the Sleep Onset Process. We model sleep onset dynamics relative to the observed behavioral, EEG, and EMG data. Our wake probability model states that as the SOP progresses from wake to sleep: •Probability of a correct behavioral response decreases •EMG squeeze amplitude decreases •Alpha power decreases •Theta power increases •Delta power increases A schematic of this model is shown in Figure 2A. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 2. A data-driven model of sleep onset process dynamics. (A) As the SOP progresses, Pr(Wake), the probability that the subject is awake, decreases. As Pr(Wake) decreases, the probability of a correct behavioral response, the EMG squeeze amplitude, and the alpha power will also decrease, while the delta and theta power will increase. (B) We can then use experimental data to estimate Pr(Wake) over time. We define state processes representing the activity of the systems underlying the motor, alpha power, and delta-theta power observations. The combined information from all states represents the level of all activity related to waking, and is used along with the behavioral task responses to estimate the wake probability curve, which tracks Pr(Wake) over time. https://doi.org/10.1371/journal.pcbi.1003866.g002 In our model, we define the wake probability Pr(Wake) as the distribution of the posterior probability (the probability of the model given the observed data) that the conditions necessary for the wake state are met: the subject is responding correctly, the EMG amplitude and alpha power are at their highest, and delta power and theta power are at their lowest. Therefore, as these conditions are met, the mode of Pr(Wake) approaches 1. This allows us to use Pr(Wake) as a metric representing the degree to which we believe the subject is awake. Moreover, we have formulated Pr(Wake) so that it also represents the distribution of the instantaneous probability a correct behavioral response, and thus directly interpretable in terms of standard behavioral paradigms. The wake probability model can be fit to experimental EEG, EMG, and behavioral data to track Pr(Wake)over time. We call the time-varying estimate of Pr(Wake) the wake probability curve. We describe wake probability in the Materials and Methods section, Interpreting Wake Probability. To implement this approach, we use a Bayesian state-space modeling framework [6], [42]–[44] (Fig. 2B). State-space modeling allows us to estimate something that is not directly observable (in this case, the probability of the subject being awake) from observations that can be directly measured (in this case, the EEG, EMG, and behavioral data). We first model the observations as a function of state processes that represent, in abstract, the level of activity in each of these systems (see Materials and Methods, State Models). These state processes are not directly observable, but their values can be inferred from the data given the structure of the model. We create three state processes: a motor activity process state xm, an alpha process state xα, and a delta-theta process state xΔθ. For each of the state processes, we define a state equation, which describes the way the states evolve over time. The state equations are designed to reflect the notion that states cannot change instantaneously, and that they are related to their past values. The motor activity process xm represents the degree of wakefulness estimated from the amplitude of the EMG during the behavioral task (Fig. 1d). As the subject becomes drowsy, the force of the squeezes will decrease and eventually revert to the underlying muscle tone. The alpha process xα represents the degree of wakefulness estimated from the spectral power in the EEG alpha band. As the subject falls asleep, the alpha power will decrease. If the subject awakens, the alpha will return (subjects are told to maintain eyes closed). In our model, the delta-theta process xΔθ represents the degree of wakefulness estimated from the spectral power in the EEG delta and theta bands. As the subject enters NREM sleep, the delta and theta will increase. If the subject awakens, the power in delta and theta will rapidly decrease. Each of the state processes can change independently, reflecting the asynchronous dynamics of the cortical and subcortical systems generating these EEG rhythms throughout the SOP. We formulate our model of wake probability to be a function of the linear combination of the three states such that xm and xα have a direct relationship to Pr(Wake), while xΔθ will have an inverse relationship to Pr(Wake). We next define the observation equations (Fig. 2A), which describe mathematically the relationship between the experimental observations (EMG, alpha, delta, theta, and binary responses) and the underlying state processes (see Materials and Methods, Observation Models). Each observation equation is constructed so that the value of the state process is high when the data indicates high activity, and low when the data indicates low activity. We also define an observation equation relating behavioral response to wakefulness, such that response probability is directly proportional to Pr(Wake). Together, the state and observations define a framework relating our experimental observations to the underlying behavioral and physiological processes, and provide an explicit model for how the aggregate activity of these processes relates to changes in behavior. Using the state and observation equations together with the data, we simultaneously estimate the hidden states and model parameters at each time, using a particle filter, which is a Bayesian sequential importance resampling method (see Supplementary Materials, Particle Filter). The particle filter evaluates all the data observations in context with model equations and computes the maximum-likelihood state and parameter values. The particle filter output is an estimate the full distribution of the posterior probability of the wake probability model, given the observed EEG, EMG, and behavioral data. In summary, our approach takes basic assumptions about the way experimental data evolves during the SOP and explicitly models them in a state-space framework. From this model, we can estimate the wake probability curve, which tracks the dynamics of the SOP by integrating simultaneously observed behavioral and physiological data. Thus, our method provides a robust, statistically-principled, and physiologically-motivated method for characterizing SOP.

Comparing SOP Dynamics for Subjects and Populations Since subjects fall asleep at different rates with different dynamics, comparing physiological activity between subjects and populations has been a difficult problem. As a result, previous studies have been limited to anecdotal analyses or static statistical analysis using categorical bins for data. Fortunately, the wake probability now allows us to compare the SOP of different subjects in a principled manner. This is because the value of Pr(Wake) provides a common point of wakefulness for the alignment of the physiological data across subjects. To characterize the population dynamics of the EEG during the SOP, we estimated the EEG spectrum of the population as a function of Pr(Wake). Specifically we calculated the median spectrum over all subjects and nights at each value of Pr(Wake). We considered values of Pr(Wake) in discrete bins of width 0.0025 between 0 and 1. We then plotted this group-level spectrum as a function of Pr(Wake). The result is a visualization that looks like a spectrogram, but displays median population spectral power as a function of frequency and Pr(Wake), rather than frequency and time. We refer to this plot as the SOP population spectrogram. Since Pr(Wake) also represents response probability, this analysis therefore characterizes the average EEG spectrum dynamics during the SOP as the behavioral response probability declines during the transition from wakefulness to sleep. The SOP population spectrogram allows us to summarize an SOP phenotype for a given population of subjects. Furthermore, we can characterize the difference in the SOP phenotype of two populations by comparing their population spectrograms. To do so, we performed a bootstrap procedure [45], [46] to compute the difference distribution for each frequency-Pr(Wake) bin using 10,000 iterations per bin. A frequence × Pr(Wake) bin was said to be significantly different between populations if zero fell outside the 2.5th and 97.5th percentiles of the difference distribution. The procedure for constructing an SOP population spectrogram is described in detail in the Materials and Methods section, Computing SOP Population Spectrograms.

Goodness-of-Fit Since wake probability is a useful abstract quantity not directly observable during the SOP, standard analyses of measurement error are not possible, as there is no ground truth against which Pr(Wake)can be compared. Instead, we can perform a likelihood analysis to assess how well a particular model of the SOP of describes the behavioral task data. We used Bayesian Monte Carlo procedures to compute the likelihood of a given model as well as compare the likelihoods of two competing models. These procedures are described in detail in the Supplementary Materials section, Bayesian Goodness-of-Fit. Clinically, the SOP is typically characterized by hypnogram-based definitions of a single moment of sleep onset. By definition, any characterization of a “sleep onset point” cleaves SOP dynamics into a unitary wake state prior to the sleep onset point and a unitary sleep following that point. Thus, while never stated outright, any definition of a sleep onset point imposes an instantaneous transition model on the SOP. Since these models assume an instantaneous wake/sleep transition, it follows that they also assume an instantaneous change in behavioral task performance. We can therefore construct a probability curve analogous to the wake probability curve for any instantaneous transition model by conservatively assuming that the subject should respond correctly with significance (95% accuracy) when deemed awake, and incorrectly with significance (5% accuracy) when deemed asleep. We can then compare these curves to the wake probability curve in order to assess the relative goodness-of-fit. The specifics of the Bayesian construction are also detailed in the Models section. To perform the goodness-of-fit analysis, we computed the likelihood distributions for the wake probability model and four different instantaneous transition models using the behavioral data across all subjects for all nights. We then computed the confidence (Bayesian credible interval) with which the wake probability model likelihood differed from that of each instantaneous transition model. Since the wake probability model incorporates information from the behavioral data, we used the posterior distribution from the time step prior to the behavioral observation in all of the goodness-of-fit analyses to insure that use of true behavioral response in the wake probability model formulation did not unfairly affect the results.

Characterizing Heterogeneity of Sleep Onset Phenotypes: Alpha Dropout Prior to Cessation of Behavioral Response In the preceding illustrative examples, there is strong agreement between the behavioral and physiological data. In practice, however, there is neurophysiological heterogeneity observed—even within healthy subjects—such that there is often a great disparity between behavioral and physiological metrics of sleep onset. In this section, we show how the wake probability curve characterizes such situations. Figure 6 shows the results from another healthy subject with a dramatically different SOP phenotype. As in the previous case, the experiment begins with a strong alpha oscillation, which eventually disappears (Fig. 6A). In this case, however, the correct responses persist long after the alpha has diminished (Fig. 6A). Moreover, there is a roughly 5-minute interval between the time the alpha mode declines and the time the theta and delta power increase. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 6. Heterogeneity in healthy subjects: An SOP phenotype with alpha power dropout before the cessation of behavioral activity. The (A) spectrogram, (B) behavioral responses, (C) the wake probability curve, (D) and the clinical hypnogram are shown for a subject with this SOP. The wake probability curve captures persistence of behavioral responses after alpha power declines, a feature that is not evident in hypnogram-based binary models of sleep onset (E). The Bayesian likelihood analysis (F) shows that wake probability significantly outperforms (99.99% Bayesian credible interval of the difference distribution falls above zero) all of the instantaneous transition models in the ability to correctly predict the behavioral responses for this subject. https://doi.org/10.1371/journal.pcbi.1003866.g006 This SOP alpha dropout phenotype with a long interval between alpha power decline and delta/theta power rise results in disagreement between standard sleep scoring and a behavioral analysis. In this period between the loss of alpha and loss of response, the hypnogram (Fig. 6D) describes the subject as being predominantly in Stage N1, with a brief period of Stage N2, and a short period of Wake when there is a short increase in alpha. Thus a standard interpretation of the hypnogram would place sleep onset at the first epoch of Stage N1, approximately 3 minutes into the SOP. This is in contrast to the behavioral data, which continues to indicate wakefulness for another 5 minutes past the first epoch of Stage N1. The wake probability curve (Fig. 6C), however, integrates all the data such that the estimated median of Pr(Wake) is still high during this period, declines slightly, and has a large uncertainty as a result of the contradicting observations. By combining both the behavioral and physiological data into the estimate of Pr(Wake), we can bridge the disparity seen between metrics that exclusively rely on ether behavior or EEG alone. The result is a model that can represent deviation from the population norm as increased uncertainty. In this analysis, 2 of the 9 subjects (Supporting Information Figures S1 and S2) clearly exhibited this alpha dropout phenotype, in which alpha power declined up to several minutes prior to the termination of correct responses and the increase of delta and theta power. For both subjects, this phenotype was present on both experimental nights. Three of the four nights had periods of scored Stage N1 during which there were correct behavioral responses. In none of the cases did we observe correct responses in the presence of strong delta and theta. This suggests that loss of alpha power, while necessary, is not sufficient for the loss of behavioral responses.

Wake Probability Outperforms Clinical Models of Sleep Onset In clinical practice, the most common definitions for the moment of sleep onset are: the first epoch of Stage N1, the first epoch of Stage N2, the first of any 3 consecutive NREM (N1 or deeper) epochs, and the first of any 10 consecutive epochs of NREM. Though not stated explicitly, any characterization of a point of sleep onset actually imposes a model on the SOP with an instantaneous sleep/wake transition, which does not agree with the continuous, dynamic transitions observed in the data. We performed a likelihood analysis comparing how well of the wake probability model and instantaneous transition models fit the behavioral data. Likelihood is a relative estimate of goodness-of-fit, and given two competing models, the one with the better fit will have a higher likelihood. The comparative likelihood analysis showed that the wake probability model significantly outperformed each of the instantaneous transition models with at least 99.99% confidence. These results are summarized in Figure 7 and in Table 1. Overall, the wake probability model fit the data the best with the largest median loglikelihood (−1589), followed by, in order of goodness-of-fit, the first epoch of N1 model (−2781), the first of 3 NREM model (−2852), the first of 10 NREM model (−3191), and by the first epoch of N2 model (−5828). PPT PowerPoint slide

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larger image TIFF original image Download: Figure 7. Goodness-of-fit analysis of the wake probability model versus instantaneous transition models. (A) Using a Bayesian Monte Carlo analysis, we compute the distribution of the total loglikelihood of each of the models given the behavioral task data across all subjects and all nights. The wake probability model significantly outperformed all of the instantaneous transition models (99.99% Bayesian credible interval of the difference distribution fell above for all models). https://doi.org/10.1371/journal.pcbi.1003866.g007 PPT PowerPoint slide

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larger image TIFF original image Download: Table 1. Bayesian goodness-of-fit analysis results. https://doi.org/10.1371/journal.pcbi.1003866.t001 To illustrate the way in which the wake probability model improves upon the instantaneous transition models, we performed the goodness-of-fit analysis on a single night of data. Figure 6E and F show, respectively, the instantaneous transition model response probabilities generated from the hypnogram, and the resultant goodness-of-fit analysis for that experimental session. This clearly shows the way in which the instantaneous transition models implicitly discretize complex dynamics of the SOP into unitary “wake” and “sleep” states, thus losing the ability to capture any nuances in state throughout. Furthermore, since current EEG-based definitions of sleep onset do not include behavioral information, the assumption that Stage N1 is equitable with “sleep” can be misleading [1], particularly for those subjects (like this one) in which behavior persists past the alpha dropout. Consequently, the wake probability model (C) fit the behavioral response data the best (F) with median loglikelihood of −41—significantly outperforming the instantaneous transition models with at least 99.99% confidence. Within the class of the instantaneous transition models (E), the first of any 10 consecutive NREM epochs model performed the best in this particular case, with a median loglikelihood of −68. In this case, the first epoch of N1 model and first of 3 consecutive NREM epochs model both provided the same response probability estimates, and each had a median loglikelihood of −113. Finally, the first epoch of N2 model performed the worst, with a median loglikelihood of −199. Overall, these results suggest that the wake probability model is a more mathematically and physiologically appropriate metric with which to track the SOP than are the current hypnogram-based metrics.