Dynamics of sleep: exploring critical
transitions and early warning signals
Susanne de Mooij
*1, Tessa Blanken
1,2, Raoul Grasman
1& Han van der Maas
1*Corresponding author: susannedemooij94@gmail.com, 1Department of Psychology, Psychological Methods, University of Amsterdam, the Netherlands, 2Department of Sleep and Cognition, Netherlands Institute for Neuroscience (an institute of the Royal Netherlands Academy of Arts and Sciences), Amsterdam, the Netherlands
Abstract
The mechanisms and dynamics of sleep are still largely unknown, although the societal impact of poor sleep quality and disorders demands more insight. The tendency to classify the complexity of sleep into distinct stages, such as in the AASM manual, has been subject for debate, because it often fails to describe characteristic changes in sleep. We used existing techniques such as automated detection algorithms and change point analysis to identify distinct changes in sleep and investigate the dynamics before these transitions. The time series recordings of a single EEG channel of two healthy participants were explored and we identified multiple distinct changes in the EEG, mostly in interplay with NREM 2. The dynamics before these changes reveal some, but not all, indicators of generic early warning signals, found in a wide class of complex systems. These early warning signals are predictive for critical transitions such that the dynamics of sleep seems to slow down. The occurrence and characteristics of critical transitions in sleep could possibly be benifical in understanding the individual and pathological differences and implications of the dynamics of sleep stage transitions.
Key words sleep stage, critical transition, early warning, change point analysis, dynamics, time
Introduction
Sleep is typically characterized by changing brain activity measured by Electroencephalography (EEG) patterns, and already in 1937 Loomis et al. classified these changes in distinct stages, spanning from wakefulness to deep sleep. Since then, this classification has been adapted numerous times and in 2007 the American Academy of Sleep Medicine (AASM) standardized the rules for sleep stage scoring, where the cyclic macrostructure of sleep is divided manually into five discrete stages or states: Stage W (Wakefulness), Stage NREM 1 & NREM 2 (light sleep), Stage NREM 3 (deep sleep) & Stage R (rapid eye movement; REM). Most sleep researchers use this classical sleep profile (i.e. the macrostructure of sleep), but manual scoring is time-consuming and leaves room for subjective interpretation, where the interrater reliability ranges between 80-90% (Moser et al., 2009; Danker-Hopfe, 2004). Furthermore, traditional sleep scoring is based upon segments with a fixed duration of 30 seconds, called epochs, and does not assign a stage transition at the actual point it occurs. If a stage shift happens in the middle of an epoch, the visual analyzer has to choose one specific stage nevertheless. The method is especially difficult to apply to elderly and patients with sleep disorders since these have abnormal, heavily fragmented sleep (Silber et al., 2007), where constant shifting between two stages within one epoch is not unusual. The current sleep stage scoring tries to classify the complex, multilayered, time-varying process of sleep into a rule-based set of a few distinct sleep stages, but is not flexible enough to identify characteristic changes in sleep. The limitations and shortcomings of the classical sleep profile are incentive to look for other ways to analyze sleep mechanisms and its dynamics.
Automated algorithms with or without rule-based classification
Over the years many studies have focused on developing an alternative to manual scoring through automatic software techniques with computerized classification algorithms such as support vector machines (SVM; Zhu, Li & Wen, 2014), decision trees (Kubat, Pfurtscheller & Flotzinger, 1994; Hanaoka, Kobayashi & Yamazaki, 2002) and neural networks (Schaltenbrand et al., 1996; Oropesa, Cycon & Jobert, 1999). All these algorithms extract each epoch from sleep recordings and score the stage according to the presence, properties and duration of a particular rhythm consisting of the following frequency bands: alpha (α; 8-14 Hz), beta (β; +13 Hz), theta (θ; 3.5-7.5 Hz) and delta (δ; 0.5-3 Hz). See Figure 1 for a visual representation of each of the
stages. Most of these algorithms are trained with the outcomes from manual scoring based upon the AASM rules and studies have found an agreement rate of around 60-80% between the two approaches, even with only a single EEG channel used (Schaltenbrand et al., 1996; Ebrahimi et
al., 2008; Fraiwan et al., 2012; Koley & Dey, 2012). These algorithms are less-time consuming and can be used to validate manual scoring. Although automatic techniques are a good alternative to classify sleep stages and find predictors that characterize sleep patterns, the algorithms are still dependent on the outcomes of manual scoring and have fixed duration of epochs.
Other automated detection studies have focused on modelling changes in EEG independent of the classical macrostructural sleep profile. For example, Kaplan et al. (2001) used a minimalistic appoach of EEG change-point segmentation in combination with cluster analysis using only the four fundamental frequency bands (delta, theta, alpha and beta) to find three basic patterns that together form the characteristic cyclic pattern of sleep: light sleep (NREM 2), deep sleep (NREM 3) and NREM 1/REM. Flexerand et al. (2002) have found that only the “extreme” AASM stages such as wake and deep sleep (NREM 3) can be detected satisfactory by using a Hidden Markov Models (HMM). Although these methods are not used frequently, the studies above present helpful tools to obtain objective information about the dynamics of sleep,
Figure 1. EEG-characterization of a healthy participant from the sample used in this study. According to the AASM manual, Stage Wake presents mixed EEG frequencies and body movement, where beta waves with low amplitude and high frequency are dominant. NREM 1 is identified by a reduction of alpha waves and the appearance of theta waves. NREM 2 shows a K-complex (a negative high voltage sharp) and/or sleep spindle burst (with a frequency range between 12-14 Hz), mixed with the NREM 1 waves. NREM 3 (deep sleep) has characteristic delta waves with a high amplitude and low frequencies. REM stage has irregular and mixed brain waves with waves in the form of sawtooth and low amplitude similar to wake and is immediately evident when the Electrooculography (EOG) detects rapid eye movements.
independent of standardized rules and fixed durations. This would allow analysis of characteristic changes in sleep in more depth.
Changes in EEG activity and early warning signals
All scoring methods essentially attempt to reveal the dynamics of sleep by classifying different stages. These dynamics can be very distinct between healthy and sleep disordered people, where the level of sleep quality depends on certain characteristics of the transitions between stages (Laffan, Caffo, Swihart, & Punjabi, 2010; Kishi et al., 2008; Wei et al., 2017). For example, patients with Chronic Insomnia Disorder (ID), have poor sleep quality and exhibit different transition characteristics than healthy subjects, such as an increased probability to switch from NREM 2 to light sleep or wake and have trouble shifting back to sleep, also known as sleep fragmentation. To understand these pathological differences, it is vital to not merily classify stages but to zoom into the changes in EEG and their characteristics starting with healthy sleep. Changes in EEG activity, could be described as critical transitions in the dynamics of sleep. Critical transitions are also known as catastrophic bifurcations, where the system is triggered by a small force and propelled towards a contrasting state once a threshold is exceeded (Scheffer et al., 2009). The simplest criterion for critical transitions is bimodality where two distinct states exist in the distribution of the data. The occurence of critical transitions is not yet formally investigated for sleep stages, but has been shown in other complex systems such as ecosystems (Scheffer et al., 2009; Dakos et al., 2008), financial markets (Bussiere & Fratzscher, 2006), and depression (van de Leemput et al., 2014). Critical transitions in complex systems are rather unpredictable. Interestingly though, there appear to be generic properties that occur in a wide class of systems before a critical point is reached. These so-called early-warning signals predict a sudden shift and give an indication of the tipping point towards another state. One commonly found phenomenon before a critical transition is called “critical slowing down” (Scheffer et al., 2009), which means that the recovery from small perturbations slows down. Two phenomena characterize critical slowing down indirectly: (1) increase in the variance of the system towards the tipping point (Dakos, Van Nes, D'Odorico, & Scheffer, 2012) and (2) elevated autocorrelation in the time series. For example, elevated temporal autocorrelation and variance in the fluctuations of the EEG data of epileptic patients are early-warning signals for an epileptic seizure (McSharry, Smith & Tarassenko, 2003). An alternative early-warning signal is “flickering”, where the system moves back and forth between states, which is also observed in epileptic seizures (Litt et al., 2001). The question is whether generic properties, called early warning-signals, are also detectable in EEG sleep activity. These detections would indicate whether there
are critical transitions between sleep stages, revealing valuable information about the dynamics of sleep. Usually early warning signals have been found and investigated in systems with only one critical transition, but in a typical night of sleep there are many transitions. If early warning signals can be found, it is interesting to investigate which sleep stages are demarcated by a critical transition. If we can find critical transitions between different stages, the next question is which types of early warning signals (e.g. increase or decrease in variance and/or elevated autocorrelation) reveal these transitions.
In the present study, we exploratory investigate different ways to model the dynamics of healthy sleep, first with automated detection techniques to find valid predictors for sleep patterns. Secondly, we use change point analysis to find the exact location of discontinuities in EEG data, since manual scoring and automatic detection techniques are restricted to fixed durations of scoring and based on the AASM rules. After detecting the changes in EEG, we look for early warning signals, generic properties such as increase in variance and autocorrelation to investigate whether these change points in the EEG are actually critical transitions, as in other complex systems. These early warning signals could be used to understand why and when changes in sleep pattern occur and eventually predict sudden changes in sleep.
Methods
ParticipantsThe data used for this study were collected by the Sleep & Cognition group of the Nederlands Herseninstituut. Participants were recruited through the Sleep Registry (Benjamins et al., 2016) and advertisement, and were screened by telephone first, followed by face-to-face interviews. Sleep recordings from two participants of the 88 in total were used, where the total consists of 46 suffering from insomnia disorder (38 females, age range 23-69 y) and 42 controls (32 females, age range 22-70 y) matched in age. The two participants used for analysis originated from the healthy control group, containing volunteers that reported to have no sleep difficulties, which was confirmed during interview. In this study, we focused on the control participants, to explore the dynamics of transitions of healthy subjects.
Protocol
The participants completed two consecutive nights of polysomnography (PSG) in a laboratory setting from 23:00 pm to 7:00 am next day. During recording days, people were asked to refrain from alcohol and drugs, and to limit themselves to a maximum of two cups of caffeinated
beverages, which were allowed only before noon. PSGs were recorded from a 256-channel LTM HydroCel EEG net and a Polygraphic Input Box (Electrical Geodesic Inc., Eugene, OR), connected to a Net Amps 300 amplifier (input impedance: 200 MΩ, A/D converter: 24 bits). The lights-out time for each participant was adaptively chosen according to individual habitual bedtime. The PSG is used to monitor brain activity (EEG). Other recordings are eye movements (EOG), muscle activity (EMG) and heart rhythm (ECG) during sleep. An expert of the Sleep & Cognition group of the Nederlands Herseninstituut scored the sleep recordings of the two participants according to the AASM. Every epoch (30 seconds) is assigned to one sleep stage (W, NREM 1, NREM 2, NREM 3, REM) and if more than one sleep stage occurred within an epoch, the greatest portion of the epoch was scored as the stage of the whole epoch. For the subsequent analyses only the second night of sleep recordings is used, since the first night serves as a screening and adaptation night. Instead of using 3 EEG channels, 2 EOG channels and EMG according to the standard rules of AASM, we restricted the analysis to one EEG channel, namely the Frontal Fz channel.
Polysomnography
In a first step, we downsampled the sampling frequency from 250 Hz to 100 Hz of the Frontal Fz channel and filtered the frequencies with a band pass filter on a range of 0.1 till 40 Hz, in order to minimize residual artefacts and reduce the size of EEG recordings using Matlab eeglab (Delorme & Makeig, 2004). The data was detrended with a gaussian kernel smoothing function to cope with non-stationarity and long trends in the data. The bandwidth was chosen in such a way that we did not overfit the data, but still removed the long-term trends in the records, according to Silverman’s (1986) rule of thumb. From the detrended, filtered and downsampled data the spectral bands 1-3 Hz (delta), 4-7 Hz (theta), 8-13 Hz (alpha), 16-31 Hz (beta) were extracted with a band-pass filter. This data is applicable to time-domain analyses but does not have any frequency details. Therefore a continuous wavelet transformation (CWT) is needed to have a time-frequency repesentation of the signal. The CWT for a signal (s) can be written as:
𝑊𝑊(𝑎𝑎, 𝑏𝑏) = �|𝑎𝑎|1 ∫ 𝑥𝑥(𝑡𝑡)𝜑𝜑(−∞∞ 𝑡𝑡−𝑏𝑏𝑎𝑎 )dt
where a is the scaling parameter, b is the translation parameter (time shifting parameter), x is the
signal function, t is time and 𝜑𝜑 is the mother wavelet. We used CWT on the preprocessed EEG data with the mother wavelet (𝜑𝜑) called morlet, since a morlet wavelet has the desirable property to optimize the time-frequency resolution (Addison, 2017). This morlet wavelet has the following form, with J as imaginary unit and ω as center frequency:
𝜑𝜑(𝑡𝑡) = 1 �𝜋𝜋 4 𝑒𝑒
−𝑡𝑡22𝑒𝑒−𝑗𝑗𝑗𝑗𝑗𝑗
Our regions of interest were identified when the power of the CWT coefficients corresponded to the four different frequency bands and these coefficients were extracted seperately. Since changes in the EEG activity are usely an interplay between the frequency bands, we computed three relative power ratios in the different frequency bands that can be used to model EEG transitions. The best extactable features from single EEG channel according to Koley & Dey (2012) were used for this purpose: (1) β/δ ratio, (2) α/δ ratio and (3) (α + β)/(θ + δ) ratio.
Data analysis
The analysis plan consists of two parts: (1) detect EEG sleep changes in both participants with statistical methods and (2) evaluate whether these changes are critical transitions based on early warning signals. In the first part we used both manual scoring and automated classifiers to shape the sleep patterns and regions for potential transitions. Firstly, a multinomial logistic regression (MLR) was used to classify sleep into stages using the scored epochs as reference and the three relative power ratios, averaged over 30 seconds, as predictors using glmnet (R core team, 2016; package "glmnet"). For developing the MLR we used K-fold cross validation on the two participants which partitions the data into k equally sized folds (segments). One fold is for validation and the other k-1 folds are used to train the model, which is repeated k times. Using this trained model, new predictions were made on test data (1/3 of the data) and compared with the scored data to investigate the performance of the classifier.
The exact location of the transitions can be detected with an independent multiple change-point analysis (CPA), that computes the significant changes in the EEG distribution by detecting distribution changes within time-ordered observations (Matteson & James, 2014). This method enables us to simultaneously identify the number and locations of change points. The epoch before and after every transition that was scored both by the expert as well as detected by the classification is selected for analysis to make sure we have the most distinct transitions detectable in the EEG signal. Note that all these selected transitions shape one signal for further analysis, where, for example, the occurrence of NREM 2- NREM 1 followed by NREM 1-Wake, would cause two times NREM 1 in a row. The CPA was restricted to detect the most significant changes (p<0.005) in the multivariate signal of the four wavelet coefficients of δ, θ, α, β frequency bands. This multivariate signal was combined with the most important feature according to the classification model. The importance of the features is calculated through a ROC curve analysis for each feature using caret (Kuhn, 2016; R package “caret”).
The second part of this study is addressed by exploring early warning signals, when approaching the tipping point before an EEG change found by the CPA. We first look at several early-warning signals in the two healthy participants, with the most important being increased variance and temporal autocorrelation as indicators of critical slowing down (Scheffer et al., 2009). The autocorrelation and variance is estimated with the "earlywarnings" R package (Dakos et al., 2012). These signals are computed 25 seconds before every detected change point originating from the change point analysis. The existence or non-existence of a visualized trend in autocorrelation and variance of all the transitions together, along with the corresponding mean kendall tau, a measure of rank correlation, should indicate whether there are critical transitions in sleep or not.
Results
The present section summarizes the obtained results starting with the classification of sleep stages to change point analysis and followed by the exploration of early warning signals.
Multinomial logistic regression (MLR) based classification
We have processed a total of 1881 epochs for the subsequent classification study of the two healthy participants in one night. Figure 1 shows the corresponding manually scored sleep stages throughout the night (hypnogram) along with the three relative power ratios features of one participant.
Figure 2. The association between the sleep stages visually scored by an expert according to AASM throughout the night (hypnogram; black line) and the three selected relative power ratio features (red, green, and blue line).
The correlation between the features and the hypnogram is ρ = .72, p < 0.001, so these features
seem promising for classification. Table 1 presents the performance of the classifier, with metrics such as precision, recall and the F-1 score for each of the five sleep stages (Wake, NREM 1, NREM 2, NREM 3, REM). Precision is the fraction of correct predictions for a certain sleep stage, whereas recall is the fraction of instances of a stage that were predicted correctly and F-1 is the harmonic mean of precision and recall. For example, the low precision of NREM 1 indicates that in only 19.4% of the cases the model predicted NREM 1 correct, indicating many false positives. The low recall in NREM 1 shows many false negatives, since in only 42.4% of the cases where sleep was scored as NREM 1, it was predicted as NREM 1. The low precision and recall results in a low F-1 score for NREM 1. The overall classification accuracy was .71, indicating the performance throughout the night was in 71% in accordance with the visual scorer. The evaluation metrics per class show that the classifier is relatively good in predicting NREM 2, NREM 3 and REM but less good in predicting wake and NREM 1.
Change point Analysis (CPA)
Only the signals were used where the manual scorer and MLR agreed on the labelled stages. Multivariate CPA was performed to find the location of change points in the EEG signal of the multivariate signal consisting of the four frequency band wavelet coefficients, along with the best classification feature according to the ROC curve analysis, namely the (α + β)/(θ + δ) ratio. Figure 3 shows eleven significant (p<0.005) change points found by CPA in the multivariate signal, where the red lines represent the change points, in a total of 26 scored epochs (see the coloured blocks in figure 3). Although we would expect 23 changes in the EEG, according to the manually and automated scored transitions in this signal, we only find half with change point
Sleep stages
Evaluation Metrics
Precision Recall F-1 score
NREM 1 .194 .424 .267
NREM 2 .779 .690 .732
NREM 3 .808 .809 .808
REM .648 .690 .668
Wake .065 .429 .113
Table 1. The average performance of the multinomial logistic regression method in sleep stage classification on two healthy participants
analysis, meaning either the scored stages are not that dinstinct in every transition or these changes are not detectable in the multivariate signal.
Nevertheless, 10 of the 11 change points found by the CPA were located in the labelled NREM 2 epochs (e.g. the light purple shaded areas): Five transitions were in the transition from and five transitions towards NREM 2. This stage is the key factor between either falling deeper in sleep (NREM 3) or waking up, which is translated in the amount of distinct changes found associated with NREM 2. The second red line can be labelled as the change point between NREM 3 and NREM 1, shown by the decrease of delta waves (upper plot) from deep sleep and increase of alpha and beta waves after the change, suggesting light sleep.
Figure 3. Multivariate change point analysis on the four frequency band wavelet coefficients (alpha, beta, theta, delta; upper four plots) along with the relative power ratio between these four bands (lower plot). The red lines show the significant change point locations and the shaded coloured areas are the labelled sleep where the manual scoring and the MLR classifier agreed upon.
Early warning signals
To explore whether critical slowing down indicates a tipping point towards another sleep stage, we investigated all 11 change points found by the CPA. Possible early warning signals predicting these changes were indications such as increased standard deviation (SD) and autocorrelation (AR1). Figure 4 shows the trends of AR1 and SD 25 seconds prior to the detected change points of every transition ordered by the transition type (e.g. NREM 1 to NREM 2). The Kendall tau was calculated to see whether the trends were significant or not, where a significant trend in either of the signals could indicate critical slowing down. For example, the red-coloured lines for both SD and AR1 visualize the three transitions from NREM 2 to NREM 1 with two significant trends of standard deviation and two significant trends of autocorrelation, where the lighter coloured lines occur later at night. Overall, the results show no visible universal trend, but the direction of the trends differs between the transition area type. For example, between the types of transitions there are indications of decrease in SD (NREM 3 to NREM 1 & NREM 2 to NREM 2), increase in SD (NREM 2 to REM & NREM 1 to NREM 2) and increase in autocorrelation (REM to NREM 2). The trends also differ within the same transition type, such as the autocorrelation in transition NREM 2 to NREM 1, where there are signs of increase and decrease in AR1. The strongest indications of critical slowing down can be found from REM to NREM 2, displaying a strong increase in AR1 in both transitions.
Discussion
In the present study, we modelled the dynamics of healthy sleep as distinct changes in EEG. We combined two different automated detection algorithms to: (a) classify the changing sleep patterns and (b) locate the exact tipping points towards another sleep state. We found multiple change points in one night with this data-driven approach, but only in less than half of the cases found by manual scoring and classification. Moreover, we explored the build-up towards these
Figure 3. Possible indications of critical slowing down: Autocorrelation (6 lower plots) and standard deviation (6 upper plots) trend 25 seconds prior to each change point found by CPA. Every transition is visualized with a different colour and all transitions are divided into transition types (e.g. N1 to N2). The lighter colours in every transition type represent the transitions occuring later at night. The kendall tau was calculated for every trend and the significance (p<0.005) of this kendall tau is depicted by rectangles and non-significance by circles.
change points in healthy sleep and found early warning signals especially associated with stage NREM 2. The strongest signs were found in the two transitions from REM to NREM 2 with increased autocorrelation and decreased variance, suggesting the dynamics of sleep slow down before the tipping point. These results suggest that a focus on critical transitions reveals a new EEG-characterization of the dynamics of sleep that would remain undetected in classic sleep analyses.
Our result with an agreement rate of 71% is similar to other automated detection studies, where they found between 60-80% agreement rate (Schaltenbrand et al., 1996; Ebrahimi et al., 2008; Fraiwan et al., 2012; Koley & Dey, 2012). Some studies also used a single EEG channel without other polygraphic signals such as EOG or EMG, but the use of just three predictors (namely the relative power ratios between the wavelet coefficients) is less common. We have shown that these are powerful features for classification. The low agreement rate between the classification and manual scoring in NREM 1 has been reported in other studies, and is probably due to the short duration of this stage (Schaltenbrand et al., 1996). The similarity between wake and NREM 1 makes it difficult to distinguish these stages with a classifier.
For locating the change points we focused on the transitions scored by both manual scoring and classification to analyze more specifically and reduce the computer load. For a more data-driven and minimalistic approach, it would be interesting to locate the changes in the EEG without a selection beforehand. Our findings show that most “scored transitions”, with fixed 30s epochs, could not be detected statistically with a distribution change, where only 11 out of 26 transitions were noted, mostly in interplay with NREM 2. Kaplan et al. (2001) found similar results, where they could distinct clearly between NREM 3, NREM 2 and NREM 1/REM. The K-complexes (brief negative high-voltage peak) and sleep spindles (burst of brain activity) characterizing NREM 2 seem to reflect such distinct beta, theta and delta bands, causing abrupt shifts towards this stage or from this stage to others, such as REM.
The current study is, to our knowledge, the first to investigate early warning signals in sleep, but it is a known phenomenon in other complex systems, ranging from ecosystems (Dakos et al., 2008) to depresssion (van de Leemput et al., 2014). Our findings of elevated autocorrelation before the abrupt shifts from REM and NREM 2 but also in certain transitions from NREM 2 to NREM 1 show the same generic properties as in these other complex systems, where elevated autocorrelation is defined as a robust indicator of slowing down (Dakos et al., 2012). Less robust, but another prime indicator, is increased variance, which we find in some of the transitions such as from NREM 2 to REM and NREM 1 to NREM 2. Decreased variance, such as from NREM 2 to NREM 1 as well as from NREM 3 to NREM 1, is less noted in other complex systems but
is also described as an early warning signal (Dakos et al., 2012). Nonetheless, more work is needed to investigate how robust these signals are and whether these results yield false positives or false negatives (Scheffer et al., 2009). False positives occur when an early warning signal is not a result of approaching a critical transition, due to chance or a confounding trend within sleep. On the contrary, false negatives are situations when no early warning signals was detected but a critical transition did occur due to the statistical difficulty of detecting an early warning signal. False negatives also arise when the transition was not preceded by a gradual approach to the threshold. Statistical procedures for reducing the false positives and negatives should be developed to ensure early warning signals are reliable.
Overall, these results have profound implications for future research in sleep. So far, dynamics of sleep have been modelled as rule-based sets of stages by manually - or occasionally with a computer detection technique- scoring fixed segments of sleep recordings. Our analysis of change points show there are few, but very clear discontinuities in EEG that shape the architecture of sleep going beyond discrete classification. Although the focus in this study was on exploring changes in healthy sleep, our approach would be very interesting for fragmented sleep, where a constant shifting between awake and sleep could be characterized by abrupt changes in the EEG. Moreover, we find indications known as early warning signals, that predict these abrupt changes in sleep. Although it is very difficult to prove what the mechanisms are behind the dynamics of sleep, the early warning signals do point out that some aspects of sleep have a universal property similar to other complex systems approaching a tipping point.
This line of evidence implies there are tipping points in sleep, known as critical transitions, where the system is triggered by a small force and propelled towards a contrasting state once a threshold is exceeded (Scheffer et al., 2009). This enables us to predict when tipping points are likely in sleep, but an open question is which forces trigger these abrupt changes. In the cusp catastrophe theory, a special type of bifurcation theory, critical transitions are modelled as sudden shifts in a system due to gradual changes of two control factors, either stimulating or blocking critical transitions (Thom & Fowler, 1975; Zeeman, 1971). In the context of sleep the two-process model of sleep regulation (Borbély, 1999) has an important role in the non-REM-REM sleep cycle, where the circadian and homeostatic process can be seen as the two control factors to cause critical transitions. Other control factors could be the level of sleep problems, arousal, stress, room temperature along with light. Further investigation is needed, with the cusp theory in mind, to investigate what kind of factors trigger certain critical transitions in sleep.
Despite the fact that this is mostly an exploratory study with a small sample, more effort must be devoted to investigate the occurrence and characteristics of abrupt changes in sleep.
Testing and applying our suggested approach on a larger and more diverse (healthy and sleep-disordered, young and elderly) group of people can prove beneficial to understand individual and pathological differences in sleep quality.
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