Two-process Model Of Sleep Regulation Research Articles

A unified mathematical model to quantify performance impairment for both chronic sleep restriction and total sleep deprivation

Performance prediction models based on the classical two-process model of sleep regulation are reasonably effective at predicting alertness and neurocognitive performance during total sleep deprivation (TSD). However, during sleep restriction (partial sleep loss) performance predictions based on such models have been found to be less accurate. Because most modern operational environments are predominantly characterized by chronic sleep restriction (CSR) rather than by episodic TSD, the practical utility of this class of models has been limited.To better quantify performance during both CSR and TSD, we developed a unified mathematical model that incorporates extant sleep debt as a function of a known sleep/wake history, with recent history exerting greater influence. This incorporation of sleep/wake history into the classical two-process model captures an individual's capacity to recover during sleep as a function of sleep debt and naturally bridges the continuum from CSR to TSD by reducing to the classical two-process model in the case of TSD. We validated the proposed unified model using psychomotor vigilance task data from three prior studies involving TSD, CSR, and sleep extension. We compared and contrasted the fits, within-study predictions, and across-study predictions from the unified model against predictions generated by two previously published models, and found that the unified model more accurately represented multiple experimental studies and consistently predicted sleep restriction scenarios better than the existing models. In addition, we found that the model parameters obtained by fitting TSD data could be used to predict performance in other sleep restriction scenarios for the same study populations, and vice versa. Furthermore, this model better accounted for the relatively slow recovery process that is known to characterize CSR, as well as the enhanced performance that has been shown to result from sleep banking.

Circadian amplitude and homeostatic buildup rate in postural control

Postural control during quiet stance is a common everyday physical activity. Sleepiness is increasingly prevalent in our 24-h society. Yet, little research exists that quantitatively links the fluctuations in sleepiness and postural control. This study quantifies the circadian amplitude and homeostatic buildup rate in postural control. With a force plate we assessed postural control in 12 participants (21–38 years) every 2h during 24h of sustained wakefulness. The sway area was 1.39±0.71mm2 at the circadian high around noon, and 4.02±0.67mm2 at the circadian low around 6 am (a 189% change, p=0.02). The circadian amplitude of the sway area was therefore 2.63mm2. The sway area was 1.92±0.64mm2 at the start of the 24-h period and 4.42±0.69mm2 at the end of the period (a 130% change, p<0.001). The homeostatic buildup rate of sway area was 0.04h−1. The circadian- and homeostatic effects on sway variability, sway velocity, sway frequency and fractal dimension were smaller but still significant. This study found that the circadian amplitude and homeostatic buildup rate are quantifiable from posturographic data, and that they have significant impact on postural control. This finding is important because it means that one could apply the framework of the famous two-process model of sleep regulation (published by Borbély in 1982) to explain the previously reported sleepiness-related changes in postural control.

A biomathematical model of the restoring effects of caffeine on cognitive performance during sleep deprivation

RationaleWhile caffeine is widely used as a countermeasure to sleep loss, mathematical models are lacking. ObjectiveDevelop a biomathematical model for the performance-restoring effects of caffeine in sleep-deprived subjects. MethodsWe hypothesized that caffeine has a multiplicative effect on performance during sleep loss. Accordingly, we first used a phenomenological two-process model of sleep regulation to estimate performance in the absence of caffeine, and then multiplied a caffeine-effect factor, which relates the pharmacokinetic–pharmacodynamic effects through the Hill equation, to estimate the performance-restoring effects of caffeine. ResultsWe validated the model on psychomotor vigilance test data from two studies involving 12 subjects each: (1) single caffeine dose of 600mg after 64.5h of wakefulness and (2) repeated doses of 200mg after 20, 22, and 24h of wakefulness. Individualized caffeine models produced overall errors that were 19% and 42% lower than their population-average counterparts for the two studies. Had we not accounted for the effects of caffeine, the individualized model errors would have been 117% and 201% larger, respectively. ConclusionsThe presented model captured the performance-enhancing effects of caffeine for most subjects in the single- and repeated-dose studies, suggesting that the proposed multiplicative factor is a feasible solution.

Factor Analysis of the Pittsburgh Sleep Quality Index in Breast Cancer Survivors

ContextSleep is a significant problem in breast cancer survivors (BCS) and measured frequently using the Pittsburgh Sleep Quality Index (PSQI). Thus, it is important to evaluate its factor structure. The two-process model of sleep regulation was the theoretical framework for this study. ObjectivesTo perform a confirmatory factor analysis of the PSQI in BCS and compare results between African-American and Caucasian BCS. MethodsThis was a secondary analysis of cross-sectional data using local and regional health care facilities and Eastern Cooperative Oncology Group referrals. The study included 1174 nondepressed BCS (90% Caucasian), with a mean age of 57 years and median PSQI global scores at the cutoff for poor sleep (median=6.00, interquartile range=4.00–9.00). Measurements included self-reported demographics, medical history, depression, and sleep. ResultsAcceptable fit was not reached for the traditional one-factor model that would be consistent with current PSQI scoring or for alternative models in the published literature from other populations. A new two-factor model (i.e., sleep efficiency and perceived sleep quality) best fit the data but nested-model comparisons by race showed different relationships by race for 1) sleep quality-sleep latency and 2) sleep efficiency-sleep quality. ConclusionResults were inconsistent with current PSQI scoring that assumes a single global factor and with previously published literature. Although a new two-factor model best fit the data, further quantitative and qualitative analyses are warranted to validate our results in other populations before revising PSQI scoring recommendations. Additional recommendations are described for research.

Factors Associated With Sleep-Wake Disturbances in Child and Adult Survivors of Pediatric Brain Tumors: A Review

To identify factors associated with sleep-wake disturbances in pediatric and adult survivors (aged older than 18 years) of pediatric brain tumors. A computerized literature search was completed using MEDLINE, CINAHL, CancerLit, Dissertation Abstracts International, and PsycINFO. The search and a personal communication with one author discovered 25 English-language research articles and case reports describing sleep-wake patterns in brain tumor survivors from 1966-2008. Disease- and treatment-related factors from direct injury to the hypothalamus results in irregular melatonin secretion and low hypocretin levels. This contributes to decreased daytime alertness, which remains the most reported sleep-wake disturbance in brain tumor survivors. Patients with craniopharyngiomas, radiation dose more than 3,500 cGy, and younger age at time of treatment experienced more severe sleep dysfunction. Patients with brain tumors experience a disruption of sleep-wake patterns associated with major dysfunction in the hypothalamic-pituitary axis, affecting both Process S (homeostasis) and Process C (circadian) from the Two-Process Model of Sleep Regulation. Various demographic-, disease-, and treatment-related variables are involved in driving the onset of sleep disturbances. Interventions are needed to improve daytime function and decrease the effect of sleep disturbances on quality of life. Current sleep literature has identified patterns of sleep disturbances in cross-sectional studies of brain tumor survivors. Rigorous longitudinal designs are needed for future studies to detect onset patterns and trajectory of sleep-wake disorders. Intervention studies are needed to impact excessive daytime sleepiness, irregular sleeping and waking patterns, and other identified sleep-wake disorders.

An Improved Methodology for Individualized Performance Prediction of Sleep-Deprived Individuals with the Two-Process Model

We present a method based on the two-process model of sleep regulation for developing individualized biomathematical models that predict performance impairment for individuals subjected to total sleep loss. This new method advances our previous work in two important ways. First, it enables model customization to start as soon as the first performance measurement from an individual becomes available. This was achieved by optimally combining the performance information obtained from the individual's performance measurements with a priori performance information using a Bayesian framework, while retaining the strategy of transforming the nonlinear optimization problem of finding the optimal estimates of the two-process model parameters into a series of linear optimization problems. Second, by taking advantage of the linear representation of the two-process model, this new method enables the analytical computation of statistically based measures of reliability for the model predictions in the form of prediction intervals. Two distinct data sets were used to evaluate the proposed method. Results using simulated data with superimposed white Gaussian noise showed that the new method yielded 50% to 90% improvement in parameter-estimate accuracy over the previous method. Moreover, the accuracy of the analytically computed prediction intervals was validated through Monte Carlo simulations. Results for subjects representing three sleep-loss phenotypes who participated in a laboratory study (82 h of total sleep loss) indicated that the proposed method yielded individualized predictions that were up to 43% more accurate than group-average prediction models and, on average, 10% more accurate than individualized predictions based on our previous method.

Sleep and sleep homeostasis in constant darkness in the rat

According to the two-process model of sleep regulation, a homeostatic Process S increases during waking and decreases during sleep. The time course of Process S can be derived on the basis of changes in vigilance states and changes in electroencephalogram slow-wave activity (SWA, activity below 4 Hz) during non-rapid eye movement (NREM) sleep. In most mouse strains, an optimal fit between S and SWA was achieved with one increasing (active during waking and REM sleep) and one decreasing time constant (active during NREM sleep) for Process S. However, in the rat, systematic deviations in the light and dark periods were observed, which were resolved by introducing different decreasing time constants between the light and dark periods. The present study shows that this difference between the rest (light) and active (dark) phases remains, and may even be larger, after animals are adapted to constant dark conditions for at least a week. In addition, the data show that the build-up rate of SWA at the onset of a NREM sleep episode is slow compared with the increase rate under light-dark conditions, and that this build-up rate changes with the circadian phase. The slow build-up rate introduces a systematic error between the simulation of Process S and SWA in NREM sleep. The circadian modulation of the build-up rate may, together with circadian changes in NREM sleep episode duration, be the source of the necessity of introducing a difference in the decreasing time constant between the rest and active phases.

Evidence for differential human slow‐wave activity regulation across the brain

The regulation of the timing of sleep is thought to be linked to the temporal dynamics of slow-wave activity [SWA, electroencephalogram (EEG) spectral power in the approximately 0.75-4.5 Hz range] in the cortical non-rapid eye movement (NREM) sleep EEG. In the two-process model of sleep regulation, SWA was used as a direct indication of sleep debt, or Process S. Originally, estimation of the latter was performed in a gross way, by measuring average SWA across NREM-REM sleep cycles, fitting an exponential curve to the values thus obtained and estimating its time constant. In later studies, SWA was assumed to be proportional to the instantaneous decay rate of Process S, rather than taken as a direct reflection of S. Following up on this, we extended the existing model of SWA dynamics in which the effects of intrusions of REM sleep and wakefulness were incorporated. For each subject, a 'gain constant' can be estimated that quantifies the efficiency of SWA in dissipating S. As the course of SWA is variable across cortical locations, local differences are likely to exist in the rate of discharge of S, eventually leading to different levels of S in different cortical regions. In this study, we estimate the extent of local differences of SWA regulation on the basis of the extended model of SWA dynamics, for 26 locations on the scalp. We observed higher efficiency of SWA in dissipation of S in frontal EEG derivations, suggesting that SWA regulation has a clear local aspect. This result further suggests that the process involved in (local) SWA regulation cannot be identical to the Process S involved (with Process C) in effectual determination of sleep timing - a single behaviour that cannot vary between locations on the scalp. We therefore propose to distinguish these two representations and characterize the former, purely SWA-related, as 'Process Z', which then is different for different locations on the scalp. To demonstrate those differences, we compare the gain constants derived for the medial EEG derivations (Fz, Cz, Pz, Oz) with each other and with the decay rate derived from SWA values per NREM-REM sleep cycle.

A new mathematical model for the homeostatic effects of sleep loss on neurobehavioral performance

The two-process model of sleep regulation makes accurate predictions of sleep timing and duration for a variety of experimental sleep deprivation and nap sleep scenarios. Upon extending its application to waking neurobehavioral performance, however, the model fails to predict the effects of chronic sleep restriction. Here we show that the two-process model belongs to a broader class of models formulated in terms of coupled non-homogeneous first-order ordinary differential equations, which have a dynamic repertoire capturing waking neurobehavioral functions across a wide range of wake/sleep schedules. We examine a specific case of this new model class, and demonstrate the existence of a bifurcation: for daily amounts of wakefulness less than a critical threshold, neurobehavioral performance is predicted to converge to an asymptotically stable state of equilibrium; whereas for daily wakefulness extended beyond the critical threshold, neurobehavioral performance is predicted to diverge from an unstable state of equilibrium. Comparison of model simulations to laboratory observations of lapses of attention on a psychomotor vigilance test (PVT), in experiments on the effects of chronic sleep restriction and acute total sleep deprivation, suggests that this bifurcation is an essential feature of performance impairment due to sleep loss. We present three new predictions that may be experimentally verified to validate the model. These predictions, if confirmed, challenge conventional notions about the effects of sleep and sleep loss on neurobehavioral performance. The new model class implicates a biological system analogous to two connected compartments containing interacting compounds with time-varying concentrations as being a key mechanism for the regulation of psychomotor vigilance as a function of sleep loss. We suggest that the adenosinergic neuromodulator/receptor system may provide the underlying neurobiology.

Individualized performance prediction of sleep-deprived individuals with the two-process model

We present a new method for developing individualized biomathematical models that predict performance impairment for individuals restricted to total sleep loss. The underlying formulation is based on the two-process model of sleep regulation, which has been extensively used to develop group-average models. However, in the proposed method, the parameters of the two-process model are systematically adjusted to account for an individual's uncertain initial state and unknown trait characteristics, resulting in individual-specific performance prediction models. The method establishes the initial estimates of the model parameters using a set of past performance observations, after which the parameters are adjusted as each new observation becomes available. Moreover, by transforming the nonlinear optimization problem of finding the best estimates of the two-process model parameters into a set of linear optimization problems, the proposed method yields unique parameter estimates. Two distinct data sets are used to evaluate the proposed method. Results of simulated data (with superimposed noise) show that the model parameters asymptotically converge to their true values and the model prediction accuracy improves as the number of performance observations increases and the amount of noise in the data decreases. Results of a laboratory study (82 h of total sleep loss), for three sleep-loss phenotypes, suggest that individualized models are consistently more accurate than group-average models, yielding as much as a threefold reduction in prediction errors. In addition, we show that the two-process model of sleep regulation is capable of representing performance data only when the proposed individualized model is used.

Moving Towards Individualized Performance Models

Moving Towards Individualized Performance Models

Optimization of Biomathematical Model Predictions for Cognitive Performance Impairment in Individuals: Accounting for Unknown Traits and Uncertain States in Homeostatic and Circadian Processes

Current biomathematical models of fatigue and performance do not accurately predict cognitive performance for individuals with a priori unknown degrees of trait vulnerability to sleep loss, do not predict performance reliably when initial conditions are uncertain, and do not yield statistically valid estimates of prediction accuracy. These limitations diminish their usefulness for predicting the performance of individuals in operational environments. To overcome these 3 limitations, a novel modeling approach was developed, based on the expansion of a statistical technique called Bayesian forecasting. The expanded Bayesian forecasting procedure was implemented in the two-process model of sleep regulation, which has been used to predict performance on the basis of the combination of a sleep homeostatic process and a circadian process. Employing the two-process model with the Bayesian forecasting procedure to predict performance for individual subjects in the face of unknown traits and uncertain states entailed subject-specific optimization of 3 trait parameters (homeostatic build-up rate, circadian amplitude, and basal performance level) and 2 initial state parameters (initial homeostatic state and circadian phase angle). Prior information about the distribution of the trait parameters in the population at large was extracted from psychomotor vigilance test (PVT) performance measurements in 10 subjects who had participated in a laboratory experiment with 88 h of total sleep deprivation. The PVT performance data of 3 additional subjects in this experiment were set aside beforehand for use in prospective computer simulations. The simulations involved updating the subject-specific model parameters every time the next performance measurement became available, and then predicting performance 24 h ahead. Comparison of the predictions to the subjects' actual data revealed that as more data became available for the individuals at hand, the performance predictions became increasingly more accurate and had progressively smaller 95% confidence intervals, as the model parameters converged efficiently to those that best characterized each individual. Even when more challenging simulations were run (mimicking a change in the initial homeostatic state; simulating the data to be sparse), the predictions were still considerably more accurate than would have been achieved by the two-process model alone. Although the work described here is still limited to periods of consolidated wakefulness with stable circadian rhythms, the results obtained thus far indicate that the Bayesian forecasting procedure can successfully overcome some of the major outstanding challenges for biomathematical prediction of cognitive performance in operational settings.

A critical review of existing mathematical models for alertness

Existing biomathematical models of human fatigue and performance are reviewed with the aim of identifying open questions and ways of improving models. Most fatigue and alertness models are based on the twoprocess model of sleep regulation. They present a mathematical formulation of the two-process model targeted on different metrics including alertness, fatigue, sleepiness, performance measures and accident risk. One of the reviewed fatigue models is completely empirical without reference to sleep regulation. Differences between the models result from the specific data set on which a model is based. These data sets determine the possible application areas for the models ranging from airline operations, car and truck drivers to industrial shift work. It is generally accepted that fatigue models are useful also for educating people about fatigue in non-standard work situations and for generating scientific hypotheses that can be tested by experiments. Important points for the improvement of models include the consideration of cumulative fatigue, interindividual differences, effects of external factors such as light on fatigue, and task-related effects. Very few models consider the task-related fatiguing effect of different activities.

Understanding sleep–wake behavior and sleep disorders in children: the value of a model

Sleep-wake problems such as night wakings, excessive crying, or difficulties in falling asleep are frequent behavioral issues during childhood. Maturational changes in sleep and circadian regulation likely contribute to the development and maintenance of such problems. This review highlights the recent research examining bioregulatory sleep mechanisms during development and provides a model for predicting sleep-wake behavior in young humans. Findings demonstrate that circadian and sleep homeostatic processes exhibit maturational changes during the first two decades of life. The developing interaction of both processes may be a key determinant of sleep-wake and crying behavior in infancy. Evidence shows that the dynamics of sleep homeostatic processes slow down in the course of childhood (i.e., sleep pressure accumulates more slowly with increasing age) enabling children to be awake for consolidated periods during the day. Another current topic is the adolescent sleep phase delay, which appears to be driven primarily by maturational changes in sleep homeostatic and circadian processes. The two-process model of sleep regulation is a valuable framework for understanding and predicting sleep-wake behavior in young humans. Such knowledge is important for improving anticipatory guidance, parental education, and patient care, as well as for developing appropriate social policies.

EEG Slow Wave Activity Regulation in Major Depression. EEG-Slow-Wave-Aktivitat bei Patienten mit Major Depression

Question of the study Sleep disturbances, including reduced slow wave activity (SWA), are among the most consistently replicated biological alterations in major depression. According to the two-process model of sleep regulation, SWA is homoeostatically regulated as a function of prior waking time. This study aimed to further elucidate SWA regulation in major depression.

Homeostatic Sleep Regulation in Adolescents

To examine the effects of total sleep deprivation on adolescent sleep and the sleep electroencephalogram (EEG) and to study aspects of sleep homeostasis. Subjects were studied during baseline and recovery sleep after 36 hours of wakefulness. Four-bed sleep research laboratory. Seven prepubertal or early pubertal children (pubertal stage Tanner 1 or 2 = Tanner 1/2; mean age 11.9 years, SD +/- 0.8, 2 boys) and 6 mature adolescents (Tanner 5; 14.2 years, +/- 1.4, 2 boys). Thirty-six hours of sleep deprivation. All-night polysomnography was performed. EEG power spectra (C3/A2) were calculated using a Fast Fourier transform routine. In both groups, sleep latency was shorter, sleep efficiency was higher, non-rapid eye movement (NREM) sleep stage 4 was increased, and waking after sleep onset was reduced in recovery relative to baseline sleep. Spectral power of the NREM sleep EEG was enhanced after sleep deprivation in the low-frequency range (1.6-3.6 Hz in Tanner 1/2; 0.8-6.0 Hz in Tanner 5) and reduced in the sigma range (11-15 Hz). Sleep deprivation resulted in a stronger increase of slow-wave activity (EEG power 0.6-4.6 Hz, marker for sleep homeostatic pressure) in Tanner 5 (39% above baseline) than in Tanner 1/2 adolescents (18% above baseline). Sleep homeostasis was modeled according to the two-process model of sleep regulation. The build-up of homeostatic sleep pressure during wakefulness was slower in Tanner 5 adolescents (time constant of exponential saturating function 15.4 +/- 2.5 hours) compared with Tanner 1/2 children (8.9 +/- 1.2 hours). In contrast, the decline of the homeostatic process was similar in both groups. Maturational changes of homeostatic sleep regulation are permissive of the sleep phase delay in the course of adolescence.

Regulation of adolescent sleep: implications for behavior.

Adolescent development is accompanied by profound changes in the timing and amounts of sleep and wakefulness. Many aspects of these changes result from altered psychosocial and life-style circumstances that accompany adolescence. The maturation of biological processes regulating sleep/wake systems, however, may be strongly related to the sleep timing and amount during adolescence-either as "compelling" or "permissive" factors. The two-process model of sleep regulation posits a fundamental sleep-wake homeostatic process (process S) working in concert with the circadian biological timing system (process C) as the primary intrinsic regulatory factors. How do these systems change during adolescence? We present data from adolescent participants examining EEG markers of sleep homeostasis to evaluate whether process S shows maturational changes permissive of altered sleep patterns across puberty. Our data indicate that certain aspects of the homeostatic system are unchanged from late childhood to young adulthood, while other features change in a manner that is permissive of later bedtimes in older adolescents. We also show alterations of the circadian timing system indicating a possible circadian substrate for later adolescent sleep timing. The circadian parameters we have assessed include phase, period, melatonin secretory pattern, light sensitivity, and phase relationships, all of which show evidence of changes during pubertal development with potential to alter sleep patterns substantially. However the changes are mediated-whether through process S, process C, or by a combination-many adolescents have too little sleep at the wrong circadian phase. This pattern is associated with increased risks for excessive sleepiness, difficulty with mood regulation, impaired academic performance, learning difficulties, school tardiness and absenteeism, and accidents and injuries.

Investigating the interaction between the homeostatic and circadian processes of sleep–wake regulation for the prediction of waking neurobehavioural performance

The two-process model of sleep regulation has been applied successfully to describe, predict, and understand sleep-wake regulation in a variety of experimental protocols such as sleep deprivation and forced desynchrony. A non-linear interaction between the homeostatic and circadian processes was reported when the model was applied to describe alertness and performance data obtained during forced desynchrony. This non-linear interaction could also be due to intrinsic non-linearity in the metrics used to measure alertness and performance, however. Distinguishing these possibilities would be of theoretical interest, but could also have important implications for the design and interpretation of experiments placing sleep at different circadian phases or varying the duration of sleep and/or wakefulness. Although to date no resolution to this controversy has been found, here we show that the issue can be addressed with existing data sets. The interaction between the homeostatic and circadian processes of sleep-wake regulation was investigated using neurobehavioural performance data from a laboratory experiment involving total sleep deprivation. The results provided evidence of an actual non-linear interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance.

Mathematical models of sleep regulation.

The level of EEG slow-wave activity (SWA) is determined by the duration of prior sleep and waking. SWA is a marker of nonREM sleep intensity and may serve as an indicator of sleep homeostasis. The two-process model of sleep regulation posits the interaction of the homeostatic Process S and the circadian Process C. Also models of neurobehavioral functions (three-process model; interactive models of alertness and cognitive throughput) are based on the concept of an interaction between homeostatic and circadian factors. Whether the interaction is linear or non-linear is still unresolved. Models may serve as a guiding principle for specifying the relationship between processes occurring at the macroscopic and microscopic level of analysis.

Hemodialysis disrupts basic sleep regulatory mechanisms: building hypotheses.

The proposition that hemodialysis may induce alterations in the sleep-wake cycle is based on two clinical observations: (a) Patients on dialysis frequently sleep during and after dialysis, and (b) the procedure often is associated with temperature elevations. A review of pertinent literature showed that sleepiness and temperature are physiologically related, and that these two variables are important indicators of sleep and circadian regulatory processes. To describe possible associations among hemodialysis, body temperature, and sleepiness; to assist in building hypotheses; and to provide direction for future research. Three exploratory studies were performed to investigate (a) dialysis-associated elevations in body temperature, (b) changes in body temperature patterns across the day, and (c) alterations in daytime sleepiness. The current study demonstrated that many patients manifest dialysis-associated episodic elevations of body temperature, changes in the circadian pattern of body temperature, and increases in daytime sleep propensity. In the context of the Two-Process Model of Sleep Regulation, these alterations provide a parsimonious explanation for the poor subjective sleep quality, prolonged sleep latency, and daytime sleepiness reported by these patients. These preliminary studies lead to the suggestion that hemodialysis may disrupt basic sleep regulatory mechanisms, and that further investigation in this area is warranted.