Biomathematical modeling of fatigue due to sleep inertia.

Biomathematical models of fatigue capture the physiology of sleep/wake regulation and circadian rhythmicity to predict changes in neurobehavioral functioning over time. We used a biomathematical model of fatigue linked to the adenosinergic neuromodulator/receptor system in the brain as a framework to predict sleep inertia, that is, the transient neurobehavioral impairment experienced immediately after awakening. Based on evidence of an adenosinergic basis for sleep inertia, we expanded the biomathematical model with novel differential equations to predict the propensity for sleep inertia during sleep and its manifestation after awakening. Using datasets from large laboratory studies of sleep loss and circadian misalignment, we calibrated the model by fitting just two new parameters and then validated the model's predictions against independent data. The expanded model was found to predict the magnitude and time course of sleep inertia with generally high accuracy. Analysis of the model's dynamics revealed a bifurcation in the predicted manifestation of sleep inertia in sustained sleep restriction paradigms, which reflects the observed escalation of the magnitude of sleep inertia in scenarios with sleep restriction to less than âˆ¼ 4 h per day. Another emergent property of the model involves a rapid increase in the predicted propensity for sleep inertia in the early part of sleep followed by a gradual decline in the later part of the sleep period, which matches what would be expected based on the adenosinergic regulation of non-rapid eye movement (NREM) sleep and its known influence on sleep inertia. These dynamic behaviors provide confidence in the validity of our approach and underscore the predictive potential of the model. The expanded model provides a useful tool for predicting sleep inertia and managing impairment in 24/7 settings where people may need to perform critical tasks immediately after awakening, such as on-demand operations in safety and security, emergency response, and health care.

Fatigue risk management based on self-reported fatigue: Expanding a biomathematical model of fatigue-related performance deficits to also predict subjective sleepiness.

Biomathematical models of fatigue can be used to predict neurobehavioral deficits during sleep/wake or work/rest schedules. Current models make predictions for objective performance deficits and/or subjective sleepiness, but known differences in the temporal dynamics of objective versus subjective outcomes have not been addressed. We expanded a biomathematical model of fatigue previously developed to predict objective performance deficits as measured on the Psychomotor Vigilance Test (PVT) to also predict subjective sleepiness as self-reported on the Karolinska Sleepiness Scale (KSS). Four model parameters were re-estimated to capture the distinct dynamics of the KSS and account for the scale difference between KSS and PVT. Two separate ensembles of datasets - drawn from laboratory studies of sleep deprivation, sleep restriction, simulated night work, napping, and recovery sleep - were used for calibration and subsequent validation of the model for subjective sleepiness. The expanded model was found to exhibit high prediction accuracy for subjective sleepiness, while retaining high prediction accuracy for objective performance deficits. Application of the validated model to an example scenario based on cargo aviation operations revealed divergence between predictions for objective and subjective outcomes, with subjective sleepiness substantially underestimating accumulating objective impairment, which has important real-world implications. In safety-sensitive operations such as commercial aviation, where self-ratings of sleepiness are used as part of fatigue risk management, the systematic differences in the temporal dynamics of objective versus subjective measures of functional impairment point to a potentially significant risk evaluation sensitivity gap. The expanded biomathematical model of fatigue presented here provides a useful quantitative tool to bridge this previously unrecognized gap.

The central cavity in trimeric glutamate transporters restricts ligand diffusion.

A prominent aqueous cavity is formed by the junction of three identical subunits in the excitatory amino acid transporter (EAAT) family. To investigate the effect of this structure on the interaction of ligands with the transporter, we recorded currents in voltage-clamped Xenopus oocytes expressing EAATs and used concentration jumps to measure binding and unbinding rates of a high-affinity aspartate analog that competitively blocks transport (ß-2-fluorenyl-aspartylamide; 2-FAA). The binding rates of the blocker were approximately one order of magnitude slower than l-Glu and were not significantly different for EAAT1, EAAT2, or EAAT3, but 2-FAA exhibited higher affinity for the neuronal transporter EAAT3 as a result of a slower dissociation rate. Unexpectedly, the rate of recovery from block was increased by l-Glu in a saturable and concentration-dependent manner, ruling out a first-order mechanism and suggesting that following unbinding, there is a significant probability of ligand rebinding to the same or neighboring subunits within a trimer. Consistent with such a mechanism, coexpression of wild-type subunits with mutant (R447C) subunits that do not bind glutamate or 2-FAA also increased the unblocking rate. The data suggest that electrostatic and steric factors result in an effective dissociation rate that is approximately sevenfold slower than the microscopic subunit unbinding rate. The quaternary structure, which has been conserved through evolution, is expected to increase the transporters' capture efficiency by increasing the probability that following unbinding, a ligand will rebind as opposed to being lost to diffusion.

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.

Numerical simulation of local pharmacokinetics of a drug after intravascular delivery with an eluting stent.

We use mathematical modelling to delineate the influence of two important factors on local pharmacokinetics of a drug delivered via an eluting stent, namely: (1) diffusional resistance of a stent coating, and (2) reversible binding of a drug to the vascular tissue. A system of differential equations that describes diffusion of the drug out of the polymeric coating of the stent into the vascular tissue and into the bloodstream, as well as reversible binding of the drug within the vascular tissue, was solved numerically and the spatial profiles of the concentration of the drug at various points of time were produced and analysed. Also, kinetic curves of the spatial average concentration of the drug within the wall were constructed, and the areas under those curves (AUC) were calculated. The simulations showed that AUC might be enhanced, if the stent is coated with a continuous layer of a drug-releasing medium with a high diffusional resistance. Both the residence time and the average concentration of the drug within the vascular wall increase in this case mainly because the coating imposes a diffusional barrier between the vascular tissue and the bloodstream, thereby reducing the wash-out. If the drug reversibly binds to the tissue, the residence time increases greatly, but the AUC for the free (unbound) drug remains unchanged, implying that the presence of the drug in the vessel is prolonged at the expense of a proportional reduction in concentration of a free drug within the tissue. These findings justify the design of eluting stents with continuous coatings with enhanced diffusional resistance and the engineering of drugs with enhanced affinity to the vascular matrix. Reversible binding to tissue may be beneficial for prolonging the presence of the drug in the target tissue, and for avoiding potential toxic peak effects of high concentrations of the free (unbound) drug.

Glutamate transporter control of ambient glutamate levels.

Accurate knowledge of the ambient extracellular glutamate concentration in brain is required for understanding its potential impacts on tonic and phasic receptor signaling. Estimates of ambient glutamate based on microdialysis measurements are generally in the range of ∼2-10µM, approximately 100-fold higher than estimates based on electrophysiological measurements of tonic NMDA receptor activity (∼25-90nM). The latter estimates are closer to the low nanomolar estimated thermodynamic limit of glutamate transporters. The reasons for this discrepancy are not known, but it has been suggested that microdialysis measurements could overestimate ambient extracellular glutamate because of reduced glutamate transporter activity in a region of metabolically impaired neuropil adjacent to the dialysis probe. We explored this issue by measuring diffusion gradients created by varying membrane densities of glutamate transporters expressed in Xenopus oocytes. With free diffusion from a pseudo-infinite 10µM glutamate source, the surface concentration of glutamate depended on transporter density and was reduced over 2 orders of magnitude by transporters expressed at membrane densities similar to those previously reported in hippocampus. We created a diffusion model to simulate the effect of transport impairment on microdialysis measurements with boundary conditions corresponding to a 100µm radius probe. A gradient of metabolic disruption in a thin (∼100µm) region of neuropil adjacent to the probe increased predicted [Glu] in the dialysate over 100-fold. The results provide support for electrophysiological estimates of submicromolar ambient extracellular [Glu] in brain and provide a possible explanation for the higher values reported using microdialysis approaches.

Dynamic circadian modulation in a biomathematical model for the effects of sleep and sleep loss on waking neurobehavioral performance.

Recent experimental observations and theoretical advances have indicated that the homeostatic equilibrium for sleep/wake regulation--and thereby sensitivity to neurobehavioral impairment from sleep loss--is modulated by prior sleep/wake history. This phenomenon was predicted by a biomathematical model developed to explain changes in neurobehavioral performance across days in laboratory studies of total sleep deprivation and sustained sleep restriction. The present paper focuses on the dynamics of neurobehavioral performance within days in this biomathematical model of fatigue. Without increasing the number of model parameters, the model was updated by incorporating time-dependence in the amplitude of the circadian modulation of performance. The updated model was calibrated using a large dataset from three laboratory experiments on psychomotor vigilance test (PVT) performance, under conditions of sleep loss and circadian misalignment; and validated using another large dataset from three different laboratory experiments. The time-dependence of circadian amplitude resulted in improved goodness-of-fit in night shift schedules, nap sleep scenarios, and recovery from prior sleep loss. The updated model predicts that the homeostatic equilibrium for sleep/wake regulation--and thus sensitivity to sleep loss--depends not only on the duration but also on the circadian timing of prior sleep. This novel theoretical insight has important implications for predicting operator alertness during work schedules involving circadian misalignment such as night shift work.