No abstract

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.

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.

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.

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.