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.

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).

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.

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.

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 (β-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.

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.

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.