Can we rely on wearable sleep-tracker devices for fatigue management?

STUDY OBJECTIVES: Wearable sleep-tracker devices are ubiquitously used to measure sleep; however, the estimated sleep parameters often differ from the gold-standard polysomnography (PSG). It is unclear to what extent we can tolerate these errors within the context of a particular clinical or operational application. Here, we sought to develop a method to quantitatively determine whether a sleep tracker yields acceptable sleep-parameter estimates for assessing alertness impairment. METHODS: Using literature data, we characterized sleep-measurement errors of 18 unique sleep-tracker devices with respect to PSG. Then, using predictions based on the unified model of performance, we compared the temporal variation of alertness in terms of the psychomotor vigilance test mean response time for simulations with and without added PSG-device sleep-measurement errors, for nominal schedules of 5, 8, or 9 hours of sleep/night or an irregular sleep schedule each night for 30 consecutive days. Finally, we deemed a device error acceptable when the predicted differences were smaller than the within-subject variability of 30 milliseconds. We also established the capability to estimate the extent to which a specific sleep-tracker device meets this acceptance criterion. RESULTS: On average, the 18 sleep-tracker devices overestimated sleep duration by 19 (standard deviation = 44) minutes. Using these errors for 30 consecutive days, we found that, regardless of sleep schedule, in nearly 80% of the time the resulting predicted alertness differences were smaller than 30 milliseconds. CONCLUSIONS: We provide a method to quantitatively determine whether a sleep-tracker device produces sleep measurements that are operationally acceptable for fatigue management.

Assessment of the unified model of performance: accuracy of group-average and individualised alertness predictions.

To be effective as a key component of fatigue-management systems, biomathematical models that predict alertness impairment as a function of time of day, sleep history, and caffeine consumption must demonstrate the ability to make accurate predictions across a range of sleep-loss and caffeine schedules. Here, we assessed the ability of the previously reported unified model of performance (UMP) to predict alertness impairment at the group-average and individualised levels in a comprehensive set of 12 studies, including 22 sleep and caffeine conditions, for a total of 301 unique subjects. Given sleep and caffeine schedules, the UMP predicted alertness impairment based on the psychomotor vigilance test (PVT) for the duration of the schedule. To quantify prediction performance, we computed the root mean square error (RMSE) between model predictions and PVT data, and the fraction of measured PVTs that fell within the models' prediction intervals (PIs). For the group-average model predictions, the overall RMSE was 43 ms (range 15-74 ms) and the fraction of PVTs within the PIs was 80% (range 41%-100%). At the individualised level, the UMP could predict alertness for 81% of the subjects, with an overall average RMSE of 64 ms (range 32-147 ms) and fraction of PVTs within the PIs conservatively estimated as 71% (range 41%-100%). Altogether, these results suggest that, for the group-average model and 81% of the individualised models, in three out of four PVT measurements we cannot distinguish between study data and model predictions.

Distributions of pore sizes and atomic densities in binary mixtures revealed by molecular dynamics simulations.

We report on the results of a molecular dynamics simulation study of porous glassy media, formed in the process of isochoric rapid quenching from a high-temperature liquid state. The transition to a porous solid occurs due to the concurrent processes of phase separation and material solidification. The study is focused on topographies of the model porous structures and their dependence on temperature and average density. To quantify the pore-size distributions, we put forth a scaling relation that provides a satisfactory data collapse in systems with high porosity. We also find that the local density of the solid domains in the porous structures is broadly distributed, and, with increasing average density, a distinct peak in the local density distribution is displaced toward higher values.

Molecular Dynamics Simulations of the Rotational and Translational Diffusion of a Janus Rod-Shaped Nanoparticle.

The diffusion of a Janus rod-shaped nanoparticle in a dense Lennard-Jones fluid is studied using molecular dynamics (MD) simulations. The Janus particle is modeled as a rigid cylinder whose atoms at each end have different interaction energies with fluid molecules, thus comprising wetting and nonwetting surfaces. We found that both rotational and translational diffusion coefficients are larger for Janus particles with lower average wettability, and these values are bound between the two limiting cases of uniformly wetting and nonwetting particles. It was also shown that values of the diffusion coefficients for displacements parallel and perpendicular to the major axis of a uniformly wetting particle agree well with analytical predictions despite a finite slip at the particle surface present in MD simulations. It was further demonstrated that diffusion of Janus particles is markedly different from that of uniform particles; namely, Janus particles preferentially rotate and orient their nonwetting ends along the displacement vector to reduce drag. This correlation between translation and rotation is consistent with the previous results on diffusive dynamics of a spherical Janus particle with two hemispheres of different wettability.

Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear.

Using molecular dynamics simulations, we study the transient response of a binary Lennard-Jones glass subjected to periodic shear deformation. The amorphous solid is modeled as a three-dimensional Kob-Andersen binary mixture at a low temperature. The cyclic loading is applied to slowly annealed, quiescent samples, which induces irreversible particle rearrangements at large strain amplitudes, leading to stress-strain hysteresis and a drift of the potential energy towards higher values. We find that the initial response to cyclic shear near the critical strain amplitude involves disconnected clusters of atoms with large nonaffine displacements. In contrast, the amplitude of shear stress oscillations decreases after a certain number of cycles, which is accompanied by the initiation and subsequent growth of a shear band.

Identifying two regimes of slip of simple fluids over smooth surfaces with weak and strong wall-fluid interaction energies.

The slip behavior of simple fluids over atomically smooth surfaces was investigated in a wide range of wall-fluid interaction (WFI) energies at low shear rates using non-equilibrium molecular dynamics simulations. The relationship between slip and WFI shows two regimes (the strong-WFI and weak-WFI regimes): as WFI decreases, the slip length increases in the strong-WFI regime and decreases in the weak-WFI regime. The critical value of WFI energy that separates these regimes increases with temperature, but it remains unaffected by the driving force. The mechanism of slip was analyzed by examining the density-weighted average energy barrier (ΔE¯) encountered by fluid atoms in the first fluid layer (FFL) during their hopping between minima of the surface potential. We demonstrated that the relationship between slip and WFI can be rationalized by considering the effect of the fluid density distribution in the FFL on ΔE¯ as a function of the WFI energy. Moreover, the dependence of the slip length on WFI and temperature is well correlated with the exponential factor exp(-ΔE¯/(kBT)), which also determines the critical value of WFI between the strong-WFI and weak-WFI regimes.

Effects of viscous heating and wall-fluid interaction energy on rate-dependent slip behavior of simple fluids.

Molecular dynamics simulations are used to investigate the rate and temperature dependence of the slip length in thin liquid films confined by smooth, thermal substrates. In our setup, the heat generated in a force-driven flow is removed by the thermostat applied on several wall layers away from liquid-solid interfaces. We found that for both high and low wall-fluid interaction (WFI) energies, the temperature of the fluid phase rises significantly as the shear rate increases. Surprisingly, with increasing shear rate, the slip length approaches a constant value from above for high WFI energies and from below for low WFI energies. The two distinct trends of the rate-dependent slip length are rationalized by examining S(G_{1}), the height of the main peak of the in-plane structure factor of the first fluid layer (FFL) together with D_{WF}, which is the average distance between the wall and FFL. The results of numerical simulations demonstrate that reduced values of the structure factor, S(G_{1}), correlate with the enhanced slip, while smaller distances D_{WF} indicate that fluid atoms penetrate deeper into the surface potential leading to larger friction and smaller slip. Interestingly, at the lowest WFI energy, the combined effect of the increase of S(G_{1}) and decrease of D_{WF} with increasing shear rate results in a dramatic reduction of the slip length.

Evolution of the pore size distribution in sheared binary glasses.

Molecular dynamics simulations are carried out to investigate mechanical properties and porous structure of binary glasses subjected to steady shear. The model vitreous systems were prepared via thermal quench at constant volume to a temperature well below the glass transition. The quiescent samples are characterized by a relatively narrow pore size distribution whose mean size is larger at lower glass densities. We find that in the linear regime of deformation, the shear modulus is a strong function of porosity, and the individual pores become slightly stretched while their structural topology remains unaffected. By contrast, with further increasing strain, the shear stress saturates to a density-dependent plateau value, which is accompanied by pore coalescence and a gradual development of a broader pore size distribution with a discrete set of peaks at large length scales.

Nonaffine rearrangements of atoms in deformed and quiescent binary glasses.

The influence of periodic shear deformation on nonaffine atomic displacements in an amorphous solid is examined via molecular dynamics simulations. We study the three-dimensional Kob-Andersen binary mixture model at a finite temperature. It is found that when the material is periodically strained, most of the atoms undergo repetitive nonaffine displacements with amplitudes that are broadly distributed. We show that particles with large amplitudes of nonaffine displacements are organized into compact clusters. With increasing strain amplitude, spatial correlations of nonaffine displacements become increasingly long-ranged, although they remain present even in a quiescent system due to thermal fluctuations.

Reversible plastic events during oscillatory deformation of amorphous solids.

The effect of oscillatory shear strain on nonaffine rearrangements of individual particles in a three-dimensional binary glass is investigated using molecular dynamics simulations. The amorphous material is represented by the Kob-Andersen mixture at the temperature well below the glass transition. We find that during periodic shear deformation of the material, some particles undergo reversible nonaffine displacements with amplitudes that are approximately power-law distributed. Our simulations show that particles with large amplitudes of nonaffine displacement exhibit a collective behavior; namely, they tend to aggregate into relatively compact clusters that become comparable with the system size near the yield strain. Along with reversible displacements there exist a number of irreversible ones. With increasing strain amplitude, the probability of irreversible displacements during one cycle increases, which leads to permanent structural relaxation of the material.

The effect of a reversible shear transformation on plastic deformation of an amorphous solid.

Langevin dynamics simulations are performed to investigate the plastic response of a model glass to a local shear transformation in a quiescent system. The deformation of the material is induced by a spherical inclusion that is gradually strained into an ellipsoid of the same volume and then reverted back into the sphere. We show that the number of cage-breaking events increases with increasing strain amplitude of the shear transformation. The results of numerical simulations indicate that the density of cage jumps is larger in the cases of weak damping or slow shear transformation. Remarkably, we also found that, for a given strain amplitude, the peak value of the density profiles is a function of the ratio of the damping coefficient and the time scale of the shear transformation.

Diffusion of a Janus nanoparticle in an explicit solvent: A molecular dynamics simulation study.

Molecular dynamics simulations are carried out to study the translational and rotational diffusion of a single Janus particle immersed in a dense Lennard-Jones fluid. We consider a spherical particle with two hemispheres of different wettabilities. The analysis of the particle dynamics is based on the time-dependent orientation tensor, particle displacement, as well as the translational and angular velocity autocorrelation functions. It was found that both translational and rotational diffusion coefficients increase with decreasing surface energy at the nonwetting hemisphere, provided that the wettability of the other hemisphere remains unchanged. We also observed that in contrast to homogeneous particles, the nonwetting hemisphere of the Janus particle tends to rotate in the direction of the displacement vector during the rotational relaxation time.

Plastic deformation of a model glass induced by a local shear transformation.

The effect of a local shear transformation on plastic deformation of a three-dimensional amorphous solid is studied using molecular dynamics simulations. We consider a spherical inclusion, which is gradually transformed into an ellipsoid of the same volume and then converted back into the sphere. It is shown that at sufficiently large strain amplitudes, the deformation of the material involves localized plastic events that are identified based on the relative displacement of atoms before and after the shear transformation. We find that the density profiles of cage jumps decay away from the inclusion, which correlates well with the radial dependence of the local deformation of the material. At the same strain amplitude, the plastic deformation becomes more pronounced in the cases of weakly damped dynamics or large time scales of the shear transformation. We show that the density profiles can be characterized by the universal function of the radial distance multiplied by a dimensionless factor that depends on the friction coefficient and the time scale of the shear event.

Dynamical heterogeneity in periodically deformed polymer glasses.

The dynamics of structural relaxation in a model polymer glass subject to spatially homogeneous, time-periodic shear deformation is investigated using molecular dynamics simulations. We study a coarse-grained bead-spring model of short polymer chains below the glass transition temperature. It is found that at small strain amplitudes, the segmental dynamics is nearly reversible over about 10^{4} cycles, while at strain amplitudes above a few percent, polymer chains become fully relaxed after a hundred cycles. At the critical strain amplitude, the transition from slow to fast relaxation dynamics is associated with the largest number of dynamically correlated monomers as indicated by the peak value of the dynamical susceptibility. The analysis of individual monomer trajectories showed that mobile monomers tend to assist their neighbors to become mobile and aggregate into relatively compact transient clusters.

Heterogeneous relaxation dynamics in amorphous materials under cyclic loading.

Molecular dynamics simulations are performed to investigate heterogeneous dynamics in amorphous glassy materials under oscillatory shear strain. We consider three-dimensional binary Lennard-Jones mixture well below the glass transition temperature. The structural relaxation and dynamical heterogeneity are quantified by means of the self-overlap order parameter and the dynamic susceptibility. We found that at sufficiently small strain amplitudes, the mean square displacement exhibits a broad subdiffusive plateau and the system undergoes nearly reversible deformation over about 10(4) cycles. Upon increasing strain amplitude, the transition to the diffusive regime occurs at shorter time intervals and the relaxation process involves intermittent bursts of large particle displacements. The detailed analysis of particle hopping dynamics and the dynamic susceptibility indicates that mobile particles aggregate into clusters whose sizes increase at larger strain amplitudes. Finally, the correlation between particle mobilities in consecutive time intervals demonstrates that dynamic facilitation becomes increasingly pronounced at larger strain amplitudes.

Interfacial friction between semiflexible polymers and crystalline surfaces.

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities, the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.

Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures.

The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. We consider a situation where the typical pattern size is smaller than the channel height and the local boundary conditions at wetting and nonwetting regions are characterized by finite slip lengths. In the case of anisotropic patterns, transverse flow profiles are reported for flows over alternating stripes of different wettability when the shear flow direction is misaligned with respect to the stripe orientation. The angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the stripe width is larger than several molecular diameters. We found that the longitudinal component of the slip velocity along the shear flow direction is proportional to the interfacial diffusion coefficient of fluid monomers in that direction at equilibrium. In case of random textures, the effective slip length and the diffusion coefficient of fluid monomers in the first layer near the heterogeneous surface depend sensitively on the total area of wetting regions.

Modeling the combined effect of surface roughness and shear rate on slip flow of simple fluids.

Molecular dynamics (MD) and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate dependence of the intrinsic slip length in the flow over an atomically flat surface is computed by MD simulations. We describe laminar flow away from a curved boundary by means of the effective slip length defined with respect to the mean height of the surface roughness. Both the magnitude of the effective slip length and the slope of its rate dependence are significantly reduced in the presence of periodic surface roughness. We then numerically solve the Navier-Stokes equation for the flow over the rough surface using the rate-dependent intrinsic slip length as a local boundary condition. Continuum simulations reproduce the behavior of the effective slip length obtained from MD simulations at low shear rates. The slight discrepancy between MD and continuum results at high shear rates is explained by examination of the local velocity profiles and the pressure distribution along the wavy surface. We found that in the region where the curved boundary faces the mainstream flow, the local slip is suppressed due to the increase in pressure. The results of the comparative analysis can potentially lead to the development of an efficient algorithm for modeling rate-dependent slip flows over rough surfaces.

Relationship between induced fluid structure and boundary slip in nanoscale polymer films.

The molecular mechanism of slip at the interface between polymer melts and weakly attractive smooth surfaces is investigated using molecular dynamics simulations. In agreement with our previous studies on slip flow of shear-thinning fluids, it is shown that the slip length passes through a local minimum at low shear rates and then increases rapidly at higher shear rates. We found that at sufficiently high shear rates, the slip flow over atomically flat crystalline surfaces is anisotropic. It is demonstrated numerically that the friction coefficient at the liquid-solid interface (the ratio of viscosity and slip length) undergoes a transition from a constant value to the power-law decay as a function of the slip velocity. The characteristic velocity of the transition correlates well with the diffusion velocity of fluid monomers in the first fluid layer near the solid wall at equilibrium. We also show that in the linear regime, the friction coefficient is well described by a function of a single variable, which is a product of the magnitude of surface-induced peak in the structure factor and the contact density of the adjacent fluid layer. The universal relationship between the friction coefficient and induced fluid structure holds for a number of material parameters of the interface: fluid density, chain length, wall-fluid interaction energy, wall density, lattice type and orientation, thermal or solid walls.

Shear rate threshold for the boundary slip in dense polymer films.

The shear rate dependence of the slip length in thin polymer films confined between atomically flat surfaces is investigated by molecular dynamics simulations. The polymer melt is described by the bead-spring model of linear flexible chains. We found that at low shear rates the velocity profiles acquire a pronounced curvature near the wall and the absolute value of the negative slip length is approximately equal to the thickness of the viscous interfacial layer. At higher shear rates, the velocity profiles become linear and the slip length increases rapidly as a function of shear rate. The gradual transition from no-slip to steady-state slip flow is associated with faster relaxation of the polymer chains near the wall evaluated from decay of the time autocorrelation function of the first normal mode. We also show that at high melt densities the friction coefficient at the interface between the polymer melt and the solid wall follows a power-law decay as a function of the slip velocity. At large slip velocities the friction coefficient is determined by the product of the surface-induced peak in the structure factor, the temperature, and the contact density of the first fluid layer near the solid wall.