A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Analysing seasonal data

Many common diseases, such as the flu and cardiovascular disease, increase markedly in winter and dip in summer. These seasonal patterns have been part of life for millennia and were first noted in ancient Greece by both Hippocrates and Herodotus. Recent interest has focused on climate change, and the concern that seasons will become more extreme with harsher winter and summer weather. We describe a set of R functions designed to model seasonal patterns in disease. We illustrate some simple descriptive and graphical methods, a more complex method that is able to model non-stationary patterns, and the case–crossover for controlling for seasonal confounding.

Performance of elite seated discus throwers in F30s classes : part II: does feet positioning matter?

Background: Studies on the relationship between performance and design of the throwing frame have been limited. Part I provided only a description of the whole body positioning. Objectives: The specific objectives were (a) to benchmark feet positioning characteristics (i.e. position, spacing and orientation) and (b) to investigate the relationship between performance and these characteristics for male seated discus throwers in F30s classes. Study Design: Descriptive analysis. Methods: A total of 48 attempts performed by 12 stationary discus throwers in F33 and F34 classes during seated discus throwing event of 2002 International Paralympic Committee Athletics World Championships were analysed in this study. Feet positioning was characterised by tridimensional data of the front and back feet position as well as spacing and orientation corresponding to the distance between and the angle made by both feet, respectively. Results: Only 4 of 30 feet positioning characteristics presented a coefficient correlation superior to 0.5, including the feet spacing on mediolateral and anteroposterior axes in F34 class as well as the back foot position and feet spacing on mediolateral axis in F33 class. Conclusions: This study provided key information for a better understanding of the interaction between throwing technique of elite seated throwers and their throwing frame.

Planar radial spots in a three-component FitzHugh-Nagumo system

Localized planar patterns arise in many reaction-diffusion models. Most of the paradigm equations that have been studied so far are two-component models. While stationary localized structures are often found to be stable in such systems, travelling patterns either do not exist or are found to be unstable. In contrast, numerical simulations indicate that localized travelling structures can be stable in three-component systems. As a first step towards explaining this phenomenon, a planar singularly perturbed three-component reaction-diffusion system that arises in the context of gas-discharge systems is analysed in this paper. Using geometric singular perturbation theory, the existence and stability regions of radially symmetric stationary spot solutions are delineated and, in particular, stable spots are shown to exist in appropriate parameter regimes. This result opens up the possibility of identifying and analysing drift and Hopf bifurcations, and their criticality, from the stationary spots described here.

Front interactions in a three-component system

The three-component reaction-diffusion system introduced in [C. P. Schenk et al., Phys. Rev. Lett., 78 (1997), pp. 3781–3784] has become a paradigm model in pattern formation. It exhibits a rich variety of dynamics of fronts, pulses, and spots. The front and pulse interactions range in type from weak, in which the localized structures interact only through their exponentially small tails, to strong interactions, in which they annihilate or collide and in which all components are far from equilibrium in the domains between the localized structures. Intermediate to these two extremes sits the semistrong interaction regime, in which the activator component of the front is near equilibrium in the intervals between adjacent fronts but both inhibitor components are far from equilibrium there, and hence their concentration profiles drive the front evolution. In this paper, we focus on dynamically evolving N-front solutions in the semistrong regime. The primary result is use of a renormalization group method to rigorously derive the system of N coupled ODEs that governs the positions of the fronts. The operators associated with the linearization about the N-front solutions have N small eigenvalues, and the N-front solutions may be decomposed into a component in the space spanned by the associated eigenfunctions and a component projected onto the complement of this space. This decomposition is carried out iteratively at a sequence of times. The former projections yield the ODEs for the front positions, while the latter projections are associated with remainders that we show stay small in a suitable norm during each iteration of the renormalization group method. Our results also help extend the application of the renormalization group method from the weak interaction regime for which it was initially developed to the semistrong interaction regime. The second set of results that we present is a detailed analysis of this system of ODEs, providing a classification of the possible front interactions in the cases of $N=1,2,3,4$, as well as how front solutions interact with the stationary pulse solutions studied earlier in [A. Doelman, P. van Heijster, and T. J. Kaper, J. Dynam. Differential Equations, 21 (2009), pp. 73–115; P. van Heijster, A. Doelman, and T. J. Kaper, Phys. D, 237 (2008), pp. 3335–3368]. Moreover, we present some results on the general case of N-front interactions.

Pulse dynamics in a three-component system : existence analysis

In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others.

Coexistence of stable spots and fronts in a three-component FitzHugh-Nagumo system

We investigate regions of bistability between different travelling and stationary structures in a planar singularly-perturbed three-component reaction-diffusion system that arises in the context of gas discharge systems. In previous work, we delineated the existence and stabil-ity regions of stationary localized spots in this system. Here, we complement this analysis by establishing the stability regions of planar travelling fronts and stationary stripes. Taken together, these results imply that stable fronts and spots can coexist in three-component systems. Numerical simulations indicate that the stable fronts never move towards stable spots but instead move away from them.

Melt textured Y123 bulk and thick film

YBa2Cu3O7-δ - 25mol%Y2BaCuO5 bars and thick films have been melt textured using a stationary furnace with a temperature gradient of 3 or 6°C/cm. Samples are heated above the peritectic reaction temperature and quenched to just above the solidification temperature and then slowly cooled below the solidification temperature. All bar shaped samples consist of 2-5 mm grains though the grain orientations strongly depend on the heat treatment conditions. The bar shows the maximum Jc of above 3,000 A/cm2, whereas the maximum Jc of 200 A/cm2 and Tczero of 88K are obtained for the thick film on (100) LaAlO3 single crystal.

Hazard based models for freeway traffic incident duration

Assessing and prioritising cost-effective strategies to mitigate the impacts of traffic incidents and accidents on non-recurrent congestion on major roads represents a significant challenge for road network managers. This research examines the influence of numerous factors associated with incidents of various types on their duration. It presents a comprehensive traffic incident data mining and analysis by developing an incident duration model based on twelve months of incident data obtained from the Australian freeway network. Parametric accelerated failure time (AFT) survival models of incident duration were developed, including log-logistic, lognormal, and Weibul-considering both fixed and random parameters, as well as a Weibull model with gamma heterogeneity. The Weibull AFT models with random parameters were appropriate for modelling incident duration arising from crashes and hazards. A Weibull model with gamma heterogeneity was most suitable for modelling incident duration of stationary vehicles. Significant variables affecting incident duration include characteristics of the incidents (severity, type, towing requirements, etc.), and location, time of day, and traffic characteristics of the incident. Moreover, the findings reveal no significant effects of infrastructure and weather on incident duration. A significant and unique contribution of this paper is that the durations of each type of incident are uniquely different and respond to different factors. The results of this study are useful for traffic incident management agencies to implement strategies to reduce incident duration, leading to reduced congestion, secondary incidents, and the associated human and economic losses.

Time-varying bispectral analysis of visually evoked multi-channel EEG

Theoretical foundations of higher order spectral analysis are revisited to examine the use of time-varying bicoherence on non-stationary signals using a classical short-time Fourier approach. A methodology is developed to apply this to evoked EEG responses where a stimulus-locked time reference is available. Short-time windowed ensembles of the response at the same offset from the reference are considered as ergodic cyclostationary processes within a non-stationary random process. Bicoherence can be estimated reliably with known levels at which it is significantly different from zero and can be tracked as a function of offset from the stimulus. When this methodology is applied to multi-channel EEG, it is possible to obtain information about phase synchronization at different regions of the brain as the neural response develops. The methodology is applied to analyze evoked EEG response to flash visual stimulii to the left and right eye separately. The EEG electrode array is segmented based on bicoherence evolution with time using the mean absolute difference as a measure of dissimilarity. Segment maps confirm the importance of the occipital region in visual processing and demonstrate a link between the frontal and occipital regions during the response. Maps are constructed using bicoherence at bifrequencies that include the alpha band frequency of 8Hz as well as 4 and 20Hz. Differences are observed between responses from the left eye and the right eye, and also between subjects. The methodology shows potential as a neurological functional imaging technique that can be further developed for diagnosis and monitoring using scalp EEG which is less invasive and less expensive than magnetic resonance imaging.

Effects of a defender on run-up velocity and ball speed when crossing a football

This study evaluated effects of defensive pressure on running velocity in footballers during the approach to kick a stationary football. Approach velocity and ball speed/accuracy data were recorded from eight football youth academy participants (15.25, SD=0.46 yrs). Participants were required to run to a football to cross it to a receiver to score against a goal-keeper. Defensive pressure was manipulated across three counterbalanced conditions: defender-absent (DA); defender-far (DF) and defender-near (DN). Pass accuracy (percentages of a total of 32 trials with 95% confidence limits in parenthesis) did not significantly reduce under changing defensive pressure: DA, 78% (55–100%); DF, 78% (61–96%); DN, 59% (40–79%). Ball speed (m·s−1) significantly reduced as defensive pressure was included and increased: DA, 23.10 (22.38–23.83); DF, 20.40 (19.69–21.11); DN, 19.22 (18.51–19.93). When defensive pressure was introduced, average running velocity of attackers did not change significantly: DA versus DF (m·s−1), 5.40 (5.30–5.51) versus 5.41 (5.34–5.48). Scaling defender starting positions closer to the start position of the attacker (DN) significantly increased average running velocity relative to the DA and DF conditions, 5.60 (5.50–5.71). In the final approach footfalls, all conditions significantly differed: DA, 5.69 (5.35–6.03); DF, 6 .22 (5.93–6.50); DN, 6.52 (6.23–6.80). Data suggested that approach velocity is constrained by both presence and initial distance of the defender during task performance. Implications are that the expression of kicking behaviour is specific to a performance context and some movement regulation features will not emerge unless a defender is present as a task constraint in practice.

On the effective hydraulic conductivity and macrodispersivity for density-dependent groundwater flow

In this paper, semi-analytical expressions of the effective hydraulic conductivity ( KE) and macrodispersivity ( αE) for 3D steady-state density-dependent groundwater flow are derived using a stationary spectral method. Based on the derived expressions, we present the dependence of KE and αE on the density of fluid under different dispersivity and spatial correlation scale of hydraulic conductivity. The results show that the horizontal KE and αE are not affected by density-induced flow. However, due to gravitational instability of the fluid induced by density contrasts, both vertical KE and αE are found to be reduced slightly when the density factor ( γ ) is less than 0.01, whereas significant decreases occur when γ exceeds 0.01. Of note, the variation of KE and αE is more significant when local dispersivity is small and the correlation scale of hydraulic conductivity is large.

Adaption of horses to a novel dynamic feeding system : movement and behavioural responses

Reasons for performing study: Many domestic horses and ponies are sedentary and obese due to confinement to small paddocks and stables and a diet of infrequent, high-energy rations. Severe health consequences can be associated with this altered lifestyle. Objectives: The aims of this study were to investigate the ability of horses to learn to use a dynamic feeder system and determine the movement and behavioural responses of horses to the novel system. Methods: A dynamic feed station was developed to encourage horses to exercise in order to access ad libitum hay. Five pairs of horses (n = 10) were studied using a randomised crossover design with each pair studied in a control paddock containing a standard hay feeder and an experimental paddock containing the novel hay feeder. Horse movement was monitored by a global positioning system (GPS) and horses observed and their ability to learn to use the system and the behavioural responses to its use assessed. Results: With initial human intervention all horses used the novel feeder within 1 h. Some aggressive behaviour was observed between horses not well matched in dominance behaviour. The median distance walked by the horses was less (P = 0.002) during a 4 h period (117 [57–185] m) in the control paddock than in the experimental paddock (630 [509–719] m). Conclusions: The use of an automated feeding system promotes increased activity levels in horses housed in small paddocks, compared with a stationary feeder.

Performance of elite seated discus throwers in F30s classes : part I: does whole body positioning matter?

Background: Studies on the relationship between performance and design of the throwing frame have been limited and therefore require further investigation. Objectives: The specific objectives were to provide benchmark information about performance and whole body positioning of male athletes in F30s classes. Study Design: Descriptive analysis. Methods: A total of 48 attempts performed by 12 stationary discus throwers in F33 and F34 classes during seated discus throwing event of 2002 International Paralympic Committee Athletics World Championships were analysed in this study. The whole body positioning included overall throwing posture (i.e. number of points of contact between the thrower and the frame, body position, throwing orientation and throwing side) and lower limb placements (i.e. seating arrangements, points of contact on the both feet, type of attachment of both legs and feet). Results: Three (25%), five (42%), one (8%) and three (25%) athletes used from three to six points of contact, respectively. Seven (58%) and five (42%) athletes threw from a standing or a seated position, respectively. A straddle, a stool or a chair was used by six (50%), four (33%) or two (17%) throwers, respectively. Conclusions: This study provides key information for a better understanding of the interaction between throwing technique of elite seated throwers and their throwing frame.

Study of particulate matter removal mechanism by using non-thermal plasma technology

Numbers of diesel engines in both stationary and mobile applications are increasing nowadays. Diesel engines emit lower Hydrocarbon (HC) and Carbon monoxide (CO) than gasoline engines. However, they can produce more nitrogen oxides (NOx) and have higher particulate matter (PM). On the other hand, emissions standards are getting stringent day by day due to considerable concerns about unregulated pollutants and particularly ultrafine particles deleterious effect on human health. Non-thermal plasma (NTP) treatment of exhaust gas is known as a promising technology for both NOx and PM reduction by introducing plasma inside the exhaust gas. Vehicle exhaust gases undergo chemical changes when exposed to plasma. In this study, the PM removal mechanism using NTP by applying high voltage pulses of up to 20 kVpp with a repetition rate of 10 kHz are investigated. It is found that, voltage increase not necessarily has a positive effect on PM removal in diesel engine emissions.