A simulation model for analysing patient activity in dermatology

We developed a general model to assess patient activity within the primary and secondary health-care sectors following a dermatology outpatient consultation. Based on observed variables from the UK teledermatology trial, the model showed that up to 11 doctor-patient interactions occurred before a patient was ultimately discharged from care. In a cohort of 1000 patients, the average number of health-care visits was 2.4 (range 1-11). Simulation analysis suggested that the most important parameter affecting the total number of doctor-patient Interactions is patient discharge from care following the initial consultation. This implies that resources should be concentrated in this area. The introduction of teledermatology (either realtime or store and forward) changes the values of the model parameters. The model provides a quantitative tool for planning the future provision of dermatology health-care.

Marker concentration patterns of labelled leaf and stem particles in the rumen of cattle grazing bermuda grass (Cynodon dactylon) analysed by reference to a raft model

Large (>1600 mum), ingestively masticated particles of bermuda grass (Cynodon dactylon L. Pers.) leaf and stem labelled with Yb-169 and Ce-144 respectively were inserted into the rumen digesta raft of heifers grazing bermuda grass. The concentration of markers in digesta sampled from the raft and ventral rumen were monitored at regular intervals over approximately 144 h. The data from the two sampling sites were simultaneously fitted to two pool (raft and ventral rumen-reticulum) models with either reversible or sequential flow between the two pools. The sequential flow model fitted the data equally as well as the reversible flow model but the reversible flow model was used because of its greater application. The reversible flow model, hereafter called the raft model, had the following features: a relatively slow age-dependent transfer rate from the raft (means for a gamma 2 distributed rate parameter for leaf 0.0740 v. stem 0.0478 h(-1)), a very slow first order reversible flow from the ventral rumen to the raft (mean for leaf and stem 0.010 h(-1)) and a very rapid first order exit from the ventral rumen (mean of leaf and stem 0.44 h(-1)). The raft was calculated to occupy approximately 0.82 total rumen DM of the raft and ventral rumen pools. Fitting a sequential two pool model or a single exponential model individually to values from each of the two sampling sites yielded similar parameter values for both sites and faster rate parameters for leaf as compared with stem, in agreement with the raft model. These results were interpreted as indicating that the raft forms a large relatively inert pool within the rumen. Particles generated within the raft have difficulty escaping but once into the ventral rumen pool they escape quickly with a low probability of return to the raft. It was concluded that the raft model gave a good interpretation of the data and emphasized escape from and movement within the raft as important components of the residence time of leaf and stem particles within the rumen digesta of cattle.

A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

Model specification tests in nonparametric stochastic regression models

In this paper, we consider testing for additivity in a class of nonparametric stochastic regression models. Two test statistics are constructed and their asymptotic distributions are established. We also conduct a small sample study for one of the test statistics through a simulated example. (C) 2002 Elsevier Science (USA).

A compartmental model of hepatic disposition kinetics: 1. Model development and application to linear kinetics

The conventional convection-dispersion model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. The extension of this model to include nonlinear kinetics and zonal heterogeneity of the liver is not straightforward and requires numerical solution of partial differential equation, which is not available in standard nonlinear regression analysis software. In this paper, we describe an alternative compartmental model representation of hepatic disposition (including elimination). The model allows the use of standard software for data analysis and accurately describes the outflow concentration-time profile for a vascular marker after bolus injection into the liver. In an evaluation of a number of different compartmental models, the most accurate model required eight vascular compartments, two of them with back mixing. In addition, the model includes two adjacent secondary vascular compartments to describe the tail section of the concentration-time profile for a reference marker. The model has the added flexibility of being easy to modify to model various enzyme distributions and nonlinear elimination. Model predictions of F, MTT, CV2, and concentration-time profile as well as parameter estimates for experimental data of an eliminated solute (palmitate) are comparable to those for the extended convection-dispersion model.

Entanglement in the steady state of a collective-angular-momentum (Dicke) model

We model the behavior of an ion trap with all ions driven simultaneously and coupled collectively to a heat bath. The equations for this system are similar to the irreversible dynamics of a collective angular momentum system known as the Dicke model. We show how the steady state of the ion trap as a dissipative many-body system driven far from equilibrium can exhibit quantum entanglement. We calculate the entanglement of this steady state for two ions in the trap and in the case of more than two ions we calculate the entanglement between two ions by tracing over all the other ions. The entanglement in the steady state is a maximum for the parameter values corresponding roughly to a bifurcation of a fixed point in the corresponding semiclassical dynamics. We conjecture that this is a general mechanism for entanglement creation in driven dissipative quantum systems.

Comparison of two population pharmacokinetic programs, NONMEM and P-PHARM, for tacrolimus

Objectives: To compare the population modelling programs NONMEM and P-PHARM during investigation of the pharmacokinetics of tacrolimus in paediatric liver-transplant recipients. Methods: Population pharmacokinetic analysis was performed using NONMEM and P-PHARM on retrospective data from 35 paediatric liver-transplant patients receiving tacrolimus therapy. The same data were presented to both programs. Maximum likelihood estimates were sought for apparent clearance (CL/F) and apparent volume of distribution (V/F). Covariates screened for influence on these parameters were weight, age, gender, post-operative day, days of tacrolimus therapy, transplant type, biliary reconstructive procedure, liver function tests, creatinine clearance, haematocrit, corticosteroid dose, and potential interacting drugs. Results: A satisfactory model was developed in both programs with a single categorical covariate - transplant type - providing stable parameter estimates and small, normally distributed (weighted) residuals. In NONMEM, the continuous covariates - age and liver function tests - improved modelling further. Mean parameter estimates were CL/F (whole liver) = 16.3 1/h, CL/F (cut-down liver) = 8.5 1/h and V/F = 565 1 in NONMEM, and CL/F = 8.3 1/h and V/F = 155 1 in P-PHARM. Individual Bayesian parameter estimates were CL/F (whole liver) = 17.9 +/- 8.8 1/h, CL/F (cutdown liver) = 11.6 +/- 18.8 1/h and V/F = 712 792 1 in NONMEM, and CL/F (whole liver) = 12.8 +/- 3.5 1/h, CL/F (cut-down liver) = 8.2 +/- 3.4 1/h and V/F = 221 1641 in P-PHARM. Marked interindividual kinetic variability (38-108%) and residual random error (approximately 3 ng/ml) were observed. P-PHARM was more user friendly and readily provided informative graphical presentation of results. NONMEM allowed a wider choice of errors for statistical modelling and coped better with complex covariate data sets. Conclusion: Results from parametric modelling programs can vary due to different algorithms employed to estimate parameters, alternative methods of covariate analysis and variations and limitations in the software itself.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Development of a generic crop model template in the cropping system model APSIM

The Agricultural Production Systems slMulator, APSIM, is a cropping system modelling environment that simulates the dynamics of soil-plant-management interactions within a single crop or a cropping system. Adaptation of previously developed crop models has resulted in multiple crop modules in APSIM, which have low scientific transparency and code efficiency. A generic crop model template (GCROP) has been developed to capture unifying physiological principles across crops (plant types) and to provide modular and efficient code for crop modelling. It comprises a standard crop interface to the APSIM engine, a generic crop model structure, a crop process library, and well-structured crop parameter files. The process library contains the major science underpinning the crop models and incorporates generic routines based on physiological principles for growth and development processes that are common across crops. It allows APSIM to simulate different crops using the same set of computer code. The generic model structure and parameter files provide an easy way to test, modify, exchange and compare modelling approaches at process level without necessitating changes in the code. The standard interface generalises the model inputs and outputs, and utilises a standard protocol to communicate with other APSIM modules through the APSIM engine. The crop template serves as a convenient means to test new insights and compare approaches to component modelling, while maintaining a focus on predictive capability. This paper describes and discusses the scientific basis, the design, implementation and future development of the crop template in APSIM. On this basis, we argue that the combination of good software engineering with sound crop science can enhance the rate of advance in crop modelling. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

Simulation of the load-unload response ratio and critical sensitivity in the lattice solid model

The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.

Impulse-response function of splanchnic circulation with model-independent constraints: theory and experimental validation

Modeling physiological processes using tracer kinetic methods requires knowledge of the time course of the tracer concentration in blood supplying the organ. For liver studies, however, inaccessibility of the portal vein makes direct measurement of the hepatic dual-input function impossible in humans. We want to develop a method to predict the portal venous time-activity curve from measurements of an arterial time-activity curve. An impulse-response function based on a continuous distribution of washout constants is developed and validated for the gut. Experiments with simultaneous blood sampling in aorta and portal vein were made in 13 anesthetized pigs following inhalation of intravascular [O-15] CO or injections of diffusible 3-O[ C-11] methylglucose (MG). The parameters of the impulse-response function have a physiological interpretation in terms of the distribution of washout constants and are mathematically equivalent to the mean transit time ( T) and standard deviation of transit times. The results include estimates of mean transit times from the aorta to the portal vein in pigs: (T) over bar = 0.35 +/- 0.05 min for CO and 1.7 +/- 0.1 min for MG. The prediction of the portal venous time-activity curve benefits from constraining the regression fits by parameters estimated independently. This is strong evidence for the physiological relevance of the impulse-response function, which includes asymptotically, and thereby justifies kinetically, a useful and simple power law. Similarity between our parameter estimates in pigs and parameter estimates in normal humans suggests that the proposed model can be adapted for use in humans.

A unified model of flames as gasdynamic discontinuities

Viewed on a hydrodynamic scale, flames in experiments are often thin so that they may be described as gasdynamic discontinuities separating the dense cold fresh mixture from the light hot burned products. The original model of a flame as a gasdynamic discontinuity was due to Darrieus and to Landau. In addition to the fluid dynamical equations, the model consists of a flame speed relation describing the evolution of the discontinuity surface, and jump conditions across the surface which relate the fluid variables on the two sides of the surface. The Darrieus-Landau model predicts, in contrast to observations, that a uniformly propagating planar flame is absolutely unstable and that the strength of the instability grows with increasing perturbation wavenumber so that there is no high-wavenumber cutoff of the instability. The model was modified by Markstein to exhibit a high-wavenumber cutoff if a phenomenological constant in the model has an appropriate sign. Both models are postulated, rather than derived from first principles, and both ignore the flame structure, which depends on chemical kinetics and transport processes within the flame. At present, there are two models which have been derived, rather than postulated, and which are valid in two non-overlapping regions of parameter space. Sivashinsky derived a generalization of the Darrieus-Landau model which is valid for Lewis numbers (ratio of thermal diffusivity to mass diffusivity of the deficient reaction component) bounded away from unity. Matalon & Matkowsky derived a model valid for Lewis numbers close to unity. Each model has its own advantages and disadvantages. Under appropriate conditions the Matalon-Matkowsky model exhibits a high-wavenumber cutoff of the Darrieus-Landau instability. However, since the Lewis numbers considered lie too close to unity, the Matalon-Matkowsky model does not capture the pulsating instability. The Sivashinsky model does capture the pulsating instability, but does not exhibit its high-wavenumber cutoff. In this paper, we derive a model consisting of a new flame speed relation and new jump conditions, which is valid for arbitrary Lewis numbers. It captures the pulsating instability and exhibits the high-wavenumber cutoff of all instabilities. The flame speed relation includes the effect of short wavelengths, not previously considered, which leads to stabilizing transverse surface diffusion terms.

Model-based analysis of anaerobic acetate uptake by a mixed culture of polyphosphate-accumulating and glycogen-accumulating organisms

An increasing number of studies shows that the glycogen-accumulating organisms (GAOs) can survive and may indeed proliferate under the alternating anaerobic/aerobic conditions found in EBPR systems, thus forming a strong competitor of the polyphosphate-accumulating organisms (PAOs). Understanding their behaviors in a mixed PAO and GAO culture under various operational conditions is essential for developing operating strategies that disadvantage the growth of this group of unwanted organisms. A model-based data analysis method is developed in this paper for the study of the anaerobic PAO and GAO activities in a mixed PAO and GAO culture. The method primarily makes use of the hydrogen ion production rate and the carbon dioxide transfer rate resulting from the acetate uptake processes by PAOs and GAOs, measured with a recently developed titration and off-gas analysis (TOGA) sensor. The method is demonstrated using the data from a laboratory-scale sequencing batch reactor (SBR) operated under alternating anaerobic and aerobic conditions. The data analysis using the proposed method strongly indicates a coexistence of PAOs and GAOs in the system, which was independently confirmed by fluorescent in situ hybridization (FISH) measurement. The model-based analysis also allowed the identification of the respective acetate uptake rates by PAOs and GAOs, along with a number of kinetic and stoichiometric parameters involved in the PAO and GAO models. The excellent fit between the model predictions and the experimental data not involved in parameter identification shows that the parameter values found are reliable and accurate. It also demonstrates that the current anaerobic PAO and GAO models are able to accurately characterize the PAO/GAO mixed culture obtained in this study. This is of major importance as no pure culture of either PAOs or GAOs has been reported to date, and hence the current PAO and GAO models were developed for the interpretation of experimental results of mixed cultures. The proposed method is readily applicable for detailed investigations of the competition between PAOs and GAOs in enriched cultures. However, the fermentation of organic substrates carried out by ordinary heterotrophs needs to be accounted for when the method is applied to the study of PAO and GAO competition in full-scale sludges. (C) 2003 Wiley Periodicals, Inc.