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.

Comparison of an ELISA and an LC/MS/MS method for measuring tacrolimus concentrations and making dosage decisions in transplant recipients

This study compared an enzyme-linked immunosorbent assay (ELISA) to a liquid chromatography-tandem mass spectrometry (LC/MS/MS) technique for measurement of tacrolimus concentrations in adult kidney and liver transplant recipients, and investigated how assay choice influenced pharmacokinetic parameter estimates and drug dosage decisions. Tacrolimus concentrations measured by both ELISA and LC/MS/MS from 29 kidney (n = 98 samples) and 27 liver (n = 97 samples) transplant recipients were used to evaluate the performance of these methods in the clinical setting. Tacrolimus concentrations measured by the two techniques were compared via regression analysis. Population pharmacokinetic models were developed independently using ELISA and LC/MS/MS data from 76 kidney recipients. Derived kinetic parameters were used to formulate typical dosing regimens for concentration targeting. Dosage recommendations for the two assays were compared. The relation between LC/MS/MS and ELISA measurements was best described by the regression equation ELISA = 1.02 . (LC/MS/MS) + 0.14 in kidney recipients, and ELISA = 1.12 . (LC/MS/MS) - 0.87 in liver recipients. ELISA displayed less accuracy than LC/MS/MS at lower tacrolimus concentrations. Population pharmacokinetic models based on ELISA and LC/MS/MS data were similar with residual random errors of 4.1 ng/mL and 3.7 ng/mL, respectively. Assay choice gave rise to dosage prediction differences ranging from 0% to 30%. ELISA measurements of tacrolimus are not automatically interchangeable with LC/MS/MS values. Assay differences were greatest in adult liver recipients, probably reflecting periods of liver dysfunction and impaired biliary secretion of metabolites. While the majority of data collected in this study suggested assay differences in adult kidney recipients were minimal, findings of ELISA dosage underpredictions of up to 25% in the long term must be investigated further.

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.

Density functional theory analysis of the influence of pore wall heterogeneity on adsorption in carbons

Density functional theory for adsorption in carbons is adapted here to incorporate a random distribution of pore wall thickness in the solid, and it is shown that the mean pore wall thickness is intimately related to the pore size distribution characteristics. For typical carbons the pore walls are estimated to comprise only about two graphene layers, and application of the modified density functional theory approach shows that the commonly used assumption of infinitely thick walls can severely affect the results for adsorption in small pores under both supercritical and subcritical conditions. Under supercritical conditions the Henry's law coefficient is overpredicted by as much as a factor of 2, while under subcritical conditions pore wall heterogeneity appears to modify transitions in small pores into a sequence of smaller ones corresponding to pores with different wall thicknesses. The results suggest the need to improve current pore size distrubution analysis methods to allow for pore wall heterogeneity. The density functional theory is further extended here to allow for interpore adsorbate interactions, and it appears that these interaction are negligible for small molecules such as nitrogen but significant for more strongly interacting heavier molecules such as butane, for which the traditional independent pore model may not be adequate.

Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Application of the Williams-Landel-Ferry model to the viscosity-temperature relationship of Australian honeys

The rheological behaviour of nine unprocessed Australian honeys was investigated for the applicability of the Williams-Landel-Ferry (WLF) model. The viscosity of the honeys was obtained over a range of shear rates (0.01-40 s(-1)) from 2degrees to 40 degreesC, and all the honeys exhibited Newtonian behaviour with viscosity reducing as the temperature was increased. The honeys with high moisture were of lower viscosity, The glass transition temperatures of the honeys, as measured with a differential scanning calorimeter (DSC), ranged from -40degrees to -46 degreesC, and four models (WLF. Arrhenius, Vogel-Tammann-Fulcher (VTF), and power-law) were investigated to describe the temperature dependence of the viscosity. The WLF was the most suitable and the correlation coefficient averaged 0.999 +/- 0.0013 as against 0.996 +/- 0.0042 for the Arrhenius model while the mean relative deviation modulus was 0-12% for the WLF model and 10-40% for the Arrhenius one. With the universal values for the WLF constants, the temperature dependence of the viscosity was badly predicted. From non-linear regression analysis, the constants of the WLF models for the honeys were obtained (C-1 = 13.7-21.1: C-2 = 55.9-118.7) and are different from the universal values. These WLF constants will be valuable for adequate modeling of the rheology of the honeys, and they can be used to assess the temperature sensitivity of the honeys. (C) 2002 Elsevier Science Ltd. All rights reserved.

Prospective independent validation of APACHE III models in an Australian tertiary adult intensive care unit

Evaluation of the performance of the APACHE III (Acute Physiology and Chronic Health Evaluation) ICU (intensive care unit) and hospital mortality models at the Princess Alexandra Hospital, Brisbane is reported. Prospective collection of demographic, diagnostic, physiological, laboratory, admission and discharge data of 5681 consecutive eligible admissions (1 January 1995 to 1 January 2000) was conducted at the Princess Alexandra Hospital, a metropolitan Australian tertiary referral medical/surgical adult ICU. ROC (receiver operating characteristic) curve areas for the APACHE III ICU mortality and hospital mortality models demonstrated excellent discrimination. Observed ICU mortality (9.1%) was significantly overestimated by the APACHE III model adjusted for hospital characteristics (10.1%), but did not significantly differ from the prediction of the generic APACHE III model (8.6%). In contrast, observed hospital mortality (14.8%) agreed well with the prediction of the APACHE III model adjusted for hospital characteristics (14.6%), but was significantly underestimated by the unadjusted APACHE III model (13.2%). Calibration curves and goodness-of-fit analysis using Hosmer-Lemeshow statistics, demonstrated that calibration was good with the unadjusted APACHE III ICU mortality model, and the APACHE III hospital mortality model adjusted for hospital characteristics. Post hoc analysis revealed a declining annual SMR (standardized mortality rate) during the study period. This trend was present in each of the non-surgical, emergency and elective surgical diagnostic groups, and the change was temporally related to increased specialist staffing levels. This study demonstrates that the APACHE III model performs well on independent assessment in an Australian hospital. Changes observed in annual SMR using such a validated model support an hypothesis of improved survival outcomes 1995-1999.

Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

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.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Simulation of the micro-physics of rocks using LSMearth

The particle-based Lattice Solid Model (LSM) was developed to provide a basis to study the physics of rocks and the nonlinear dynamics of earthquakes (MORA and PLACE, 1994; PLACE and MORA, 1999). A new modular and flexible LSM approach has been developed that allows different microphysics to be easily included in or removed from the model. The approach provides a virtual laboratory where numerical experiments can easily be set up and all measurable quantities visualised. The proposed approach provides a means to simulate complex phenomena such as fracturing or localisation processes, and enables the effect of different micro-physics on macroscopic behaviour to be studied. The initial 2-D model is extended to allow three-dimensional simulations to be performed and particles of different sizes to be specified. Numerical bi-axial compression experiments under different confining pressure are used to calibrate the model. By tuning the different microscopic parameters (such as coefficient of friction, microscopic strength and distribution of grain sizes), the macroscopic strength of the material and can be adjusted to be in agreement with laboratory experiments, and the orientation of fractures is consistent with the theoretical value predicted based on Mohr-Coulomb diagram. Simulations indicate that 3-D numerical models have different macroscopic properties than in 2-D and, hence, the model must be recalibrated for 3-D simulations. These numerical experiments illustrate that the new approach is capable of simulating typical rock fracture behaviour. The new model provides a basis to investigate nucleation, rupture and slip pulse propagation in complex fault zones without the previous model limitations of a regular low-level surface geometry and being restricted to two-dimensions.

Cost comparison of hospital- and home-based treatment models for acute chronic obstructive pulmonary disease

This trial compared the cost of an integrated home-based care model with traditional inpatient care for acute chronic obstructive pulmonary disease (COPD). 25 patients with acute COPD were randomised to either home or hospital management following request for hospital admission. The acute care at home group costs per separation ($745, CI95% $595-$895, n = 13) were significantly lower (p < 0.01) than the hospital group ($2543, CI95% $1766-$3321, n = 12). There was an improvement in lung function in the hospital-managed group at the Outpatient Department review, decreased anxiety in the Emergency Department in the home-managed group and equal patient satisfaction with care delivery. Acute care at home schemes can substitute for usual hospital care for some patients without adverse effects, and potentially release resources. A funding model that allows adequate resource delivery to the community will be needed if there is a move to devolve acute care to community providers.

Fitting genetic models to twin data with binary and ordered categorical responses: A comparison of structural equation modelling and Bayesian hierarchical models

We compare Bayesian methodology utilizing free-ware BUGS (Bayesian Inference Using Gibbs Sampling) with the traditional structural equation modelling approach based on another free-ware package, Mx. Dichotomous and ordinal (three category) twin data were simulated according to different additive genetic and common environment models for phenotypic variation. Practical issues are discussed in using Gibbs sampling as implemented by BUGS to fit subject-specific Bayesian generalized linear models, where the components of variation may be estimated directly. The simulation study (based on 2000 twin pairs) indicated that there is a consistent advantage in using the Bayesian method to detect a correct model under certain specifications of additive genetics and common environmental effects. For binary data, both methods had difficulty in detecting the correct model when the additive genetic effect was low (between 10 and 20%) or of moderate range (between 20 and 40%). Furthermore, neither method could adequately detect a correct model that included a modest common environmental effect (20%) even when the additive genetic effect was large (50%). Power was significantly improved with ordinal data for most scenarios, except for the case of low heritability under a true ACE model. We illustrate and compare both methods using data from 1239 twin pairs over the age of 50 years, who were registered with the Australian National Health and Medical Research Council Twin Registry (ATR) and presented symptoms associated with osteoarthritis occurring in joints of the hand.