Optimal design for model discrimination and parameter estimation for itraconazole population pharmacokinetics in cystic fibrosis patients

Optimal sampling times are found for a study in which one of the primary purposes is to develop a model of the pharmacokinetics of itraconazole in patients with cystic fibrosis for both capsule and solution doses. The optimal design is expected to produce reliable estimates of population parameters for two different structural PK models. Data collected at these sampling times are also expected to provide the researchers with sufficient information to reasonably discriminate between the two competing structural models.

Estimating variable returns to scale production frontiers with alternative stochastic assumptions

Two stochastic production frontier models are formulated within the generalized production function framework popularized by Zellner and Revankar (Rev. Econ. Stud. 36 (1969) 241) and Zellner and Ryu (J. Appl. Econometrics 13 (1998) 101). This framework is convenient for parsimonious modeling of a production function with returns to scale specified as a function of output. Two alternatives for introducing the stochastic inefficiency term and the stochastic error are considered. In the first the errors are added to an equation of the form h(log y, theta) = log f (x, beta) where y denotes output, x is a vector of inputs and (theta, beta) are parameters. In the second the equation h(log y,theta) = log f(x, beta) is solved for log y to yield a solution of the form log y = g[theta, log f(x, beta)] and the errors are added to this equation. The latter alternative is novel, but it is needed to preserve the usual definition of firm efficiency. The two alternative stochastic assumptions are considered in conjunction with two returns to scale functions, making a total of four models that are considered. A Bayesian framework for estimating all four models is described. The techniques are applied to USDA state-level data on agricultural output and four inputs. Posterior distributions for all parameters, for firm efficiencies and for the efficiency rankings of firms are obtained. The sensitivity of the results to the returns to scale specification and to the stochastic specification is examined. (c) 2004 Elsevier B.V. All rights reserved.

Using the floatability characterisation test rig for industrial flotation plant design

Industrial flotation plant design is a complex process involving many aspects, one of which is the use of pilot-scale plants to test industrial plant flow sheets. Once test work on a pilot-scale has been performed, scale-up of these results to the full-scale plant must be performed. This paper describes scale-up test work performed on the Floatability Characterisation Test Rig (FCTR). The FCTR is a self-contained, highly instrumented mobile pilot plant designed to determine flotation model parameters and to develop and validate flotation plant modelling, scale-up and simulation methodologies.

A D-optimal designed population pharmacokinetic study of itraconazole capsules and solution in adults with cystic fibrosis

Background: Oral itraconazole (ITRA) is used for the treatment of allergic bronchopulmonary aspergillosis in patients with cystic fibrosis (CF) because of its antifungal activity against Aspergillus species. ITRA has an active hydroxy-metabolite (OH-ITRA) which has similar antifungal activity. ITRA is a highly lipophilic drug which is available in two different oral formulations, a capsule and an oral solution. It is reported that the oral solution has a 60% higher relative bioavailability. The influence of altered gastric physiology associated with CF on the pharmacokinetics (PK) of ITRA and its metabolite has not been previously evaluated. Objectives: 1) To estimate the population (pop) PK parameters for ITRA and its active metabolite OH-ITRA including relative bioavailability of the parent after administration of the parent by both capsule and solution and 2) to assess the performance of the optimal design. Methods: The study was a cross-over design in which 30 patients received the capsule on the first occasion and 3 days later the solution formulation. The design was constrained to have a maximum of 4 blood samples per occasion for estimation of the popPK of both ITRA and OH-ITRA. The sampling times for the population model were optimized previously using POPT v.2.0.[1] POPT is a series of applications that run under MATLAB and provide an evaluation of the information matrix for a nonlinear mixed effects model given a particular design. In addition it can be used to optimize the design based on evaluation of the determinant of the information matrix. The model details for the design were based on prior information obtained from the literature, which suggested that ITRA may have either linear or non-linear elimination. The optimal sampling times were evaluated to provide information for both competing models for the parent and metabolite and for both capsule and solution simultaneously. Blood samples were assayed by validated HPLC.[2] PopPK modelling was performed using FOCE with interaction under NONMEM, version 5 (level 1.1; GloboMax LLC, Hanover, MD, USA). The PK of ITRA and OH‑ITRA was modelled simultaneously using ADVAN 5. Subsequently three methods were assessed for modelling concentrations less than the LOD (limit of detection). These methods (corresponding to methods 5, 6 & 4 from Beal[3], respectively) were (a) where all values less than LOD were assigned to half of LOD, (b) where the closest missing value that is less than LOD was assigned to half the LOD and all previous (if during absorption) or subsequent (if during elimination) missing samples were deleted, and (c) where the contribution of the expectation of each missing concentration to the likelihood is estimated. The LOD was 0.04 mg/L. The final model evaluation was performed via bootstrap with re-sampling and a visual predictive check. The optimal design and the sampling windows of the study were evaluated for execution errors and for agreement between the observed and predicted standard errors. Dosing regimens were simulated for the capsules and the oral solution to assess their ability to achieve ITRA target trough concentration (Cmin,ss of 0.5-2 mg/L) or a combined Cmin,ss for ITRA and OH-ITRA above 1.5mg/L. Results and Discussion: A total of 241 blood samples were collected and analysed, 94% of them were taken within the defined optimal sampling windows, of which 31% where taken within 5 min of the exact optimal times. Forty six per cent of the ITRA values and 28% of the OH-ITRA values were below LOD. The entire profile after administration of the capsule for five patients was below LOD and therefore the data from this occasion was omitted from estimation. A 2-compartment model with 1st order absorption and elimination best described ITRA PK, with 1st order metabolism of the parent to OH-ITRA. For ITRA the clearance (ClItra/F) was 31.5 L/h; apparent volumes of central and peripheral compartments were 56.7 L and 2090 L, respectively. Absorption rate constants for capsule (kacap) and solution (kasol) were 0.0315 h-1 and 0.125 h-1, respectively. Comparative bioavailability of the capsule was 0.82. There was no evidence of nonlinearity in the popPK of ITRA. No screened covariate significantly improved the fit to the data. The results of the parameter estimates from the final model were comparable between the different methods for accounting for missing data, (M4,5,6)[3] and provided similar parameter estimates. The prospective application of an optimal design was found to be successful. Due to the sampling windows, most of the samples could be collected within the daily hospital routine, but still at times that were near optimal for estimating the popPK parameters. The final model was one of the potential competing models considered in the original design. The asymptotic standard errors provided by NONMEM for the final model and empirical values from bootstrap were similar in magnitude to those predicted from the Fisher Information matrix associated with the D-optimal design. Simulations from the final model showed that the current dosing regimen of 200 mg twice daily (bd) would provide a target Cmin,ss (0.5-2 mg/L) for only 35% of patients when administered as the solution and 31% when administered as capsules. The optimal dosing schedule was 500mg bd for both formulations. The target success for this dosing regimen was 87% for the solution with an NNT=4 compared to capsules. This means, for every 4 patients treated with the solution one additional patient will achieve a target success compared to capsule but at an additional cost of AUD $220 per day. The therapeutic target however is still doubtful and potential risks of these dosing schedules need to be assessed on an individual basis. Conclusion: A model was developed which described the popPK of ITRA and its main active metabolite OH-ITRA in adult CF after administration of both capsule and solution. The relative bioavailability of ITRA from the capsule was 82% that of the solution, but considerably more variable. To incorporate missing data, using the simple Beal method 5 (using half LOD for all samples below LOD) provided comparable results to the more complex but theoretically better Beal method 4 (integration method). The optimal sparse design performed well for estimation of model parameters and provided a good fit to the data.

A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.

Emulation of random output simulators

Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty. This thesis develops a novel sequential screening method to reduce the set of simulator variables considered during emulation. This screening method is shown to require fewer simulator evaluations than existing approaches. Utilising the lower dimensional active variable set simplifies subsequent emulation analysis. For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. Through a series of simulation experiments on both synthetic and real world simulators, the emulators inferred on optimal designs with replicated observations are shown to outperform equivalent models inferred on space-filling replicate-free designs in terms of both model parameter uncertainty and predictive variance.

Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

The design, evaluation and costing of biomass gasifiers

The objective of this study has been to enable a greater understanding of the biomass gasification process through the development and use of process and economic models. A new theoretical equilibrium model of gasification is described using the operating condition called the adiabatic carbon boundary. This represents an ideal gasifier working at the point where the carbon in the feedstock is completely gasified. The model can be used as a `target' against which the results of real gasifiers can be compared, but it does not simulate the results of real gasifiers. A second model has been developed which uses a stagewise approach in order to model fluid bed gasification, and its results have indicated that pyrolysis and the reactions of pyrolysis products play an important part in fluid bed gasifiers. Both models have been used in sensitivity analyses: the biomass moisture content and gasifying agent composition were found to have the largest effects on performance, whilst pressure and heat loss had lesser effects. Correlations have been produced to estimate the total installed capital cost of gasification systems and have been used in an economic model of gasification. This has been used in a sensitivity analysis to determine the factors which most affect the profitability of gasification. The most important influences on gasifier profitability have been found to be feedstock cost, product selling price and throughput. Given the economic conditions of late 1985, refuse gasification for the production of producer gas was found to be viable at throughputs of about 2.5 tonnes/h dry basis and above, in the metropolitan counties of the United Kingdom. At this throughput and above, the largest element of product gas cost is the feedstock cost, the cost element which is most variable.

Computer aided design and manufacture for three dimensional milling

Advances in both computer technology and the necessary mathematical models capable of capturing the geometry of arbitarily shaped objects has led to the development in this thesis of a surface generation package called 'IBSCURF' aimed at providing a more economically viable solution to free-form surface manufacture. A suit of computer programs written in FORTRAN 77 has been developed to provide computer aids for every aspect of work in designing and machining free-form surfaces. A vector-valued parametric method was used for shape description and a lofting technique employed for the construction of the surface. The development of the package 'IBSCURF' consists of two phases. The first deals with CAD. The design process commences in defining the cross-sections which are represented by uniform B-spline curves as approximations to give polygons. The order of the curve and the position and number of the polygon vertices can be used as parameters for the modification to achieve the required curves. When the definitions of the sectional curves is complete, the surface is interpolated over them by cubic cardinal splines. To use the CAD function of the package to design a mould for a plastic handle, a mathematical model was developed. To facilitate the integration of design and machining using the mathematical representation of the surface, the second phase of the package is concerned with CAM which enables the generation of tool offset positions for ball-nosed cutters and a general post-processor has been developed which automatically generates NC tape programs for any CNC milling machine. The two phases of these programs have been successfully implemented, as a CAD/CAM package for free-form surfaces on the VAX 11/750 super-minicomputer with graphics facilities for displaying drawings interactively on the terminal screen. The development of this package has been beneficial in all aspects of design and machining of free form surfaces.

An experimental analysis of operating conditions in cold roll-forming

A detailed literature survey confirmed cold roll-forming to be a complex and little understood process. In spite of its growing value, the process remains largely un-automated with few principles used in set-up of the rolling mill. This work concentrates on experimental investigations of operating conditions in order to gain a scientific understanding of the process. The operating conditions are; inter-pass distance, roll load, roll speed, horizontal roll alignment. Fifty tests have been carried out under varied operating conditions, measuring section quality and longitudinal straining to give a picture of bending. A channel section was chosen for its simplicity and compatibility with previous work. Quality measurements were measured in terms of vertical bow, twist and cross-sectional geometric accuracy, and a complete method of classifying quality has been devised. The longitudinal strain profile was recorded, by the use of strain gauges attached to the strip surface at five locations. Parameter control is shown to be important in allowing consistency in section quality. At present rolling mills are constructed with large tolerances on operating conditions. By reduction of the variability in parameters, section consistency is maintained and mill down-time is reduced. Roll load, alignment and differential roll speed are all shown to affect quality, and can be used to control quality. Set-up time is reduced by improving the design of the mill so that parameter values can be measured and set, without the need for judgment by eye. Values of parameters can be guided by models of the process, although elements of experience are still unavoidable. Despite increased parameter control, section quality is variable, if only due to variability in strip material properties. Parameters must therefore be changed during rolling. Ideally this can take place by closed-loop feedback control. Future work lies in overcoming the problems connected with this control.

The design of environmental test rigs

Product reliability and its environmental performance have become critical elements within a product's specification and design. To obtain a high level of confidence in the reliability of the design it is customary to test the design under realistic conditions in a laboratory. The objective of the work is to examine the feasibility of designing mechanical test rigs which exhibit prescribed dynamical characteristics. The design is then attached to the rig and excitation is applied to the rig, which then transmits representative vibration levels into the product. The philosophical considerations made at the outset of the project are discussed as they form the basis for the resulting design methodologies. It is attempted to directly identify the parameters of a test rig from the spatial model derived during the system identification process. It is shown to be impossible to identify a feasible test rig design using this technique. A finite dimensional optimal design methodology is developed which identifies the parameters of a discrete spring/mass system which is dynamically similar to a point coordinate on a continuous structure. This design methodology is incorporated within another procedure which derives a structure comprising a continuous element and a discrete system. This methodology is used to obtain point coordinate similarity for two planes of motion, which is validated by experimental tests. A limitation of this approach is that it is impossible to achieve multi-coordinate similarity due to an interaction of the discrete system and the continuous element at points away from the coordinate of interest. During the work the importance of the continuous element is highlighted and a design methodology is developed for continuous structures. The design methodology is based upon distributed parameter optimal design techniques and allows an initial poor design estimate to be moved in a feasible direction towards an acceptable design solution. Cumulative damage theory is used to provide a quantitative method of assessing the quality of dynamic similarity. It is shown that the combination of modal analysis techniques and cumulative damage theory provides a feasible design synthesis methodology for representative test rigs.

Management information:design of a system for change identification

This thesis deals with the problem of Information Systems design for Corporate Management. It shows that the results of applying current approaches to Management Information Systems and Corporate Modelling fully justify a fresh look to the problem. The thesis develops an approach to design based on Cybernetic principles and theories. It looks at Management as an informational process and discusses the relevance of regulation theory to its practice. The work proceeds around the concept of change and its effects on the organization's stability and survival. The idea of looking at organizations as viable systems is discussed and a design to enhance survival capacity is developed. It takes Ashby's theory of adaptation and developments on ultra-stability as a theoretical framework and considering conditions for learning and foresight deduces that a design should include three basic components: A dynamic model of the organization- environment relationships; a method to spot significant changes in the value of the essential variables and in a certain set of parameters; and a Controller able to conceive and change the other two elements and to make choices among alternative policies. Further considerations of the conditions for rapid adaptation in organisms composed of many parts, and the law of Requisite Variety determine that successful adaptive behaviour requires certain functional organization. Beer's model of viable organizations is put in relation to Ashby's theory of adaptation and regulation. The use of the Ultra-stable system as abstract unit of analysis permits developing a rigorous taxonomy of change; it starts distinguishing between change with in behaviour and change of behaviour to complete the classification with organizational change. It relates these changes to the logical categories of learning connecting the topic of Information System design with that of organizational learning.

The design of novel antifolates against pneumocystis carinii

The pneumonia caused by Pneumocystis carinii is ultimately responsible for the death of many acquired immunodeficiency syndrome (AIDS) patients. Large doses of trimethoprim and pyrimethamine in combination with a sulphonamide and/or pentamidine suppress the infection but produce serious side-effects and seldom prevent recurrence after treatment withdrawal. However, the partial success of the aforementioned antifolates, and also trimetrexate used alone, does suggest dihydrofolate reductase (DHFR) as a target for the development of antipneumocystis agents. From the DHFR inhibitory activities of 3'-substituted pyrimethamine analogues it was suggested that the 3'-(3'',3''-dimethyltriazen-1''-yl) substituent may be responsible for the greater activity for the P.carinii over the mammalian enzyme. Crystallographic and molecular modeling studies revealed considerable geometrical and electronic differences between the triazene and the chemically related formamidine functions that may account for the differences in DHFR inhibitory profiles. Structural and electronic parameters calculated for a series of 3'-(3'',3''-disubstitutedtriazen-1''-yl) pyrimethamine analogues did not correlate with the DHFR inhibitory activities. However, the in vitro screening against P.carinii DHFR revealed that the 3''-hydroxyethyl-3''-benzyl analogue was the most active and selective. Models of the active sites of human and P.carinii DHFRs were constructed using DHFR sequence and structural homology data which had identified key residues involved in substrate and cofactor binding. Low energy conformations of the 3'',3''-dimethyl and 3''-hydroxyethyl-3''-benzyle analogues, determined from nuclear magnetic resonance studies and theoretical calculations, were docked by superimposing the diaminopyrimidine fragment onto a previously docked pyrimethamine analogue. Enzyme kinetic data supported the 3''-hydroxyethyl-3''-benzyl moiety being located in the NADPH binding groove. The 3''-benzyl substituent was able to locate to within 3 AA of a valine residue in the active site of P.carinii DHFR thereby producing a hydrophobic contact. The equivalent residue in human DHFR is threonine, more hydrophilic and less likely to be involved in such a contact. This difference may account for the greater inhibitory activity this analogue has for P.carinii DHFR and provide a basis for future drug design. From an in vivo model of PCP in immunosuppressed rats it was established that the 3"-hydroxyethyl-3"-benzyl analogue was able to reduce the.P.carinii burden more effectively with increasing doses, without causmg any visible signs of toxicity. However, equivalent doses were not as effective as pentamidine, a current treatment of choice for Pneumocystis carinii pneumonia.

The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing

Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

Aspects of design for a spare parts provisioning system

This thesis describes an investigation by the author into the spares operation of compare BroomWade Ltd. Whilst the complete system, including the warehousing and distribution functions, was investigated, the thesis concentrates on the provisioning aspect of the spares supply problem. Analysis of the historical data showed the presence of significant fluctuations in all the measures of system performance. Two Industrial Dynamics simulation models were developed to study this phenomena. The models showed that any fluctuation in end customer demand would be amplified as it passed through the distributor and warehouse stock control systems. The evidence from the historical data available supported this view of the system's operation. The models were utilised to determine which parts of the total system could be expected to exert a critical influence on its performance. The lead time parameters of the supply sector were found to be critical and further study showed that the manner in which the lead time changed with work in progress levels was also an important factor. The problem therefore resolved into the design of a spares manufacturing system. Which exhibited the appropriate dynamic performance characteristics. The gross level of entity presentation, inherent in the Industrial Dynamics methodology, was found to limit the value of these models in the development of detail design proposals. Accordingly, an interacting job shop simulation package was developed to allow detailed evaluation of organisational factors on the performance characteristics of a manufacturing system. The package was used to develop a design for a pilot spares production unit. The need for a manufacturing system to perform successfully under conditions of fluctuating demand is not limited to the spares field. Thus, although the spares exercise provides an example of the approach, the concepts and techniques developed can be considered to have broad application throughout batch manufacturing industry.