Prospective evaluation of a D-optimal designed population pharmacokinetic study

Recently, methods for computing D-optimal designs for population pharmacokinetic studies have become available. However there are few publications that have prospectively evaluated the benefits of D-optimality in population or single-subject settings. This study compared a population optimal design with an empirical design for estimating the base pharmacokinetic model for enoxaparin in a stratified randomized setting. The population pharmacokinetic D-optimal design for enoxaparin was estimated using the PFIM function (MATLAB version 6.0.0.88). The optimal design was based on a one-compartment model with lognormal between subject variability and proportional residual variability and consisted of a single design with three sampling windows (0-30 min, 1.5-5 hr and 11 - 12 hr post-dose) for all patients. The empirical design consisted of three sample time windows per patient from a total of nine windows that collectively represented the entire dose interval. Each patient was assigned to have one blood sample taken from three different windows. Windows for blood sampling times were also provided for the optimal design. Ninety six patients were recruited into the study who were currently receiving enoxaparin therapy. Patients were randomly assigned to either the optimal or empirical sampling design, stratified for body mass index. The exact times of blood samples and doses were recorded. Analysis was undertaken using NONMEM (version 5). The empirical design supported a one compartment linear model with additive residual error, while the optimal design supported a two compartment linear model with additive residual error as did the model derived from the full data set. A posterior predictive check was performed where the models arising from the empirical and optimal designs were used to predict into the full data set. This revealed the optimal'' design derived model was superior to the empirical design model in terms of precision and was similar to the model developed from the full dataset. This study suggests optimal design techniques may be useful, even when the optimized design was based on a model that was misspecified in terms of the structural and statistical models and when the implementation of the optimal designed study deviated from the nominal design.

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.

Optimal design of smart structures using bonded plezoelectrics for vibration control

Smart material technology has become an area of increasing interest for the development of lighter and stronger structures which are able to incorporate actuator and sensor capabilities for collocated control. In the design of actively controlled structures, the determination of the actuator locations and the controller gains, is a very important issue. For that purpose, smart material modelling, modal analysis methods, control and optimization techniques are the most important ingredients to be taken into account. The optimization problem to be solved in this context presents two interdependent aspects. The first one is related to the discrete optimal actuator location selection problem which is solved in this paper using genetic algorithms. The second is represented by a continuous variable optimization problem, through which the control gains are determined using classical techniques. A cantilever Euler-Bernoulli beam is used to illustrate the presented methodology.

Full Bridge MMC Converter Optimal Design to HVDC Operational Requirements

This project is funded by RTE, Paris, France

Optimal design for correlated processes with input-dependent noise

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models. © 2013 Elsevier Inc. All rights reserved.

Toward Optimal Design of Piezoelectric Transducers Based on Multifunctional and Smoothly Graded Hybrid Material Systems

This work explores the design of piezoelectric transducers based on functional material gradation, here named functionally graded piezoelectric transducer (FGPT). Depending on the applications, FGPTs must achieve several goals, which are essentially related to the transducer resonance frequency, vibration modes, and excitation strength at specific resonance frequencies. Several approaches can be used to achieve these goals; however, this work focuses on finding the optimal material gradation of FGPTs by means of topology optimization. Three objective functions are proposed: (i) to obtain the FGPT optimal material gradation for maximizing specified resonance frequencies; (ii) to design piezoelectric resonators, thus, the optimal material gradation is found for achieving desirable eigenvalues and eigenmodes; and (iii) to find the optimal material distribution of FGPTs, which maximizes specified excitation strength. To track the desirable vibration mode, a mode-tracking method utilizing the `modal assurance criterion` is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept. The optimization algorithm is constructed based on sequential linear programming, and the concept of continuum approximation of material distribution. To illustrate the method, 2D FGPTs are designed for each objective function. In addition, the FGPT performance is compared with the non-FGPT one.

Optimal design of periodic functionally graded composites with prescribed properties

The computational design of a composite where the properties of its constituents change gradually within a unit cell can be successfully achieved by means of a material design method that combines topology optimization with homogenization. This is an iterative numerical method, which leads to changes in the composite material unit cell until desired properties (or performance) are obtained. Such method has been applied to several types of materials in the last few years. In this work, the objective is to extend the material design method to obtain functionally graded material architectures, i.e. materials that are graded at the local level (e.g. microstructural level). Consistent with this goal, a continuum distribution of the design variable inside the finite element domain is considered to represent a fully continuous material variation during the design process. Thus the topology optimization naturally leads to a smoothly graded material system. To illustrate the theoretical and numerical approaches, numerical examples are provided. The homogenization method is verified by considering one-dimensional material gradation profiles for which analytical solutions for the effective elastic properties are available. The verification of the homogenization method is extended to two dimensions considering a trigonometric material gradation, and a material variation with discontinuous derivatives. These are also used as benchmark examples to verify the optimization method for functionally graded material cell design. Finally the influence of material gradation on extreme materials is investigated, which includes materials with near-zero shear modulus, and materials with negative Poisson`s ratio.

Balancing the number and size of sites: An economic approach to the optimal design of cluster samples

The design of randomized controlled trials entails decisions that have economic as well as statistical implications. In particular, the choice of an individual or cluster randomization design may affect the cost of achieving the desired level of power, other things being equal. Furthermore, if cluster randomization is chosen, the researcher must decide how to balance the number of clusters, or sites, and the size of each site. This article investigates these interrelated statistical and economic issues. Its principal purpose is to elucidate the statistical and economic trade-offs to assist researchers to employ randomized controlled trials that have desired economic, as well as statistical, properties. (C) 2003 Elsevier Inc. All rights reserved.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Optimal design for active damping in sandwich structures using the Direct MultiSearch method

This paper addresses the problem of optimal positioning of surface bonded piezoelectric patches in sandwich plates with viscoelastic core and laminated face layers. The objective is to maximize a set of modal loss factors for a given frequency range using multiobjective topology optimization. Active damping is introduced through co-located negative velocity feedback control. The multiobjective topology optimization problem is solved using the Direct MultiSearch Method. An application to a simply supported sandwich plate is presented with results for the maximization of the first six modal loss factors. The influence of the finite element mesh is analyzed and the results are, to some extent, compared with those obtained using alternative single objective optimization. (C) 2013 Elsevier Ltd. All rights reserved.

Optimal design for active damping in sandwich structures using the Direct MultiSearch method

This paper addresses the problem of optimal positioning of surface bonded piezoelectric patches in sandwich plates with viscoelastic core and laminated face layers. The objective is to maximize a set of modal loss factors for a given frequency range using multiobjective topology optimization. Active damping is introduced through co-located negative velocity feedback control. The multiobjective topology optimization problem is solved using the Direct MultiSearch Method. An application to a simply supported sandwich plate is presented with results for the maximization of the first six modal loss factors. The influence of the finite element mesh is analyzed and the results are, to some extent, compared with those obtained using alternative single objective optimization.

Optimal design and operation of compact simulated moving bed processes for enantioseparations

Simulated moving bed (SMB) chromatography is attracting more and more attention since it is a powerful technique for complex separation tasks. Nowadays, more than 60% of preparative SMB units are installed in the pharmaceutical and in the food in- dustry [SDI, Preparative and Process Liquid Chromatography: The Future of Process Separations, International Strategic Directions, Los Angeles, USA, 2002. http://www. strategicdirections.com]. Chromatography is the method of choice in these ¯elds, be- cause often pharmaceuticals and ¯ne-chemicals have physico-chemical properties which di®er little from those of the by-products, and they may be thermally instable. In these cases, standard separation techniques as distillation and extraction are not applicable. The noteworthiness of preparative chromatography, particulary SMB process, as a sep- aration and puri¯cation process in the above mentioned industries has been increasing, due to its °exibility, energy e±ciency and higher product purity performance. Consequently, a new SMB paradigm is requested by the large number of potential small- scale applications of the SMB technology, which exploits the °exibility and versatility of the technology. In this new SMB paradigm, a number of possibilities for improving SMB performance through variation of parameters during a switching interval, are pushing the trend toward the use of units with smaller number of columns because less stationary phase is used and the setup is more economical. This is especially important for the phar- maceutical industry, where SMBs are seen as multipurpose units that can be applied to di®erent separations in all stages of the drug-development cycle. In order to reduce the experimental e®ort and accordingly the coast associated with the development of separation processes, simulation models are intensively used. One impor- tant aspect in this context refers to the determination of the adsorption isotherms in SMB chromatography, where separations are usually carried out under strongly nonlinear conditions in order to achieve higher productivities. The accurate determination of the competitive adsorption equilibrium of the enantiomeric species is thus of fundamental importance to allow computer-assisted optimization or process scale-up. Two major SMB operating problems are apparent at production scale: the assessment of product quality and the maintenance of long-term stable and controlled operation. Constraints regarding product purity, dictated by pharmaceutical and food regulatory organizations, have drastically increased the demand for product quality control. The strict imposed regulations are increasing the need for developing optically pure drugs.(...)

Optimal design in conjoint analysis

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Optimal design for dose finding studies on safety and efficacy

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009