I-optimal Design Research Articles

Algorithms for i-optimal designs for ordinal response: a literature approach

In many cases, the reseachers face the problem how to design the experiment which deal with the real situation. This is because the designs on literature do not suit the case. To solve the problem, optimal design can be an alternative. There are two approaches on optimal design: an analytical and a computational approach. An algorithm in the computational approach is needed to find an optimal design. The optimal design is a part of experimental design which seeks the design based on a certain criterion. The criterion which focuses on presicion of prediction variance is I-optimality criterion. Limited literatures address the I- optimality criterion for ordinal response. Most of literatures address to developing algorithms of other optimality criteria for General Linear Model. As the response is ordinal, hence the ordinal response belongs to non-linear model.

A prototype of a low-cost eyelid cleaning foaming solution for symptom management in patients with chronic blepharitis: An I-optimal mixture experimental design

lepharitis is a common chronic eye condition that causes eyelid inflammation, leading to inflamed, irritated, sticky and itchy eyelids and flaking of the skin. For its treatment, patients often need indefinite use of an eyelid cleaning solution which usually cost more than 20 USD per 80 ml bottle and lasts, on average, one month. For those patients unable to afford the treatment, physicians recommend the use of a do it yourself (DIY) solution. However, the efficacy of DIY eyelid solutions might fluctuate according to the type of blepharitis present in the patient and inadequate pH stabilization of the solution might promote additional itchiness, irritation, and dryness of the skin and eyes. Thus, we propose an optimized DIY solution prototype for symptom management in patients with chronic blepharitis. The formulation contains a significant ratio of tea tree oil and resulted in suitable pH and foam expansion values. The low cost and ease of preparation of the designed formulation make it an affordable, effective alternative in the treatment of chronic blepharitis.

A nonlinear multidimensional knapsack problem in the optimal design of mixture experiments

Mixture experiments usually involve various constraints on the proportions of the ingredients of the mixture under study. In this paper, inspired by the fact that the available stock of certain ingredients is often limited, we focus on a new type of constraint, which we refer to as an ingredient availability constraint. This type of constraint substantially complicates the search for optimal designs for mixture experiments. One difficulty, for instance, is that the optimal number of experimental runs is not known a priori. The resulting optimal experimental design problem belongs to the class of nonlinear nonseparable multidimensional knapsack problems. We present a variable neighborhood search algorithm as well as a mixed integer nonlinear programming approach to tackle the problem to identify D- and I-optimal designs for mixture experiments when there is a limited stock of certain ingredients, and we show that the variable neighborhood search algorithm is highly competitive in terms of solution quality and computing time.

INVESTIGATION OF CRITICAL MATERIAL ATTRIBUTES OF NANOCELLULOSE IN TABLETS

Objective: The present work aims to compare powder flow properties and post-compression characteristics of acid hydrolysis nanocellulose (AH-NC) a novel excipient with microcrystalline cellulose (MCC PH200) to demonstrate the application and performance of AH-NC.
 Methods: I-optimal design was applied separately for both the excipient, i.e., MCC PH200 and AH-NC. Independent variables were MCC PH200 as diluent (X1), AH-NC as diluent (X1), starch as disintegrant (X2), and PVP K30 as dry binder (X3). The dependent variables in design were Carr’s index (CI) (R1), angle of repose (AR) (R2), hardness (R3), friability (R4), disintegration time (DT) (R5), and T90 (R6).
 Results: Fourier-transform infrared spectroscopy (FTIR) and differential scanning calorimetry studies showed the compatibility of the drug with an excipient. CI was found in the range of 8%–17.84% for MCC PH200 and 5.25%–11.94% for AH-NC. AR was found in the range of 31.48–37.66 for MCC PH200 and 29.62–35.30 for AH-NC. The values of friability, DT, and T90 were almost identical in both the cases.
 Conclusion: Not only does AH-NC demonstrates better flow properties but also problems of weight variation and content uniformity are not observed when compared to MCC PH200. Hence, AH-NC is more suitable as an excipient for modern high-speed rotary tablet press.

Synthesis, characterization, rheological and self-assembly behavior of polyelectrolytes hydrophobically modified with high styrene content: Effect of external parameters on thickening properties and nano-associations

Acrylamide (AM)/2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS)/styrene (St) (AMAS) and AM/sodium styrenesulfonate (SSS)/St (AMSS) polyelectrolytes were synthesized by micellar copolymerization method and then characterized using 1H-NMR, rheometry, viscometry, dynamic light scattering (DLS) and water solubility analyses. It was found that polyelectrolytes are not soluble in the water due to their high length of St blocks (NH=15.4); however, a significant self-assembly behavior of St nano-sized associations was observed by adding a low amount of SDS (10 mM) to the aqueous solution, resulting in the improved rheological behavior of the corresponding solutions. Effect of the external stimuli including emulsifier (SDS) and electrolyte (NaCl) concentration and temperature on the reduced viscosity of polyelectrolyte solutions was also studied using I-optimal design. Based on the viscosity measurements, notable thickening ability for aqueous solutions of both the AMAS and AMSS samples were observed at a SDS concentration of 6.5 mM, NaCl concentration of 0.55 wt% and temperature of 25 °C, which was further confirmed using oscillatory frequency sweep and dynamic light scattering measurements. Moreover, the higher thickening ability was observed for the AMSS aqueous solution in comparison with the AMAS one.

A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments

We propose a class of subspace ascent methods for computing optimal approximate designs that covers existing algorithms as well as new and more efficient ones. Within this class of methods, we construct a simple, randomized exchange algorithm (REX). Numerical comparisons suggest that the performance of REX is comparable or superior to that of state-of-the-art methods across a broad range of problem structures and sizes. We focus on the most commonly used criterion of D-optimality, which also has applications beyond experimental design, such as the construction of the minimum-volume ellipsoid containing a given set of data points. For D-optimality, we prove that the proposed algorithm converges to the optimum. We also provide formulas for the optimal exchange of weights in the case of the criterion of A-optimality, which enable one to use REX and some other algorithms for computing A-optimal and I-optimal designs. Supplementary materials for this article are available online.

I-Optimal design of poly(lactic-co-glycolic) acid/hydroxyapatite three-dimensional scaffolds produced by thermally induced phase separation.

In bone tissue engineering, 3D scaffolds are often designed to have adequate modulus while taking into consideration the requirement for a highly porous network for cell seeding and tissue growth. This paper presents the design optimization of 3D scaffolds made of poly(lactic-co-glycolic) acid (PLGA) and nanohydroxyapatite (nHA), produced by thermally induced phase separation (TIPS). Slow cooling at a rate of 1°C/min enabled a uniform temperature and produced porous scaffolds with a relatively uniform pore size. An I-optimal design of experiments (DoE) with 18 experimental runs was used to relate four responses (scaffold thickness, density, porosity, and modulus) to three experimental factors, namely the TIPS temperature (-20°C, -10°C, and 0°C), PLGA concentration (7%, 10%, and 13% w/v), and nHA content (0%, 15%, and 30% w/w). The response surface analysis using JMP® software predicted a temperature of -18.3°C, a PLGA concentration of 10.3% w/v, and a nHA content of 30% w/w to achieve a thickness of 3 mm, a porosity of 83%, and a modulus of ~4 MPa. The set of validation scaffolds prepared using the predicted factor levels had a thickness of 3.05 ± 0.37 mm, a porosity of 86.8 ± 0.9 %, and a modulus of 3.57 ± 2.28 MPa.

Response Surface Methodology for Optimization of Ultrasound-Assisted Transdermal Delivery and Skin Retention of Asenapine Maleate

Asenapine maleate (ASP) is an antipsychotic agent used in the treatment of schizophrenia and bipolar disorder. It has extremely low oral bioavailability of < 2%, necessitating the utilization of alternate route of administration. The objective of this work is to study and optimize the sonophoretic transdermal delivery and skin retention of ASP statistically, in Sprague-Dawley rat skin, using response surface methodology in Design of Experiments (DoE). I-optimal design was employed, using the ultrasound (US) parameters viz., duration of US application, amplitude of US, and mode of US application (simultaneous application or pretreatment) as the input variables. Steady-state flux (Jss) of ASP and amount of drug retained in skin after 24 h was taken as the output responses. The model and dependent variables were found to be significant and representative of the data and response surface. While passive diffusion yielded Jss of 2.575 μg/cm2/h, the same values with US application ranged from 8.18 to 127.68 μg/cm2/h. Passive diffusion of drug showed 46.22 ± 5.2 μg/cm2 of ASP retained in 24 h, while US application resulted in 99.07 to 1495.6 μg/cm2 of drug retained in skin in 24 h. Based on the findings from optimization studies, 30 min of US application, with amplitude of 27–28, and simultaneous application mode was found to achieve the optimal transdermal drug flux, with slightly lower retention values in skin. The study found that the sonophoretic transdermal permeation and retention of ASP in vitro could be optimized using response surface methodology.

Natural Frequency prediction of FDM manufactured parts using ANN approach

Abstract This research study demonstrates the use of machine learning tools for the prediction of dynamic mechanical characteristics of parts produced by the Fused Deposition Modeling (FDM) process. In this regard, I-optimal design of experiments was followed with raster angle, air gap, build orientation and number of contours as independent variables together with natural frequency as the mechanical part characteristic for investigation. Accordingly, a Artificial Neural Network (ANN) model was trained using the Bayesian regularization function. Finally, the trained ANN model was validated by performing multiple confirmation runs which provided predictions generally within 5% accuracy.

I-Optimal Design of Hierarchical 3D Scaffolds Produced by Combining Additive Manufacturing and Thermally Induced Phase Separation.

The limitations in the transport of oxygen, nutrients, and metabolic waste products pose a challenge to the development of bioengineered bone of clinically relevant size. This paper reports the design and characterization of hierarchical macro/microporous scaffolds made of poly(lactic-co-glycolic) acid and nanohydroxyapatite (PLGA/nHA). These scaffolds were produced by combining additive manufacturing (AM) and thermally induced phase separation (TIPS) techniques. Macrochannels with diameters of ~300 μm, ~380 μm, and ~460 μm were generated by embedding porous 3D-plotted polyethylene glycol (PEG) inside PLGA/nHA/1,4-dioxane or PLGA/1,4-dioxane solutions, followed by PEG extraction using deionized (DI) water. We have used an I-optimal design of experiments (DoE) and the response surface analysis (JMP® software) to relate three responses (scaffold thickness, porosity, and modulus) to the four experimental factors affecting the scaffold macro/microstructures (e.g., PEG strand diameter, PLGA concentration, nHA content, and TIPS temperature). Our results indicated that a PEG strand diameter of ~380 μm, a PLGA concentration of ~10% w/v, a nHA content of ~10% w/w, and a TIPS temperature around -10°C could generate scaffolds with a porosity of ~90% and a modulus exceeding 4 MPa. This paper presents the steps for the I-optimal design of these scaffolds and reports on their macro/microstructures, characterized using scanning electron microscopy (SEM) and micro-computed tomography (micro-CT).

Analytical QbD-Integrated Method Development and Validation of Silver Sulphadiazine in Pure Drug and Topical Nanocarrier(s)

Current work aims at Analytical Quality by Design (AQbD)-based development and validation of stability-indicating chromatographic method for quantification of silver sulphadiazine (SSD) in bulk and pharmaceutical dosage forms. The first stage of AQbD approach involved defining QTP (Quality Target Profile) usually referred to as ATP (Analytical Target Profile). Screening studies were performed employing a 78-Taguchi design. The composition of mobile phase, pH of water and injection volume were identified as critical method parameters (CMPs) and were systematically optimized using I-optimal design for evaluating CAAs, namely theoretical plates, tailing factor and % assay. Chromatographic separation was carried out using C-18 column with water containing glacial acetic acid (5 mL in 255 mL water, pH adjusted to 2.5) and mixture of acetonitrile:methanol (75: 25, v/v) in the ratio of 80: 20 (v/v) as mobile phase at flow rate of 0.7 mL/min at 254 nm. The method was validated as per ICH recommended guidelines. Further, forced degradation studies and application of the developed method for the estimation of SSD in marketed, liposomal and organogel systems indicated no significant change in retention time. In conclusion, the studies successfully ratify the utility of AQbD approach for developing highly sensitive liquid chromatographic method for SSD estimation.

Improving the biopharmaceutical attributes of mangiferin using vitamin E-TPGS co-loaded self-assembled phosholipidic nano-mixed micellar systems

The current research work encompasses the development, characterization, and evaluation of self-assembled phospholipidic nano-mixed miceller system (SPNMS) of a poorly soluble BCS Class IV xanthone bioactive, mangiferin (Mgf) functionalized with co-delivery of vitamin E TPGS. Systematic optimization using I-optimal design yielded self-assembled phospholipidic nano-micelles with a particle size of < 60 nm and > 80% of drug release in 15 min. The cytotoxicity and cellular uptake studies performed using MCF-7 and MDA-MB-231 cell lines demonstrated greater kill and faster cellular uptake. The ex vivo intestinal permeability revealed higher lymphatic uptake, while in situ perfusion and in vivo pharmacokinetic studies indicated nearly 6.6- and 3.0-folds augmentation in permeability and bioavailability of Mgf. In a nutshell, vitamin E functionalized SPNMS of Mgf improved the biopharmaceutical performance of Mgf in rats for enhanced anticancer potency.

Quasi-Newton algorithm for optimal approximate linear regression design: Optimization in matrix space

Given a linear regression model and an experimental region for the independent variable, the problem of finding an optimal approximate design calls for minimizing a convex optimality criterion over a convex set of information matrices of feasible approximate designs. For numerical solution pure gradient methods are often used by design theorists, as vertex direction, vertex exchange, multiplicative algorithms, or combinations hereof. These methods have two major deficiencies: a slow convergence rate after a quick but rough approximation to the optimum, and often a large support of the obtained nearly optimal design. The latter feature is related to the fact that the methods optimize in the space of design measures which is usually of high or even infinite dimension, whereas the dimension of the information matrices is often small or moderate. For such situations a quasi-Newton method is revisited which was originally established by Gaffke & Heiligers (1996). In the present paper new possibilities of its application are demonstrated. The algorithm optimizes in matrix space. It shows a good global and an excellent local convergence behavior resulting in an accurate approximation of the optimum. A crucial subroutine solves convex quadratic minimization over the set of information matrices via repeated linear minimization over that set, providing thus the quasi-Newton step of the algorithm. This may also be of interest as a tool for computing an approximate design from a given information matrix and such that the support size of the design keeps Carathéodory’s bound. Illustrations are given for D- and I-optimality in particular multivariate random coefficient regression models and for T-optimal discriminating design in univariate polynomial models. Moreover, the behavior of the algorithm is tested for cases of larger dimensions: D- and I-optimal design for a third order polynomial model in several variables on a discretized cube.

Investigation of the tableting behavior of Ibuprofen DC 85 W

The aim of the present study was to investigate the tableting behavior of Ibuprofen DC 85 W with special focus on the tablet disintegration time, the tablet crushing strength, and the sticking tendency to punch surfaces. To simulate production conditions, tableting was conducted on a rotary press, equipped with three compaction stations. An I-optimal design of experiments was used to analyze the influence of the pre-compaction, the intermediate compaction, and the main compaction force on the two responses: tablet disintegration time and crushing strength. It was shown that Ibuprofen DC 85 W showed a good tableting behavior with regard to both responses. The tablet disintegration was considerably affected by the maximum compaction force applied, but was also slightly affected by preceding compaction events. The tablet crushing strength was mainly affected by the maximum applied compaction force independent of the order of these forces. The sticking tendency of Ibuprofen DC 85 W was compared with that two other ibuprofen powder formulations in long-term tableting runs. Compared to the other two formulations, sticking was considerably lower with Ibuprofen DC 85 W. The sticking tendency was not influenced by the addition of an intermediate compaction force, but was remarkably reduced by the choice of the punch tip coating.

Development and optimization of in-situ forming microparticles for long term controlled delivery of deslorelin acetate

Deslorelin is a nonapeptide analogue of the natural gonadotropin releasing hormone or luteinizing hormone releasing hormone used in the treatment of prostate cancer, endometriosis and uterine fibroids. In-situ forming microparticles were developed for deslorelin using smart, biodegradable polymer i.e. PLGA. Different formulations were designed, prepared and evaluated by employing response surface, I-optimal design. To determine the optimized formulation, numerical and graphical optimization techniques were employed. The resulting optimized formulation was evaluated for other physicochemical parameters viz., rheology, particle size distribution, surface morphology of the particles, peptide conformation stability in the formulation and stability study at different environmental conditions. It was concluded that the optimized deslorelin acetate ISFM formulation effectively extended the peptide release for 30 days while maintaining its conformational stability during the period of study. The optimized ISFM formulation was found to be stable at 5°C ± 2°C and 25°C ± 2°C during 6 months stability studies.

Selection of a design for response surface

Box-Behnken, Central-Composite, D and I-optimal designs were compared using statistical tools. Experimental trials for all designs were generated. Random uniform responses were simulated for all models. R-square, Akaike and Bayesian Information Criterion for the fitted models were noted. One–way ANOVA and Tukey’s multiple comparison test were performed on these parameters. These models were evaluated based on the number of experimental trials generated in addition to the results of the statistical analyses. D-optimal design generated 12 trials in its model, which was lesser in comparison to both Central Composite and Box-Behnken designs. The R-square values of the fitted models were found to possess a statistically significant difference (P<0.0001). D-optimal design not only had the highest mean R-square value (0.7231), but also possessed the lowest means for both Akaike and Bayesian Information Criterion. The D-optimal design was recommended for generation of response surfaces, based on the assessment of the above parameters.

The construction of [formula omitted]- and [formula omitted]-optimal designs for mixture experiments with linear constraints on the components

Mixture experiments in which linear constraints are imposed on the components of the mixture are used extensively in practice. The problem of constructing designs which are in some sense optimal for this experimental setting is not straightforward. More specifically, the design space is a polytope embedded in a regular simplex. In the present paper, a new approach to the problem, which builds on the fact that points in the polytope can be represented as convex combinations of the vertices of that polytope, is introduced. Some theory underpinning this idea and rooted in the notion of barycentric coordinates is developed and algorithms for the construction of exact and approximate D- and I-optimal designs for the Scheffé model are delineated. The methodology is illustrated by means of examples involving three- and four-component mixtures.

Optimal design of experiments for excipient compatibility studies

A crucial stage in the development of medical drugs is to study which additives, usually called excipients, impact the active ingredient stability. This type of study is generally named an excipient compatibility study and requires a mixture experiment. Subsequently, the effect of the storage conditions, more specifically the relative humidity and temperature, on the stability is investigated. This so-called accelerated life test involves a factorial type of experiment. It has become, however, customary to include the storage conditions in the compatibility study. This provides valuable information concerning potential interactions between excipient combinations and storage conditions. Experiments that combine a mixture experiment with a factorial experiment are generally named mixture-process variable experiments. A limited number of designs for mixture-process variable experiments are available in the literature. One problem is that the proposed designs offer little flexibility. Another is that the required number of runs becomes prohibitively large for large numbers of mixture components. In this paper, we examine flexible, optimal designs for realistic mixture-process variable experiments. Our motivation is to provide guidance to pharmaceutical formulation scientists concerning state-of-the art models and designs for excipient compatibility studies. Using several proof-of-concept examples, we demonstrate that I-optimal designs offer both flexibility and small variances of prediction. We also discuss a real-life example, which could be used as a blueprint for future studies. Because many excipient compatibility studies are not completely randomized, we pay special attention to their logistics and to the resulting randomization restrictions, which lead to split-plot and strip-plot experiments.

Effects of Process and Design Parameters on Granule Size Distribution in a Continuous High Shear Granulation Process

Wet granulation is widely used in the pharmaceutical industry. This advantageous technology is capable of enhancing compression and powder handling, decreasing ingredient segregation, and promoting blend and content uniformity. Currently, a high level of interest exists in the continuous version of this technology, both by the US Food and Drug Administration (FDA), and by pharmaceutical manufacturers. In this paper, a continuous high shear wet granulation process was examined based on a placebo formulation comprising 70% ∂-lactose monohydrate and 30% microcrystalline cellulose (Avicel® PH101). Granulation was then carried out in a continuous high shear mixer granulator, Glatt GCG 70. The impact of two process variables (rotation speed and liquid/solid (L/S) ratio) and two design parameters (blade configuration and nozzle position) were evaluated via an I-optimal design. Multi-factor analysis of variance (ANOVA) indicated that rotation speed and L/S ratio dominated the granulation process and had the most significant effects on granule size distribution (GSD). The largest granule mass median diameter was obtained at the lowest rotation speed and highest L/S ratio. The granulation mechanism underlying this continuous process was examined using a wetting and nucleation regime map. For the cases studied here, the mechanical dispersion regime controlled the formation of granule nuclei, leading to a broad GSD and a limited growth ratio.

Characterization and dynamic mechanical analysis of PC-ABS material processed by fused deposition modelling: An investigation through I-optimal response surface methodology

Fused deposition modelling (FDM) is one of the most widely used layered manufacturing technology in various industries due to its capability to create complex parts at the lowest cost. But when it comes to the mechanical properties, the advantage of FDM is not ideal for every application. This is due to the fact that the mechanical properties of the fabricated parts by FDM strongly related to the fabrication parameters in which the material is being processed, and so how to improve them is worthy of study. Many researchers have examined the influence of varying parameters on the characteristics of FDM manufactured prototypes. FDM manufactured parts are always subjected to static and dynamic loading conditions in a wide range of industries. However, former researches only focused on the mechanical properties under static loading conditions, but none of them provided a systematic study on the effect of FDM fabrication parameters on the mechanical performance under thermal-mechanical cyclic loading. This study investigates the effect of manufacturing parameters on dynamic mechanical performance of the processed parts by FDM through computer-generated optimal design based on I-optimal design. Scanning Electron Microscope (SEM) was used to study the microstructures of some specimens. The results show that dynamic mechanical performance of the manufactured parts is greatly influenced by processing conditions. The results also show that computer-generated optimal design based on I-optimal design is superior over the conventional experimental designs as it is able to simultaneously consider several factors at different levels with less number of experiments than traditional designs.