Multivariate Analyses of a Production Formulation Optimization Experiment

Three prominent multivariate statistical analyses, canonical correlation analysis (CCA), principal component analysis (PCA) and CAS-Regression analysis (CAS-R) are appropriately applied to the formulation optimization data associated with Product-T for determining a set of key excipient/process variables and a set of key response variables to be used in monitoring the future performance of the optimizated formula. CCA which considers both sets of variables simultaneously in a single analysis, successfully delineated two key parameters, one for each set. PCA which considers only the response variables concurred with the CCA results and CAS-R which considers each response variable separately also concurred. Even though CCA is a predominant technique, adjunct results of PCA and CAS-R could be supplemented for a comprehensive interpretation. It is recommended that all three analyses be carried out and interpreted appropriately.     

Multivariate Methods in the Development of a New Tablet Formulation: Optimization and Validation

In a previous study of the development of a tablet formulation approximately 100 excipients were characterized in screening experiments using multivariate design. Acceptable values for important responses were obtained with some of the formulations. The relationships between the properties of the excipients and the responses were evaluated using PLS. In this study additional experiments were performed in order to validate models obtained from the screening study and to find a formulation of suitable composition with desired tablet properties. A formulation with the desired disintegration time was found with the additional experiments and the agreement between observed and predicted values was fair for the tablets that did disintegrate. A limitation of this study was that tablets from four experiments did not disintegrate within the set time limit. The lack of agreement between observed and predicted values of these four experiments was probably due to the nature of one of the factors in the design. Considering the reduced experimental design the results are still encouraging.     

Robustness Testing of a Tablet Formulation Using Multivariate Design

ABSTRACT

A total of 45 experiments were carried out to evaluate the robustness of two similar tablet formulations—a product of two strengths—with respect to normal batch-to-batch variation of the excipients and the active pharmaceutical ingredient. The formulations consist of 10 ingredients. Because of the differing amounts of active pharmaceutical ingredients, the two formulations also differ in the amounts of two of the diluents and one of the binders. The excipients and active pharmaceutical ingredient were characterized in terms of multiple variables, and principal properties were calculated with principal component analysis. A Plackett and Burman design was applied to the principal properties. The relationships between the design factors and two responses, mean disintegration time and mean crushing strength, were evaluated by using regression methods. Both formulations were found to be robust under controlled conditions.     

Formulation Optimization of a Hydrocolloid Dressing

A methodology of mixture experiments has been applied to the formulation of a multicomponent hydrocolloid dressing. Using an extreme vertices statistical design, a semi-occlusive dressing composed of dextran, phospholipid, glycerol and sodium lauryl sulphate has been formulated, which checks evaporative water loss (EWL) from the excised wound surface of rats to an optimum level.     

Formulation Optimization of a Hydrocolloid Dressing

Abstract

A methodology of mixture experiments has been applied to the formulation of a multicomponent hydrocolloid dressing. Using an extreme vertices statistical design, a semi-occlusive dressing composed of dextran, phospholipid, glycerol and sodium lauryl sulphate has been formulated, which checks evaporative water loss (EWL) from the excised wound surface of rats to an optimum level.     

Development and Optimization of a Methotrexate Topical Formulation

A topical methotrexate (MTX) formulation that would achieve optimal drug buildup in the epidermis and diminish potential systemic toxicity could be of great utility in the treatment of a variety of hyperproliferative skin disorders. In an attempt to develop an optimized MTX topical formulation containing pharmaceutically acceptable excipients, a 2³ factorial design was used to investigate the effects of a fatty alcohol, propylene glycol, and ethanol on the in vitro skin permeation and uptake of MTX. In vitro skin permeation studies were performed using excised human epidermis mounted in flow-through diffusion cells. The results of steady-state flux and skin uptake of MTX from these formulations ranged from 0.035 to 0.315 μg/cm²/hr and 1.146 to 7.929 μg/cm², respectively. Response surface analysis was used to determine the optimum formulation in terms of skin permeation and uptake of MTX.

An optimized cream formulation was developed and compared to a gel formulation containing 3% Azone in hairless mice to evaluate the uptake of MTX in the treated and untreated skin sites as well as the distribution of MTX in the blood and liver following topical application. The results of the in vivo study demonstrated the localization of MTX at the treated site for both formulations without significant uptake of MTX in the distant untreated epidermis and dermis. The levels of MTX in the blood and liver following topical application of the optimized cream were significantly less than those of the gel formulation with 3% Azone.     

Development and Optimization of a Methotrexate Topical Formulation

Abstract

A topical methotrexate (MTX) formulation that would achieve optimal drug buildup in the epidermis and diminish potential systemic toxicity could be of great utility in the treatment of a variety of hyperproliferative skin disorders. In an attempt to develop an optimized MTX topical formulation containing pharmaceutically acceptable excipients, a 2³ factorial design was used to investigate the effects of a fatty alcohol, propylene glycol, and ethanol on the in vitro skin permeation and uptake of MTX. In vitro skin permeation studies were performed using excised human epidermis mounted in flow-through diffusion cells. The results of steady-state flux and skin uptake of MTX from these formulations ranged from 0.035 to 0.315 μg/cm²/hr and 1.146 to 7.929 μg/cm², respectively. Response surface analysis was used to determine the optimum formulation in terms of skin permeation and uptake of MTX.

An optimized cream formulation was developed and compared to a gel formulation containing 3% Azone in hairless mice to evaluate the uptake of MTX in the treated and untreated skin sites as well as the distribution of MTX in the blood and liver following topical application. The results of the in vivo study demonstrated the localization of MTX at the treated site for both formulations without significant uptake of MTX in the distant untreated epidermis and dermis. The levels of MTX in the blood and liver following topical application of the optimized cream were significantly less than those of the gel formulation with 3% Azone.     

Multivariate Methods in Developing an Evolutionary Strategy for Tablet Formulation

The aim of this study was to develop a new strategy for choosing excipients in tablet formulation. Multivariate techniques such as principal component analysis (PCA) and experimental design were combined in a multivariate design for screening experiments. Of a total 87 investigated excipients, the initial screening experiments contained 5 lubricants, 9 binders, and 5 disintegrants, and 35 experiments were carried out. Considering a reduced factorial design was used, the resulting PCA and partial least squares (PLS) models offered good insight into the possibilities of tablet formulation. It also offered solutions to the problems and clearly gave directions for optimum formulations. Further, it offered several alternatives for achieving quality formulations. Additional experiments conducted to validate and verify the usefulness of the model were successful, resulting in several tablets of good quality. The conclusion is that a multivariate strategy in tablet formulation is efficient and can be used to reduce the number of experiments drastically. Combining multivariate characterization, physicochemical properties, experimental design, multivariate design, and PLS would lead to an evolutionary strategy for tablet formulation. Since it includes a learning strategy that continuously incorporates data for new compounds and from conducted experiments, this would be an even more powerful tool than expert systems.     

Optimization of Disintegration Time and Crushing Strength of a Tablet Formulation

Abstract

In an experiment with a factorial design, the following aspects were scrutinized: the impact on disintegration time and crushing strength caused by the loss-on-drying of the granulation; the granule-size distribution; the lubricant concentration; the compression force; and the pre-compression. Both with regard to disintegration time and crushing strength, these factors were found to have a significant influence: the loss-on-drying of the granulation; the fraction less than 0.150 mm; the concentration of magnesium stearate; and the compression force. A reduction of the tablet disintegration time was obtained by means of an increase of the granulation moisture; by an increase of the fine fraction; or by a reduction of the lubricant concentration or the compression force. The tablet crushing strength was increased by reducing the deviation of the granulation loss-on-drying from approximately 4.6 %; by a reduction of the fine fraction; by decreasing the lubricant concentration; or by increasing the compression force. The fraction larger than 0.300 mm had no significant influence; nor did the pre-compression. Further, there were no significant interactions.

By means of superimposing contour plots of disintegration time and crushing strength, a region was obtained where the requirements of disintegration time and crushing strength could be satisfied by controlling the processing variables.     

Optimization of Disintegration Time and Crushing Strength of a Tablet Formulation

In an experiment with a factorial design, the following aspects were scrutinized: the impact on disintegration time and crushing strength caused by the loss-on-drying of the granulation; the granule-size distribution; the lubricant concentration; the compression force; and the pre-compression. Both with regard to disintegration time and crushing strength, these factors were found to have a significant influence: the loss-on-drying of the granulation; the fraction less than 0.150 mm; the concentration of magnesium stearate; and the compression force. A reduction of the tablet disintegration time was obtained by means of an increase of the granulation moisture; by an increase of the fine fraction; or by a reduction of the lubricant concentration or the compression force. The tablet crushing strength was increased by reducing the deviation of the granulation loss-on-drying from approximately 4.6 %; by a reduction of the fine fraction; by decreasing the lubricant concentration; or by increasing the compression force. The fraction larger than 0.300 mm had no significant influence; nor did the pre-compression. Further, there were no significant interactions.

By means of superimposing contour plots of disintegration time and crushing strength, a region was obtained where the requirements of disintegration time and crushing strength could be satisfied by controlling the processing variables.     

Multivariate Methods in the Development of a New Tablet Formulation: Excipient Mixtures and Principal Properties

ABSTRACT

A tablet formulation for direct compression has previously been studied using multivariate design. An optimization study of one of the most important tablet properties, disintegration time, revealed that excipients with Principal Properties (PP's) that were predicted as suitable by the model were not represented within the studied material.

The feasibility of using mixtures of excipients in the multivariate approach to tablet formulation to solve this problem has been investigated in the present study. By mixing different excipients of the same excipient class, it should be possible to obtain mixtures with the predicted PP's, which in turn should give a formulation with the desired properties. In order to investigate the utility of this approach, separate mixture designs were applied to both binders and fillers (diluents).

As reported here, the Partial Least Squares Projections to Latent Structures (PLS) model developed in the previously published screening study has been validated in the sense that the interesting region of the PP space identified in it has been shown to contain excipients, pure or mixed, that give the formulation suitable properties. Formulations with suitable properties were found with the mixture experiments. The local models also offer several alternatives for the composition of the formulation that yield the desired disintegration time.     

Canonical Correlation Analysis of Formulation Optimization Experiments

Formulation optimization experiments are primarily composed of two groups of variables, a set of independent variables and a set of dependent variables. Simultaneous consideration of all the variables in a single analysis is desirable since it provides an opportunity to study the interrelationships of all variables, independent as well as dependent at the same time and imparts an in-depth insight into the entire system as a whole. A multivariate statistical analysis, known as canonical correlation analysis, has indeed this capability. In addition, the analysis has the capacity of extracting the maximum possible correlation, called canonical correlation, between the variables of the two sets. The larger the value of the canonical correlation (0.90 or above), the higher is the predictability of one set from the other set. The analysis produces two composite canonical functions, one for each set. They can be used to streamline the subsequent search process associated with the full-fledged optimization analysis. The analysis also has the cardinal property to rank-order the variables in each set according to their relative contributions to the canonical prediction function, and to delineate the most important variable in each set. This information can be useful in monitoring the future performance of the formulation in a time-and-cost effective manner and in selecting variables for future experiments. All the relevant features of the analysis have been depicted in this paper in the context of a mobile phase composition optimization experiment.     

Optimization in Development of Acetaminophen Syrup Formulation

ABSTRACT

Formulation of acetaminophen syrup could be developed by an optimization technique to reduce the time and cost of study. Cosolvents were used in the formulation because of the low solubility of acetaminophen in water. They were composed of polyethylene glycol 4000, propylene glycol, sorbitol solution, and glycerin. Their effects on the solubility of acetaminophen and the pH of formulations were investigated. Effects on taste and price were calculated based on their properties. Simulation study of the effect of cosolvents upon the formulation scores was performed, using an algorithm based upon a simulated annealing concept to achieve the global optima and heuristic optimization concept to accelerate convergence. The program written as a Visual Basic module within Microsoft Access 97 was used to simulate and assess the optimal cosolvent amounts to achieve the most desirable formulations automatically according to the specified criteria. Formulators could customize the optimal formulation according to their needs and cost constraints by redefining the desirable outcomes in the source code of the program.     

Optimization of a Slow-Release Tablet Formulation Containing Sodium Sulfathiazole and a Montmorillonite Clay

Abstract

A slow-release tablet formulation containing high levels of a montomorillonite clay, Veegum F®, was initially developed by trial and error. The present study was undertaken to utilize an approach involving statistics with the aid of computer science to develop a formula with desired characteristics. An experimental design for five factors was employed. The five factors consisted of levels of various components and the amount of compressional force applied while tableting. The response or dependent variables included tablet weight uniformity, hardness and friability; and percent drug in solution after 3 hours of dissolution testing. The response variables were fitted to a second-order polynomial with the five formulation factors as the independent variables. The resulting equations were used to optimize the formulation with respect to the response variables. The results indicated that a formulation with the desired characteristics could be predicted by the technique.     

Optimization of a Slow-Release Tablet Formulation Containing Sodium Sulfathiazole and a Montmorillonite Clay

A slow-release tablet formulation containing high levels of a montomorillonite clay, Veegum F®, was initially developed by trial and error. The present study was undertaken to utilize an approach involving statistics with the aid of computer science to develop a formula with desired characteristics. An experimental design for five factors was employed. The five factors consisted of levels of various components and the amount of compressional force applied while tableting. The response or dependent variables included tablet weight uniformity, hardness and friability; and percent drug in solution after 3 hours of dissolution testing. The response variables were fitted to a second-order polynomial with the five formulation factors as the independent variables. The resulting equations were used to optimize the formulation with respect to the response variables. The results indicated that a formulation with the desired characteristics could be predicted by the technique.     

Formulation of an Experiment for Detecting New Long-Range Forces

An experimental scheme is proposed for detecting new long-range forces by utilizing a spherical cavity excavated from a sphere and placing a fixed torsion balance within it. It is shown that for the optimal distance between the axes of rotation of the sphere, the cavity, and the torsion balance and for a spatial parameter 10–12 cm, the ultimate attainable sensitivity in the parameter exceeds the present level by roughly a factor of 10⁵.     

Cataplasm-Based Controlled Drug Delivery: Development and Optimization of a Novel Formulation

The objective of the present study was to study the formulation variables involved in the development of a novel plasterlike preparation (cataplasm) and to optimize important formulation variables with an aim to maximize the in vitro release of the drug with minimum lag time. Cataplasm was prepared by dispersing a model drug (ibuprofen), humectant (glycerol), adhesive (Indopol H100®), polymer (Carbopol C934P®) with other formulation ingredients in a beaker with an open-blade impeller. The paste was cast on a nonocclusive backing membrane and dried overnight. The diffusion of the model drug was studied across a cellulosic membrane using Franz's diffusion cells. The amounts of three formulation variables, carbopol (X₁), glycerol (X₂), and indopol (X₃) were studied at three levels, and a face-centered cubic design was used to maximize the flux. An optimization procedure for maximum flux and minimum lag time predicted a flux of 97.22 mcg/cm²/hr at X₁ (2% w/w), X₂ (11.75% w/w), and X₃ (6% w/w). An experimental patch prepared with the above concentrations yielded a flux of 90.7 mcg/cm²/hr.     

某型内燃机车驾驶室阻尼优化降噪分析

为降低某型号内燃机车驾驶室噪声,对驾驶室结构上的阻尼材料进行布局优化设计。建立驾驶室声学数值模型,采用基于模态的声-振耦合法计算驾驶室声学响应,提取驾驶员耳旁声压级找出噪声声压峰值处所对应的振动频率;对驾驶室进行板块贡献量分析,找到对噪声声压峰值处噪声贡献较大的壁板;为了降低39 Hz、73 Hz、110 Hz频率处噪声,建立拓扑优化数值模型求解自由阻尼的优化布局,构建优化后的数值模型计算5 Hz～120 Hz驾驶室声学响应,结果表明自由阻尼材料的优化布局能够降低驾驶室内噪声。     

跨区域灭火救援圈的提出与优化

针对目前我国灭火救援的现状,作者提出了建立灭火救援圈,以快速、有效地跨区域处置重大灾害事故。该文设计了灭火救援圈半径计算的数学模型;并对确定后的灭火救援圈,设计了增加投资后的优化模型。研究成果在实践应用中取得了一定的效果。