Optimizing analytical methods using sequential response surface methodology. Application to the pararosaniline determination of formaldehyde

Sequential response surface methodology is a general procedure to re-optimize common analytical methods on the basis of the application of the response surface methodology and of a new approach to the steepest ascent method. This procedure, which is easy to apply, consists of estimating an analytical function relating the response with the experimental parameters by means of a second-degree polynomial. Thus, a 2nd order design covering the total experimental domain is used and when a maximum is obtained, the characteristics of the response surface are confirmed using a new design, which is obtained contracting the first one. In the proposed methodology, Box-Behnken designs are used because they offer advantages in comparison with second order designs more frequently used in the steepest ascent method (central composite designs), i.e. fewer experiments are needed, they are more efficient, they can be moved through the experimental domain and they can even be easily contracted or expanded.     

Modeling the adsorption of dyes onto activated carbon by using experimental designs

We used experimental design methodologies to obtain the response surface of the adsorption process for three acid dyes used in the dyeing step of a tanning process. The dyes were Acid Red 97, Acid Orange 61 and Acid Brown 425. The adsorption process was evaluated determining the concentrations of individual and total dyes remaining in solution at the end of the process. These concentrations were determined simultaneously in a single step using sequential injection analysis with multivariate curve resolution alternating least squares (SIA-MCR-ALS). This method involves fractional factorial designs and the steepest ascent method to find a zone of efficient adsorption and a response surface-modeling step to fit the relevant adsorption factors for the response.     

响应面法优化海藻酸钠-壳聚糖-粉末活性炭生物微胶囊制备工艺

采用响应面法优化了海藻酸钠-壳聚糖-粉末活性炭生物微胶囊(SA-CA-PAC)的制备工艺.在单因素实验的基础上.应用PIackett-Burman实验设计筛选影响微胶囊机械强度的重要参数,采用最陡爬坡实验逼近最大区域后,利用Box-Behnken设计确定重要参数的最佳水平.结果表明,影响微胶囊机械强度的重要参数为壳聚糖...     

Medium Optimization Based on Statistical Methodologies for Pristinamycins Production by <Emphasis Type="Italic">Streptomyces pristinaespiralis</Emphasis>

The optimization of nutrient levels for the production of pristinamycins by Streptomyces pristinaespiralis CGMCC 0957 in submerged fermentation was carried out using the statistical methodologies based on the Plackett–Burman design, the steepest ascent method, and the central composite design (CCD). First, the Plackett–Burman design was applied to evaluate the influence of related nutrients in the medium. Soluble starch and MgSO₄·7H₂O were then identified as the most significant nutrients with a confidence level of 99%. Subsequently, the concentrations of the two nutrients were further optimized using response surface methodology of CCD, together with the steepest ascent method. Accordingly, a second-order polynomial regression model was finally fitted to the experimental data. By solving the regression equation from the model and analyzing the response surface, the optimal levels for soluble starch and MgSO₄·7H₂O were determined as 20.95 and 5.67g/L, respectively. Under the optimized medium, the yield of pristinamycins in the shake flask and 5-L bioreactor could reach 1.30 and 1.01g/L, respectively, which is the highest yield reported in literature to date.     

A study of robustness with multivariate calibration. Application to the polarographic determination of benzaldehyde

A procedure to evaluate the robustness of an analytical method when there are changes in some experimental variables, when using multivariate calibration, is proposed. The procedure consists of analysing the root mean square error of prediction (RMSEP) as a response to a Plackett–Burman experimental design, through which the influence of several experimental factors on the prediction capability of the multivariate partial least squares (PLS) models built is studied. Two different ways of analysing the experimental design response are considered: establishing the residual variance with replicates and using Lenth's method. The proposed methodology has been applied to estimate the robustness of the polarographic determination of benzaldehyde when PLS calibration is used.     

Modeling and optimization of biopolymer (Polyhydroxyalkanoates) production from ice cream residue by novel statistical experimental design

Polyhydroxyalkanoates (PHAs) are thermoplastic polyesters synthesized by Ralstonia eutropha and other bacteria as a form of intracellular carbon and energy storage and are accumulated as lipid inclusions in the cytoplasm of these bacteria. The modeling and optimization of PHA production by fermentation from industrial waste (ice cream residue) was studied by employing statistical experimental design methods. A series of iterative experimental designs was used to find optimal factor conditions (medium components and fermentation process time) in the order of fractional factorial design, path of steepest ascent, and full factorial augmented with axial design (rotational central composite design). An optimal range characterized by lipid (15 mg/mL) and % lipid (88%) values was found and further investigated to verify the optimal conditions for PHA production from ice cream (56.68 mL of ice cream or 56.68% ice cream in water [v/v], 5.03 mL of buffer, 1 mL of mineral salts solution, 100 muL of trace element solution, 100 mL of seed culture, and 213.76 h of fermentation time).     

Application of response surface methodologies in capillary electrophoresis

A fast method of determining ascorbic acid and isoascorbic acid by capillary zone electrophoresis with a photodiode array detector was developed. Response surface methodologies based on three-level, three-variable designs, such as the Box-Behnken design, central composite face-centered and full fractional design, were used comparatively for optimization of buffer pH, buffer concentration and operation voltage. Statistical interpretation of the variables concerning different responses, such as resolution and migration time of the last migrated analyte, were performed. The optimum conditions of these variables were predicted using a second-order polynomial model fitted to the results obtained by applying three designs. The response surface plots using three experimental designs revealed a separation optimum with Tris–HCl buffer of pH 8.5, a concentration of 50 mM, and an operation voltage of 30 kV. The significance of the statistical designs were confirmed by the generally good agreement obtained between predicted responses and actual experimental data. We concluded that experimental designs offer a rapid means of optimizing several variables and provide an efficient test for the robustness of the analytical method.     

Development and optimization of a method for analyzing biodiesel mixtures with non-aqueous reversed phase liquid chromatography

Biodiesel (a mixture of fatty acid esters) is normally analyzed using gas chromatography/flame ionization detection, as specified by the ASTM D6584 and EN14105 standards. This paper proposes a binary gradient method for analyzing biodiesel mixtures using non-aqueous reverse phase HPLC with a UV detector capable of overcoming the drawbacks of the gas chromatographic technique normally used. The new analytical method was developed by means of a statistical sensitivity analysis applied to the main parameters influencing the recording, using the full factorial design method combined with the Yates algorithm and the steepest ascent optimization procedure. The present study shows the influence of the main biodiesel mixture separation analysis parameters. The resulting tool proved valid for analyzing not only biodiesel but also any traces of unreacted oil.     

Response surface methodology (RSM) as a tool for optimization in analytical chemistry

A review about the application of response surface methodology (RSM) in the optimization of analytical methods is presented. The theoretical principles of RSM and steps for its application are described to introduce readers to this multivariate statistical technique. Symmetrical experimental designs (three-level factorial, Box-Behnken, central composite, and Doehlert designs) are compared in terms of characteristics and efficiency. Furthermore, recent references of their uses in analytical chemistry are presented. Multiple response optimization applying desirability functions in RSM and the use of artificial neural networks for modeling are also discussed.     

Application of design-of-experiments procedures to optimize efficiently pretreatment of lipase for use in a nonaqueous reaction

A variety of different pretreatments can improve the performance of enzymes in nonpolar reaction media. These pretreatments have primarily been studied in isolation; however, interactions between some pairs of pretreatments are known to exist. The presence of these interactions complicates the design of an optimum multifactor pretreatment. Modern design-of-experiments techniques allow the simultaneous optimization of two or more variables. To improve the performance of lipase in a model reaction, we used a technique called the method of steepest ascent to optimize three variables simultaneously: pretreatment pH and sodium phosphate concentration, and the concentration of acetic acid (one of the reactants) in the reaction mixture. In only 26 experimental runs, this optimization process determined a combination of variable settings that yielded a reaction product approx 180 times faster than achieved with untreated enzyme. Evidence is presented to demonstrate that locating this optimum with single-factor experiments would be inefficient. This article demonstrates the efficiency of the method of steepest ascent particularly for evaluation of enzymatic reaction conditions exhibiting significant interactions.     

Modelling and graphic interpretation of response surface in chemical analysis

The complicated effects of several factors on an analytical signal can be studied comprehensively only by an experimental design in which the additive and non-additive effects of these factors are included in one experimental run, with simultaneous variation of the values of all factors. From the law of mass action, it is shown that systems in which the analytical signal is produced by a species formed during a chemical reaction (i.e., for spectrophotometry) can be described by a model based on quasi-linear regressions with squares and products of variables. The regression coefficients can be evaluated by means of factorial designs at three levels. Interpretation of results in the case of two or three independent variables is simplified by using a graphic method in which the complex effects of factors on the dependent variable are represented as an empirical response surface. In the case of regression with three independent variables, the response surface is four-dimensional; its dimensionality is reduced to three by several three-dimensional representations. The shapes of the response surfaces described by the response functions and the adequacy of the models are discussed.     

Chemometric Methods for the Study of Toxic Metals on the Growth of Plants: Use of Experimental Design and Response Surface Methodology

Abstract

Chemometrics is a recent discipline concerned, principally, with the application of mathematics and statistics to laboratory systems. One way in which the chemometrician can aid the environmental analytical chemist is via planned experimental designs. In this paper the importance of experimental design is illustrated and the main considerations prior to experimentation, namely, degrees of freedom, analytical errors, coding and modelling, are outlined. This is exemplified by a study of the influence of potentially toxic heavy metals on the growth of barley seedlings. Undesigned univariate experiments suggest that Tl is probably more toxic than Cd. A three factor central composite design is reported, to study the relative toxicities of Tl, Cd and Pb and also of Tl, Fe and Zn. The paper exemplifies how much information can be obtained from the resultant experimental response data. Multilinear regression can be employed to produce a quadratic model: this can be interpreted graphically by reconstructed univariate response curves and 3-dimensional response surfaces. Analysis of variance is a statistical method for computing how well the model has been fitted, taking into account analytical errors. With the aid of modern graphical computing, a variety of confidence intervals can be displayed for both univariate and bivariate responses. The usefulness of the design can be visualised by displaying leverage over and outside the experimental region. Finally future trends in multivariate response methodology are discussed.     

Desirability functions as response in a d‐optimal design for evaluating the extraction and purification steps of six tranquillizers and an anti‐adrenergic by liquid chromatography‐tandem mass spectrometry

Internal standards can be added at different stages of an analytical procedure. When they are added at the beginning of a multiresidue method and their behavior is not exactly the same as that of the analytes, the intended correction for small variations within the analytical process could not be achieved. Because of this, in the present work, the use of d ‐optimal designs together with desirability functions is proposed to state the experimental response under study. The overall desirability function used relates two analytical criteria: to assess a similar chemical behavior of each analyte in relation to its internal standard and to avoid a significant reduction of the absolute peak area of the internal standards. This strategy has been applied to the analysis of the effect of four factors related to the extraction and purification steps of six tranquillizers and a β‐blocker from pig muscle analyzed by liquid chromatography–tandem mass spectrometry. The effect of those factors has been evaluated by means of an ad hoc d ‐optimal design consisting of only 11 experiments. The resulting levels of the four factors that enable to achieve the greatest overall desirability have also been compared with those obtained when either the standardized or absolute peak area has been considered as response. Differences in both the significant factors and their optimum levels have been observed. It is noticeable that the experimental effort necessary to study the effect of the factors has been reduced by more than 50% thanks to the d ‐optimal design. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluating the significance threshold in robustness testing. A critical discussion on the influence of time in molecular fluorescence spectrometry

Robustness experiments are performed in analytical chemistry to assess the behaviour of an analytical procedure under conditions slightly different from those of the experimental optimum. This work presents a study of robustness applied to a previously proposed fluorescent methodology using two replicated 2(7-4) saturated fractional factorial designs. A comparison is established between three different ways to test the significance of the effects of the variables involved on the response signal. Critical discussions about the most appropriate threshold to be introduced when testing for significance of the factors and the influence of the time necessary to carry out the experiments are included.     

Multi-objective optimisation strategy based on desirability functions used for chromatographic separation and quantification of l-proline and organic acids in vinegar

An optimisation strategy based on desirability functions together with experimental design has been used to optimise a chromatographic method applied to the separation and quantification of l-proline and seven organic acids in vinegar samples. Chromatographic problems often force to reach a compromise between different experimental variables in order to achieve the best chromatographic separation. The importance of the use of multi-objective optimisation methods lies in the ability to cope with this kind of problems. The quality of the multicriteria optimisation method was tested through the validation of the analytical parameters of the final chromatographic method developed. The versatility of this methodology allows to use it in other chromatographic applications resulting in a suitable adaptive procedure to solve new analytical problems. Furthermore, the determination of l-proline and organic acids in vinegar is useful for several industrial goals such as the correct monitoring of fermentation, for the study of nutrient needs at all times during the twofold fermentation process and for the detection of possible adulterations in the final product.     

Decision protocol for checking robustness with previous outlier detection in the validation of analytical methods

A general procedure based on variation of experimental design for checking robustness in the validation of analytical methods is presented. This procedure, which is easy to apply, consists in estimating the main total effects, in detecting outliers, checking the curvature and in determining the main side effects. Two methodologies based on the analysis of a) the residuals from the reduced model and b) the replicates from the reconstructed design were employed for the detection of outliers. In further studies, general experimental design principles were applied using two- and three-level factorial designs. In some cases, a dummy variable was introduced in order not to modify the structure of the designs utilized.     

A new approach to response surface development for detailed gas‐phase and surface reaction kinetic model optimization

We propose a new method for constructing kinetic response surfaces used in the development and optimization of gas‐phase and surface reaction kinetic models. The method, termed as the sensitivity analysis based (SAB) method, is based on a multivariate Taylor expansion of model response with respect to model parameters, neglecting terms higher than the second order. The expansion coefficients are obtained by a first‐order local sensitivity analysis. Tests are made for gas‐phase combustion reaction models. The results show that the response surface obtained with the SAB method is as accurate as the factorial design method traditionally used in reaction model optimization. The SAB method, however, presents significant computational savings compared to factorial design. The effect of including the partial and full third order terms was also examined and discussed. The SAB method is applied to optimization of a relatively complex surface reaction mechanism where large uncertainty in rate parameters exists. The example chosen is laser‐induced fluorescence signal of OH desorption from a platinum foil in the water/oxygen reaction at low pressures. We introduce an iterative solution mapping and optimization approach for improved accuracy. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 94–106, 2004     

Robust and non-parametric statistics in the evaluation of figures of merit of analytical methods. Practices for students

A set of laboratory practices is proposed in which evaluation of the quality of the analytical measurements is incorporated explicitly by applying systematically suitable methodology for extracting the useful information contained in chemical data. Non-parametric and robust techniques useful for detecting outliers have been used to evaluate different figures of merit in the validation and optimization of analytical methods. In particular, they are used for determination of the capability of detection according to ISO 11843 and IUPAC and for determination of linear range, for assessment of the response surface fitted using an experimental design to optimize an instrumental technique, and for analysis of a proficiency test carried out by different groups of students. The tools used are robust regression, least median of squares (LMS) regression, and some robust estimators as median absolute deviation (m.a.d.) or Huber estimator, which are very useful as an alternatives to the usual centralization and dispersion estimators.     

Decision protocol for checking robustness with previous outlier detection in the validation of analytical methods

A general procedure based on variation of experimental design for checking robustness in the validation of analytical methods is presented. This procedure, which is easy to apply, consists in estimating the main total effects, in detecting outliers, checking the curvature and in determining the main side effects. Two methodologies based on the analysis of a) the residuals from the reduced model and b) the replicates from the reconstructed design were employed for the detection of outliers. In further studies, general experimental design principles were applied using two- and three-level factorial designs. In some cases, a dummy variable was introduced in order not to modify the structure of the designs utilized. Received: 30 October 1998 / Revised: 19 April 1999 / Accepted: 6 May 1999