Some practical advice on polynomial regression analysis from blocked response surface designs

It is often necessary to run response surface designs in blocks. In this paper the analysis of data from such experiments, using polynomial regression models, is discussed. The definition and estimation of pure error in blocked designs are considered. It is recommended that pure error is estimated by assuming additive block and treatment effects, as this is more consistent with designs without blocking. The recovery of inter-block information using REML analysis is discussed, although it is shown that it has very little impact if thc design is nearly orthogonally blocked. Finally prediction from blocked designs is considered and it is shown that prediction of many quantities of interest is much simpler than prediction of the response itself.

Optimization of cyclodextrin glucanotransferase production from Bacillus clausii E16 in submerged fermentation using response surface methodology

Cyclodextrin glucanotransferase production from Bacillus clausii E16, a new bacteria isolated from Brazilian soil samples was optimized in shake-flask cultures. A 2 4 full-factorial central composite design was performed to optimize the culture conditions, using a response surface methodology the combined effect among the soluble starch concentration, the peptone concentration, the yeast extract concentration, and the initial pH value of the culture medium was investigated. The optimum concentrations of the components, determined by a 2(4) full-factorial central composite design, were 13.4 g/L soluble starch, 4.9 g/L peptone, 5.9 g/L yeast extract, and initial pH 10.1. Under these optimized conditions, the maximum cyclodextrin glucanotransferase activity was 5.9 U/mL after a 48-h fermentation. This yield was 68% higher than that obtained when the microorganism was cultivated in basal culture medium.

Optimisation of a continuous flash fermentation for butanol production using the response surface methodology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Use of Response Surface Methodology in Optimization of Lactic Acid Production: Focus on Medium Supplementation, Temperature and pH Control

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evaluation of the Naturally Acquired Antibody Immune Response to the Pv200L N-terminal Fragment of Plasmodium vivax Merozoite Surface Protein-1 in Four Areas of the Amazon Region of Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Optimization of xylanase production by Bacillus circulans D1 in submerged fermentation using response surface methodology

In this work, a 3(3) factorial design was performed with the aim of optimizing the culture conditions for xylanase production by an alkalophilic thermophilic strain of Bacillus circulans, using response surface methodology. The variables involved in this study were xylan concentration (X-1), pH (X-2) and cultivation time (X-3). The optimal response region was approached without using paths of steepest ascent. Statistical analysis of results showed that, in the range studied, only pH did not have a significant effect on xylanase production. A second-order model was proposed to represent the enzymic activity as a function of xylan concentration (X-1) and cultivation time (X-3). The optimum xylan concentration and cultivation time were 5 g/l and 48 h, respectively. Under these conditions, the model predicted a xylanase activity of 19.1 U/ml. (C) 2002 Elsevier B.V. Ltd. All rights reserved.

Row-column response surface designs

Factorial experiments are widely used in industry to investigate the effects of process factors on quality response variables. Many food processes, for example, are not only subject to variation between days, but also between different times of the day. Removing this variation using blocking factors leads to row-column designs. In this paper, an algorithm is described for constructing factorial row-column designs when the factors are quantitative, and the data are to be analysed by fitting a polynomial model. The row-column designs are constructed using an iterative interchange search, where interchanges that result in an improvement in the weighted mean of the efficiency factors corresponding to the parameters of interest are accepted. Some examples illustrating the performance of the algorithm are given.

Optimisation of conditions for the extraction of casearins from Casearia sylvestris using response surface methodology

Optimal conditions for the extraction of casearins from Casearia sylvestris were determined using response surface methodology. The maceration and sonication extraction techniques were performed using a 3 x 3 x 3 full factorial design including three acidity conditions, three solvents of different polarities and three extraction times. The yields and selectivities of the extraction of casearins were significantly influenced by acidity conditions. Taking into account all variables tested, the optimal conditions for maceration extraction were estimated to involve treatment with dichloromethane saturated with ammonium hydroxide for 26 h. Similar yields and selectivities for casearins were determined for sonication extraction using the same solvent but for the much shorter time of I h. The best results for stabilisation of the fresh plant material were obtained using leaves that had been oven dried at 40 degrees C for 48 h. Copyright (c) 2006 John Wiley & Sons, Ltd.

Difference variance dispersion graphs for comparing response surface designs with applications in food technology

Variance dispersion graphs have become a popular tool in aiding the choice of a response surface design. Often differences in response from some particular point, such as the expected position of the optimum or standard operating conditions, are more important than the response itself. We describe two examples from food technology. In the first, an experiment was conducted to find the levels of three factors which optimized the yield of valuable products enzymatically synthesized from sugars and to discover how the yield changed as the levels of the factors were changed from the optimum. In the second example, an experiment was conducted on a mixing process for pastry dough to discover how three factors affected a number of properties of the pastry, with a view to using these factors to control the process. We introduce the difference variance dispersion graph (DVDG) to help in the choice of a design in these circumstances. The DVDG for blocked designs is developed and the examples are used to show how the DVDG can be used in practice. In both examples a design was chosen by using the DVDG, as well as other properties, and the experiments were conducted and produced results that were useful to the experimenters. In both cases the conclusions were drawn partly by comparing responses at different points on the response surface.

OPTIMIZATION OF EXTRUSION COOKING PROCESS FOR CHICKPEA (CICER-ARIETINUM, L) DEFATTED FLOUR BY RESPONSE-SURFACE METHODOLOGY

Response surface methodology was employed to optimize the production of a snack food from chickpea. The independent variables, process temperature (123-137-degrees-C) and feed moisture (13-27% d.s.b.) were selected at five levels (rotatable five level composite design: - square-root 2, -1, 0, 1, + square-root 2) in the extrusion of defatted chickpea flour. Response variables were expansion ratio, shear strength of the extrudate and sensory preference assessed by an untrained panel. Expansion ratio increased steadily with decrease in feed moisture similar to cereal extrusion. Regions of maxima were observed for sensory preference and shear strength, and these two product attributes were linearly related. The most acceptable chickpea snack was rated higher than a commercial corn snack.

Response of rat bone marrow cells to commercially pure titanium submitted to different surface treatments

Objectives. Alterations in the commercially pure titanium (cpTi) surface may be undertaken to improve its biological properties. The aim of this study is to investigate the biocompatibility of cpTi submitted to different surface treatments.Methods. The cpTi surfaces were prepared so that machined and blasted surfaces, either acid etched or not, were compared using rat bone marrow cells cultured to differentiated into osteoblast. For attachment evaluation, cells were cultured for 4 and 24 h. Cell morphology was evaluated after 3 days. After 7, 14, and 21 days cell proliferation was evaluated. Total protein content and alkaline phosphatase (ALP) activity were evaluated after 14 and 21 days. For bone-like nodule formation, cells were cultured for 21 days. Data were compared by analysis of variance.Results. Cell attachment, cell morphology, cell proliferation, and ALP activity were not affected by surface treatments. Total. protein content was reduced by blasted and acid etched surface. Bone-Like nodule formation was significantly reduced by blasted, acid etched, and a combination of both blasted and acid etched surfaces.Conclusions. Based on these results, it can be suggested that cpTi surfaces that were submitted only to machining treatment favor the final event of osteoblastic differentiation of the rat bone marrow cells, evidenced by increased bone-Like nodule formation. (C) 2003 Elsevier B.V. Ltd. All rights reserved.

Characterization of glycerol kinase from baker's yeast: Response surface modeling of the enzymatic reaction

The present study describes a methodology of dosage of glycerol kinase (GK) from baker's yeast. The standardization of the activity of the glycerol kinase from baker's yeast was accomplished using the diluted enzymatic preparation containing glycerol phosphate oxidase (GPO) and glycerol kinase. The mixture was incubated at 60 degrees C by 15 min and the reaction was stopped by the SDS solution addition. A first set of experiments was carried out in order to investigate the individual effect of temperature (7), pH and substrate concentration (S), on GK activity and stability. The pH and temperature stability tests showed that the enzyme presented a high stability to pH 6.0-8.0 and the thermal stability were completely maintained up to 50 degrees C during 1 h. The K(m) of the enzyme for glycerol was calculated to be 2 mM and V(max) to be 1.15 U/mL. In addition, modeling and optimization of reaction conditions was attempted by response surface methodology (RSM). Higher activity values will be attained at temperatures between 52 and 56 degrees C, pH around 10.2-10.5 and substrate concentrations from 150 to 170 mM.This low cost method for glycerol kinase dosage in a sequence of reactions is of great importance for many industries, like food, sugar and alcohol. RSM showed to be an adequate approach for modeling the reaction and optimization of reaction conditions to maximize glycerol kinase activity. (C) 2007 Elsevier B.V. All rights reserved.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

Use of soybean oil fry waste for economical biosurfactant production by isolated Pseudomonas aeruginosa using response surface methodology

The present study sought biotensoactive production from soybean oil fry waste using Pseudomonas aeruginosa ATCC 10145 and Pseudomonas aeruginosa isolated from the soil of a petroleum station having undergone gasoline and diesel oil spills. The results of the experiments were analyzed using a complete factorial experimental design, investigating the concentration of soybean oil waste, ammonia sulfate and residual brewery yeast. Assays were performed in 250-mL Erlenmeyer beakers containing 50 mL of production medium, maintained on a rotary shaker at 200 rpm and a temperature of 30±1 °C for a 48-hour fermentation period. Biosurfactant production was monitored through the determination of rhamnose, surface tension and emulsification activity. The Pseudomonas aeruginosa ATCC 10145 strain and isolated Pseudomonas aeruginosa were able to reduce the surface tension of the initial mexlium from 61 mN/m to 32.5 mN/m and 30.0 mN/m as well as produce rhamnose at concentrations of 1.96 and 2.89 g/L with emulsification indices of 96% and 100%, respectively.

Optimization of a synbiotic formulation of soy yoghurt containing yacon extract by response surface methodology

A synbiotic yoghurt based on a combination of soymilk and yacon water extract (from yacon root tubers) was developed as a novel food product fermented with a probiotic culture of Enterococcus faecium CRL 183 and Lactobacillus helveticus ssp jugurti 4l6. Response surface methodology (RSM) was used to optimize the independent variables soymilk protein concentration and percentage of yacon extract in the formulation through a Central Composite Rotatable Design (CCRD), consisting of a 22 factorial design with two levels (-1, +1), two central points (0) and four axial points (± a, 0) (0, ± α). The responses were assessed by consumer acceptance tests. The optimization indicated that a formulation with a soymilk protein concentration of 1.74g/L and 25.86% of yacon extract gave the best average values, 5.91 for the taste and 6.00 for the overall impression responses. The formulation with 40% of yacon extract and the same concentration of soymilk protein achieved similar acceptance values: taste (5.94) and overall impression (5.87), however, with the extra yacon, it probably had a greater content of prebiotic fructooligosaccharides. Consequently, both formulations may give useful functional foods, with sensory properties comparable with those of soy yoghurt (control formulation). Copyright © 2010 by New Century Health Publishers.