Response surface models to predict broiler performance and applications for economic analysis

A study was carried out to elaborate response surface models using broiler performance data recovered from literature in order to predict performance and elaborate economic analyses. Nineteen studies published between 1995 and 2005 were retrieved using the systematic literature review method. Weight gain and feed conversion data were collected from eight studies that fulfilled the pre-established inclusion criteria, and a response surface model was adjusted using crude protein, environmental temperature, and age as independent variables. The models produced for weight gain (r² = 0.93) and feed conversion (r² = 0.85) were accurate, precise, and not biased. Protein levels, environmental temperature and age showed linear and quadratic effects on weight gain and feed conversion. There was no interaction between protein level and environmental temperature. Age and crude protein showed interaction for weight gain and feed conversion, whereas interaction between age and temperature was detected only for weight gain. It was possible to perform economic analyses to determine maximum profit as a function of the variables that were included in the model. It was concluded that the response surface models are effective to predict the performance of broiler chickens and allow the elaboration of economic analyses to optimize profit.

Optimization of acid hydrolysis from the hemicellulosic fraction of Eucalyptus grandis residue using response surface methodology

Biotechnological conversion of biomass into fuels and chemicals requires hydrolysis of the polysaccharide fraction into monomeric sugars. Hydrolysis can be performed enzymatically and with dilute or concentrate mineral acids. The present study used dilute sulfuric acid as a catalyst for hydrolysis of Eucalyptus grandis residue. The purpose of this paper was to optimize the hydrolysis process in a 1.41 pilot-scale reactor and investigate the effects of the acid concentration, temperature and residue/acid solution ratio on the hemicellulose removal and consequently on the production of sugars (xylose, glucose and arabinose) as well as on the formation of by-products (furfural, 5-hydroxymethylfurfural and acetic acid). This study was based on a model composition corresponding to a 2 3 orthogonal factorial design and employed the response surface methodology (RSM) to optimize the hydrolysis conditions, aiming to attain maximum xylose extraction from hemicellulose of residue. The considered optimum conditions were: H2SO4 concentration of 0.65%, temperature of 157 degrees C and residue/acid solution ratio of 1/8.6 with a reaction time of 20 min. Under these conditions, 79.6% of the total xylose was removed and the hydrolysate contained 1.65 g/l glucose, 13.65 g/l xylose, 1.55 g/l arabinose, 3.10 g/l acetic acid, 1.23 g/l furfural and 0.20 g/l 5-hydroxymethylfurfural. (c) 2006 Published by Elsevier Ltd.

Multistratum response surface designs

Response surface designs are usually described as if the treatments have been completely randomized to the experimental units. However, in practice there is often a structure to the units, implying the need for blocking. If, in addition, some factors are more difficult to vary between units than others, a multistratum structure arises naturally. We present a general strategy for constructing response surface designs in multistratum unit structures. Designs are constructed stratum by stratum, starting in the highest stratum. In each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata, allowing-for all the effects that have to be estimated. Three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set. Finally, some practical considerations in randomization are discussed.

An algorithm for arranging response surface designs in small blocks

We consider the problem of blocking response surface designs when the block sizes are prespecified to control variation efficiently and the treatment set is chosen independently of the block structure. We show how the loss of information due to blocking is related to scores defined by Mead and present an interchange algorithm based on scores to improve a given blocked design. Examples illustrating the performance of the algorithm are given and some comparisons with other designs are made. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Variance dispersion graphs for comparing blocked response surface designs

In this paper, we extend the use of the variance dispersion graph (VDG) to experiments in which the response surface (RS) design must be blocked. Through several examples we evaluate the prediction performances of RS designs in non-orthogonal block designs compared with the equivalent unblocked designs and orthogonally blocked designs. These examples illustrate that good prediction performance of designs in small blocks can be expected in practice. Most importantly, we show that the allocation of the treatment set to blocks can seriously affect the prediction properties of designs; thus, much care is needed in performing this allocation.

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)

Response surface optimization of D(-)-lactic acid production by Lactobacillus SMI8 using corn steep liquor and yeast autolysate as an alternative nitrogen source

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.