Optimization central composite design

The experimental designs discussed in Chapters 24-26 for optimization can be used also for finding the product composition or processing condition that is optimal in terms of sensory properties. In particular, central composite designs and mixture designs are much used. The analysis of the sensory response is usually in the form of a fully quadratic function of the experimental factors. The sensory response itself may be the mean score of a panel of trained panellists. One may consider such a trained panel as a sensitive instrument to measure the perceived intensity useful in describing the sensory characteristics of a food product. 

This model is capable of estimating both linear and non-linear effects observed experimentally. Hence, it can also be used for optimization of the desired response with respect to the variables of the system. Two popular response surface designs are central composite designs and Box-Behnken designs. Box-Behnken designs were not employed in the experimental research described here and will therefore not be discussed further, but more information on Box-Behnken designs can be obtained from reference [15]. 

Based on the obtained response surface, a second roimd of optimization follows, using the steepest ascent method where the direction of the steepest slope indicates the position of the optimum. Alternatively, a quadratic model can be fitted around a region known to contain the optimum somewhere in the middle. This so-called central composite design contains an imbedded factorial design with centre... 

A fully central comp osite design was applied to optimize monolaurin synthesis. A three factorial design was proven effective to establish the influence of the variables on the monolaurin synthesis. The central composite design procedure was adopted to optimize variables affecting the monolaurin molar fraction. 

Once the variables having the greatest influence on the responses were identified, a 20-run central composite design was used to optimize the levels of these variables (18). A design matrix was developed (Table 2) and the true values for the variables were determined (Table 3). 

In the second optimization step, the exact values of the three variables that were identified to have significant effects on nisin and/or lactic acid production were determined using a central composite design (Table 2). The coded and actual values of each variable are given in Table 3. The fermentation media (pH 6.5) were composed of 50 g/L of whey, 5 g/L of polypeptone, 1 g/L of Tween-80, and 30 g/L of CaC03, and the predetermined amount of the three variables was assigned by the central composite design. The content of nisin and lactic acid after 24 h of fermentation at 30°C was measured and are presented as responses in Table 2. 

Li et al. (2007) reported the use of dry biomass, Rhizopus oryzae (R. oryzae) IF04697, whole cell-catalyzed methanolysis of soybean oil for biodiesel (methyl ester) in rm-butanol system. Changing one separate factor at a time (COST), live-level-four-factor Central Composite Design (CCD) were used to evaluate the effects of synthesis conditions, such as tert-butanol to oil volume ratio, methanol to oil molar ratio, water content, and dry biomass amount. Biodiesel yields of 72% were obtained under the optimal conditions using the proposed model for prediction. 

Rotthauser, B., Kraus, G., and Schmidt, P. C. (1998), Optimization of an effervescent tablet formulations containing spray-dried L-leucine and polyethylene glycol 6000 as lubricants using a central composite design, Eur. J. Pharm. Biopharm., 46, 85-94. 

Cocaine has been extracted from coca leaves and the optimization procedure was investigated by means of a central composite design [17]. Pressure, temperature, nature, and percentage of polar modifier were studied. A rate of 2 mL/min CO2 modified by the addition of 29 % water in methanol at 20 M Pa for 10 min allowed the quantitative extraction of cocaine. The robustness of the method was evaluated by drawing response surfaces. The same compound has also been extracted by SEE from hair samples [18-20]. 

PSE was applied to the rapid extraction of cocaine and benzoylecgonine from coca leaves [31]. Several parameters including the nature of the extracting solvent, the pressure, temperature, extraction, addition of alkaline substances, and sample granulometry were investigated. Critical parameters were pressure, temperature, and extraction time. They were optimized by means of a central composite design. It was demonstrated that an extraction time of 10 min was sufficient to extract cocaine quantitatively at 80 °C and 20 MPa. 

The central composite design was often selected because of the limited number of experiments needed to sample the response surfaces. In the separation of As and Se species in tap water, the analysis of isoresponse curves allowed the determination of optimum chromatographic conditions and the robustness of the method [77]. The same design was also used to study the influence of an organic modifier and IPR concentration on retention of biogenic amines in wines. To obtain a compromise between resolution and chromatographic time, optimization through a multi-criteria approach was followed [78]. 

Once the right set of parameters has been identified, computer-aided optimization using modified sequential simplex or central composite design methods can be applied to further hne-tune the separation under investigation, as has been published for the optimization of reverse-phase HPLC [17-20] and chiral separations [21-23]. 

Probably, the very long time used in most cases could be significantly reduced by using a multivariate optimization approach focusing on interrelated variables. Figure 5.4 shows a surface response from a central composite design for [HCI]-ultrasound exposure for the determination of tin in coal acidified slurries [6]. 

Example Optimization of a synthetic procedure by response surface modelling from a central composite design. Enamine synthesis by a modified TiCl -method... 

TABLE 2.18. Responses studied in the circumscribed central composite design (Table 2.14 with lal = 1.68, five center point replicates (exp 15-19)) applied during the optimization phase of the development of a chiral enantioseparation method in Reference 28 migration time of the first and the second enantiomer (t i and t j), and resolution between the two enantiomers Rs... 

Several studies have employed chemometric designs in CZE method development. In most cases, central composite designs were selected with background electrolyte pH and concentration as well as buffer additives such as methanol as experimental factors and separation selectivity or peak resolution of one or more critical analyte pairs as responses. For example, method development and optimization employing a three-factor central composite design was performed for the analysis of related compounds of the tetracychne antibiotics doxycycline (17) and metacychne (18). The separation selectivity between three critical pairs of analytes were selected as responses in the case of doxycycline while four critical pairs served as responses in the case of metacychne. In both studies, the data were htted to a partial least square (PLS) model. The factors buffer pH and methanol concentration proved to affect the separation selectivity of the respective critical pairs differently so that the overall optimized methods represented a compromise for each individual response. Both methods were subsequently validated and applied to commercial samples. 

TABLE 5.2. A central composite design nsed for the optimization of a separation of nenrotransmitter amino acids. Adapted from Reference 62... 

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