Method optimization response surface designs

When from initial experiments, conditions that indicate the enantioselectivity of the system towards a given enantiomer pair or towards a limited series of substances are known, one might optimize their separation. To obtain optimal conditions, the different chemometric techniques used for method optimization in classic chromatographic or electrophoretic separations can also be applied for the chiral ones. Different experimental design approaches, using both screening and response surface designs can be In Reference 331, for... 

Method development and optimization are started with review of the currently available methods within the company or in literature. Available methods are used as a starting point and evaluated against the method requirements set in the method definition. If necessary the method is optimized or redeveloped in order to fulfill the requirements. DOE tools (response surface design) are preferentially applied to obtain the best optimal conditions in terms of robustness. Application of DOE methodology is not new in chromatography and DOE is frequently applied also for enantiomeric separations in Especially in... 

In the screening phase of method development and in robustness tests, the factors usually are examined at two levels (-1, +1). On the other hand, in the response surface designs, applied in method optimization, the factors are examined at three or more levels, depending on the applied design (see further). 

In this method optimization phase, response surface designs or sequential optimization methods are apphed.The main difference between the two is that for a response surface design the experimental domain enclosed by the design is expected to contain the optimum, while a sequential optimization method can be applied in situations where the experimental region containing the optimal result is not a priori known. Another difference is that the sequential methods allow optimization of only one response, while with response surface designs several responses can be considered simultaneously (see further). 

A.2.3. Example of an Applied Response Surface Design. In the optimization phase of the development of a CE method for the chiral enantio-separation of a nonsteroidal anti-inflammatory drug (28), a circumscribed CCD was performed. The applied symmetrical response surface design is as shown in Table 2.14, with a = 2 f = 1.68. The center point (experiment 15 in Table 2.14) was replicated five times (experiments 15-19). 

Merkuryeva G (2005) Response Surface-based Simulation Metamodelling Methods, Dolgui A, Soldek J, Zaikin O (eds) Supply Chain Optimization Prod-uct/Process Design, Facility, Location and Flow Control. Springer, Berlin et al.,pp 205-216... 

In reference 20, a typical robustness test is not performed, but a study on the influence of peak measurement parameters is reported on the outcome. The study is special in the sense that no physicochemical parameter in the experimental runs is changed, but only data measurement and treatment-related parameters. These parameters can largely affect the reported results, as shown earlier, and in that sense they do influence the robusmess of the method. The different parameters (see above) were first screened in a two-level D-optimal design (9 factors in 10 experiments). The most important were then examined in a face-centered CCD, and conclusions were drawn from the response surfaces plots. 

Initial screens can be distinguished between methods that are used to determine what factors are most important, and follow-up screens that allow optimization and improvement of crystal quality (Table 14.1). In experimental design, this is known as the Box-Wilson strategy (Box et al., 1978). The first group of screens is generally based on a so-called factorial plan which determines the polynomial coefficients of a function with k variables (factors) fitted to the response surface. It can be shown that the number of necessary experiments n increases with 2 if all interactions are taken into account. Instead of running an unrealistic, large number of initial experiments, the full factorial matrix can... 

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... 

In the response surface strategy that was discussed in Section 2.3 standard response surface techniques are used to generate two response surface models, one for the mean response and one for the standard deviation of the response (or some function of the standard deviation). The standard deviation measures the stability of the response to the environmental variation. Standard analysis can reveal which factors affect the mean only, which only affect the variability, and which affect both the mean and the variability. The researcher can then apply optimization methods or construct contour plots of the mean and standard deviation response surfaces to determine settings of the design variables that will give a mean response that is close to the target with minimum variation. 

Chowdhury and Fard (2001) presented a method for estimating dispersion effects from robust design experiments with right censored data. Kim and Lin (2002) proposed a method to determine optimal design factor settings that take account of both location and dispersion effects when there are multiple responses. They based their approach on response surface models for location and dispersion of each response variable. 

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]. 

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]. 

---