Chemometrical optimization methods

Obviously (1) higher order terms may be further included in the equation (2) more than two factors can be used to describe the system and higher order interaction terms may be present (3) some terms of Equation 3.32 can, under simpler circumstances, be omitted, for example, in a simple two-factor first-order model, the fourth, fifth, and sixth terms in the right member of Equation 3.32 are missing and 

FIGURE 3.5 Two-level-three-factor experimental design with geometrically balanced tet-rahedric subset (T). 

This model is composite because it consists of the overlapping of a star design with 2k+ factor combinations, and a two level -factor design with 2 factor combinations to give a total of 2 -i- -i-1 treatments. 

We now illustrate some recent examples of chemometrical modeling of IPC systems for the sake of clarity. In the framework of a quality by design approach, statistically designed experiments were used to optimize the IPC condition for the analysis of atomoxetine and impurities and demonstrate method robustness. 

A five-factor (buffer concentration, pH, IPR and organic solvent concentrations, and column temperature) two-level fractional factorial design with four center points was performed. The center points of the design were the midpoints of the range for each factor. The response from the design did not focus on bare retention but on resolution, and particularly on the separation of potential impurities around the main peak. Peak tailing, run time and backpressure were also considered chromatographic responses [76]. 

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PRISMA Chemometric optimization method of IMGE (isoselective multisolvent gradient elution). 

Experimental design can be very helpful, and a number of chemometric optimization methods are... 

Experimental design can be very helpful, and a number of chemometric optimization methods are present in the literature. Neural network models provided a good prediction power and a great versatility, without the need to develop any equations. 

Variable selection is an optimization problem. An optimization method that combines randomness with a strategy that is borrowed from biology is a technique using genetic algorithms—a so-called natural computation method (Massart et al. 1997). Actually, the basic structure of GAs is ideal for the purpose of selection (Davis 1991 Hibbert 1993 Leardi 2003), and various applications of GAs for variable selection in chemometrics have been reported (Broadhurst et al. 1997 Jouan-Rimbaud et al. 1995 Leardi 1994, 2001, 2007). Only a brief introduction to GAs is given here, and only from the point of view of variable selection. 

It is most often the case that raw data from analytical instruments needs to be treated by one or more operations before optimal results can be obtained from chemometric modeling methods. Although such pre-treatments often result in improved model performance, it is critically important to understand the inherent assumptions of these pretreatment methods in order to use them optimally. 

IPC-MS/MS was used to quantify heterocyclic aromatic amines in meat-based infant foods [30], The separation of biogenic amines was chemometrically optimized when they were determined in wines [31] a sensitive and selective method to determine 12 biogenic amines regardless of the characteristics of the vegetal food matrix was successfully validated [32], Determination of soybean proteins in commercial products was performed by fast IPC using an elution gradient and acetic acid as the IPR [33],... 

The attempts that have been made to utilize true chemometric optimization of operating conditions in CEC are unclear in most of the studies done utilizing CEC. This has been done for many years in GC and HPLC, as well as in CE, but there are no obvious articles that have appeared which have utilized true chemometric software approaches to optimization in CEC [57-59]. It is not clear that any true method optimization has been performed or what analytical figures of merit were used to define an optimized set of conditions for biopolymer analysis by CEC. It is also unclear as to why a specific stationary phase (packing) was finally selected as the optimal support in these particular CEC applications for biopolymers. In the future, it is hoped that more sophisticated optimization routines, especially computerized chemometrics (expert systems, theoretical software, or simplex/optiplex routines) will be employed from start to finish. 

Dejaegher, B. and Vander Heyden, Y. (2009) Chapter 17 Sequential optimization methods, in Comprehensive Chemometrics,Wo. 1 (eds. S. Brown, R.Tauler, and B. Walczak), Elsevier, Oxford, pp. 547-575. 

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. 

Normal-phase, bonded-phase columns are likely underutilized for separations where they should be the method of choice. This is due both to the ease of use of reversed-phase, bonded-phase columns, discussed next, and also to the many problems inherent in the use of bare silica and alumina. Very straightforward method development in normal-phase chromatography can be performed by combining the solvent and stationary-phase selectivity triangles. The three columns, each used with the three recommended modifiers, should provide the maximum difference in selectivity available. These nine experiments, used in conjunction with chemometric optimization schemes, should then provide a ratio-... 

Hammond, M.H., Riedel, C.J., Rose-Pehrsson, S.L. and Williams, F.W., 2004. Training set optimization methods for a probabilistic neural network, Chemometrics and Intelligent... 

Baseline separation was achieved between the candidate drug and the two metabohtes after extraction of the compounds from human plasma following protein precipitation. The LOQ was improved by a factor of 5 for the HPLC-MS/MS method after chemometric optimization. The UPLC-MS/MS method resulted in much lower operational cost, and therefore it was decided to optimize that method. Significant factors from the experimental screening were optimized via central com-... 

The variable selection methods have been also adopted for region selection in the area of 3D QSAR. For example, GOLPE [31] was developed with chemometric principles and q2-GRS [32] was developed based on independent CoMFA analyses of small areas of near-molecular space to address the issue of optimal region selection in CoMFA analysis. Both of these methods have been shown to improve the QSAR models compared to original CoMFA technique. 

Procedures used vary from trial-and-error methods to more sophisticated approaches including the window diagram, the simplex method, the PRISMA method, chemometric method, or computer-assisted methods. Many of these procedures were originally developed for HPLC and were apphed to TLC with appropriate changes in methodology. In the majority of the procedures, a set of solvents is selected as components of the mobile phase and one of the mentioned procedures is then used to optimize their relative proportions. Chemometric methods make possible to choose the minimum number of chromatographic systems needed to perform the best separation. 

Multivariate chemometric techniques have subsequently broadened the arsenal of tools that can be applied in QSAR. These include, among others. Multivariate ANOVA [9], Simplex optimization (Section 26.2.2), cluster analysis (Chapter 30) and various factor analytic methods such as principal components analysis (Chapter 31), discriminant analysis (Section 33.2.2) and canonical correlation analysis (Section 35.3). An advantage of multivariate methods is that they can be applied in... 

Advanced mathematical and statistical techniques used in analytical chemistry are often referred to under the umbrella term of chemometrics. This is a loose definition, and chemometrics are not readily distinguished from the more rudimentary techniques discussed in the earlier parts of this chapter, except in terms of sophistication. The techniques are applied to the development and assessment of analytical methods as well as to the assessment and interpretation of results. Once the province of the mathematician, the computational powers of the personal computer now make such techniques routinely accessible to analysts. Hence, although it would be inappropriate to consider the detail of the methods in a book at this level, it is nevertheless important to introduce some of the salient features to give an indication of their value. Two important applications in analytical chemistry are in method optimization and pattern recognition of results. 

A comprehensive two-volume Handbook of Chemometrics and Qualimetrics has been published by D. L. Massart et al. (1997) and B. G. M. Vandeginste et al. (1998) predecessors of this work and historically interesting are Chemometrics A Textbook (Massart et al. 1988), Evaluation and Optimization of Laboratory Methods and Analytical Procedures (Massart et al. 1978), and The Interpretation of Analytical Chemical Data by the Use of Cluster Analysis (Massart and Kaufmann 1983). A classical reference is still Multivariate Calibration (Martens and Naes 1989). A dictionary with extensive explanations containing about 1700 entries is The Data Analysis Handbook (Frank and Todeschini 1994). 

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