Doehlert matrix: a chemometric tool for analytical chemistry-review

A review of the use of the Doehlert matrix as a chemometric tool for the optimization of methods in analytical chemistry and other sciences is presented. The theoretical principles of Doehlert designs are described, including the coded values for the use of this matrix involving two, three, four and five variables. The advantages of this matrix in comparison with other response surface designs, such as central composite and Box-Behnken, designs are discussed. Finally, 57 references concerning the application of Doehlert matrices in the optimization of procedures involving spectroanalytical, electroanalytical and chromatographic techniques are considered.     

Response surface methodology (RSM) as a tool for optimization in analytical chemistry

A review about the application of response surface methodology (RSM) in the optimization of analytical methods is presented. The theoretical principles of RSM and steps for its application are described to introduce readers to this multivariate statistical technique. Symmetrical experimental designs (three-level factorial, Box-Behnken, central composite, and Doehlert designs) are compared in terms of characteristics and efficiency. Furthermore, recent references of their uses in analytical chemistry are presented. Multiple response optimization applying desirability functions in RSM and the use of artificial neural networks for modeling are also discussed.     

Chemometric tools in electroanalytical chemistry: Methods for optimization based on factorial design and response surface methodology

The aim of this paper is to give a brief overview of chemometric techniques based on factorial designs and response surface methodologies used in the optimization of electroanalytical methods. Chemometric techniques have several important advantages over one-way optimization for analytical applications, including a relatively low cost, a reduced number of experiments, and possibilities to evaluate interactions among variables. These techniques also enable the selection of optimal experimental conditions, helping to avoid trivial mistakes during optimization. Despite these facts, chemometric techniques have rarely been applied to electroanalytical data, especially in comparison with their use in spectroscopy. The application of chemometric methods in electroanalytical chemistry has been mostly used for solving overlapping signals, multivariate calibration methods, model identification and optimization of analytical procedures. This review is focused on the latter applications and overviews the role of full or fractional factorial designs (first-order designs), as well as second-order designs, such as central composite, Doehlert and Box-Behnken designs, for optimization of electroanalytical methods. A discussion of chemometric-related advantages is also given for stripping analyses, flow injection systems with amperometric detection, differential pulse voltammetry, square wave voltammetry and electrochemical sensor preparation.     

Statistical designs and response surface techniques for the optimization of chromatographic systems

This paper describes fundamentals and applications of multivariate statistical techniques for the optimization of chromatographic systems. The surface response methodologies: central composite design, Doehlert matrix and Box-Behnken design are discussed and applications of these techniques for optimization of sample preparation steps (extractions) and determination of experimental conditions for chromatographic separations are presented. The use of mixture design for optimization of mobile phases is also related. An optimization example involving a real separation process is exhaustively described. A discussion about model validation is presented. Some applications of other multivariate techniques for optimization of chromatographic methods are also summarized.     

Comparison of Full Factorial Design,Central Composite Design,and Box-Behnken Design in Chromatographic Method Development for the Determination of Fluconazole and Its Impurities

This paper presents the development and optimization of a liquid chromatographic method for the determination of fluconazole and its impurities by experimental design methodology. Four experimental design types were applied: two-level full factorial design, central composite design, Box-Behnken design, and three-level full factorial design. The advantages and drawbacks of each design are described and detailed statistical evaluation of mathematical models was performed. The central composite design and three-level full factorial design created significantly better models comparing to the other methods. As the central composite design requires a smaller number of experiments, its models were used for theoretical examination of experimental space. Multiobjective optimization aiming to achieve maximal separation of all investigated substances and minimal analysis duration was performed by a grid point search. The defined optimal separation was achieved on a C₁₈ (125 mm × 4 mm, 5 µm particle size) column with a mobile phase consisting of acetonitrile and water (5 mM ammonium formate) (15:85, v/v); a column temperature of 25°C; a flow rate of 1.2 mL min^?1; and a detection wavelength of 260 nm.     

Erratum to: Multiple Response Optimization of a HPLC Method for the Determination of Enantiomeric Purity of S-Ofloxacin

The aim of the study was to develop a new HPLC method for direct chiral separation of Ofloxacin enantiomers using polar non-aqueous mobile phase by application of response surface methodology. Rotatable central composite design (CCD) with eight factorial points, six axial points and six replications in central point was used to evaluate the influence of three independent variables (concentration of methanol, diethylamine and flow rate) on the output responses (capacity factor of first peak, tailing factors of both the enantiomers, resolution between the Ofloxacin enantiomers, retention time of the last peak and chromatographic optimization function). Further, CCD data were combined with multiple response optimization in order to obtain a set of optimal experimental conditions (% methanol/hexane/acetonitrile-43.33/10/46.62 (v/v), % acetic acid/diethylamine-0.4/0.2 and flow rate as 1.4 mL min⁻¹) leading to the most desirable compromise between resolution and analysis time. The method demonstrated good correlation between observed and predicted responses. The developed method was validated according to ICH guidelines and applied for quantitative analysis of two commercially available tablets Zenoflox (Ofloxacin) and Glevo (Levofloxacin). Good agreement was found between the assay results and the label claim of the marketed formulations by showing good %recovery and %CV. The study resulted in a better chromatographic system for the determination of Ofloxacin enantiomers.

     

Considerations on the modelling and optimisation of resolution of ionisable compounds in extended pH-range columns

The problems associated to the modelling and optimisation of the chromatographic resolution of mixtures involving ionisable solutes at varying pH and acetonitrile content are discussed. Several retention models that separate the contributions of solute, column and stationary phase, were used. The retention was predicted with low errors in large pH domains (2-12), which was an essential requirement to face the optimisation of resolution. The selected mixture was particularly problematic under the viewpoint of resolution, owing to the excessively diverse acid-base behaviour of solutes. This variety led to sudden drops in retention at different pH for each solute, yielding numerous peak crossing, which made finding shared regions of high resolution especially difficult. Conventional resolution diagrams for these situations are scarcely informative, since both the overall and the worst elementary resolutions drop to zero if at least two compounds remain overlapped, even when all the others are baseline resolved. A new chromatographic objective function is proposed to address this drawback. This function, called "limiting peak count", is based on the limiting peak purity concept, and measures the success in the resolution focusing on the resolved solutes, in contrast to conventional resolution assessments that attend mainly to the least resolved solutes. Limiting peak count yields the same result as conventional assessments when full resolution is possible, but it is also able to discriminate the maximal resolving power in low-resolution situations. It offers a different perspective to that given by the complementary mobile phases approach, and the computation is far simpler.     

Study of elution behaviour with gradient voltage in CEC using methacrylate monolithic columns

A theoretical study on the retention behaviour and chromatographic performance of neutral solutes using a lauryl methacrylate‐based monolithic column under voltage gradient mode in CEC was carried out. Through a flexible mathematical function based on a modified Gaussian model, the peak shape of compounds was firstly fitted under constant and gradient voltage. Using the peak shape parameters and retention time, the estimation of global chromatographic performance, efficiency and peak capacity under several voltage conditions was performed. The influence of voltage gradient on the separation efficiency is discussed and simple equations are presented to calculate retention and peak widths under voltage gradient conditions. A comparison in terms of chromatographic performance of a test mixture of neutral solutes under constant and gradient voltage modes was also carried out. The experiments carried out under gradient voltage showed better efficiencies (172 000 plates/m) and lower peak widths than those obtained under constant voltage (52 000 plates/m).     

Novel experimental design paradigm for development of eco-friendly gradient chromatographic method for simultaneous determination of metronidazole and spiramycin

This work describes the innovative experimental design-assisted development of a green gradient chromatographic method for concomitant analysis of metronidazole (MTR) and spiramycin (SPR). Two different designs including fractional factorial and Box-Behnken designs were implemented for screening and optimization steps, respectively. The optimum chromatographic conditions involved a mobile phase consisting of ethanol and 20 mM sodium dihydrogen phosphate solution (pH adjusted to 2.5) in the ratio 2:98 (v/v) for 2 min then the ratio changed to 30:70 (v/v). The flow rate was 1.3 mL/minute. Separation and analysis were performed on X-bridge C18 (150 mm × 4.6 mm × 3.5 μm) column with diode array detector set at 230 nm. Column oven temperature was 40°C. A linear response was acquired over the range of 5–125 μg/mL for both drugs. Detection and quantitation limits were 0.86 and 2.62 μg/mL for MTR and 0.92 and 2.83 μg/mL for SPR, respectively. The method was implemented for determination of both drugs in three tablet formulations. The method was proved to be green as evaluated by three assessment tools. The application of experimental designs assists in development of a robust green chromatographic method in gradient elution mode for determination of both drugs within reasonable time.     

QSPR modeling: graph connectivity indices versus line graph connectivity indices

Five QSPR models of alkanes were reinvestigated. Properties considered were molecular surface-dependent properties (boiling points and gas chromatographic retention indices) and molecular volume-dependent properties (molar volumes and molar refractions). The vertex- and edge-connectivity indices were used as structural parameters. In each studied case we computed connectivity indices of alkane trees and alkane line graphs and searched for the optimum exponent. Models based on indices with an optimum exponent and on the standard value of the exponent were compared. Thus, for each property we generated six QSPR models (four for alkane trees and two for the corresponding line graphs). In all studied cases QSPR models based on connectivity indices with optimum exponents have better statistical characteristics than the models based on connectivity indices with the standard value of the exponent. The comparison between models based on vertex- and edge-connectivity indices gave in two cases (molar volumes and molar refractions) better models based on edge-connectivity indices and in three cases (boiling points for octanes and nonanes and gas chromatographic retention indices) better models based on vertex-connectivity indices. Thus, it appears that the edge-connectivity index is more appropriate to be used in the structure-molecular volume properties modeling and the vertex-connectivity index in the structure-molecular surface properties modeling. The use of line graphs did not improve the predictive power of the connectivity indices. Only in one case (boiling points of nonanes) a better model was obtained with the use of line graphs.     

Simple and Efficient Solution for Robustness Testing in Gradient Elution Liquid Chromatographic Methods

In this paper, an efficient way for robustness testing of gradient elution liquid chromatographic methods is proposed and tested on model mixtures comprising cilazapril, hydrochlorothiazide, and their degradation products, solutes that differ not only in polarities, but also in solubility and absorption characteristics. In general, the robustness could be tested with respect to various responses: resolution, retention factor, selectivity factor, change of detector response, etc. In chromatographic methods, the separation of the adjacent peaks is mandatory, and, consequently, the resolution is usually used as response. In isocratic elution methods, the resolution threshold depends on many factors, such as sizes of adjacent peaks, peak shapes, and asymmetry factor. At the same time, the situation is even more complex in gradient elution methods, because separation depends on a larger number of parameters, such as gradient profile, column geometry, mobile phase flow rate, column equilibration between gradient runs, etc. To ensure baseline separation, the authors propose application of separation criterion (s) as response and indirect modeling in the robustness evaluation. Examined response in this approach is represented by the difference between the retention time of the beginning of the peak and the retention time of the end of the previously eluting peak of the critical pair. Moreover, the proposed methodology included reusing experiments from the optimization phase to define a robust chromatographic region without increasing the number of experiments. It was shown that method robustness can be easily and efficiently evaluated by this methodology.     

离子色谱线性梯度淋洗分离阴离子的计算机模拟

建立了使用氢氧化钠淋洗液时用计算机模拟离子色谱梯度淋洗分离阴离子的新方法,研究了在线性梯度淋洗过程中不同时间阴离子在色谱柱中的位置及所在位置的淋洗液浓度,得出阴离子在不同时间的容量因子、迁移速度,通过积分得到保留时间。再根据离子色谱峰峰形变化的规律,得到色谱峰峰形的参数。模拟色谱图保留值与实验值的相对误差小于5%,模拟色谱图的色谱峰峰形与实验所得到的色谱图的色谱峰峰形也非常接近。     

Development of an HPLC Assay Methodology for a Desonide Cream with Chemometrics Assisted Optimization

A new reversed-phase liquid chromatographic method for the separation and simultaneous quantification of desonide, sorbic acid, methylparaben, propyl gallate, and the major degradation product of desonide in a hydrophilic cream was developed with the aid of experimental design, resolution loss functions, and chemometrics methods. A strategy involving a screening phase and a fractional factorial design revealed the most influent chromatographic variables (pH and organic solvent content). The arc tangent resolution function was adopted as the optimization loss function. These variables were further optimized using a central composite design. Multivariate curve resolution and partial least squares regression were tested to optimize the chromatographic run time. The latter revealed to be superior in terms of precision and allowed the validation of a method with a total run time 3 times lower (approximately 8 min). The experimental design and chemometrics models enabled an efficient use of time and resources in predicting the optimum separation conditions for the desonide formulation. The validation of the resulting method according to the current ICH guidelines confirmed its selectivity, linearity, accuracy, and precision.     

Combined effect of solvent content, temperature and pH on the chromatographic behaviour of ionisable compounds II: benefits of the simultaneous optimisation

A previously reported eight-parameter mechanistic model [Part I of this work, J. Chromatogr. A 1163 (2007) 49] was applied to optimise the separation of 11 ionisable compounds (nine diuretics and two beta-blockers), considering solvent content, temperature and pH as experimental factors. The data from 21 experiments, arranged in a central composite design, were used to model the retention. Local models were used to predict efficiency and peak asymmetry. The optimisation strategy, based on the use of peak purity as chromatographic objective function and derived concepts, was able to find the most suitable experimental conditions yielding full resolution in reasonable analysis times. It also allowed a detailed inspection of the separation capability of the studied factors, and of the consequences of the shifts in the protonation constants originated by changes in solvent content and temperature. The size of the resolution structures suggested that the ranked importance of the factors was pH, organic solvent and temperature, giving rise to relatively narrow domains of full resolution. The three factors were found, however, worthwhile in the optimisation of selectivity. Predicted optimal conditions corresponding to two different optimal resolution regions were verified experimentally. In spite of the difficulties associated to the use of pH as optimisation factor, satisfactory agreement was found in both cases.     

Factorial analysis optimization of a Diltiazem kinetic spectrophotometric quantification method

A Diltiazem kinetic spectrophotometric method was optimized by factorial analysis. The experimental method is based on a two-stage reaction of Diltiazem with hydroxylamine and a ferric salt: in the first stage there is a hydroxamic acid formation; and, in the second stage there is a red colour complex ferric hydroxamate formation. The variables under investigation were: solvent; hydroxylamine, sodium hydroxide and ammonium ferric sulphate concentrations; volume of perchloric acid; and, temperature. The responses of the reactional system were the maximum absorbance, the wavelength and the reaction time at maximum absorbance. Experimental design methodologies were used in the optimization. Fractional and full factorial designs followed by optimization Box-Behnken and central composite experimental designs were used. The observed optimum conditions were: methanol as reaction solvent; hydroxylamine concentration of 9.375%; sodium hydroxide concentration of 18.750%; ferric reagent concentration of 2.000%; minimum volume of perchloric acid to neutralize the sodium hydroxide; and, room temperature as reaction temperature. With this set of experimental conditions a reaction time of 10.5 s with maximum colour development at 512 nm wavelength was achieved.