Derringer's Desirability Function Research Articles

OPTIMIZATION OF SEPARATION OF FLAVONOIDS IN MICELLAR LIQUID CHROMATOGRAPHY USING EXPERIMENTAL DESIGN AND DERRINGER'S DESIRABILITY FUNCTION

Derringer's desirability function was used to simultaneous optimization of resolution and analysis time of five flavonoids myricetin, quercetin, hesperetin, naringenin, and apigenin in MLC. The factors studied were the concentration of sodium dodecyl sulfate [SDS], alkyl chain length of the alcohol (N), volume percentage of alcohol (Vm), volume percentage of acetic acid (AcOH) in mobile phase, and flow rate. The experiments were performed according to a face-centered cube half fractional central composite design to map the chromatographic response surface. The chromatographic response functions (CRFs) were formed using two sigmoidal desirability functions and were considered as the responses of design. The qualities of the obtained chromatograms in each experiment were calculated using CRF and model was built by the use of multiple linear regression (MLR) to correlate the obtained CRFs to the experimental factors and their interactions. The developed MLR model showed good descriptive and predictive ability (R2 = 0.9530 and F = 21.88). The optimum mobile phase composition for separation of interested flavonoids using a C18 column was [SDS] = 0.040 mol L−1; 11.2 % v/v butanol, 1.4 % v/v AcOH with flow rate of 1.1 mL/min. The efficiency of prediction of polynomial model was confirmed by performing the experiment under the predicted optimal conditions.

Chaotropic agents in liquid chromatographic method development for the simultaneous analysis of levodopa, carbidopa, entacapone and their impurities

The simultaneous pharmaceutical analysis of multi-component drugs represents a challenge due to a large total number of analytes present in the sample. These analytes are not only the active pharmaceutical ingredients, but also the impurities that might follow the active substances. The aim of this study was to develop an efficient reversed-phase LC method for the simultaneous analysis of antiparkinsonian drugs levodopa, carbidopa and entacapone along with their six related impurities. For the achievement of desirable separation, different acids with anions possessing different properties according to Hofmeister classification (ortho-phosphoric, trifluoroacetic and perchloric acid) were tested. Finally, in order to draw the unbiased conclusions when optimizing the analytical method, for the final tuning of the gradient program, Box–Behnken experimental design and Derringer's desirability function were used. The experiments were performed on Zorbax Extend C18, 150mm×4.6mm, 5μm particle size column with the UV detection at 280nm and mobile phase flow rate of 1mL/min. The optimal mobile phase consisted of methanol and 20mM trifluoroacetic acid (pH 2.0 adjusted with NaOH), while their ratio is changed according to previously defined gradient program. The method was tested for selectivity, sensitivity, linearity, accuracy and precision, and proved to be suitable for routine qualitative and quantitative analysis of levodopa, carbidopa, entacapone and their impurities in their mixture.

Separation system suitability (3S): a new criterion of chromatogram classification in HPLC based on cross-evaluation of separation capacity/peak symmetry and its application to complex mixtures of anthraquinones

A comparison of chromatograms obtained in a series of separation conditions for a given complex mixture may be done with a series of chromatographic descriptors. In this study, we used two descriptors: the number of critical pairs and symmetry of peaks, further rescaled and converted to the corresponding critical pairs' coefficient (CPc) and symmetry coefficient (Sc). Considering the difficulty of appreciating global separation quality using CPc and Sc criteria separately, as their respective values are usually uncorrelated, a double-criteria cross-evaluation system was required. For that purpose we tested the commonly used multi-criteria decision-making method - Derringer's desirability function (D) - as well as the recently introduced sum of ranking differences (SRD). To facilitate the graphical comparison of both approaches, the desirability function (D) was used in the inverse form (Dinv). The advantages and drawbacks of both evaluation methods, especially the respective under- or over-evaluation of outliers, caused us to introduce a new ranking approach, separation system suitability (3S). The obtained suitability rankings for the three tested approaches (Dinv, SRD and 3S) are different; nevertheless, 3S appears to be the most balanced and the easiest to interpret as well. The approach developed for selection of suitable systems was applied to the problem of separation of complex mixtures through the analysis of a series of standards of anthraquinone derivatives. To judge the pertinence of this evaluation, a sample containing a number of natural anthraquinones extracted from the bark of Indian mulberry (Morinda citrifolia) was analysed. In conclusion, the proposed methodology for the cross-evaluation of the series of chromatograms using single specific descriptors (CPc and Sc) through a global composite descriptor (3S) significantly simplifies the decision that separation systems are the most suitable for the separation of complex target mixtures of compounds.

Systematic optimisation of coupled microwave-assisted extraction-solid phase extraction for the determination of pesticides in infant milk formula via LC–MS/MS

An extraction method consisting of both microwave-assisted extraction (MAE) and solid phase extraction (SPE) was developed to extract pesticides of different polarities in infant milk formula. An experimental central face composite design was established to evaluate the effects of several MAE variables simultaneously such as temperature and pH of extractant. With Derringer desirability function, all pesticides were optimally extracted at 102 °C within 20 min with 4.56 mL of extractant consisting of 0.1% of water in methanol at pH 12. Extraction efficiency was subsequently analysed with LC-MS/MS. The extraction recoveries ranging from 72% to 111% were obtained for all pesticides at fortification level of 5-100 μg kg(-1) with relative standard deviations (RSDs) of less than 8%. Compared with Soxhlet/SPE, the MAE/SPE method utilised less solvent and higher recoveries were achieved with a shorter extraction time.

Chemometric technique for the optimization of chromatographic system: Simultaneous HPLC determination of Rosuvastatin, Telmisartan, Ezetimibe and Atorvastatin used in combined cardiovascular therapy

Developed and optimized a validated isocratic reverse phase HPLC separation of Rosuvastatin, Telmisartan, Ezetimibe and Atorvastatin in pharmaceutical preparation using response surface methodology. The separation was carried out by using phenomenex C18 column (15cm×4.6mm id, 5μm particle size) and UV detection at 239nm. The ranges of the independent variables used for the optimization were MeCN: 33–38%, buffer conc.: 10–20mM and flow rate: 1–2ml/min. The influence of these independent variables on the output responses: capacity factor of the first peak (k1), resolutions of the 2nd and 3rd peak (Rs2,3), and capacity factor of the fifth peak (k5) were evaluated. Using this strategy, a mathematical model was defined and a response surface was derived for the separation. The three responses were simultaneously optimized by using Derringer's desirability functions. Optimum conditions chosen for the assay were MeCN, MeOH, 20mM K2HPO4 (pH 3.0±0.2) solution (34.27:20:45.73 v/v/v) and flow rate 2ml/min. Total chromatographic analysis time per sample was approximately 10min. The optimized assay condition was validated as per the ICH guidelines and applied for the quantitative analysis of Rosavel EZ, Avas-EZ and Lipisar 20 tablet. The developed method was simple, accurate and precise. Hence, it can be employed for the routine analysis in quality control laboratories.

OPTIMIZATION OF LIQUID CHROMATOGRAPHIC METHOD FOR THE SEPARATION OF FOLIC ACID AND ITS TWO IMPURITIES

In this article, the multiobjective optimization of reversed-phase high-performance liquid chromatography (RP-HPLC) method for the analysis of folic acid and its two impurities, p-aminobenzoic acid and N-(4-aminobenzoyl)-L-glutamic acid, is presented. During the preliminary study, the independent variables whose impact should be further examined in the optimization were defined (acetonitrile content in the mobile phase, molarity of sodium 1-heptanesulfonate in the aqueous phase, and pH of the aqueous phase). The face-centered central composite design was chosen for the method optimization. As the dependent variables, the separation between the impurities and the retention factor of folic acid were followed. The analysis of variance (ANOVA) test was done, and good correlation among results was confirmed. For the more accurate and reliable optimization, Derringer's desirability function was applied. On the basis of restrictions adopted for the selected targets, the resulting optimal composition of the mobile phase was acetonitrile −3 mM sodium 1-heptanesulfonate (5.3:94.7 V/V), pH of the aqueous phase adjusted to 2.1 with the concentrated ortho-phosphoric acid. Furthermore, the method was subjected to method validation. It proved to be reliable and suitable for the routine analysis of investigated substances in active pharmaceutical ingredients, as well as in pharmaceutical preparations.

Simultaneous optimization of the resolution and analysis time of flavonoids in reverse phase liquid chromatography using Derringer's desirability function

The chemometrics approach was applied for simultaneous optimization of resolution and analysis time of seven flavonoids in reverse phase liquid chromatography. Derringer's desirability function, a multi-criteria decision making method, was used for the evaluation of two different chromatographic performance goals including resolution and analysis time. The selected flavonoids belong to different classes of flavonoids including: flavonols (myricetin, morin, quercetin and kaempferol) flavones (apigenin and luteolin) and flavanones (naringenin). The effect of five experimental factors on a chromatographic response function, formed using two sigmoidal desirability functions, was investigated. The sigmoidal functions were used to transform the optimization criteria, resolution and analysis time, into the desirability values. The factors studied were percentages of methanol, phosphoric acid and THF in mobile phase as well as flow rate and temperature. A rotatable, orthogonal central composite design was used to map the chromatographic response surface and then calculated chromatographic response functions were fitted to a polynomial model. The obtained regression model was characterized by both descriptive and predictive ability (R2=0.96). The model was verified, as good agreement was observed between the predicted and experimental values of the chromatographic response function in the optimal condition. The most effective factor on retention of flavonoids was percentage of methanol in mobile phase followed by temperature, flow rate, THF and H3PO4 percentages. Optimum condition for separation of flavonoids was as follows: methanol:0.4% phosphoric acid in water:THF (45.3:54.4:0.3, v/v/v) as mobile phase with flow rate of 1mLmin−1 at 30°C. The optimum condition was applied for separation of flavonoids of Satureja sahendica Bornm. which is an endemic medicinal plant of Iran.

Desirability-based optimization and its sensitivity analysis for the perindopril and its impurities analysis in a microemulsion LC system

In the current paper the application of multiobjective optimization (MOOP) technique, via Derringer's desirability function, to a microemulsion liquid chromatographic (MELC) method is described. Chromatographic separation of perindopril tert-butylamine and its four impurities was selected as the case study. Central composite design (CCD) with fractional factorial design, ±0.5 α star design and four replications in central point was applied for a response surface study, in order to examine in depth the effects of the most important factors. As factors that influence the system mostly (i) content of ethyl acetate and (ii) butyl acetate in composite internal phase, (iii) content of sodium dodecyl sulfate (surfactant) and (iv) n-butanol (co-surfactant), as well as (v) pH of the mobile phase were selected. Retention factor of (a) perindoprilat and (b) impurity Y 31 and (c) resolution factor for impurities Y 32 and 33 were chosen for simultaneous optimization. By adjustment of the importance coefficients and weights, according to defined objectives, the optimal mobile phase composition was predicted to be: 0.24% w/v butyl acetate, 0.3% w/v ethyl acetate, 2% w/v SDS, 7.75% w/v n-butanol and pH of the mobile phase 3.7. The sensitivity analysis of desirability function for these optimal conditions was conducted for the first time in LC separations, by applying a sensitivity procedure. The performed sensitivity analysis confirmed that the higher overall desirability does not necessarily mean a better solution. The accuracy of prediction might be affected if the optimal levels of input variables, achieved from several design points, end up with equal settings and different corresponding overall desirability. In our study this was not the issue, which confirmed the adequacy of predicted optimum.

Method development and validation for optimised separation of salicylic, acetyl salicylic and ascorbic acid in pharmaceutical formulations by hydrophilic interaction chromatography and response surface methodology

This paper introduces a design of experiments (DOE) approach for method optimisation in hydrophilic interaction chromatography (HILIC). An optimisation strategy for the separation of acetylsalicylic acid, its major impurity salicylic acid and ascorbic acid in pharmaceutical formulations by HILIC is presented, with the aid of response surface methodology (RSM) and Derringer's desirability function. A Box-Behnken experimental design was used to build the mathematical models and then to choose the significant parameters for the optimisation by simultaneously taking both resolution and retention time as the responses. The refined model had a satisfactory coefficient ( R 2 > 0.92, n = 27). The four independent variables studied simultaneously were: acetonitrile content of the mobile phase, pH and concentration of buffer and column temperature each at three levels. Of these, the concentration of buffer and its cross-product with pH had a significant, positive influence on all studied responses. For the test compounds, the best separation conditions were: acetonitrile/22 mM ammonium acetate, pH 4.4 (82:18, v/v) as the mobile phase and column temperature of 28 °C. The methodology also captured the interaction between variables which enabled exploration of the retention mechanism involved. It would be inferred that the retention is governed by a compromise between hydrophilic partitioning and ionic interaction. The optimised method was further validated according to the ICH guidelines with respect to linearity and range, precision, accuracy, specificity and sensitivity. The robustness of the method was also determined and confirmed by overlying counter plots of responses which were derived from the experimental design utilised for method optimisation.

Multiple response optimization of vegetable oils fatty acid composition to improve biodiesel physical properties

The effect of fatty acids chain length (LC) and its interaction with unsaturation degree (UD) on important biodiesel quality parameters was studied. Low calorific value, kinematic viscosity, flash point, cetane number and cold filter plugging point of biodiesel blends covering a wide range of fatty acids were analyzed. Analytical results were processed with statistical regression to obtain a prediction model for each property, combining LC and UD. Due to the antagonistic effects of the chemical composition over quality properties, the Derringer desirability function was proposed to allow the most suitable fatty acid composition. This target was achieved considering an average of 1.26 double bounds and 17 carbon atoms. A set of combinations of LC and UD values that provides a biodiesel that fits the European standard EN 14214 was proposed. It was found that a reduction of FAME LC allows a lower UD while keeping biodiesel specifications under the standard limits.

Multi‐objective optimization strategy based on desirability functions used for electrophoratic separation and quantification of rosiglitazone and glimepiride in plasma and formulations

Multiple response simultaneous optimization employing Derringer's desirability function was used for the development of a capillary electrophoresis method for the simultaneous determination of rosiglitazone (RSG) and glimepiride (GLM) in plasma and formulations. Twenty experiments, taking the two resolutions, the analysis time, and the capillary current as the responses with three important factors--buffer morality, volte and column temperature--were used to design mathematical models. The experimental responses were fitted into a second order polynomial and the six responses were simultaneously optimized to predict the optimum conditions for the effective separation of the studied compounds. The separation was carried out by using capillary zone electrophoresis (CZE) with a silica capillary column and diode array detector at 210 nm. The optimum assay conditions were 52 mmol l⁻¹ phosphate buffer, pH 7, and voltage of 22 kV at 29 °C. The method showed good agreement between the experimental data and predictive value throughout the studied parameter space. The assay limit of detection was 0.02 µg ml⁻¹ and the effective working range at relative standard deviation (RSD) of ≤ 5% was 0.05-16 µg ml⁻¹ (r = 0.999) for both drugs. Analytical recoveries of the studied drugs from spiked plasma were 97.2-101.9 ± 0.31-3.0%. The precision of the assay was satisfactory; RSD was 1.07 and 1.14 for intra- and inter-assay precision, respectively. The proposed method has a great value in routine analysis of RSG and GLM for its therapeutic monitoring and pharmacokinetic studies.

Desirability function combining metabolic stability and functionality of peptides

The evaluation of peptides as potential therapeutic or diagnostic agents requires the consideration of several criteria that are targeted around two axes: functionality and metabolic stability. Most often, a compromise has to be made between these mutually opposing characteristics. In this study, Derringer's desirability function, a multi-criteria decision-making method, was applied to determine the best peptide for opioid studies in a single figure-of-merit. The penetration of the blood-brain barrier (BBB) determines the biological functionality of neuropeptides in the brain target tissue, and consists of an influx and an efflux component. The metabolic stability in the two concerned tissues, i.e. plasma and brain, are taken into consideration as well. The overall selection of the peptide drug candidate having the highest BBB-drugability is difficult due to these conflicting responses as well as the different scalings of the four biological parameters under consideration. The highest desirability, representing the best BBB-drugability, was observed for dermorphin. This peptide is thus the most promising drug candidate from the set of eight opioid peptides that were investigated. The least desirable candidate, with the worst BBB influx and/or metabolic stability, was found to be CTAP. Validation of the desirability function by in vivo medical imaging showed that dermorphin and DAMGO penetrate the BBB, whereas EM-1 and TAPP did not. These results are thus consistent with those obtained with the desirability evaluation. To conclude, the multi-criteria decision method was proven to be useful in biomedical research, where a selection of the best candidate based on opposing characteristics is often required.

Dual CD system‐modified MEEKC method for the determination of clemastine and its impurities

A dual system of CDs was used for the first time in MEEKC with the aim of determining clemastine and its three main related impurities in both drug substances and tablets. The addition of methyl-β-cyclodextrin and heptakis(2,6-di-O-methyl)-β-cyclodextrin to the microemulsion pseudo-stationary phase was essential to increase the resolving power of the system to obtain a baseline separation among the compounds. The best microemulsion composition was identified by mixture design and the effects of the factors concentrations of CDs and voltage were investigated by a response surface study applying a Central Composite Design. In both cases, Derringer's desirability function made it possible to find the global optimum, which corresponded to the following combination: microemulsion, 89.8% 10 mM borate buffer pH 9.2, 1.5% n-heptane and 8.7% of SDS/n-butanol in 1:2 ratio; 18 mM methyl-β-cyclodextrin, 38 mM heptakis(2,6-di-O-methyl)-β-cyclodextrin, 17 kV. By applying these conditions, the separation was completed in about 5.5 min. The method was validated following International Conference on Harmonisation guidelines and was applied to a real sample of clemastine tablets.

Evolving neural network optimization of cholesteryl ester separation by reversed-phase HPLC

Cholesteryl esters have antimicrobial activity and likely contribute to the innate immunity system. Improved separation techniques are needed to characterize these compounds. In this study, optimization of the reversed-phase high-performance liquid chromatography separation of six analyte standards (four cholesteryl esters plus cholesterol and tri-palmitin) was accomplished by modeling with an artificial neural network–genetic algorithm (ANN-GA) approach. A fractional factorial design was employed to examine the significance of four experimental factors: organic component in the mobile phase (ethanol and methanol), column temperature, and flow rate. Three separation parameters were then merged into geometric means using Derringer’s desirability function and used as input sources for model training and testing. The use of genetic operators proved valuable for the determination of an effective neural network structure. Implementation of the optimized method resulted in complete separation of all six analytes, including the resolution of two previously co-eluting peaks. Model validation was performed with experimental responses in good agreement with model-predicted responses. Improved separation was also realized in a complex biological fluid, human milk. Thus, the first known use of ANN-GA modeling for improving the chromatographic separation of cholesteryl esters in biological fluids is presented and will likely prove valuable for future investigators involved in studying complex biological samples. FigureANN-derived response surface plot for two interacting factors and overall response Electronic supplementary materialThe online version of this article (doi:10.1007/s00216-010-3778-5) contains supplementary material, which is available to authorized users.

Chemometric Approach for Simultaneous Optimization of Resolution and Analysis Time in CCC

The chemometric approach combining Box-Behnken response surface model and Derringer's desirability function was applied for simultaneous optimization of resolution and analysis time in countercurrent chromatography (CCC). The mergence of the two parameters was accomplished using the Derringer's desirability function with subsequent optimization by a Box-Behnken response surface design. The developed model was checked by statistical analysis. By implementing the optimal flow rate, rotation speed and temperature predicted by the validated model, enhanced resolution between two similar analytes (phenol and resorcinol) was achieved in a reasonable time. The analyses and results obtained in this paper will benefit to improve the efficiency of CCC separation.

Cyclodextrin-MEEKC for the analysis of oxybutynin and its impurities

The development of a cyclodextrin-MEEKC method for the analysis of oxybutynin and five related impurities is described. Experimental design strategies were applied in order to reach baseline separation of the compounds in a short analysis time. Mixture design made it possible to find the best composition for the microemulsion acting as pseudostationary phase, which was constituted by 89.1% 10 mM borate buffer pH 9.2, 1.7% n-heptane, 9.2% SDS/ n-butanol in 1:2 ratio. The addition of (2-hydroxypropyl)-β-cyclodextrin to the background electrolyte was found to improve analysis performance. A Doehlert design, for the factors cyclodextrin concentration and voltage, was carried out and Derringer desirability function led to the identification of 18 mM and 29 kV as the optimal values. Applying the optimum conditions, separation of all the compounds, including the enantiomers of impurity 1, was obtained in less than 12 min. The method was validated according to ICH guidelines for drug assay and determination of impurities and was applied to oxybutynin tablet analysis.

Possibility of predicting separations in supercritical fluid chromatography with the solvation parameter model

In order to obtain a selection of optimal chromatographic columns for the separation of chlorotriazine pesticides in packed column supercritical fluid chromatography (pSFC), a multi-criteria approach is applied. For this purpose, prediction of the separations is carried out, based on quantitative structure–retention relationships, then Derringer's desirability function is proposed to determine the stationary phase that will result in the most desirable separation. The best SFC separation obtained was then optimized using a mobile phase gradient. Besides, the accuracy of the solvation parameter model as SFC retention predictive model is assessed.

Combined column–mobile phase mixture statistical design optimization of high-performance liquid chromatographic analysis of multicomponent systems

A statistical approach for the simultaneous optimization of the mobile and stationary phases used in reversed-phase liquid chromatography is presented. Mixture designs using aqueous mixtures of acetonitrile (ACN), methanol (MeOH) and tetrahydrofuran (THF) organic modifiers were performed simultaneously with column type optimization, according to a split-plot design, to achieve the best separation of compounds in two sample sets: one containing 10 neutral compounds with similar retention factors and another containing 11 pesticides. Combined models were obtained by multiplying a linear model for column type, C8 or C18, by quadratic or special cubic mixture models. Instead of using an objective response function, combined models were built for elementary chromatographic criteria (retention factors, resolution and relative retention) of each solute or pair of solutes and, after their validation, the global separation was accomplished by means of Derringer's desirability functions. For neutral compounds a 37:12:8:43 (v/v/v/v) percentage mixture of ACN:MeOH:THF:H2O with the C18 column and for pesticides a 15:15:70 (v/v/v) ACN:THF:H2O mixture with the C8 column provide excellent resolution of all peaks.

Computer-assisted optimization of liquid-liquid extraction for HPLC analysis of domperidone and pantoprazole in human plasma

Summary This paper deals with optimization of a liquid-liquid extraction procedure for simultaneous HPLC analysis of domperidone and pantoprazole in human plasma. Central composite design and Derringer's desirability function were used to optimize the concentration of KOH and the volume of ethyl acetate as the main factors affecting the liquid-liquid extraction procedure. After extraction, the analytes were separated quantitatively on a C18 column with 10 mM pH 7.0 phosphate buffer-methanol-acetonitrile 48.46:20:31.54 (υ/υ) as mobile phase at a flow rate of 1.20 mL min−1 and with UV detection at 285 nm. It was concluded that extraction recovery of both the analytes was affected by KOH concentration and that recovery of pantoprazole was affected by ethyl acetate (extraction solvent) volume. Extraction recovery under optimum extraction conditions was 93.52% for domperidone and 92.72% for pantoprazole. The optimized extraction method was validated. Linearity was established for six levels in the ranges 10–1000 ng mL−1 for pantoprazole and 15–1000 ng mL−1 for domperidone. The lower limit of quantitation (LLOQ) and detection (LOD) were estimated as 9.84 and 5.91 ng mL−1, respectively, for pantoprazole and 14.56 and 8.79 ng mL−1 for domperidone. The optimized method was linear, specific, accurate, and precise; the high recovery (>92%) and low relative standard deviation (<2.5%) enable reliable quantification of these analytes in spiked human plasma.

Purity determination of yunaconitine reference standard using HPLC with experimental design and response surface optimization

Experimental design and response surface methodology have been used for the development of the stability-indicating HPLC method for the purity determination of yunaconitine reference standard. Significant factors including the contents of ACN, perchloric acid, triethylamine (TEA), and column temperature were optimized using a Box-Behnken design. A mixture of crude yunaconitine extract and degradation solutions of yunaconitine under stress conditions was chromatogramed. The normalized peak area of total impurities, the retention time of yunaconitine, and the resolutions between yunaconitine and its adjacent peaks were selected as optimization criteria. Derringer desirability function of the multicriteria and the tested factors were used to establish 3-D response surfaces. The optimal condition was achieved with a mobile phase of ACN/water (30:70, containing 0.125% perchloric acid and 1.0% TEA) at a column temperature of 37.5 degrees C. The method was validated and shown comparable to that of phase solubility analysis. As a result, the newly developed method can be used to determine the chromatographic purity and stability of the yunaconitine reference standard.