Pareto-optimal front as a tool to study the behaviour of experimental factors in multi-response analytical procedures

This work presents a methodology to analyse the behaviour of an analytical procedure, above all when optimization of the procedure is needed. The methodology starts by the design of an experiment suitable to fit response surfaces to some analytical responses of interest in the problem being studied. Then, a pareto-optimal front is estimated that accounts for the optimal possibly trading-off solutions among the responses. The analysis of the behaviour of the optimal values of the response surfaces and the experimental conditions that provide these values allows going deeply into the analytical procedure.     

Improving the visualization of the Pareto-optimal front for the multi-response optimization of chromatographic determinations

The paper shows tools to visualize and more easily interpret the effect that some experimental factors may exert on analytical responses of interest when optimization of several responses is needed.It is based on an adaptation of the parallel coordinate plot, a tool for graphical representation of points in multidimensional spaces that, theoretically and contrary to the usual Cartesian plots, does not have limits in the dimension of the points being depicted.The joint use of the Pareto-optimal solutions and their visualization allows a deeper knowledge about the problem at hand as well as the wise selection of the conditions of experimental factors for achieving specific goals about the responses.Although the methodology is for a general use, the procedure, its interpretation and usefulness is shown with several analytical cases in chromatography. The first one refers to the experimental conditions to obtain simultaneously the maximum allowable area for both the peak of the malachite green and its metabolite leucomalachite green in fish by liquid chromatography with tandem mass spectrometry detection (LC–MS/MS). The second one is about the simultaneous determination of steroid hormones estrone and 17-α-ethinylestradiol by gas chromatography–mass spectrometry (GC/MS). In the last case, the chromatographic separation by GC/MS of the diastereoisomers, α- and β-estradiol is needed taking into account that these hormones have the same mass fragments.     

The construction of simultaneous optimal experimental designs for several polynomials in the calibration of analytical methods

In this paper a criterion is described for the construction of experimental designs for the evaluation of calibration models in analytical chemistry. The proposed criterion seeks a compromise between the D-optimal designs for estimating the parameters of different polynomial models. A computer algorithm is presented for a sequential construction of experimental designs using the optimality criterion. The performance of the optimality criterion and the computer algorithm is elaborated for the problem of discrimination between a first- to a third-degree polynomial for the calibration of analytical methods. An experimental design consisting of replicate measurements at five distinct levels equally spaced over the calibration range proved a good solution.     

An appraisal of experimental designs: Application to enantioselective capillary electromigration techniques

Enantioresolution processes are vital tools for investigating the enantioselectivities of chiral compounds. An analyst resolves to optimize enantioresolution conditions once they are determined. Generally, optimization is conducted by a one-factor-at-a-time (OFAT) approach. Although this approach may determine an adequate condition for the method, it does not often allow the estimation of the real optimum condition. Experimental designs are conducive for the optimization of enantioresolution methods via capillary electromigration techniques (CETs). They can efficiently extract information from the behavior of a method and enable the estimation of the real optimum condition. Furthermore, the application of the analytical quality by design (AQbD) approach to the development of CET-based enantioselective methods is a trend. This article (i) offers an overview of the application of experimental designs to the development of enantioselective methods from 2015 to mid-2020, (ii) reveals the experimental designs that are presently employed in CET-based enantioresolutions, and (iii) offers a critical point of view on how the different experimental designs can aid the optimization of enantioresolution processes by considering the method parameters.     

Quality by Design approach in the development of a solvent-modified micellar electrokinetic chromatography method: Finding the design space for the determination of amitriptyline and its impurities

A solvent-modified micellar electrokinetic chromatography method was set up for the simultaneous determination of the tricyclic antidepressant amitriptyline (AMI) and its main impurities. The method was developed following Quality by Design (QbD) principles according to ICH Guideline Q8(R2). QbD approach made it possible to find the design space (DS), where quality was assured. After a scouting phase, aimed at selecting a suitable capillary electrophoresis pseudostationary phase, risk assessment tools were employed to define the critical process parameters (CPPs) to be considered in a screening phase (applied voltage, concentration and pH of the background electrolyte, concentration of the surfactant sodium dodecyl sulphate, of the cosurfactant n-butanol and of the organic modifiers acetonitrile and urea). The effects of the seven selected CPPs on critical quality attributes (CQAs), namely resolution values between critical peak pairs and analysis time, were investigated throughout the knowledge space by means of a symmetric screening matrix. Response surface study was then carried out on four selected CPPs by applying a Doehlert Design. Monte-Carlo simulations were performed in order to estimate the probability of meeting the desired specifications on CQAs, and thus to define the DS by means of a risk of failure map. Additional points at the edges of the DS were tested in order to verify the requirements for CQAs to be fulfilled. A control strategy was implemented by defining system suitability tests. The developed method was validated following ICH Guideline Q2(R1), including robustness assessment by Plackett–Burman design, and was applied to the analysis of real samples of amitriptyline coated tablets.     

The application of experimental design to the robustness testing of a method for the determination of drug-related impurities by capillary electrophoresis

Summary Robustness testing of capillary electrophoresis methods is an important part of method validation. Appropriate use of experimental designs can be employed in this robustness testing. In this study experimental designs were used in the assessment of a capillary electrophoresis method used to determine drug related impurities. Initially a fractional factorial screening design was used to identify the critical parameters which were found to be pH and voltage. A central composite design was then performed to evaluate the response surfaces for pH and voltage which showed operation at the optimum pH and voltage values.     

Development and validation of an HPLC method for the determination of process-related impurities in pridinol mesylate, employing experimental designs

A simple high performance liquid chromatographic method for the determination of process-related impurities in bulk drug of the central anticholinergic compound pridinol mesylate, has been developed and validated. Spectroscopically characterized synthetic impurities were used as standards. The chromatographic separation was optimized employing an experimental design strategy, and was achieved on a C₁₈ column with a mobile phase containing 50 mM potassium phosphate buffer (pH 6.4), MeOH and 2-propanol (20:69:11, v/v/v), delivered at a flow rate of 1.0 mL min⁻¹. UV detection was performed at 245 nm. The optimized method was thoroughly validated, demonstrating to be selective, when the chromatogram was recorded with a diode-array detector and peak purities were evaluated (>0.9995). The method is robust and linear (r² > 0.99) over the range 0.05-2.5% (5-250% with regards to the 1% specification limit for both process-related impurities); it is also precise, regarding repeatability (RSD ≤ 1.5% for all of the analytes) and intermediate precision aspects and LOQ values for the impurities are below 0.01%. Method accuracy, evidenced by low bias of the results and analyte recoveries in the range of 99.1-102.7%, was assessed at five analyte concentration levels. The usefulness of the determination was also demonstrated through the analysis of different lots of pridinol mesylate bulk substance. The results indicate that the method is suitable for the quality control of the bulk manufacturing of pridinol mesylate drug substance.     

Analytical quality by design in the development of a cyclodextrin‐modified capillary electrophoresis method for the assay of metformin and its related substances

Quality by Design (QbD) is a new paradigm of quality to be applied to pharmaceutical products and processes, recently encouraged by International Conference on Harmonisation guidelines. In this paper QbD approach was applied to the development of a CE method for the simultaneous assay of metformin hydrochloride (MET) and its main impurities. QbD strategy was focused on electrophoretic process understanding, and the analytical method was thoroughly evaluated by applying risk assessment and chemometric tools. Method scouting allowed CD‐CZE based on the addition of carboxymethyl‐β‐CD to Britton‐Robinson acidic buffer to be chosen as operative mode. Seven critical process parameters (CPPs) were selected, related to capillary, injection, BGE and instrumental settings. The effect of the different levels of the CPPs on critical quality attributes (CQAs), e.g. critical resolution values and analysis time, was evaluated in a screening study. Response surface methodology led to draw contour plots and sweet spot plots. The definition of design space was accomplished by applying Monte‐Carlo simulations, thus identifying by risk of failure maps a multivariate zone where the CQAs fulfilled the requirements with a selected probability. Finally, a control strategy was designed and the method was applied to a real sample of MET tablets.     

Optimization of a pressurized liquid extraction method by experimental design methodologies for the determination of fluoroquinolone residues in infant foods by liquid chromatography

In the present study, we have developed a method based on pressurized liquid extraction (PLE) and liquid chromatography with fluorescence detection (LC-FLD) for the determination of residues of fluoroquinolones (FQs) in infant food products. PLE extraction has been optimized by the application of experimental design methodologies. Initially, a fractional factorial design (FFD) was used to screen the significance of four extraction parameters: solvent composition, temperature, pressure and number of cycles. The most significant factors, identified by ANOVA analysis, were the solvent composition, temperature and pressure, which were further optimized with the aid of a face centred design (FCD) and the desirability function. The optimized operating PLE conditions were as follows: ACN/o-phosphoric acid 50 mM pH 3.0 (80:20, v/v), 80 °C, 2000 psi and three extraction cycles of 5 min. Under these conditions, recoveries of the target FQs varied between 69% and 107% with RSDs below 9%. The whole method was validated according to the Commission Decision 2002/657/EC guidelines. The proposed method has been successfully applied to the analysis of different infant food products bought in local supermarkets and pharmacies. The results showed the presence of residues of enrofloxacin in a non-compliant baby food sample corresponding to a chicken-based formulation, which were also confirmed and quantified by LC–MS/MS analysis.     

Development and validation of a HPLC method for the determination of voriconazole in pharmaceutical formulation using an experimental design

A rapid and sensitive RP-HPLC method with UV detection (260 nm) for routine analysis of voriconazole in a pharmaceutical formulation (Vfend^®) was developed. Chromatography was performed with mobile phase containing a mixture of acetonitrile and water (50:50, v/v) with flow rate was of 1.0 ml min⁻¹. Quantitation was accomplished with internal standard method. The procedure was validated for linearity (correlation coefficient = 0.9999), accuracy, robustness and intermediate precision. Experimental design was used for validation of robustness and intermediate precision. To test robustness, three factors were considered. Percentage of acetonitrile in mobile phase, flow rate and p^H; an increase in the flow rate results in a decrease of the drug found concentration, while the percentage of organic modifier and p^H have no important effect on the response. For intermediate precision measure the variables considered were: analyst, equipment and number of days. The R.S.D. value (0.45%, n = 24) indicated a good precision of the analytical method. The proposed method was simple, highly sensitive, precise and accurate and retention time less than 4 min indicating that the method is useful for routine quality control.     

Characterization and optimization by experimental design of a liquid chromatographic method for the separation of hydroxylated polychlorinated biphenyls on a polar-embedded stationary phase

Traditionally, the determination of hydroxylated polychlorinated biphenyls (OH-PCBs) has been carried out by gas chromatography (GC). However, the gas chromatographic behavior and sensitivity of this type of hydroxylated compounds are not always satisfactory, hence a prior derivatization of the OH-PCBs must be performed. Therefore, the development of liquid chromatographic methods should prove to be a very interesting task aimed at dealing with the instrumental determination of OH-PCBs. Taking into account that octadecylsilane stationary phases are not the most adequate for the separation of isobaric compounds, an amide-type column has been tested. For the development of the method, the Response Surface Methodology was used, based on a Box-Wilson Central Composite experimental design. The initial content of methanol in the mobile phase, the gradient time, and the concentration and the pH value of the buffer were chosen as relevant experimental parameters. A global optimum was obtained by selecting the elution time, the sensitivity and the overall resolution as responses to optimize. The developed method for liquid chromatography presented a very good resolution and sensitivity, and a reasonably short analysis time. In addition, a retention study was conducted in order to survey the different interactions that take place in the separation process, showing that hydrogen bonding is the main interaction between OH-PCBs and the amide-type stationary phase. However, a substantial contribution of dispersion forces was present in methanol contents in the mobile phase below 65%. Besides, the pH value of the mobile phase was found to be the most important parameter to control the hydrogen bond forces and therefore, to regulate the OH-PCBs separation.     

Optimization of the operating conditions using factorial designs for determination of uranium by inductively coupled plasma optical emission spectrometry

A critical evaluation of the determination of uranium by inductively coupled plasma optical emission spectrometry was performed using factorial designs (2³) involving the factors: acid concentration, radio frequency power and nebulizer gas flow rate. All of the experiments in this study were made for five emission lines, in the presence of nitric and hydrochloric acid. The results demonstrated that, between nitric and hydrochloric acid, the determinations in the presence of nitric acid were most sensitive. The factorial design showed that the nebulizer gas flow rate was the most significant among the factors studied for the five emission lines. Calcium in concentrations of 10 mg L⁻¹ was observed to cause suppression of the emission intensity for some lines. Iron (at least up to 10 mg L⁻¹) did not interfere in the emission intensity of uranium across the five lines studied. Another experiment evaluated simultaneously the effect of 13 other elements, and the results demonstrated that these elements did not affect the emission intensity of uranium for the lines chosen. The optimized method, using the line at 385.957 nm, allows the determination of uranium with limit of quantification of 31 μg L⁻¹ and precision expressed as RSD lower than 2.2% for uranium concentrations of either 500 or 1000 μg L⁻¹. The accuracy was confirmed by analysis of two laboratory reference materials. The developed method was applied to the determination of uranium in an industrial effluent collected from uranium-producing mine in Caetite City, Brazil. The sample was analyzed by inductively coupled plasma mass spectrometry ICP-MS, and the observed recovery was satisfactory.     

MultiSimplex and experimental design as chemometric tools to optimize a SPE-HPLC-UV method for the determination of eprosartan in human plasma samples

A chemometric approach was applied for the optimization of the extraction and separation of the antihypertensive drug eprosartan from human plasma samples. MultiSimplex program was used to optimize the HPLC-UV method due to the number of experimental and response variables to be studied. The measured responses were the corrected area, the separation of eprosartan chromatographic peak from plasma interferences peaks and the retention time of the analyte.The use of an Atlantis dC18, 100 mm × 3.9 mm i.d. chromatographic column with a 0.026% trifluoroacetic acid (TFA) in the organic phase and 0.031% TFA in the aqueous phase, an initial composition of 80% aqueous phase in the mobile phase, a stepness of acetonitrile of 3% during the gradient elution mode with a flow rate of 1.25 mL/min and a column temperature of 35 ± 0.2 °C allowed the separation of eprosartan and irbesartan used as internal standard from plasma endogenous compounds. In the solid phase extraction procedure, experimental design was used in order to achieve a maximum recovery percentage. Firstly, the significant variables were chosen by way of fractional factorial design; then, a central composite design was run to obtain the more adequate values of the significant variables. Thus, the extraction procedure for spiked human plasma samples was carried out using C8 cartridges, phosphate buffer pH 2 as conditioning agent, a drying step of 10 min, a washing step with methanol-phosphate buffer (20:80, v/v) and methanol as eluent liquid. The SPE-HPLC-UV developed method allowed the separation and quantitation of eprosartan from human plasma samples with an adequate resolution and a total analysis time of 1 h.     

Validation of a high-performance liquid chromatographic method for determination of isoflavonoids in soybeans. Study of the extraction procedure by experimental design

Summary An improved analytical method, reversed-phase high-performance liquid chromatography on a narrow-bore C₁₈ column, has been developed for the simultaneous determination of genistein, daidzein, formononetin, and biochanin A. The method was validated in terms of detection limits, quantitation limits (LOQ), linearity, and precision.LOQ in the 0.04–0.1 μg mL⁻¹ range were calculated, enabling determination of these compounds of nutritional concern at trace levels. Good linearity was demonstrated over three orders of magnitude of concentration for each analyte (r ²=0.998–1.000). The intra-day repeatability was evaluated in terms ofRSD (%) at two concentration levels for each analyte (RSD (%) <1.8%). Good inter-day reproducibility of data was proved by performing homoscedasticity and ANOVA tests (P>0.05 at the 95% confidence level). The method was applied to the determination of genistein and daidzein in yellow soybeans, after optimization of the method for extraction of isoflavonoid aglycones from soybeans by experimental design, i.e. central composite design. Extraction recoveries up to 87±4% were obtained when the corresponding glycosidic forms (genistin and daidzin) were added to soybean samples.     

A new multiresponse optimization approach in combination with a D-Optimal experimental design for the determination of biogenic amines in fish by HPLC-FLD

A new strategy to approach multiresponse optimization in conjunction to a D-optimal design for simultaneously optimizing a large number of experimental factors is proposed. The procedure is applied to the determination of biogenic amines (histamine, putrescine, cadaverine, tyramine, tryptamine, 2-phenylethylamine, spermine and spermidine) in swordfish by HPLC-FLD after extraction with an acid and subsequent derivatization with dansyl chloride. Firstly, the extraction from a solid matrix and the derivatization of the extract are optimized. Ten experimental factors involved in both stages are studied, seven of them at two levels and the remaining at three levels; the use of a D-optimal design leads to optimize the ten experimental variables, significantly reducing by a factor of 67 the experimental effort needed but guaranteeing the quality of the estimates. A model with 19 coefficients, which includes those corresponding to the main effects and two possible interactions, is fitted to the peak area of each amine. Then, the validated models are used to predict the response (peak area) of the 3456 experiments of the complete factorial design. The variability among peak areas ranges from 13.5 for 2-phenylethylamine to 122.5 for spermine, which shows, to a certain extent, the high and different effect of the pretreatment on the responses. Then the percentiles are calculated from the peak areas of each amine. As the experimental conditions are in conflict, the optimal solution for the multiresponse optimization is chosen from among those which have all the responses greater than a certain percentile for all the amines. The developed procedure reaches decision limits down to 2.5 μg L⁻¹ for cadaverine or 497 μg L⁻¹ for histamine in solvent and 0.07 mg kg⁻¹ and 14.81 mg kg⁻¹ in fish (probability of false positive equal to 0.05), respectively.     

Optimization of modified dispersive liquid–liquid microextraction coupled with high‐performance liquid chromatography for the simultaneous preconcentration and determination of nitrazepam and midazolam drugs: An experimental design

A simple, sensitive, and rapid microextraction method, namely, ultrasound‐assisted surfactant‐enhanced emulsification microextraction based on the solidification of floating organic droplet method coupled with high‐performance liquid chromatography was developed for the simultaneous preconcentration and determination of nitrazepam and midazolam. The significant parameters affecting the extraction efficiency were considered using Plackett–Burman design as a screening method. To obtain the optimum conditions with consideration of the selected significant variables, a Box–Behnken design was used. The microextraction procedure was performed using 29.1 μL of 1‐undecanol, 1.36% (w/v) of NaCl, 10.0 μL of sodium dodecyl sulfate (25.0 μg mL^?1), and 1.0 μL of Tween80 (25.0 μg mL^?1) as an emulsifier in an extraction time of 20.0 min at pH 7.88. In order to investigate the validation of the developed method, some validation parameters including the linear dynamic range, repeatability, limit of detection, and recoveries were studied under the optimum conditions. The detection limits of the method were 0.017 and 0.086 ng mL^?1 for nitrazepam and midazolam, respectively. The extraction recovery percentages for the drugs studied were above 91.0 with acceptable relative standard deviation. The proposed methodology was successfully applied for the determination of these drugs in a number of human serum samples.     

Optimization of alcohol‐assisted dispersive liquid–liquid microextraction by experimental design for the rapid determination of fluoxetine in biological samples

A sensitive and rapid method based on alcohol‐assisted dispersive liquid–liquid microextraction followed by high‐performance liquid chromatography for the determination of fluoxetine in human plasma and urine samples was developed. The effects of six parameters on the extraction recovery were investigated and optimized utilizing Plackett–Burman design and Box–Benken design, respectively. According to the Plackett–Burman design results, the volume of disperser solvent, extraction time, and stirring speed had no effect on the recovery of fluoxetine. The optimized conditions included a mixture of 172 μL of 1‐octanol as extraction solvent and 400 μL of methanol as disperser solvent, pH of 11.3 and 0% w/v of salt in the sample solution. Replicating the experiment in optimized condition for five times, gave the average extraction recoveries equal to 90.15%. The detection limit of fluoxetine in human plasma was obtained 3 ng/mL, and the linearity was in the range of 10–1200 ng/mL. The corresponding values for human urine were 4.2 ng/mL with the linearity range from 10 to 2000 ng/mL. Relative standard deviations for intra and inter day extraction of fluoxetine were less than 7% in five measurements. The developed method was successfully applied for the determination of fluoxetine in human plasma and urine samples.     

Evaluation of microwave-assisted digestion condition for the determination of metals in fish samples by inductively coupled plasma mass spectrometry using experimental designs

This paper describes the development of a compromised single-stage microwave-assisted digestion condition for multi-element determination in fish samples by inductively coupled plasm: mass spectrometry using experimental designs. A Plackett–Burman design was carried out as a multivariate strategy to investigate the main effects of the following parameter on microwave-assisted nitric acid digestion: microwave irradiation time, ramp time, digestion temperature, microwave power limit and the addition of hydrogen peroxide or hydrochloric acid. The most significant microwave setting parameters (radiation time, ramp and temperature) were further evaluated by response surface methodology under Box–Behnken design, while others were kept constant. The influences of different parameters vary according to metal element, thus the working conditions were established as a compromise within optimum region found for each targeted element which ensures quantitative recoveries and time efficiency. The compromised conditions are: ramp to 185°C in 10.5?min then hold for 14.5?min with 1600W (50%) of microwave power, using reagent mixture composed of 2.5?mL nitric acid, 0.5?mL hydrochloric acid and 7.0?mL water. Good agreements were demonstrated between measured and certified values with respect to DORM-3, DOLT-4 and ECM-CE278 and this method was successfully applied for metals determination in tilapia tissues.     

Optimization of a solid-phase microextraction procedure for the determination of herbicides by micellar electrokinetic chromatography

The use of a different optimization procedure that involves Experimental Design (ED) and Artificial Neural Networks (ANN) for the off-line coupling solid-phase microextraction-micellar electokinetic chomatography (SPME-MEKC) is presented. This combination of ED and ANN, mathematical tools not previously used in SPME-MEKC optimization, allowed us to obtain good extraction efficiencies in the SPME procedure for the determination of a group of eleven triazine herbicides in groundwater samples. Both extraction and desorption steps were carried out by solution stirring at 900 rpm. Optimal conditions for the off-line SPME procedure were: extraction with a poly(dimethylsiloxane)/divinylbenzene SPME fiber for 120 min, 10% (w/v) NaCl, desorption time 40 min, and 70% (v/v) of methanol/buffer as desorption mixture. Detection limits lay between 0.80 microg L(-1) and 4.89 microg L(-1). Finally, the optimized method was applied to the determination of these compounds in spiked and non-spiked groundwater samples using a previously optimized MEKC separation.