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Evaluation of the quantitative performances of supercritical fluid chromatography: From method development to validation Amandine Dispas a,∗ , Pierre Lebrun a,b , Eric Ziemons a , Roland Marini a , Eric Rozet a,b , Philippe Hubert a a b
University of Liege (ULg), CIRM, Laboratory of Analytical Chemistry, 1 Avenue de l’Hôpital, B36, B-4000 Liège, Belgium Arlenda s.a., Liège, Belgium
a r t i c l e
i n f o
Article history: Received 28 November 2013 Received in revised form 15 January 2014 Accepted 17 January 2014 Available online xxx Keywords: Supercritical fluid chromatography (SFC) Ultra high performance supercritical fluid chromatography (UHPSFC) Ultra high performance liquid chromatography (UHPLC) Quantitative performances Method validation Total error approach
a b s t r a c t Recently, the number of papers about SFC increased drastically but scientists did not truly focus their work on quantitative performances of this technique. In order to prove the potential of UHPSFC, the present work discussed about the different steps of the analytical life cycle of a method: from development to validation and application. Moreover, the UHPSFC quantitative performances were evaluated in comparison with UHPLC, which is the main technique used for quality control in the pharmaceutical industry and then could be considered as a reference. The methods were developed using Design Space strategy, leading to the optimization of robust method. In this context, when the Design Space optimization shows guarantee of quality, no more robustness study is required prior to the validation. Then, the methods were geometrically transferred in order to reduce the analysis time. The UHPSFC and UHPLC methods were validated based on the total error approach using accuracy profile. Even if UHPLC showed better precision and sensitivity, UHPSFC method is able to give accurate results in a dosing range larger than the 80–120% range required by the European Medicines Agency. Consequently, UHPSFC results are valid and could be used for the control of active substance in a finished pharmaceutical product. Finally, UHPSFC validated method was used to analyse real samples and gave similar results than the reference method (UHPLC). © 2014 Elsevier B.V. All rights reserved.
1. Introduction Supercritical fluid chromatography (SFC) is an old technique hidden in the shadow of gas chromatography (GC) and liquid chromatography (LC) for almost fifty years [1,2]. Recently, the interest of manufacturers and scientists for SFC increased leading to the development and the improvement of the SFC instrumentation. Moreover, the involvement of SFC in the worldwide effort for green chemistry helped to its success. Ultra high performance supercritical fluid chromatography (UHPSFC) is now presented as a really powerful technique complementary to GC and LC. Nowadays, the advantages and interests of SFC, such as high throughput or improved chromatographic performances, are worldwide approved. Although the number of publications increased significantly in recent years, most scientists did not truly consider (UHP)SFC as a quantitative method but more for fundamental studies and chiral applications. Moreover, few publications
∗ Corresponding author. Tel.: +32 4366 4319; fax: +32 4366 4317. E-mail address: [email protected] (A. Dispas).
described validation process of SFC method. The validation of chiral separation of a drug compound was previously described [3] assessing several validation criteria such as selectivity, linearity and precision. Unfortunately, surprising results (i.e. intraday repeatability with relative standard deviation (RSD) value of 9%) were mentioned without explanation about acceptance criteria. Xiang et al. described the validation of nine chiral compounds considering repeatability and linearity [4]. Whang et al. described partial validation of SFC method, considering the selectivity as critical in order to demonstrate the orthogonality between two methods [5]. Only one publication presents the validation results SFC method for the quality control of medicines [6]. In the evaluation of the precision criterion, the intra-day RSD values were superior than the inter-day RSD for some concentration levels. Thus, these peculiar results cannot be considered as adequate indicators of the quantitative performances of the method. Moreover, the accuracy was tested using standards addition method; unfortunately, the dosing range investigated was not the same than the other criteria tested (precision and linearity). To our best of knowledge, a full validation considering total error approach of SFC method was not yet published.
http://dx.doi.org/10.1016/j.chroma.2014.01.046 0021-9673/© 2014 Elsevier B.V. All rights reserved.
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Validation is one of the main steps in analytical method life cycle. The aim of validation process is to demonstrate the analytical performances of the developed analytical method in accordance to its intended use. Validation of analytical methods is well established and described in the literature. Nevertheless, despite many regulatory documents (GMP, ISO, FDA, etc.) the conclusion about the method acceptance criteria remains confused. For that purpose, Hubert et al. proposed a common strategy for the validation of quantitative an analytical method [7–10], introducing the concept of total error approach as a decision tool. In the pharmaceutical industry, the validation of analytical procedure is required before its use in the quality control (QC) laboratory. The objective of the present work is to investigate the life cycle of a UHPSFC method from development to validation, including its application to real samples. The concept of Quality by Design (QbD) is now well established in pharmaceutical development. The QbD is defined by ICH Q8 R2 [11] as “a systematic approach to development that begins with predefined objectives and emphasises product and process understanding based on sound science and quality risk management”. Furthermore, the QbD concept was recently introduced in the field of analytical method development and validation [12,13]. Indeed, an analytical method can be seen as a process that must have an output of acceptable quality. Borman et al. [14] demonstrated that the QbD concept for manufacturing processes could also be applied to analytical methods. Design of Experiments (DoE) considering risk management by means of error propagation is considered as a keystone to optimize process in the QbD environment [15]. In this context, the Design Space (DS) was introduced as a key component of analytical method development [13,16]. The DS is defined as “the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality” [1]. Thus, the DS is a subspace of the experimental domain in which the assurance of quality has been proved. As previously described [16], the Design Space could be defined as a region of an experimental domain – – where the posterior probability that the critical quality attributes (CQAs) are within acceptance criteria , is higher than a specified quality level , conditionally on the available data. DS = {x0 ∈ : P(CQAs ∈ |x0 , data} ≥
(1)
CQAs provide some indications about the overall achievement of the analytical method. In chromatography, CQAs may be the resolution (Rs) or the separation (S) of a critical pair of peaks, while the acceptance criteria may be Rs > 1.5 and/or S > 0. In this context, a result given as a predictive probability that the CQAs will be within the acceptance interval establishes the assurance of quality. For chromatographic method development, the DS could be defined as the space of chromatographic conditions that will ensure the quality of the separation. Therefore, the method robustness is guaranteed inside the DS limits. Method robustness should be evaluated prior or post validation step. Only a few examples of SFC robustness studies were published [17]. The interest of robust optimization strategy, especially for SFC methods development, was previously described [18,19]. USP requires robustness evaluation, before the initiation of method validation during the development/optimization step [20]. This important step is no more required if robust method optimization was performed and acceptable guarantee level was found. Thus, DS strategy fulfils the USP recommendations and at the same time allows speeding up the analytical life cycle. The main objective of this work is to investigate the interest of UHPSFC as a quantitative method used for the quality control of manufactured medicines. For that purpose, robust method optimization and validation QbD compliant were performed. Because of their weight in the current pharmaceutical therapy, antibiotics
drugs were selected using the following model compounds: phenoxymethylpenicillin (penicillin V), doxycycline, levofloxacin, metronidazole, amoxicilline, trimethoprim and clindamycin. These drugs are frequently used in Democratic Republic of Congo (DRC) [21]. Counterfeiters are very active in developing countries, such as DRC, where medicines are largely used such as antibiotics and antiparasitics. In this context, the development of screening analytical methods that can simultaneously trace several molecules is an essential strategy in order to fight against poor quality medicines. Caffeine was included in the studied model mixture as system suitability compound. The studied compounds, their structures, pKa and log P are shown in Table 1. Nowadays, the most popular method used for the quality control in pharmaceutical industry is HPLC because of the wide range of compounds that could be analysed and the good quantitative performances of the technique. Previously, a HPLC method was developed for the screening of a wide range of antibiotic drugs [21] using DS strategy. This method was transferred to UHPLC in order to get a faster technique. UHPLC could be used as a reference quantitative technique to evaluate and compare the potential of UHPSFC in the field of quantitative analysis, considering the analytical performances (method validation) and the analysis of real samples. 2. Material and methods 2.1. Chemicals and reagents Levofloxacine (99.0%) was purchased from Molekula Limited (Dorset, UK). Amoxicilline (99.1%), caffeine (100.1%) clindamycin (95.8%), doxycycline (97.6%), metronidazole (99.9%), penicillin-V (100.2%) and trimethoprim (99.2%) were provided by Fagron N.V. (Waregem, Belgium). Methanol (HPLC gradient grade) was purchased from J.T. Baker (Deventer, Netherlands). 2-Propanol (HPLC gradient grade), nheptane (HPLC grade), ammonium acetate (98.0%, analytical grade), hydrochloric acid (37%, analytical grade) and formic acid (98%, analytical grade) were obtained from Merck Millipore (Darmstadt, Germany). Carbon dioxide (99.995%) was purchased from Westfalen (Brussels, Belgium). Ultrapure water was obtained from a Milli-Q Plus 185 water purification system (Millipore, Billerica, MA, USA). 2.2. Standard samples preparation 2.2.1. Mixture preparation According to their UV absorbance and solubility, the antibiotics were divided in three groups. All stock solutions were prepared in pure methanol. Stock solution of group 1 (S1 ) was obtained by dissolving 40 mg of penicillin-V, 50 mg of doxycycline, 25 mg of levofloxacine and 20 mg of metronidazole in a volumetric flask of 5.0 mL. Solution stock of group 2 (S2 ) was obtained by dissolving 10 mg of amoxicilline in a volumetric flask of 5.0 mL. Solution stock of group 3 (S3 ) was obtained by dissolving 20 mg of caffeine and 25 mg of trimethoprim in a volumetric flask of 20.0 mL. All stock solutions were sonicated in an ultrasonic bath for 12 min to ensure a complete dissolution. Stock solutions were stored at −27 ◦ C. Intermediate and working solution were prepared daily by dilution of stock solutions. Intermediate solution (SI) was prepared by dissolving, and diluting in 2-propanol, 100 mg of clindamycin, 1.0 mL of S1 , 2.0 mL of S2 and 1.0 mL of S3 in a volumetric flask of 10.0 mL. Working solution was obtained by diluting SI twice in 2-propanol/n-heptane (50/50, v/v) mixture. Thus, the final sample diluent is a mixture methanol/2-propanol/n-heptane (20/55/25, v/v/v). This solvent
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Table 1 Structure, pKa , and log P (octanol/water, at 25 ◦ C), found on Clarke’s Analysis of Drugs and Poisons (Medicines Complete Browser).
composition is quite apolar in order to guarantee a good peak shape while keeping the compounds solubility. All these solutions were prepared protected from light to avoid degradation of light-sensitive antibiotics. The sample preparation could be modified according to specific requirements for quantitative analysis. The amount of API in the pharmaceutical product and/or targeted concentration and/or the matrix (excipients) should require some changes like described in Sections 2.2.2 and 2.2.4 for the quantification of amoxicillin in capsules.
2.2.2. UHPSFC calibration and validation standards preparation For the calibration standards (CS), a stock solution was prepared by dissolving 150 mg of amoxicilline with a solution of 0.1% formic acid in methanol in a volumetric flask of 100.0 mL. The solution was sonicated for 60 min to ensure a complete dissolution, followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted in order to obtain final concentration of 375, 562.5, 750, 937.5 and 1125 g/mL. For the validation standard (VS), a stock solution was prepared by dissolving 150 mg of amoxicilline, 2.25 mg of an excipient
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mixture (talc/magnesium stearate 2/1 (m/m)) with a solution of 0.1% formic acid in methanol in a volumetric flask of 100.0 mL. The solution was sonicated for 60 min to ensure a complete dissolution, followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted in order to obtain final concentration of 375, 562.5, 750, 937.5 and 1125 g/mL. The VS were independently prepared in the matrix (three independent repetitions per series), in such a way to mimic as much as possible the corresponding antibiotic formulation and its routine analysis. The validation experiments were tested by means of four series (one series per day). Each CS and VS solution is composed of a mixture methanol/2propanol/n-heptane (75/12.5/12.5, v/v/v) solvent. All these solutions were prepared protected from light to avoid degradation of light-sensitive antibiotics. Furthermore, the sonication was performed in a cooled bath to avoid temperature increase. 2.2.3. UHPLC calibration and validation standards preparation For the calibration standards (CS), a stock solution was prepared by dissolving 10 mg of amoxicilline with water in a volumetric flask of 100.0 mL. The solution was sonicated for 20 min followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted in water in order to obtain final concentration of 50, 80, 100, 120, 150 g/mL. For the validation standard (VS), a stock solution was prepared by dissolving 100 mg of amoxicilline, 1.5 mg of an excipient mixture (talc/magnesium stearate 2/1 (m/m)) with water in a volumetric flask of 100.0 mL. The solution was sonicated for 20 min followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted in water in order to obtain final concentration of 50, 80, 100, 120, 150 g/mL. The VS were independently prepared in the matrix (three independent repetitions per series), in such a way to mimic as much as possible the corresponding antibiotic formulation and its routine analysis. The validation experiments were tested by means of three series (one series per day). All these solutions were prepared protected from light to avoid degradation of light-sensitive antibiotics. 2.2.4. Preparation of real samples The developed and validated methods were applied to the identification and assay of amoxicillin in capsules marketed in Democratic Republic of Congo. The content of 20 capsules was removed as completely as possible and was mixed together. For UHPSFC, a quantity equivalent to 500 mg of amoxicillin was transferred to a 500.0 mL volumetric flask and dissolved with a solution of 0.1% formic acid in methanol. The solution was sonicated for 60 min followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted with a 2propanol–n-heptane (50/50, v/v) mixture solvent in order to obtain concentration of 750 g/mL. For UHPLC, a quantity equivalent to 500 mg of amoxicillin was transferred to a 500.0 mL volumetric flask and dissolved with water. The solution was sonicated for 20 min followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted with water in order to obtain concentration of 100 g/mL. Three independent sample solutions were prepared for each analysis. All these solutions were prepared protected from light to avoid degradation of light-sensitive antibiotics. 2.3. Instrumentation 2.3.1. UHPSFC equipment A Waters Acquity UPC2® equipped with a PDA detector was used to carry out the UHPSFC experiments. The injector was equipped with a 10 L loop operating in the partial loop with needle
overfill mode, with methanol and methanol/2-propanol/n-heptane (1/4/5, v/v/v) as strong and weak needle wash, respectively. Chromatograms were recorded at wavelengths ranging from 210 nm to 400 nm with a step of 1.2 nm and with an acquisition frequency of 20 points/s. Peaks were integrated at a wavelength of 220 nm. The chromatographic columns employed in this study were a Acquity BEH 2-ethylpyridine (3 mm id × 100 mm, 1.7 m), a Acquity BEH 2-ethylpyridine (3 mm id × 50 mm, 1.7 m), a Acquity BEH (3 mm id × 100 mm, 1.7 m) all from Waters (Milford, USA), and a Kinetex Hilic (2.1 mm id × 150 mm, 2.6 m) from Phenomenex (Torrance, USA). 2.3.2. UHPLC equipment A Waters Acquity UPLC® equipped with a PDA detector was used to carry out the UHPLC experiments. The injector was equipped with a 10 L loop operating in the partial loop with needle overfill mode, with water/methanol (95/5; v/v) and water/methanol (5/95; v/v) as weak and strong needle wash, respectively. Chromatograms were recorded at wavelengths ranging from 210 nm to 400 nm with a step of 1.2 nm and with an acquisition frequency of 20 points/s. Peaks were integrated at a wavelength of 220 nm. The chromatographic column employed in this study was a Acquity BEH C18 (2.1 mm id × 50 mm, 1.7 m) from Waters. The UHPLC method used in the present study was described previously [21]. 2.4. Design of Experiments 2.4.1. Chromatographic screening design In order to select the appropriated stationary and mobile phase before the method optimization, a screening design was built. The factors were: stationary phase chemistry and modifier type. Bare silica, BEH silica and BEH 2-ethylpyridine were selected as stationary phases. Methanol and ethanol were selected as modifier. The objective was to maximize the chromatographic performances of SFC; for that purpose, sub 2 m or core-shell particles were selected. To evaluate the main effect of the factors and their interactions a full factorial design comprising 6 experiments was tested. The others chromatographic parameters were kept constant. The mobile phase flow rate was set at 2 mL min−1 . The analyses were performed in gradient mode, starting by an isocratic step (2 min, 5% modifier), then a gradient to linearly modify the co-solvent proportion from 5 to 20% in 5 min. The column outlet pressure and the temperature were set at 120 bars and 40 ◦ C, respectively. The autosampler temperature and the injected volume were set at 4 ◦ C and 5 L, respectively. 2.4.2. Method optimization design Method development was focused on the gradient profile optimization. Indeed, three factors were selected: the isocratic time (tiso ) before the gradient, the gradient time (tgrad ) to linearly modify the proportion of modifier and the proportion of methanol in the mobile phase at the end of the gradient (%MeOH). A total of 17 experiments were defined by a rotatable inscribed central composite design. The central point (i.e. tiso 1.5 min, tgrad 9 min, % MeOH 25%) was independently repeated three times. The 17 experiments were required to optimize the method and to assess the robustness. To our opinion, it is less experiment than making firstly the optimization and then performing the robustness study. Factors and their respective levels are summarized in Table 2. These factors were selected to investigate their effect on the selectivity, especially for the gradient time and %MeOH. Isocratic time should impact the separation of the less retained compounds. Very rapid equilibration between experiments led to perform the DoE on two days thanks to the additive-free mobile phase.
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Levels
tiso (min) tgrad (min) %MeOH
0.5 3 20
5
3. Results and discussion 3.1. Method development
0.9 5.55 22
1.5 9 25
2.1 12.55 28
2.5 15 30
The others factors were kept constant during the experimental design. As described in Section 3.1, the selected column was BEH 2-ethylpyridine with methanol as modifier. The mobile phase flow rate was set at 2 mL min−1 . The column outlet pressure and the temperature were set at 120 bars and 40 ◦ C, respectively. The temperature was not a factor of the DoE for two mains reasons: (i) the experimental domain is restricted taking into account the instability of antibiotics; (ii) it was not necessary to demonstrate the temperature robustness because all the SFC systems are thermostatically controlled. The column outlet pressure was fixed at a pressure SFC compliant enabling the use gradient involving large amount of modifier. Indeed, the elution of polar compounds in SFC could require using methanol or other co-solvent up to 40–50% in the mobile phase. The presence of methanol led to an increase of viscosity, the pressure in the system is higher than neat CO2 mobile phase. After the gradient, a 2 min isocratic plateau at the maximal value of %MeOH was applied to elute all the compounds and the column was reconditioned for 5 min prior to the next injection. The autosampler temperature and the injected volume were set at 4 ◦ C and 5 L, respectively. 2.5. Response modelling and Design Space computation As previously described [13,16], the retention times at the beginning, the apex and the end of each peak (respectively tB , tR and tE ) were measured. The studied response was the logarithm of the apparent retention factor termed kapp (i.e. log (ktR ) with kapp tR = (tR − t0 )/t0 , where t0 is the column dead time). These responses were modelled by a multivariate polynomial equation using a stepwise regression maximizing the adjusted coefficient of 2 ). The objective of this statistical approach is to determination (Radj obtain a high quality parsimonious model. Retention times were predicted using the developed model. Separation (S) was selected as critical quality attributes (CQA) [16,18], defined as the difference between the retention time at the beginning of the second peak and the retention time at the end of the first peak of a critical peak pair (i.e. S = tB2 − tE1 ). The errors obtained for the predicted retention times are propagated to the CQA. As described by Lebrun et al. [16], Monte-Carlo simulations were used to obtain the distribution of S from the joint posterior distribution of tB , tR and tE of the critical pair, for a given chromatographic condition. Considering the distribution of tR and S, the probability for S to be higher than 0 was used to compute the DS. Thus, the DS defines the sub-space of the experimental domain where the predictive probability to have S > 0 is higher than a predefined quality level. 2.6. Software JMP 10.0.0 was used to build the Design of Experiments. An algorithm was set up to develop a Bayesian model and to compute the DS using Monte-Carlo simulations. The algorithm was written in R 2.13, which is available as free-ware for most operating systems [22]. HPLC calculator [23] was used to perform the geometric calculations of UHPSFC and UHPLC method transfers. E-noval® V3.0 software (Arlenda, Belgium) was used to compute the results of the analytical validation.
3.1.1. Screening design results The objective of this screening was to find quickly chromatographic conditions for the method development design. The interest of adding additives in the mobile phase was previously described [24,25], especially in order to improve peak shape. However, in the present project, the aim was to fix chromatographic conditions without using additive in the mobile phase for three mains reasons: (i) modifier/CO2 mobile phase enables reduced equilibration and wash time of the column and then speed up the analysis protocol; (ii) several studies and the manufacturer’s recommendations suggested the adsorption or the modification on/of the stationary phase [26,27] leading to use one column with only one additive and then to increase the cost of method development; (iii) antibiotics are unstable compounds: basic pH and very acid pH lead to degradation of these compounds. Only three or four compounds were eluted on the Kinetex Hilic column (considering EtOH or MeOH as modifier) with very wide peaks. Seven compounds were eluted on the BEH column with MeOH as modifier; unfortunately, additive such as ammonia is often advisable to get good peak shape [25] especially for basic compound. Then, the combination of BEH 2-EP stationary phase and methanol as modifier was the unique combination enabling the retention and elution of all the compounds. 3.1.2. Optimization design results 3.1.2.1. Response modelling. The model was established using amoxicilline as model compound because it was the last eluted compound (more polar compound in the present study). Indeed, to our experience, the chromatographic behaviour of polar compound is really influenced by the conditions, i.e. the gradient slope and the modifier amount. Furthermore, on the basis of our knowledge of chromatography modelling, the peaks with higher retention times are more affected by predictive uncertainty. Thus, using amoxicilline as a model compound enabled to take into account the highest experimental and the predictive uncertainty. An original empirical model, described in Eq. (2), was developed involving the principal effects of the factors and their interactions. 2 log(ktR ) = ˇ0 + ˇ1 · tiso + ˇ2 · tgrad + ˇ3 · %MeOH + ˇ4 · tgrad
+ ˇ5 · tiso · tgrad + ˇ6 · tiso · tgrad · %MeOH + ε
(2)
where ˇ0 ,. . .,ˇ6 are the estimated parameters of the model and ε is the residuals of the model. The good agreement between the retention times predicted by the model and those observed demonstrate the good adequacy of the model (Fig. 1). The residuals were observed within the [−0.4; 0.4] minute interval; except one outlier value of −0.6 min. These residuals values include the experimental (analytical) and the model variability. The consideration of both variabilities (i.e. analytical and modelling) is required when predicting for robust optimization. Furthermore, using Monte-Carlo simulations from the prediction errors, the predictive probability for S to be greater than 0 min was calculated as shown in Fig. 2. These three images represent a two-dimensional probability surface with one of the factors being fixed at optimum. The DS ( = 0.38) is encircled by a black line. 3.1.2.2. Optimal separation. One optimal separation was identified at tg 12 min, tiso 2.3 min and % MeOH set at 22% with a minimal quality level of 0.38. The chromatogram recorded at the optimal condition is presented in Fig. 3. This figure illustrates the rather
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Fig. 3. Top: predicted UHPSFC chromatogram and predictive uncertainty (shaded grey area) at the optimal condition: tiso 2.3 min; tgrad 12 min; % MeOH 22%. Bottom: respective experimental chromatogram. Elution order: (1) caffeine; (2) clindamycine; (3) metronidazole; (4) doxycycline; (5) penicillin V; (6) trimethoprim; (7) levofloxacine; (8) amoxicilline.
3.2. Method transfer Fig. 1. Modelling results and corresponding residuals. Top: predicted vs. experimental retention times; bottom: corresponding residuals plots.
good adequacy between the predicted and observed sixth first peak of the chromatogram. Some differences could be observed between predicted and observed, especially for the antepenultimate and the penultimate compound. The variability of prediction was illustrated by simulated chromatograms taking into account the predictive uncertainty (shaded grey area). As shown in Fig. 3 this area is wider for the three last eluted peaks than the others, indicating a potential lack of prediction quality. This is corroborated by the value of the quality level; meaning that practically it is expected to obtain S > 0 with a probability not more than 0.4. Notice this probability calculation is often conservative as it accounts for model uncertainty. Better model could lead to a better probability of success, but empirical linear models have been preferred for their simplicity and easy understanding of factor effects. Nevertheless, the peaks were baseline separated at the experimental optimal condition. The DS strategy led to the optimization of a quality method to separate and detect several antibiotic drugs. Moreover, the DoEDS methodology used is fully QbD compliant in that the ways for improvement and better chromatographic behaviour understanding are identified.
In order to get a rapid method to perform routine analysis, the developed UHPSFC method was transferred to a shorter column. Moreover, the use of a shorter column (50 mm × 3 mm, 1.7 m instead of 100 mm × 3 mm, 1.7 m) enabled to work at higher flow rate (3 mL min−1 instead of 2 mL min−1 ) while keeping a quite similar pressure in the system in order to speed up a little be more the analysis. The geometric transfer was successfully performed using the three classical rules of LC method transfer thanks to the method sufficient robustness. However, the pressures measured on the two columns were slightly different (≈10 bars), impacting a little bit on fluid density and hence retention and selectivity are modified. Nevertheless, the amount of modifier used slightly decreased the influence of CO2 density on the polarity of mobile phase. Despite these changes on fluid density, previous work [19] showed the successful use of this methodology for robust SFC method transfer. In the same way, the LC method previously developed using DS strategy [21] was transferred to sub 2 m short column in order to compare UHPSFC and UHPLC methods. The two methods parameters are summarized in Table 3. 3.3. Validation To assess the validity of the UHPSFC and UHPLC methods, total error approach validation using accuracy profile based on tolerance
Fig. 2. Probability surfaces (i.e. P(S > 0)). (a) % MeOH vs. gradient time (min), (b) gradient time (min) vs. isocratic times (min), (c) %MeOH vs. isocratic time (min). The DS ( = 38.5%) is encircled by a dark line.
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Table 3 Summary of UHPSFC and UHPLC validated methods.
intervals was carried out [7–10]. The tolerance interval used is a ˇexpectation tolerance interval, which defines an interval where it is expected that a defined proportion ˇ of future results will fall. The accuracy profile coming from the method validation is represented in Fig. 4 where the plain red line represents the relative bias. The dashed blue lines represent the ˇ-expectation tolerance limits at 95% probability level, which links ˇ-expectation tolerance intervals calculated for each concentration level of the validation standards, taking into account their estimated intermediate standard deviation and their bias. If the ˇ-expectation tolerance limits are comprised in the predefined acceptance limits (black dotted lines) the method can be considered as valid and guarantees that every future result will fall in the acceptance limits with at least a probability previously defined. All the validation criteria required by ICH Q2 R1 guidelines are fulfilled using total error approach [10]. As showed in Fig. 4, the dosing range validated in UHPSFC is different than the one validated in UHPLC. The difference values between the methods are related the lower sensitivity of (UHP)SFC–UV than (U)HPLC–UV, mainly explained by the difference of solvating power between supercritical fluids and liquids. In this study, the method was validated prior to its use in a QC laboratory for the manufactured medicines control. The European Medicines Agency (E.M.A.) defined some specifications “the specifications for release of the finished product must be comply with the criteria defined by Directive 75/318/EEC as amended, i.e. ± 5% for the assay of active substance(s)”. Then, the acceptance limits were fixed at ±5% for the dosing range.
3.3.2. Trueness and precision Trueness expressed in term of relative bias (%) was assessed from the validation standards at five concentration levels. The precision was then determined by computing the relative standard deviation (RSD (%)) for repeatability and between-series intermediate precision at each concentration level of validation standards. The relative bias values and RSD are presented in Tables 4 and 5 for UHPSFC and UHPLC results, respectively. Regarding precision criterion, UHPLC method showed lower RSD values (
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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Evaluation of the quantitative performances of supercritical fluid chromatography: From method development to validation Amandine Dispas a,∗ , Pierre Lebrun a,b , Eric Ziemons a , Roland Marini a , Eric Rozet a,b , Philippe Hubert a a b
University of Liege (ULg), CIRM, Laboratory of Analytical Chemistry, 1 Avenue de l’Hôpital, B36, B-4000 Liège, Belgium Arlenda s.a., Liège, Belgium
a r t i c l e
i n f o
Article history: Received 28 November 2013 Received in revised form 15 January 2014 Accepted 17 January 2014 Available online xxx Keywords: Supercritical fluid chromatography (SFC) Ultra high performance supercritical fluid chromatography (UHPSFC) Ultra high performance liquid chromatography (UHPLC) Quantitative performances Method validation Total error approach
a b s t r a c t Recently, the number of papers about SFC increased drastically but scientists did not truly focus their work on quantitative performances of this technique. In order to prove the potential of UHPSFC, the present work discussed about the different steps of the analytical life cycle of a method: from development to validation and application. Moreover, the UHPSFC quantitative performances were evaluated in comparison with UHPLC, which is the main technique used for quality control in the pharmaceutical industry and then could be considered as a reference. The methods were developed using Design Space strategy, leading to the optimization of robust method. In this context, when the Design Space optimization shows guarantee of quality, no more robustness study is required prior to the validation. Then, the methods were geometrically transferred in order to reduce the analysis time. The UHPSFC and UHPLC methods were validated based on the total error approach using accuracy profile. Even if UHPLC showed better precision and sensitivity, UHPSFC method is able to give accurate results in a dosing range larger than the 80–120% range required by the European Medicines Agency. Consequently, UHPSFC results are valid and could be used for the control of active substance in a finished pharmaceutical product. Finally, UHPSFC validated method was used to analyse real samples and gave similar results than the reference method (UHPLC). © 2014 Elsevier B.V. All rights reserved.
1. Introduction Supercritical fluid chromatography (SFC) is an old technique hidden in the shadow of gas chromatography (GC) and liquid chromatography (LC) for almost fifty years [1,2]. Recently, the interest of manufacturers and scientists for SFC increased leading to the development and the improvement of the SFC instrumentation. Moreover, the involvement of SFC in the worldwide effort for green chemistry helped to its success. Ultra high performance supercritical fluid chromatography (UHPSFC) is now presented as a really powerful technique complementary to GC and LC. Nowadays, the advantages and interests of SFC, such as high throughput or improved chromatographic performances, are worldwide approved. Although the number of publications increased significantly in recent years, most scientists did not truly consider (UHP)SFC as a quantitative method but more for fundamental studies and chiral applications. Moreover, few publications
∗ Corresponding author. Tel.: +32 4366 4319; fax: +32 4366 4317. E-mail address: [email protected] (A. Dispas).
described validation process of SFC method. The validation of chiral separation of a drug compound was previously described [3] assessing several validation criteria such as selectivity, linearity and precision. Unfortunately, surprising results (i.e. intraday repeatability with relative standard deviation (RSD) value of 9%) were mentioned without explanation about acceptance criteria. Xiang et al. described the validation of nine chiral compounds considering repeatability and linearity [4]. Whang et al. described partial validation of SFC method, considering the selectivity as critical in order to demonstrate the orthogonality between two methods [5]. Only one publication presents the validation results SFC method for the quality control of medicines [6]. In the evaluation of the precision criterion, the intra-day RSD values were superior than the inter-day RSD for some concentration levels. Thus, these peculiar results cannot be considered as adequate indicators of the quantitative performances of the method. Moreover, the accuracy was tested using standards addition method; unfortunately, the dosing range investigated was not the same than the other criteria tested (precision and linearity). To our best of knowledge, a full validation considering total error approach of SFC method was not yet published.
http://dx.doi.org/10.1016/j.chroma.2014.01.046 0021-9673/© 2014 Elsevier B.V. All rights reserved.
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Validation is one of the main steps in analytical method life cycle. The aim of validation process is to demonstrate the analytical performances of the developed analytical method in accordance to its intended use. Validation of analytical methods is well established and described in the literature. Nevertheless, despite many regulatory documents (GMP, ISO, FDA, etc.) the conclusion about the method acceptance criteria remains confused. For that purpose, Hubert et al. proposed a common strategy for the validation of quantitative an analytical method [7–10], introducing the concept of total error approach as a decision tool. In the pharmaceutical industry, the validation of analytical procedure is required before its use in the quality control (QC) laboratory. The objective of the present work is to investigate the life cycle of a UHPSFC method from development to validation, including its application to real samples. The concept of Quality by Design (QbD) is now well established in pharmaceutical development. The QbD is defined by ICH Q8 R2 [11] as “a systematic approach to development that begins with predefined objectives and emphasises product and process understanding based on sound science and quality risk management”. Furthermore, the QbD concept was recently introduced in the field of analytical method development and validation [12,13]. Indeed, an analytical method can be seen as a process that must have an output of acceptable quality. Borman et al. [14] demonstrated that the QbD concept for manufacturing processes could also be applied to analytical methods. Design of Experiments (DoE) considering risk management by means of error propagation is considered as a keystone to optimize process in the QbD environment [15]. In this context, the Design Space (DS) was introduced as a key component of analytical method development [13,16]. The DS is defined as “the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality” [1]. Thus, the DS is a subspace of the experimental domain in which the assurance of quality has been proved. As previously described [16], the Design Space could be defined as a region of an experimental domain – – where the posterior probability that the critical quality attributes (CQAs) are within acceptance criteria , is higher than a specified quality level , conditionally on the available data. DS = {x0 ∈ : P(CQAs ∈ |x0 , data} ≥
(1)
CQAs provide some indications about the overall achievement of the analytical method. In chromatography, CQAs may be the resolution (Rs) or the separation (S) of a critical pair of peaks, while the acceptance criteria may be Rs > 1.5 and/or S > 0. In this context, a result given as a predictive probability that the CQAs will be within the acceptance interval establishes the assurance of quality. For chromatographic method development, the DS could be defined as the space of chromatographic conditions that will ensure the quality of the separation. Therefore, the method robustness is guaranteed inside the DS limits. Method robustness should be evaluated prior or post validation step. Only a few examples of SFC robustness studies were published [17]. The interest of robust optimization strategy, especially for SFC methods development, was previously described [18,19]. USP requires robustness evaluation, before the initiation of method validation during the development/optimization step [20]. This important step is no more required if robust method optimization was performed and acceptable guarantee level was found. Thus, DS strategy fulfils the USP recommendations and at the same time allows speeding up the analytical life cycle. The main objective of this work is to investigate the interest of UHPSFC as a quantitative method used for the quality control of manufactured medicines. For that purpose, robust method optimization and validation QbD compliant were performed. Because of their weight in the current pharmaceutical therapy, antibiotics
drugs were selected using the following model compounds: phenoxymethylpenicillin (penicillin V), doxycycline, levofloxacin, metronidazole, amoxicilline, trimethoprim and clindamycin. These drugs are frequently used in Democratic Republic of Congo (DRC) [21]. Counterfeiters are very active in developing countries, such as DRC, where medicines are largely used such as antibiotics and antiparasitics. In this context, the development of screening analytical methods that can simultaneously trace several molecules is an essential strategy in order to fight against poor quality medicines. Caffeine was included in the studied model mixture as system suitability compound. The studied compounds, their structures, pKa and log P are shown in Table 1. Nowadays, the most popular method used for the quality control in pharmaceutical industry is HPLC because of the wide range of compounds that could be analysed and the good quantitative performances of the technique. Previously, a HPLC method was developed for the screening of a wide range of antibiotic drugs [21] using DS strategy. This method was transferred to UHPLC in order to get a faster technique. UHPLC could be used as a reference quantitative technique to evaluate and compare the potential of UHPSFC in the field of quantitative analysis, considering the analytical performances (method validation) and the analysis of real samples. 2. Material and methods 2.1. Chemicals and reagents Levofloxacine (99.0%) was purchased from Molekula Limited (Dorset, UK). Amoxicilline (99.1%), caffeine (100.1%) clindamycin (95.8%), doxycycline (97.6%), metronidazole (99.9%), penicillin-V (100.2%) and trimethoprim (99.2%) were provided by Fagron N.V. (Waregem, Belgium). Methanol (HPLC gradient grade) was purchased from J.T. Baker (Deventer, Netherlands). 2-Propanol (HPLC gradient grade), nheptane (HPLC grade), ammonium acetate (98.0%, analytical grade), hydrochloric acid (37%, analytical grade) and formic acid (98%, analytical grade) were obtained from Merck Millipore (Darmstadt, Germany). Carbon dioxide (99.995%) was purchased from Westfalen (Brussels, Belgium). Ultrapure water was obtained from a Milli-Q Plus 185 water purification system (Millipore, Billerica, MA, USA). 2.2. Standard samples preparation 2.2.1. Mixture preparation According to their UV absorbance and solubility, the antibiotics were divided in three groups. All stock solutions were prepared in pure methanol. Stock solution of group 1 (S1 ) was obtained by dissolving 40 mg of penicillin-V, 50 mg of doxycycline, 25 mg of levofloxacine and 20 mg of metronidazole in a volumetric flask of 5.0 mL. Solution stock of group 2 (S2 ) was obtained by dissolving 10 mg of amoxicilline in a volumetric flask of 5.0 mL. Solution stock of group 3 (S3 ) was obtained by dissolving 20 mg of caffeine and 25 mg of trimethoprim in a volumetric flask of 20.0 mL. All stock solutions were sonicated in an ultrasonic bath for 12 min to ensure a complete dissolution. Stock solutions were stored at −27 ◦ C. Intermediate and working solution were prepared daily by dilution of stock solutions. Intermediate solution (SI) was prepared by dissolving, and diluting in 2-propanol, 100 mg of clindamycin, 1.0 mL of S1 , 2.0 mL of S2 and 1.0 mL of S3 in a volumetric flask of 10.0 mL. Working solution was obtained by diluting SI twice in 2-propanol/n-heptane (50/50, v/v) mixture. Thus, the final sample diluent is a mixture methanol/2-propanol/n-heptane (20/55/25, v/v/v). This solvent
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Table 1 Structure, pKa , and log P (octanol/water, at 25 ◦ C), found on Clarke’s Analysis of Drugs and Poisons (Medicines Complete Browser).
composition is quite apolar in order to guarantee a good peak shape while keeping the compounds solubility. All these solutions were prepared protected from light to avoid degradation of light-sensitive antibiotics. The sample preparation could be modified according to specific requirements for quantitative analysis. The amount of API in the pharmaceutical product and/or targeted concentration and/or the matrix (excipients) should require some changes like described in Sections 2.2.2 and 2.2.4 for the quantification of amoxicillin in capsules.
2.2.2. UHPSFC calibration and validation standards preparation For the calibration standards (CS), a stock solution was prepared by dissolving 150 mg of amoxicilline with a solution of 0.1% formic acid in methanol in a volumetric flask of 100.0 mL. The solution was sonicated for 60 min to ensure a complete dissolution, followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted in order to obtain final concentration of 375, 562.5, 750, 937.5 and 1125 g/mL. For the validation standard (VS), a stock solution was prepared by dissolving 150 mg of amoxicilline, 2.25 mg of an excipient
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mixture (talc/magnesium stearate 2/1 (m/m)) with a solution of 0.1% formic acid in methanol in a volumetric flask of 100.0 mL. The solution was sonicated for 60 min to ensure a complete dissolution, followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted in order to obtain final concentration of 375, 562.5, 750, 937.5 and 1125 g/mL. The VS were independently prepared in the matrix (three independent repetitions per series), in such a way to mimic as much as possible the corresponding antibiotic formulation and its routine analysis. The validation experiments were tested by means of four series (one series per day). Each CS and VS solution is composed of a mixture methanol/2propanol/n-heptane (75/12.5/12.5, v/v/v) solvent. All these solutions were prepared protected from light to avoid degradation of light-sensitive antibiotics. Furthermore, the sonication was performed in a cooled bath to avoid temperature increase. 2.2.3. UHPLC calibration and validation standards preparation For the calibration standards (CS), a stock solution was prepared by dissolving 10 mg of amoxicilline with water in a volumetric flask of 100.0 mL. The solution was sonicated for 20 min followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted in water in order to obtain final concentration of 50, 80, 100, 120, 150 g/mL. For the validation standard (VS), a stock solution was prepared by dissolving 100 mg of amoxicilline, 1.5 mg of an excipient mixture (talc/magnesium stearate 2/1 (m/m)) with water in a volumetric flask of 100.0 mL. The solution was sonicated for 20 min followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted in water in order to obtain final concentration of 50, 80, 100, 120, 150 g/mL. The VS were independently prepared in the matrix (three independent repetitions per series), in such a way to mimic as much as possible the corresponding antibiotic formulation and its routine analysis. The validation experiments were tested by means of three series (one series per day). All these solutions were prepared protected from light to avoid degradation of light-sensitive antibiotics. 2.2.4. Preparation of real samples The developed and validated methods were applied to the identification and assay of amoxicillin in capsules marketed in Democratic Republic of Congo. The content of 20 capsules was removed as completely as possible and was mixed together. For UHPSFC, a quantity equivalent to 500 mg of amoxicillin was transferred to a 500.0 mL volumetric flask and dissolved with a solution of 0.1% formic acid in methanol. The solution was sonicated for 60 min followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted with a 2propanol–n-heptane (50/50, v/v) mixture solvent in order to obtain concentration of 750 g/mL. For UHPLC, a quantity equivalent to 500 mg of amoxicillin was transferred to a 500.0 mL volumetric flask and dissolved with water. The solution was sonicated for 20 min followed by filtration with 0.20 m PTFE syringe filtration disks. Then the solution was diluted with water in order to obtain concentration of 100 g/mL. Three independent sample solutions were prepared for each analysis. All these solutions were prepared protected from light to avoid degradation of light-sensitive antibiotics. 2.3. Instrumentation 2.3.1. UHPSFC equipment A Waters Acquity UPC2® equipped with a PDA detector was used to carry out the UHPSFC experiments. The injector was equipped with a 10 L loop operating in the partial loop with needle
overfill mode, with methanol and methanol/2-propanol/n-heptane (1/4/5, v/v/v) as strong and weak needle wash, respectively. Chromatograms were recorded at wavelengths ranging from 210 nm to 400 nm with a step of 1.2 nm and with an acquisition frequency of 20 points/s. Peaks were integrated at a wavelength of 220 nm. The chromatographic columns employed in this study were a Acquity BEH 2-ethylpyridine (3 mm id × 100 mm, 1.7 m), a Acquity BEH 2-ethylpyridine (3 mm id × 50 mm, 1.7 m), a Acquity BEH (3 mm id × 100 mm, 1.7 m) all from Waters (Milford, USA), and a Kinetex Hilic (2.1 mm id × 150 mm, 2.6 m) from Phenomenex (Torrance, USA). 2.3.2. UHPLC equipment A Waters Acquity UPLC® equipped with a PDA detector was used to carry out the UHPLC experiments. The injector was equipped with a 10 L loop operating in the partial loop with needle overfill mode, with water/methanol (95/5; v/v) and water/methanol (5/95; v/v) as weak and strong needle wash, respectively. Chromatograms were recorded at wavelengths ranging from 210 nm to 400 nm with a step of 1.2 nm and with an acquisition frequency of 20 points/s. Peaks were integrated at a wavelength of 220 nm. The chromatographic column employed in this study was a Acquity BEH C18 (2.1 mm id × 50 mm, 1.7 m) from Waters. The UHPLC method used in the present study was described previously [21]. 2.4. Design of Experiments 2.4.1. Chromatographic screening design In order to select the appropriated stationary and mobile phase before the method optimization, a screening design was built. The factors were: stationary phase chemistry and modifier type. Bare silica, BEH silica and BEH 2-ethylpyridine were selected as stationary phases. Methanol and ethanol were selected as modifier. The objective was to maximize the chromatographic performances of SFC; for that purpose, sub 2 m or core-shell particles were selected. To evaluate the main effect of the factors and their interactions a full factorial design comprising 6 experiments was tested. The others chromatographic parameters were kept constant. The mobile phase flow rate was set at 2 mL min−1 . The analyses were performed in gradient mode, starting by an isocratic step (2 min, 5% modifier), then a gradient to linearly modify the co-solvent proportion from 5 to 20% in 5 min. The column outlet pressure and the temperature were set at 120 bars and 40 ◦ C, respectively. The autosampler temperature and the injected volume were set at 4 ◦ C and 5 L, respectively. 2.4.2. Method optimization design Method development was focused on the gradient profile optimization. Indeed, three factors were selected: the isocratic time (tiso ) before the gradient, the gradient time (tgrad ) to linearly modify the proportion of modifier and the proportion of methanol in the mobile phase at the end of the gradient (%MeOH). A total of 17 experiments were defined by a rotatable inscribed central composite design. The central point (i.e. tiso 1.5 min, tgrad 9 min, % MeOH 25%) was independently repeated three times. The 17 experiments were required to optimize the method and to assess the robustness. To our opinion, it is less experiment than making firstly the optimization and then performing the robustness study. Factors and their respective levels are summarized in Table 2. These factors were selected to investigate their effect on the selectivity, especially for the gradient time and %MeOH. Isocratic time should impact the separation of the less retained compounds. Very rapid equilibration between experiments led to perform the DoE on two days thanks to the additive-free mobile phase.
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Levels
tiso (min) tgrad (min) %MeOH
0.5 3 20
5
3. Results and discussion 3.1. Method development
0.9 5.55 22
1.5 9 25
2.1 12.55 28
2.5 15 30
The others factors were kept constant during the experimental design. As described in Section 3.1, the selected column was BEH 2-ethylpyridine with methanol as modifier. The mobile phase flow rate was set at 2 mL min−1 . The column outlet pressure and the temperature were set at 120 bars and 40 ◦ C, respectively. The temperature was not a factor of the DoE for two mains reasons: (i) the experimental domain is restricted taking into account the instability of antibiotics; (ii) it was not necessary to demonstrate the temperature robustness because all the SFC systems are thermostatically controlled. The column outlet pressure was fixed at a pressure SFC compliant enabling the use gradient involving large amount of modifier. Indeed, the elution of polar compounds in SFC could require using methanol or other co-solvent up to 40–50% in the mobile phase. The presence of methanol led to an increase of viscosity, the pressure in the system is higher than neat CO2 mobile phase. After the gradient, a 2 min isocratic plateau at the maximal value of %MeOH was applied to elute all the compounds and the column was reconditioned for 5 min prior to the next injection. The autosampler temperature and the injected volume were set at 4 ◦ C and 5 L, respectively. 2.5. Response modelling and Design Space computation As previously described [13,16], the retention times at the beginning, the apex and the end of each peak (respectively tB , tR and tE ) were measured. The studied response was the logarithm of the apparent retention factor termed kapp (i.e. log (ktR ) with kapp tR = (tR − t0 )/t0 , where t0 is the column dead time). These responses were modelled by a multivariate polynomial equation using a stepwise regression maximizing the adjusted coefficient of 2 ). The objective of this statistical approach is to determination (Radj obtain a high quality parsimonious model. Retention times were predicted using the developed model. Separation (S) was selected as critical quality attributes (CQA) [16,18], defined as the difference between the retention time at the beginning of the second peak and the retention time at the end of the first peak of a critical peak pair (i.e. S = tB2 − tE1 ). The errors obtained for the predicted retention times are propagated to the CQA. As described by Lebrun et al. [16], Monte-Carlo simulations were used to obtain the distribution of S from the joint posterior distribution of tB , tR and tE of the critical pair, for a given chromatographic condition. Considering the distribution of tR and S, the probability for S to be higher than 0 was used to compute the DS. Thus, the DS defines the sub-space of the experimental domain where the predictive probability to have S > 0 is higher than a predefined quality level. 2.6. Software JMP 10.0.0 was used to build the Design of Experiments. An algorithm was set up to develop a Bayesian model and to compute the DS using Monte-Carlo simulations. The algorithm was written in R 2.13, which is available as free-ware for most operating systems [22]. HPLC calculator [23] was used to perform the geometric calculations of UHPSFC and UHPLC method transfers. E-noval® V3.0 software (Arlenda, Belgium) was used to compute the results of the analytical validation.
3.1.1. Screening design results The objective of this screening was to find quickly chromatographic conditions for the method development design. The interest of adding additives in the mobile phase was previously described [24,25], especially in order to improve peak shape. However, in the present project, the aim was to fix chromatographic conditions without using additive in the mobile phase for three mains reasons: (i) modifier/CO2 mobile phase enables reduced equilibration and wash time of the column and then speed up the analysis protocol; (ii) several studies and the manufacturer’s recommendations suggested the adsorption or the modification on/of the stationary phase [26,27] leading to use one column with only one additive and then to increase the cost of method development; (iii) antibiotics are unstable compounds: basic pH and very acid pH lead to degradation of these compounds. Only three or four compounds were eluted on the Kinetex Hilic column (considering EtOH or MeOH as modifier) with very wide peaks. Seven compounds were eluted on the BEH column with MeOH as modifier; unfortunately, additive such as ammonia is often advisable to get good peak shape [25] especially for basic compound. Then, the combination of BEH 2-EP stationary phase and methanol as modifier was the unique combination enabling the retention and elution of all the compounds. 3.1.2. Optimization design results 3.1.2.1. Response modelling. The model was established using amoxicilline as model compound because it was the last eluted compound (more polar compound in the present study). Indeed, to our experience, the chromatographic behaviour of polar compound is really influenced by the conditions, i.e. the gradient slope and the modifier amount. Furthermore, on the basis of our knowledge of chromatography modelling, the peaks with higher retention times are more affected by predictive uncertainty. Thus, using amoxicilline as a model compound enabled to take into account the highest experimental and the predictive uncertainty. An original empirical model, described in Eq. (2), was developed involving the principal effects of the factors and their interactions. 2 log(ktR ) = ˇ0 + ˇ1 · tiso + ˇ2 · tgrad + ˇ3 · %MeOH + ˇ4 · tgrad
+ ˇ5 · tiso · tgrad + ˇ6 · tiso · tgrad · %MeOH + ε
(2)
where ˇ0 ,. . .,ˇ6 are the estimated parameters of the model and ε is the residuals of the model. The good agreement between the retention times predicted by the model and those observed demonstrate the good adequacy of the model (Fig. 1). The residuals were observed within the [−0.4; 0.4] minute interval; except one outlier value of −0.6 min. These residuals values include the experimental (analytical) and the model variability. The consideration of both variabilities (i.e. analytical and modelling) is required when predicting for robust optimization. Furthermore, using Monte-Carlo simulations from the prediction errors, the predictive probability for S to be greater than 0 min was calculated as shown in Fig. 2. These three images represent a two-dimensional probability surface with one of the factors being fixed at optimum. The DS ( = 0.38) is encircled by a black line. 3.1.2.2. Optimal separation. One optimal separation was identified at tg 12 min, tiso 2.3 min and % MeOH set at 22% with a minimal quality level of 0.38. The chromatogram recorded at the optimal condition is presented in Fig. 3. This figure illustrates the rather
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Fig. 3. Top: predicted UHPSFC chromatogram and predictive uncertainty (shaded grey area) at the optimal condition: tiso 2.3 min; tgrad 12 min; % MeOH 22%. Bottom: respective experimental chromatogram. Elution order: (1) caffeine; (2) clindamycine; (3) metronidazole; (4) doxycycline; (5) penicillin V; (6) trimethoprim; (7) levofloxacine; (8) amoxicilline.
3.2. Method transfer Fig. 1. Modelling results and corresponding residuals. Top: predicted vs. experimental retention times; bottom: corresponding residuals plots.
good adequacy between the predicted and observed sixth first peak of the chromatogram. Some differences could be observed between predicted and observed, especially for the antepenultimate and the penultimate compound. The variability of prediction was illustrated by simulated chromatograms taking into account the predictive uncertainty (shaded grey area). As shown in Fig. 3 this area is wider for the three last eluted peaks than the others, indicating a potential lack of prediction quality. This is corroborated by the value of the quality level; meaning that practically it is expected to obtain S > 0 with a probability not more than 0.4. Notice this probability calculation is often conservative as it accounts for model uncertainty. Better model could lead to a better probability of success, but empirical linear models have been preferred for their simplicity and easy understanding of factor effects. Nevertheless, the peaks were baseline separated at the experimental optimal condition. The DS strategy led to the optimization of a quality method to separate and detect several antibiotic drugs. Moreover, the DoEDS methodology used is fully QbD compliant in that the ways for improvement and better chromatographic behaviour understanding are identified.
In order to get a rapid method to perform routine analysis, the developed UHPSFC method was transferred to a shorter column. Moreover, the use of a shorter column (50 mm × 3 mm, 1.7 m instead of 100 mm × 3 mm, 1.7 m) enabled to work at higher flow rate (3 mL min−1 instead of 2 mL min−1 ) while keeping a quite similar pressure in the system in order to speed up a little be more the analysis. The geometric transfer was successfully performed using the three classical rules of LC method transfer thanks to the method sufficient robustness. However, the pressures measured on the two columns were slightly different (≈10 bars), impacting a little bit on fluid density and hence retention and selectivity are modified. Nevertheless, the amount of modifier used slightly decreased the influence of CO2 density on the polarity of mobile phase. Despite these changes on fluid density, previous work [19] showed the successful use of this methodology for robust SFC method transfer. In the same way, the LC method previously developed using DS strategy [21] was transferred to sub 2 m short column in order to compare UHPSFC and UHPLC methods. The two methods parameters are summarized in Table 3. 3.3. Validation To assess the validity of the UHPSFC and UHPLC methods, total error approach validation using accuracy profile based on tolerance
Fig. 2. Probability surfaces (i.e. P(S > 0)). (a) % MeOH vs. gradient time (min), (b) gradient time (min) vs. isocratic times (min), (c) %MeOH vs. isocratic time (min). The DS ( = 38.5%) is encircled by a dark line.
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Table 3 Summary of UHPSFC and UHPLC validated methods.
intervals was carried out [7–10]. The tolerance interval used is a ˇexpectation tolerance interval, which defines an interval where it is expected that a defined proportion ˇ of future results will fall. The accuracy profile coming from the method validation is represented in Fig. 4 where the plain red line represents the relative bias. The dashed blue lines represent the ˇ-expectation tolerance limits at 95% probability level, which links ˇ-expectation tolerance intervals calculated for each concentration level of the validation standards, taking into account their estimated intermediate standard deviation and their bias. If the ˇ-expectation tolerance limits are comprised in the predefined acceptance limits (black dotted lines) the method can be considered as valid and guarantees that every future result will fall in the acceptance limits with at least a probability previously defined. All the validation criteria required by ICH Q2 R1 guidelines are fulfilled using total error approach [10]. As showed in Fig. 4, the dosing range validated in UHPSFC is different than the one validated in UHPLC. The difference values between the methods are related the lower sensitivity of (UHP)SFC–UV than (U)HPLC–UV, mainly explained by the difference of solvating power between supercritical fluids and liquids. In this study, the method was validated prior to its use in a QC laboratory for the manufactured medicines control. The European Medicines Agency (E.M.A.) defined some specifications “the specifications for release of the finished product must be comply with the criteria defined by Directive 75/318/EEC as amended, i.e. ± 5% for the assay of active substance(s)”. Then, the acceptance limits were fixed at ±5% for the dosing range.
3.3.2. Trueness and precision Trueness expressed in term of relative bias (%) was assessed from the validation standards at five concentration levels. The precision was then determined by computing the relative standard deviation (RSD (%)) for repeatability and between-series intermediate precision at each concentration level of validation standards. The relative bias values and RSD are presented in Tables 4 and 5 for UHPSFC and UHPLC results, respectively. Regarding precision criterion, UHPLC method showed lower RSD values (
