Multivariate optimization and evaluation of quaternary mixture in bulk and co-formulated dosage forms by central composite design

The current study describes the use of central composite design for multivariate optimization of resolution and retention time, taking into account different critical method parameters like organic phase, pH, flow rate, and wavelength for risk assessment. The chromatographic method for the assay of the most effective anti-viral regimen (EPCLUSA, DARVONI, and HARVONI) was developed. An experimental design was presented by sequential investigation of four independent parameters. The method was developed using XTERRA C18 (250 mm × 4.6 mm, 5 μm particle size) column in isocratic mode using potassium dihydrogen phosphate buffer (pH adjusted to 5) and acetonitrile (50:50 % v/v) as mobile phase at a flow rate of 1.0 ml/min and UV detection wavelength of 260 nm. The separation of four drugs with fine resolution and preferable retention times was achieved. Retention times of four drugs were found to be 2.96, 3.91, 7.15, and 11.94 min for daclatasvir, sofosbuvir, velpatasvir, and ledipasvir, respectively. The percentage accuracy of labelled claim was in the range of 99–102%, and the pooled %RSD for repeatability, precision, and accuracy was less than 2%. The suggested method was applied for quantification and identification of studied drugs in tablets; the results agreed with the label claim and were validated according to the ICH guidelines. The optimized method can be used for pharmacokinetic and quality control studies.


Background
The fast-developing resistance to anti-viral drugs due to rapid viral cell mutation in HIV and hepatitis C virus has garnered researchers worldwide to focus on combination therapy and in analysing the efficacy and toxicity of drugs that act on different targets. Over the past two decades, the researchers worked immensely to identify new molecular targets (structural and non-structural proteins), and trials were still going on to develop drugs which were selectively toxic to viruses without causing harm to the host cell. Researchers also aided in improving the efficacy of study by developing HCV replicon cell culture lines for pharmacokinetic and clinical investigations. Despite all the advancements, the anti-viral drug research was still running at a slower pace than expected, so it is the due responsibility of the analytical chemist to develop a method for simultaneous estimation of anti-viral drugs in clinical samples and dosage forms, to make the analysis of drug cost-effective, timesaving, and efficient to demarcate the toxic and therapeutic doses of drugs. The complexity involved in the analysis of effective anti-viral treatment regimen was eased by developing a single simple, robust, and selective analytical method for simultaneous assessment of antiviral drugs such as sofosbuvir, velpatasvir, ledipasvir, and daclatasvir using quality-based drug design principles.
HCV therapy was initially started using a combination of pegylated interferon and ribavarin drugs, until protease inhibitors boceprevir and telaprevir were identified as potent targeted therapies. Later, the advancement in diagnostic tools and molecular target discovery (NS5A, NS5B, and NS3/4A) brought to light drugs like simprevir. But the intense results in therapy were noticed only after the discovery of sofosbuvir. This potent molecule was now available in combination with different drugs such as velpatasvir, daclatasvir, and ledipasvir to treat hepatitis [1][2][3].
Quality by design (QbD) helps in understanding and monitoring the process based on quality risk management and sound science [9]. This method also offers a good regulatory flexibility compared to normal one factor at a time (OFAT) experiments [10]. QbD provides information about significant parameters of the method and their interactions in a broader prospect [11,12]. It helps to create a method operable design region which eases the work of the analytical chemist and regulatory bodies [13][14][15]. It also reduces the cost, analysis time, and the number of experimental trials [16,17]. The quality of HPLC methods has become increasingly important in a QbD environment [18,19]. Thorough literature studies indicated the availability of methods for the analysis of drugs individually or as a combination in a binary mixture, plasma or dosage form, but to date, no analytical method was tried to assay this quaternary mixture in bulk or dosage forms [20][21][22][23][24][25][26]. Thus, this article portrays important concepts, such as central composite design to analyse the four anti-viral drugs, i.e. sofosbuvir, velpatasvir, ledipasvir, and daclatasvir by RP-HPLC.

Chemicals and apparatus
The Shimadzu HPLC (Detector model: SPD20A, Pump model: LC-20 AD) with a UV-visible detector was used for the method development and quantification. LC solutions software was used for processing and monitoring the output signal. The chromatographic column XTERRA RP-18 (250 mm × 4.6 mm, 5 μm), rheodyne syringe loading manual sample injector (20 μl) was used for the analysis of drugs. The design used for the analysis of LC experiments was the Sigma Tech analytical QbD software. Shimadzu AUX 220 model analytical balance, Elico pH meter, and REMI model Centrifuge were utilized for this work. API (sofosbuvir, velpatasvir, ledipasvir, and daclatasvir) were obtained as a gift sample from Hetero Drugs Private Limited. Analytical grade potassium dihydrogen orthophosphate, sodium hydroxide, potassium hydroxide, di-sodium hydrogen orthophosphate, HPLC grade acetonitrile, and methanol were acquired from Merck, Mumbai. Pharmaceutical tablet dosage forms such as ECLUPSA, HARVONI, and DAR-VONI were procured from local pharmacies.

Preparation of mobile phase
Acetonitrile and potassium dihydrogen phosphate buffer, pH adjusted to 5.0, was taken in the ratio of 50:50 % v/v and filtered through a 0.45-μm membrane filter and sonicated to degas. Acetonitrile and water in the ratio of 50: 50 % v/v were used as diluents.

Preparation of standard solution
Ten milligrams of each standard drug was accurately weighed and transferred into four different 10-ml volumetric flasks, followed by the addition of 7 ml diluent to dissolve. The solution was then sonicated for 15 min and diluted to the mark with diluent to prepare a 1000-μg/ ml concentrated solution.

Chromatographic conditions
In order to study the effect of controlled input factors on responses, they were systematically varied in an experimental design known as "design of experiment" (DOE). DOE was twofold and comprises screening and optimization carried out sequentially [27]. Screening focuses on discriminating the critical method parameters using screening designs such as two-level full or fractional factorial designs in most cases. These designs screen the method parameters that have the ability to affect the analytical method response. The full and fractional design will explore many parameters by setting each on two levels, i.e. higher and lower. Its conclusion helps in identifying the most significant parameters among many others that were involved in the design.
Four variables were selected with their lower and upper values, using the Sigmatech software for screening, and 16 experimental trials were obtained. Based on the results, some of the variables were selected and fixed for the optimization. The selected significant factors are further studied using more comprehensive designs to set the most influential factors at levels that enhance analytical CQAs simultaneously. It provides a base for scientific understanding of the relation between quantities of input variables (CMP) and output response which will show a considerable effect on the method performance and ATP [17,19]. The central composite design was utilized to determine the significant variables and optimize the chromatographic conditions with the lowest number of runs. From the screening results, wavelength and organic phases were fixed as dependent variables, and % of organic phase, aqueous phase pH, and flow rate were selected as variables for optimization with its lower and upper values reported in Table 1. These variables were placed in the Sigmatech software, and 8 experimental trials were obtained. Based on the results, a method was developed with the optimized conditions. The chromatographic trials suggested by the system were performed using Shimadzu HPLC with XTERRA RP 18 (250 mm × 4.6 mm × 5 μ) column at UV detection wavelength 260 nm.

Method validation
The method operable design region (MODR) constructed from contour plots controls the variations in the response [11,28]. The optimized chromatographic method parameters were verified and validated as per standard guidelines [29][30][31][32].

Specificity
The spectra obtained from the synthetic mixture of standard solutions and commercial formulations were compared to assess the specificity of the method [33]. The chromatograms of blank, placebo, standard, and commercial formulations were examined to determine any additional peaks appearing at the retention time of sofosbuvir, velpatasvir, ledipasvir, and daclatasvir.

Linearity and range
Sofosbuvir aliquots of 0.6, 1.2, 1.8, 2.4, 3.0, and 3.6 ml were withdrawn from the stock solution 1000 μg/ml and were diluted to 10 ml such that the final concentration of sofosbuvir is in the range of 60-360 μg/ml. Velpatasvir and ledipasvir aliquots of 0.4, 0.6, 0.8, 1.0, 1.2, and 1.4 ml were withdrawn from their respective stock solution 1000 μg/ml and diluted to 10 ml with diluent such that the final concentration of velpatasvir and ledipasvir was in the range of 40-140 μg/ml. Daclatasvir aliquots of 0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 ml were withdrawn from the stock solution 1000 μg/ml and diluted to 10 ml with diluent such that the final concentration of daclatasvir in the range of 20-120 μg/ml was obtained; 20 μl of each concentration was injected, and a calibration curve was plotted by taking peak area on the Y-axis and concentration of drug on the X-axis.

Accuracy
The accuracy of the method was determined by spiking known concentration of standard drugs (80%, 100%, and 120%) to their respective formulation three times in a sequence. The parameters like percent recovery and per cent relative standard deviation of all the four drugs were calculated accurately to justify the study.

Precision
The drugs sofosbuvir (60,180, and 360 μg/ml), velpatasvir (40, 80, and 140 μg/ml), ledipasvir (40, 80, and 180 μg/ml), and daclatasvir (20, 60, and 120 μg/ml) were injected at each concentration level, and their peak areas were noted in triplicate on the same day and on three different days of the same week for intra-and inter-day precision studies. Parameters like per cent relative standard deviation in peak area and retention time of corresponding drug peaks were calculated as part of the validation.

LOD and LOQ
From the linearity data, the limit of detection and quantification was calculated using the following formula.
where σ is the standard deviation of the response, and S is the slope of the calibration curve of the analytes.

Preliminary studies
Authentication of drugs was done by determination of melting point, UV absorption spectra (λ max ), and FT-IR. The results of these studies were compared with the reference values and found to be within the limit of acceptance. The individual standard solutions (10 μg/ml) of four drugs in diluent (acetonitrile: water, 50:50 % v/v) were analysed in a UV spectrophotometer ranging from 200 to 400 nm. From the overlain spectrum of four drugs, the wavelength 260 nm was selected for estimation in order to get maximum responses for four analytes [29,33].

Screening studies
The critical process parameters such as organic phase, aqueous phase (pH), flow rate, wavelength, and interactions between the factors, which can affect the chromatographic responses such as theoretical plate number and retention time, were screened by using experimental design.

AQbD approach method optimization
In order to determine optimum chromatographic conditions, selected variables were screened using a factorial experimental design (2 3 ). Software-designed experimental  trials were performed with respect to three variables such as % organic phase (X 1 ), aqueous phase pH (X 2 ),and flow rate (X 3 ) to obtain theoretical plate number as method control response for four drugs. The software suggested central composite experimental design (CCD) was evaluated for the effect of individual factors on the response in the form of a contour plot.

Statistical analysis
Statistical analysis of experimental observations was performed to evaluate significant factors that affect the chromatographic response and were tabulated in Tables  2 and 3. Polynomial equations for the prediction of responses were obtained as follows (Eqs. 1 to 4) for sofosbuvir, velpatasvir, ledipasvir, and daclatasvir.
(Y-response of respective drug; b 0 -intercept; b 1, b 2 , and b 3 -regression coefficients of variables X 1 , X 2 , and X 3 , respectively; b 12 , b 13 , and b 23 -regression coefficients for two factor interactions between variables; and b 123 -  coefficient for three factor interactions between three variables). Statistical data analysis of sofosbuvir exhibited X 1 (% organic phase) as the significant factor owing to the highest SS ratio (85.815%) at b 1 combination. The negative sign of the coefficient indicates that the lower the % organic phase, the higher is the plate number of the chromatographic system. The next best SS ratio (5.8307%) was obtained at b 3 combination, i.e. X 3 variable, so the flow rate was also an important factor. The negative sign of the coefficient indicates that the lower the flow rate, the higher the response of the chromatographic system. The SS ratio (5.689%) was obtained at b 2 combination, i.e. X 2 variable, so the pH was also an important factor.
Statistical data analysis of velpatasvir, ledipasvir, and daclatasvir exhibited X 1 (% organic phase) as the significant factor owing to the highest SS ratios (90.19%, 90.94%, and 56.36%) at b 1 combination. The positive sign of the coefficient indicates that higher the % organic phase in the mobile phase, the higher is the response (theoretical plates number) of the chromatographic system. The SS ratio of velpatasvir and ledipasvir (4.39% and 4.16%) was obtained at b 13 combination, i.e.; X 1 X 3 variable, so the interaction of % organic phase (X 1 ) and flow rate (X 3 ) has an influence on the chromatographic system. The negative sign of the coefficient indicates that the lower the interaction, the better the response of the chromatographic system. The SS ratio of daclatasvir (12.206%) indicated pH as an influential factor.
Analysis of results (ANOVA) showed curvature effect was significant. The curvature effect showed a 95% confidence level. This indicates X 1 , X 2 , and X 3 along with interactions were highly significant at a 95% confidence level. Hence, it is mandatory to select a central composite design. The central composite design of sofosbuvir, velpatasvir, ledipasvir, and daclatasvir with its responses (theoretical plate number) was reported in Table 4.

Contour plot
The method was optimized based on contour plots drawn by varying % organic phase and pH keeping flow rate constant. The plots are as shown in Figs. 1, 2, 3, and 4. The % organic phase has a prominent effect on theoretical plate number for the four drugs and indicates that organic modifier above + 1 level (70%) and below −1 level (30%) decreases the response. The aqueous phase (pH) of the mobile phase showed a significant effect on the four drugs and indicates that pH above + 1 (7) and below −1 (4) decreases the response. Hence, % organic phase at mid-level and the pH at a lower level can be preferred to reduce the cost of the experiment.

Optimized experimental conditions
To optimize the HPLC parameters, several mobile phase compositions, changes in pH, and changes in flow rate     were attempted. A satisfactory separation of the drugs was obtained by XTERRA RP18 (250 × 4.6 mm, 5 μ) column eluted with acetonitrile and potassium dihydrogen phosphate buffer of pH 5.0 in the ratio of 50: 50 % v/v by isocratic elution pattern at a flow rate of 1.0 ml/ min with a detection wavelength of 260 nm for sofosbuvir, velpatasvir, ledipasvir, and daclatasvir.
The injection volume of 20 μl at 25°C temperature afforded the best separation of these analytes. The retention time was found to be 2.96 min for daclatasvir, 3.91 min for sofosbuvir, 7.15 min for velpatasvir, and 11.94 min for ledipasvir. The optimized method conditions were shown in Table 5. The chromatograms of trial methods were as shown in Fig. 5, and its peak results were reported in Table 6.

Method validation
The method was optimized and validated according to ICH Q2 (R1) [32] guidelines. A linear response was willful over the examined concentration range of 60-360 μg/ml for sofosbuvir, 40-140 μg/ml for velpatasvir, 40-140 μg/ml for ledipasvir, and 20-120 μg/ml for daclatasvir. Chromatograms of blank and placebo had a dearth of the peak at the retention time of title drugs indicated the specificity of the method. The accuracy of   the method was validated by recovery studies and was found to be significant under specification limits, with afforded recovery of 98.8-101% for sofosbuvir, 99-102% for velpatasvir, 97-105% for ledipasvir, and 96-105% for daclatasvir. The % RSD values for intra-day and interday precision were less than 2.0, which endorsed the good repeatability of the proposed method. Predicted response of optimized method parameters in the robust process (MODR of contour plot) was verified experimentally, and no significant change in retention time, peak area, and tailing factor and plate count by deliberate variations in method parameters was observed. The results of the system suitability test and validation were represented in Table 7.

Assay of marketed dosage form
The proposed method was evaluated by the assay of commercially available tablet dosage forms. The results obtained were compared with the corresponding labelled amounts and reported in Table 8. The % assay results of sofosbuvir and velpatasvir in EPCLUSA was found to be 102.7% and 100.2%, sofosbuvir and ledipasvir in HAR-VONI found to be 102% and 98.9%, and % assay of sofosbuvir and daclatasvir in DARVONI was found to be 102% and 101.7%, respectively. The %RSD was less than 2, which indicates the accuracy of the proposed method. The assay chromatograms of respective drugs were shown in Figs. 6, 7, and 8, respectively.

Discussion
The rising need for multi-drug anti-viral therapy shapes novel challenges in analytical research. The complexity in separating the drugs with different physico-chemical properties from the quaternary mixtures and applying them to the pharmacokinetic study was eased by AQbD.
The research mainly focused on developing a method that has very little run time in just 16 experimental trials, which makes it more sustainable. The statistical outcomes also granted excellent linearity and specificity. The merits of the method such as low LOQ, high resolution, and good theoretical plate number compared to some peer journals [21][22][23][24] suggest its use for in vitro and in vivo characterization of novel formulation and in quality control. The central composite design suggested an increase in flow rate to obtain high resolution, and acidic pH in separating the basic components is good due to their more likeliness for protonation/ionization. The method catches its credibility by showing a resolution (> 2), tailing factor (0.9-1.2), capacity factor (1-10), number of theoretical plates (> 2000), and very good HETP.

Conclusion
To our present knowledge no trials have been made yet to assay all four anti-viral drugs in a mixture. So, the robust, reproducible, sensitive, specific, inexpensive analytical method for simultaneous assessment of anti-viral drugs in co-formulated dosage forms has been developed using a central composite design. The proposed single (low consumption of solvent) analytical method can be employed for routine quality control analysis and pharmacokinetics studies of combined anti-viral drugs of sofosbuvir/velpatasvir, sofosbuvir/ledipasvir, and sofosbuvir/daclatasvir simultaneously.