QBD APPROACH TO ANALYTICAL METHOD DEVELOPMENT AND ITS VALIDATION FOR ESTIMATION OF LENVATINIB IN BULK AND PHARMACEUTICAL FORMULATION

Objective: The objective of this research was to develop a simple, very rapid, sensitive, accurate, precise reverse phase High-Performance Liquid Chromatography (RP-HPLC) technique for the estimation of Lenvatinib in bulk and its dosage form. Methods : To perform this study, we employed a central composite design (CCD) to make method robust and effective to create chromatographic database. The factor screening studies were performed using 2-factor 10-runs. The factors were selected as the mobile phase ratio and buffer pH. Results: The desirability value of the optimized model was found to be 0.869 and The optimized chromatographic condition was achieved on Enable C18 analytical column with 0.01M Ammonium acetate buffer pH 3.84: methanol (33.17:66.83 v/v) as the mobile phase and flow rate of 1 ml min-1 and detection wavelength was set to 240 nm. The retention time of Lenvatinib was found to be 5.122 min. Linearity was established for Lenvatinib in the range of 10-50 µg/ml with a correlation coefficient (r2=0.9995). The accuracy values were found to be in the range of 98–102%. Intraday precision and Interday precision were in prescribed (Less than 0.98% RSD). Robustness was found to be less than 1.22% RSD. Conclusion: The proposed method was useful for best analysis of Lenvatinib in Bulk pharmaceutical dosage forms. Central Composite Design was an effective tool for the proposed RP-HPLC method.

According to the previous study, we got bioanalytical method development, RP-HPLC method development and their validation, stability indicating method development etc but nobody went for statistical approach like Quality by design due that we selected Lenvatinib.
Quality by Design is a novel approach to estimate Lenvatinib in bulk as well as a pharmaceutical formulation. Central composite design gave runs for optimization. In this study, we selected no of mobile phases, pH of aqueous phase and flow rate. No one went for such a chromatographic variation and their observation.
Objectives of the present research were to develop routine analytical method development and its validation by using quality by design approach. We have used central composite design and quadratic model. We have succeeded in optimizing overall model with desirability 0.869.

Preliminary analysis of drug
Color and texture of Lenvatinib were compared with reported characters mentioned in the drug bank.
Solubility of Lenvatinib was determined sparingly soluble in acetic acid and slightly soluble in water, N, N-dimethylformamide, methanol, N-methylpyrrolidone, and pyridine. UV analysis was carried out by scanning the solution of Lenvatinib at 200-400 nm [1][2][3].

Central composite designs
The most popular response surface method (RSM) design is the central composite design (CCD). A CCD has three groups of design points: Independent factors are retention Time, peak area, theoretical Plate and peak asymmetry. The C 18 column has been selected for routine analytical method.
Factorial design has flexibility to change/add/delete any parameter at any time when our experiment is going on. it provides facility to give standard run at one time at only one mobile phase. Three independent factors have been selected. Mobile phases are selected as Buffer: Methanol, Water: Methanol and Water: Acetonitrile [4][5][6][7][8][9].
Dependent factors were selected as mobile Phase, pH of buffer and independent factors were retention time, peak area, theoretical plate and peak asymmetry. C 18 Column used for the separation of Lenvatinib. Mobile phases selected as phosphate buffer: acetonitrile, ammonium acetate buffer: methanol and water: methanol. Central Composite Factorial design facilitates only one mobile phase like ammonium acetate buffer: Methanol, change pH range: 4-6 mmol/l and change mobile phase proportion range: 60-70% (consider organic phase).
When all above ranges put in Central Composite design, it gave 10 run at different pH and Mobile phase proportion with flow rate is maintained constant at 1 ml/min followed by same procedure for each mobile phase. Total runs of design are 30. After completion of all trials, screening and optimization is done for best desirability value that is 1.00. Optimization means finding an alternative with the most cost effective or highest achievable performance under the given constraints, by maximizing desired factors and minimizing undesired ones. In comparison, maximization means trying to attain the highest or maximum result or outcome without regard to cost or expense. Trails suggested by software are as given in table no 4 [4][5][6][7][8][9].  [4][5][6][7][8][9].

Preparation of stock solutions of lenvatinib
Stock solution was prepared by dissolving 10 mg Lenvatinib in methanol and then diluted with methanol in 10 ml of volumetric flask to get concentration of 1000 µg/ml. From the resulting solution 0.4 ml was diluted to 10 ml with methanol to obtain concentration of 40 µg/ml of Lenvatinib and labeled as standard stock Lenvatinib [4][5][6][7][8][9].

Selection of detection wavelength
From the standard stock solution further dilutions were done using water and scanned over the range of 200-400 nm and the spectra were overlain. It was observed that drug showed considerable absorbance at 240 nm.

Optimization
Screening design for suitable chromatographic condition • Ammonium acetate buffer: Acetonitrile; Some peaks observed with high peak asymmetric factor, more retention time and less theoretical Plates: Overall observations were partially satisfactory.
• Ammonium acetate buffer: Methanol: Peaks observed with less peak asymmetry, less retention time and more theoretical plates: Overall observations were Extremely Satisfactory.
• Water: Methanol: Some proportions did not show peaks and some proportion did not have good peak properties: Overall observations were Dissatisfactory.

Effect of independent variables on retention time (X)
After applying experimental design, the suggested Response Surface Linear Model was found to be significant with model F value of 80.20, p value less than 0.005 and R 2 value of 0.9901. There is only a 0.04% chance that a "Model F-Value" this large could occur due to noise. Values of % C. V. and adjusted R 2 were 5.82 and 0.9778, respectively [4][5][6][7][8][9]. Fit summary: Surface Linear Model was suggested by the software.

ANOVA: ANOVA of developed central composite model for retention time (X)
Values of "Prob>F" (p-value) less than 0.0500 indicate model terms are significant. In this case A and C are significant model terms (table 3).

Effect of independent variables on asymmetric factor (Y)
After applying experimental design, the suggested Response Surface Linear Model was found to be significant with model F value of 7.59, p value less than 0.005 and R 2 value of 0.9047. There is only a 3.60% chance that a "Model F-Value" this large could occur due to noise.

Effect of independent variables on theoretical plates (Z)
After applying experimental design, suggested Response Surface Linear Model was found to be significant with model F value of 18.10, p value less than 0.005 and R 2 value of 0.9577. There is only a 0.75% chance that a "Model F-Value" this large could occur due to noise. Values of % C. V. and adjusted R 2 were 8.16 and 0.9048 respectively [4][5][6][7][8][9].

The equation for response surface quadratic model is as follows
Theoretical Plates =-3.09773E+005+9274.53098 *Mobile Phase+4091.85610 *pH of Buffer +136.60000 *Mobile Phase *pH of Buffer-73.19750 *Mobile Phase2-1536.68750 *pH of Buffer2 fig. 4 shows a graphical representation of pH of buffer (B) and amount of Methanol (A), as increases in pH does not showed change in retention time (X), but increase in amount of Methanol showed decreases the retention time.
Fit summary: Response Surface Quadratic Model was suggested by the software.

ANOVA: ANOVA of developed central composite model for theoretical plates (Z)
Values of "Prob>F" (p-value) less than 0.0500 indicate model terms are significant. In this case, A and C are significant model terms (table 5)

Method validation
The proposed HPLC method was validated in terms of system suitability, specificity, precision, accuracy and robustness as per the International Conference on Harmonization (ICH) guidelines (7).

System suitability
System-suitability tests are an integral part of method development and are used to ensure the adequate performance of the chromatographic system ( fig. 6) Retention time, the number of theoretical plates (N) and tailing factor (T) were evaluated for six replicate injections of the drug at a concentration of 40 µg/ml. The results which are given in table 7 and  table 8 were within acceptable limits [4][5][6][7][8][9][10][11][12][13]. Theoretical plates 12458

Specificity
The effect of excipients and other additives usually present in the dosage form of Lenvatinib in the determination under optimum conditions was investigated. Lenvatinib showed a peak at a retention time of 5.112 min. The mobile phase designed for the method resolved the drug very efficiently. The Retention time of Lenvatinib was 5.113±0.0098 min. The wavelength 240 nm was selected for detection because; it resulted in better detection sensitivity for the drug. The peak for Lenvatinib from the tablet formulation was Lenvatinib [4][5][6][7][8][9][10][11][12][13].

Robustness
Robustness is a measure of the capacity of a method to remain unaffected by small but deliberate variations in the method conditions and is indications of the reliability of the method. A method is robust, if it is unaffected by small changes in operating conditions. To determine the robustness of this method, the experimental conditions were deliberately altered at three different levels and retention time and chromatographic response was evaluated. One factor at a time was changed to study the effect. Variation of Wavelength and Temperature had no significant effect on the retention time and chromatographic response of the 40 µg/ml solution, indicating that the method was robust. The results are shown in table 12 [4][5][6][7][8][9][10][11][12][13].

CONCLUSION
Our current experiment illustrates the development and validation of a simple, rapid, and very sensitive RP-HPLC method developed for the determination of Lenvatinib in pure form and dosage forms. This developed experiment overcomes the drawbacks that have been found in the other reported method where no need to use the isocratic method, more retention time, and complex extraction for this simple method. Also, this method is money-saving as it needs less expensive instrumentations, solvents, and reagents. The high accuracy, precision, and sensitivity make this simple method be a reliable and reproducible method to be applied in quality control.