Advancing Quality and Environmental Responsibility: A Stability-Indicating LC Method Development for Lenvatinib Through QbD and Green Chemistry

A Quality by Design (QbD) systematic and analytical approach was used to develop a novel and sensitive Lenvatinib stability-indicating method. The ICH Q1A(R2) and Q3 guidelines were implemented to determine Lenvatinib degradation behavior under various environmental conditions. The QbD approach implementation has screening and optimization stages.The Placket–Burman design was used to assess primary parameters, and Response Surface Design (RSD) to optimize critical factors. The drug degradation was examined under different degradation conditions, including acidic, basic, oxidative, neutral, thermal, and photolytic conditions. Separation was achieved using a Shimadzu® C18 column (250 mm × 4.6 mm, particle size 5 µ) with the mobile phase consisted of Acetonitrile: 10 mM ammonium acetate at pH 3.5 (39:61, v/v) at a flow rate 0.8 mL/min. The run time was 20 min and the wavelength used was 245 nm. The drug found sensitive toward acid and base hydrolysis, resulting in the generation of five degradation products. These products were successfully identified using the optimized LC–MS compatible analytical method. The optimized method was found to be sensitive, reproducible, specific, and robust, with a linearity range of 10 to 60 mg/mL and a correlation coefficient (R2 = 0.9993). The greenness score of the analytical method was calculated, revealing that the developed method is environmentally friendly.


Introduction
The Stability-Indicating Method (SIAM) has gained recognition for its significance in various areas, such as product quality assurance, regulatory compliance, formulation optimization, customer satisfaction, and batch-to-batch variation correction.The SIAM is an established analytical testing approach used to detect process impurities and degradation products in active ingredients, following specified product specifications.Its application ensures product quality, regulatory adherence, optimized formulations, customer confidence, and the rectification of batch inconsistencies [1].Regulatory guidelines, such as ICH Q1A (R2), ICH Q3B (R2), Q6A, and FDA 21 CFR Section 211, require the validation of stability-indicating methods [2].Recent drug recalls, such as Advil, Delsam ointment, and Acyclovir tablets, have been caused by stability-indicating issues during storage, highlighting the importance of determining the distance between the drug peak and potential degradation product peaks [3].These recalls also raise concerns about the reliability and safety of the pharmaceutical industry as a whole.Stability testing is a critical component in assessing the efficacy of drugs or medications, as the average shelf life of chemical compounds is only 3-5 years due to degradation from environmental factors like heat, light, humidity, and pH [4].The International Conference on Harmonization (ICH) guidelines provide standardized procedures that consider safety, efficacy, and quality factors.Stability-indicating methods are essential for analyzing the impact of chemical, physical, or microbial variables in various environmental conditions on the efficacy and integrity of the final formulation [5].
Lenvatinib is an inhibitor of multiple tyrosine kinase receptors [VEGFR-2 (KDR), VEGFR-1 (FLT1), FGFR-2, FGFR-4, and FGFR-3] and is primarily used as a firstline treatment for unrespectable hepatocellular carcinoma (HCC) [6].It is also approved for the treatment of radioactive iodine-refractory differentiated thyroid cancer (DTC) and advanced renal cell carcinoma (RCC).Additionally, it is used in combination therapy with Everolimus for advanced RCC treatment [7,8].Lenvatinib is slightly soluble in methanol and completely soluble in acetonitrile and acetone, but very slightly soluble in water.Chemically, it is 4-{3-chloro-4-[(cyclopropylcarbamoyl)amino]phenoxy}-7-methoxyquinoline-6-carboxamide, with a pKa value of 5.05 and a log P value of 3.30 (Fig. 1) [9].However, under certain environmental conditions, functional groups, such as quinoline, methoxy, phenoxy, and amide, can be susceptible to degradation.Therefore, it is important to investigate the critical variables that affect the generation, separation, and qualification of degradation products using appropriate techniques.This research can help determine the expiry date, reset window, and storage conditions of the final product and provide necessary packaging specifications for handling Lenvatinib [10,11].
The QbD approach is utilized for the development of a stability-indicating method for the API of Lenvatinib.Employing QbD principles to the production and delivery of pharmaceutical products and services under a SIAM framework can guarantee that products meet required quality standards and comply with regulatory requirements.ICH Q8 guidance defines the concept of QbD, which is dependent on scientific and risk-based product development with predefined objectives to mitigate challenges, such as inconsistency in quality, product performance, and robustness [12,13].This approach has garnered the attention of regulatory bodies and the pharmaceutical industry as it helps achieve well-defined objectives and ease of risk management.The scientific knowledge acquired can be used to select method controller settings and manage identified risks [14,15].To ensure an impact on the methods developed, green analytical methodology is necessary for analytical research, and the importance of green methods is rapidly growing across various analytical procedures [16].The goal of green analytical chemistry is to provide a safer and cost-effective analytical technique.The methodology reduces the cost of method development by minimizing the quantity of solvent employed and eliminating solvent waste [17,18].The environmentally friendly analytical chemistry procedure involves analyzing the smallest possible samples with the smallest sample size possible [19,20] QbD and Green Chemistry can help develop analytical methods that are more efficient, effective, and environmentally friendly.By considering the impact of critical factors on the quality of the method and the environment, QbD and Green Chemistry can ensure that analytical methods are developed with the right quality attributes, while minimizing the use of hazardous substances and waste [21][22][23].The utilization of 12 principles to assess the environmental friendliness of an analysis technique, employing resources like the National Environmental Methods Index (NEMI) is being revamped through the development of a novel tool known as GAPI (Green Analytical Procedure Index) [24].This advanced tool evaluates the greenness of an analytical method across various stages, ranging from sample preparation to final method optimization.Parameters, such as waste generation, energy consumption, sample automation and downsizing, sample quantity, and reagent toxicity, are all taken into account within the AGREE scale, a specialized evaluation tool used to assess analytical greenness.Experts in the field of "Green Chemistry" employ or devise efficient assessment methods that eliminate waste and solely employ non-hazardous chemicals [25,26].
In-depth drug literature revealed that only a limited number of articles focused on the stability study of Lenvatinib.The Indian Pharmacopeia includes a monograph on Lenvatinib; however, it lacks data on impurities.The related substance method described in the Indian Pharmacopeia employs phosphate buffer with gradient programming.Nevertheless, the SIAM (Stability-Indicating Assay Method) developed by Jahnvi Bandla et al. for Lenvatinib incorporates a derivatizing agent, ortho-phosphoric acid, as a mobile phase.This choice makes it less than optimal for effectively resolving degradation peaks under diverse stress conditions [27].Pratiksha Bang et al. reported the development of an HPTLC (High-Performance Thin-Layer Chromatography) method to assess the stability of Lenvatinib by isolating and identifying two degradation products.However, the increased use of organic solvents in this method had a detrimental impact on the GAC (Green Analytical Chemistry) score.Furthermore, the method did not achieve the desired level of effectiveness in separating all degradation products [28].Additionally, Maheen Sultana et al. developed a UPLC (Ultra-Performance Liquid Chromatography) technique for simultaneous quantification of Lenvatinib and Dasatinib impurities.However, the method employed sodium phosphate buffer, which is incompatible with LC-MS/MS (Liquid Chromatography-Mass Spectrometry/Mass Spectrometry) studies.Moreover, the proposed technique failed to separate all potential degradation products of Lenvatinib [29,30].
All previous research and pharmacopeia references lack method efficiency, effective separation of degradation products, and a green technique compatible with LC-MS/MS.Therefore, the objective of this study is to establish new stability-indicating analytical procedures (SIAM) utilizing the QbD approach.By adopting this approach, companies can ensure that stability methods meet criteria, such as peak resolution, robustness, selectivity, specificity, and accuracy, which are essential for product approval and drug quality monitoring.
With that in mind, our aim was to develop a novel isocratic HPLC mass compatible method that is environmentally friendly and employs the QbD approach to separate all degradants in compliance with ICH standards, taking into consideration the multivariate approach and green chemistry, which is emerging as a trend in the analytical field.

Chemicals and Reagents
A gift sample of Lenvatinib (99.9% purity) was received from Intas Pharmaceuticals Limited, located in Ahmedabad, Gujarat, India, along with a certificate of analysis.HPLC-grade methanol (MeOH) and acetonitrile (ACN) were procured from SD Fine Chemicals in Mumbai, India.HPLC-grade water was prepared by filtering collected milli-Q water using the Millipore Milli-Q Plus system (Millipore, Milford, MA, USA).Analytical-grade ammonium formate (NH 4 HCO 2 ), formic acid (HCOOH), hydrochloric acid (HCl), sodium hydroxide (NaOH), and hydrogen peroxide (H 2 O 2 ) were sourced from Research-Lab Fine Industries in Mumbai.

Equipment and Instruments
The Shimadzu LC 2010 CHT High-Performance Liquid Chromatography was utilized, along with an autosampler and a Photodiode array (PDA) detector equipped with Lab Solutions software, for the acquisition and analysis of chromatographic data.The Lab India pH meter was employed to monitor the buffer pH, while the sample compounds were weighed using the Presissa XB220 analytical balance from India.For the degradation studies, a high precision water bath with a temperature controller was obtained from Meta-Lab Ltd (Mumbai, India).To identify the functional group, Fourier-Transform Infrared Spectrophotometer (FTIR-RX1) was utilized.The mobile phase was filtered using 0.45 µm membrane filters.Electrosonic industries (Mumbai, India) provided the Ultrasonic bath (L-45) used for sonication of the HPLC mobile phase.Thermal degradation was conducted using a hot air oven from Meta-Lab Ltd (Mumbai, India).The method was optimized using State-Ease Design-Expert software version 13.0 ® , licensed version.

Solution Preparation
Preparation of Standard Solution 10 mg of Lenvatinib was weighed accurately, dissolved in acetonitrile (1 mL), and then diluted with methanol to make a final volume of 10 mL, resulting in a concentration of 1000 µg/mL (stock solution).From the stock solution, 1 mL was pipetted out and transferred into a 10 mL volumetric flask.It was further diluted up to 10 mL with the respective stressor, resulting in a concentration of 100 µg/mL.

Preparation of Working Solution
10 mg of Lenvatinib was weighed and transferred into a 10 mL volumetric flask.Stressors, such as HCl, NaOH, and H 2 O 2 , were added to create a 1000 ppm solution.The sample was placed in a round bottom flask and the flask was then immersed in a water bath at a specific temperature.Samples were collected at designated time intervals (0 min, 6 h, 12 h).Subsequently, the collected samples of HCl and NaOH were neutralized using the opposite stressor, and another sample was diluted with ACN to a final volume of 1 mL, resulting in a 100 ppm solution.These 100 ppm solutions were then injected into an HPLC and LC-MS system for further analysis.

Solution Preparation for Degradation Study
Stressor solution preparation -To prepare a 1 N HCl solution, 8.8 mL of HCl was dissolved in 100 mL of Millipore water.Subsequently, a series of dilutions were prepared to obtain 0.1 N and 0.5 N HCl solutions.This was achieved by dissolving 0.88 mL and 4.4 mL, respectively, from the stock solution in 100 mL of Millipore water.To prepare a stock solution of 1 N NaOH, 0.4 g of NaOH was dissolved in 100 mL of Millipore water.To produce 0.1 N and 0.5 N HCl, a series of dilutions were made by dissolving 0.4 g and 2 g of the stock solution in 100 mL of Millipore water, respectively.A 3% H 2 O 2 solution was prepared by adding 2.3 mL of hydrogen peroxide (H 2 O 2 ) to 100 mL of Millipore water.Similarly, a 5% H 2 O 2 solution was prepared by adding 3.9 mL of H 2 O 2 to 100 mL of Millipore water, and a 10% H 2 O 2 solution was made by adding 7.8 mL of H 2 O 2 to 100 mL of Millipore water.
Lenvatinib (10 mg) was accurately weighed and transferred into a volumetric flask.To dissolve the API, 2 mL of acetonitrile was added to the flask.The volume was then adjusted to 10 mL by adding the relevant stressors, resulting in a concentration of 1000 µg/mL.At predetermined intervals, 1 mL of the solution was collected and diluted to 10 mL with a mixture of (ACN:Water; 50:50, v/v) to create a working solution with a concentration of 100 µg/mL.Hydrolytic degradation experiments (acidic, alkaline, and neutral) were conducted at temperatures of 60 °C, 70 °C, and 80 °C.After the acid and alkaline degradation experiments, the samples were promptly neutralized to minimize the potential for secondary degradation.The impact of different concentrations of H 2 O 2 (1%, 6%, and 10%) on oxidative degradation was investigated.For thermal degradation, solid samples were placed in an oven at 80 °C for 12 h.Photolytic degradation was achieved by exposing solid-state and solution samples (ACN: water, 50:50, v/v) to light.

Implementation of Quality by Design Approach for SIAM Method Development
Pharmaceutical Quality by Design (QbD) is an analytical approach to pharmaceutical method development that is systematic, comprehensive, and risk-based.It focuses on achieving predefined goals and emphasizes the importance of process control for stability-indicating analytical method development (SIAM) [31,32].The term Analytical Quality by Design (AQbD) refers to the development of analytical methods using the quality by design approach [33].In AQbD, the first step involves identifying the Quality Target Product Profile (QTPP), the analytical target profile (ATP), Critical method attributes, and Critical method parameters [15,34], as shown in Table S1.
Lenvatinib (100 µg/mL) evaluated at various forced degradation conditions.The analysis revealed the drug's susceptibility toward acidic and alkaline hydrolysis.Among these conditions, the acid hydrolysis resulted in the highest percentage of drug degradation with formation of degradation product peaks.Consequently, a solution of 100 µg/ mL acid hydrolysis was selected for further screening and optimization.In the screening and the optimization designs, peak resolution was employed as the response variable.This measure served as an indicator of how effectively the stability-indicating technique separated the drug peak from the degradation peaks.In line with ICH Q9 guidelines, critical factors must undergo evaluation through risk identification and ranking.This process allows the determination of the factors that pose the greatest threat to the success of the critical factor methodology [35].

Risk Assessment
Critical method parameters (CMPs) refer to high-risk variables identified through risk assessment, which have a significant impact on the listed Critical Analytical Attributes (CAAs) [36].By conducting a risk assessment, various critical parameters that affect the method's performance and their underlying causes were identified [37].Analytical method development is influenced by method parameters, instrumental settings (such as reaction time, solvent preparation, sample preparation, flow rate, mobile phase ratio, and chromatographic mode), and other factors.Considering their criticality and their influence on the CAAs of the method, high-risk method factors were identified and further investigated using an appropriate screening and experimental optimization strategy [38].

Screening Using Plackett-Burman Design
After the establishment of Quality Target Product Profiles (QTPPs) and Critical Quality Characteristics (CQAs), the ICH Q9 quality risk management tool was employed to screen key parameters [39].The risk assessment tool, along with the Ishikawa (Fishbone) diagram, identified eleven significant factors that required further analysis using the Plackett-Burman design (Design-Expert 13).As the resolution is a critical response variable among all peaks, it was examined as the response variable.The design findings were converted into Pareto charts and half-normal plots to demonstrate how the independent component influenced the required response.Crucial elements were identified and implemented to create a responsive surface for the optimization approach [40].

Response Surface Optimization
Following the initial screening phase, an influential factor that significantly impacted the response variable, specifically the peak resolution, was recognized.This finding sparked an additional investigation into secondary parameters.To explore these additional measures, Response Surface Design (RSD) methodology was employed [41,42].The use of Response Surface Design (RSD)-optimal design enables the examination of the impacts and interrelationships among various factors on one or multiple response variables.In this study, a design consisting of 25 trials was implemented to assess the resolution as the response variable.Statistical computations, such as ANOVA analysis, model development, desirability plot analysis, derivation of polynomial equations, contour plot analysis, as well as the calculation of F-values and p-values, were conducted using Design-Expert v13, which is a process-oriented approach to performance management [43].To optimize chromatographic parameters, a four-factor and five-level Response Surface Design (RSD) was employed to estimate the primary interaction and quadratic effects of the factors on the critical response variables [8].

Method Validation
The proposed method for assessing stability has been demonstrated to comply with the ICH guideline Q2 (R1).To evaluate the system suitability variables of the proposed method, including peak area, asymmetry, theoretical plate, and retention time, the % RSD data were calculated based on five replicate standards.To establish linearity, six replicates (n = 6) were conducted at each dosage using serial dilutions of the acid degradation solution across a concentration range of 10-60 mg/mL.Accuracy, which measures the consistency of results obtained from the analysis method, was determined by running triplicates at 20, 40, and 60 ng/mL for three consecutive days (Interday and Intraday).The accuracy of the method was also tested by spiking three different concentrations of the substance (80%, 100%, and 120% of the drug) and determining the proportion of recovery for each sample solution.Limits of detection (LOD) and quantification (LOQ) were established by analyzing a series of known concentrations within the linear range, with a signalto-noise ratio of 3:1 for LOD and 10:1 for LOQ.Samples were prepared, injected into the system, and the detection and quantification limits of the system were verified based on the calculated theoretical values.Precision was assessed by evaluating the method's ability to detect a wide range of other factors, such as degradants, excipients, impurities, and more [44][45][46].

Preliminary Analysis
The initial investigation into the degradation analysis involved an extensive review of published literature, with a focus on developing a chromatographic method to detect and measure Lenvatinib.Utilizing water and water with 0.1% formic acid as the aqueous phase, and methanol and acetonitrile as the organic phase, and employing a flow rate ranging from 0.6 to 1.2 mL/min, various combinations of mobile phases were tested.Preliminary high-performance liquid chromatography (HPLC) tests demonstrated that using a buffer as the aqueous phase enabled the separation of degradation peaks from the substance.To determine the appropriate pH of the buffer, the pKa value of Lenvatinib, which is 5.05, was utilized as a guideline, as peak separation requires a buffer pH within two units of the drug's pKa value.All the initial assessment data was collected and thoroughly examined, with a comprehensive study conducted on the Quality Target Product Profile (QTPP), Critical Quality Attributes (CQA), and Critical Material Attributes (CMAs) as shown in Table S1.

Placket Burman Screening Design
The ICH Q9 guideline was used for the risk assessment and analysis.Screening method include primary parameter screening and secondary parameter screening.A Fishbone diagram (Fig. 2), was developed using the specified Critical Quality Attributes (CQA), Critical Process Parameters (CPP), and Critical Material Attributes (CMA) (Table S1).The selected parameters were studied for risk assessment.A Systematic risk assessment, significant process variables and essential techniques that may influence potential CQAs were identified as secondary parameters as shown in Fig. S1.These secondary parameters were studied with a Plackett-Burman design to screen the most significant parameters, which have influence on chromatogram system suitability parameters.Total selected eleven factors with two levels were studied based on design suggested by software as shown in Table 1.Each factor was assigned a level of high, moderate, or low relative chance, indicating its impact on the selected response variable.The independent variables were isolated through a series of brief experiments following a two-level, multifactorial approach.It is crucial to have resolution between degradation products and drug hence resolution was considered as response variable.The eleven factors were identified and studied at two levels: low (− 1) and high (+ 1).These factors included mobile-phase organic composition, pH, column temperature, flow rate, degradation sample duration, type of buffer, wavelength, column length, type of organic phase, and type of column.According to preliminary results, the Lenvatinib found less stable with methanol.Therefore, acetonitrile (ACN) and methanol (MeOH) were studied as categorical factor "type of organic phase" and studied at two levels in this study.
A method development involves using a mobile phase with a different proportion of the aqueous phase compared to the organic phase.In the initial experiments, when water:ACN was used as the mobile phase, the degradation peak of the drug was not effectively separated.To address this issue, ammonium acetate (AA) and ammonium formate (AF) were selected as volatile buffers due to their compatibility with the LC-MS/MS technique and were further investigated.The buffer pH was chosen in the range of 2 pH, with ammonium acetate (pKa = 4.76) and ammonium formate (pKa = 3.74) used as starting materials.Two different mobile phase ratios of organic phase:aqueous phase ((30:70, v/v), (− 1) and (40:60, v/v), (+ 1)) were selected as factors for comparison.Since the resolution and peak separation depend on the mobile phase pH, values of 3.5 (− 1) and 4.0 (+ 1) were chosen based on drug pKa value.The flow rate of the mobile phase investigated was 0.8 mL/min (− 1) and 1.0 mL/min (+ 1).The column chemistry, which involves multiple cross-linked carbons, alters the polarity of the silica within the column, thereby influencing chromatographic separation.The Van Demeter equation relates the linear velocity of the mobile phase to the variation per unit length of the separation column, taking into account its physical, kinetic, and thermodynamic properties.Two different column sizes and types were examined, both with a fixed diameter of 150 cm (− 1) and 250 cm (+ 1).Using both relatively polar (C8) and nonpolar (C18; Shimadzu, 4.6 × 250 mm, 5 µ) columns, reducing the column diameter reduces the amount of organic solvent required to establish the environmentally friendly method.Since the C18 column is more hydrophobic, it allows increased interaction between the confined mobile phase and the analyte.As a result, the sample elutes more slowly and separates more distinctly.Peaks obtained using the C8 (or octadecyl) column are more pronounced and have a shorter retention time.Tri-fluoroacetic acid (TFA) and acetic acid (AA) were selected for their ability to modify the peak structure.The peak purity index and the absorbance depend on the wavelength of the drug and its degradation product.Therefore, two wavelength maxima, 200 nm and 250 nm, were chosen for Lenvatinib and tested.According to Van't Hoff's equation, the column temperature affects the viscosity of the mobile phase, leading to changes in adsorption energy and thus altering the drug's retention time.Furthermore, increasing the column temperature raises the dielectric constant, causing the aqueous component of the mobile phase to behave more like an organic solvent, thereby reducing the amount of organic solvent needed.Therefore, experiments were conducted at temperatures of 10 °C (− 1) and 30 °C (+ 1).As shown in Table S2, all of the aforementioned variables were evaluated at two levels with 8 hours and 12 hours of samples of degradation.
Additional samples were examined and subjected to HPLC analysis using Design-Expert v13.The Pareto chart tool was employed to identify the most important variables.Pareto charts provide a visual representation of the relationship between the length of each bar and the regression coefficient, which are derived from multivariate regression analysis.The statistical parameters Bonferroni limit and t-value were utilized to identify secondary parameters that required further optimization.From the statistical analysis, it was determined that the concentration of the stressor, degradation sample, column type, column length, detection wavelength, and column temperature had only marginal effects.Therefore, these variables were kept constant for further research.The conventional Pareto ranking analysis revealed that variables, such as mobile phase organic composition, buffer pH, flow rate, and column temperature, had a significant impact on the method's critical analytical attributes (CAAs).Consequently, these factors were selected as critical method parameters (CMPs) and were subjected to a comprehensive analysis for analytical optimization using Design-Expert v13 response surface design.The Plackett-Burman screening design, coupled with the desirability function, was employed to identify the main, interaction, and quadratic effects of these variables on parameters, such as retention time, peak area, peak tailing factor, theoretical plates, and peak separation.

Method Optimization by Response
The secondary parameter screening was further carried out by Plackett-Burman design that revealed, the mobile phase composition, buffer pH, flow rate, and buffer type are critical variables that need further optimization.Using the expert v13 response surface matrix, fewer experimental trials were required without compromising the model's orthogonal nature to select the optimum design.Response surface design is utilized in order to optimize the specified four parameter at two levels.The four critical factors at five levels studied with optimal response surface design having 25 experiments.The selected parameters are examined throughout in the range from low to high, as shown in Table 2.The selected four critical factors were (A) Mobile-Phase Organic Composition (Organic: Buffer; v/v), (B) buffer pH; (C) Flow rate (mL/min), and (D) Column Temperature.To optimize four components for three levels, the response surface design is employed.Selected response variable was degradation peak resolution relative to drug peak resolution.The objective was to examine the main effect, interaction effect, and quadratic impacts of key factors on a subset of response variables, including resolution between degradation peaks RS I, RS II, RS III, and RS IV, where RS I defines resolution between peak 1 and peak 2 of degradant.
All the trials listed in Table 3 were conducted, and the resolution values were collected for numerical and graphical optimization purposes.A mathematical model was created for each response variable (RS I, RS II, RS III, and RS IV), and ANOVA was performed to carry out statistical calculations.The statistical values for the model p-value, R 2 , and adjusted R 2 were examined to determine the significance of the models, as shown in Table S3.The calculated R 2 values for all response variables were close to 0.8, indicating that the models could explain a significant amount of variation in the responses.The summary statistics from the quadratic mathematical model indicated that the R 2 and adjusted R 2 values for all response variables were reasonably consistent.The polynomial equation expresses the response variables in terms of factor additions and subtractions.The coded polynomial equation and the p-value indicate that four factors have a significant influence on each response variable.Based on the statistics presented in Table S3, the fitted model showed a good fit to the experimental results, with a p-value less than 0.05 and a lack-of-fit greater than 0.05.
The design generates the polynomial quadratic equation, as shown in Table S3.The equation provided is a mathematical expression that represents a linear regression model with multiple variables.It can be interpreted as follows: In the given equation, factors D, AB, AC, AD, C 2 , and D 2 have positive coefficients, indicating a positive relationship.This means that an increase in these variables is associated with an increase in the predicted value of Y. On the other hand, factors A, B, C, BC, BD, CD, A 2 , and B 2 have negative coefficients, indicating a negative relationship.This means that an increase in these variables is associated with a decrease in the predicted value of Y. Overall, this equation represents a predictive model where the value of Y is estimated based on the values of the independent variables (A, B, C, D) and their interactions, taking into consideration both linear and nonlinear relationships between the variables.
The model was statistically significant and utilized for both numerical and graphical optimization purposes.By employing software-based numerical optimization, multiple predictions of variable desirability were generated.The HPLC injection of the sample was conducted under specific conditions to achieve a desirability value of 1, allowing for a comparison between the anticipated (software) and actual resolution, as shown in Fig. 3. Consequently, critical parameters, such as mobile phase composition (X1) and pH (X2), were chosen for optimization, while the Flow rate (X3) and Buffer type (X4) were set to 0.8 mL/min and ammonium acetate (AA), respectively.The influence of factors X1 and X2 on the resolution, acting as the response variable, was illustrated through the counterplot depicted in Fig. S2.Further optimization was carried out graphically, incorporating constraints.The design space displayed in Fig. 4 represents the robust working area that fulfills the requirement of a stability-indicating method, with a resolution value exceeding 1.5 between each peak.
The overlay plot highlights the yellow zone, indicating the optimal conditions for the procedure as provided by the  design expert software.Within this range, the Lenvatinib stability indication approach is deemed the most reliable and feasible.The optimal conditions for this approach were found to be a mobile-phase composition of [(ACN: 10 mM of ammonium acetate buffer, pH optimized to 3.5 using acetic acid) (39:61; v/v) at 0.8 mL/min, for run time 20 min], which attained a desirability of 1.0, as shown in Fig. 6.Through graphical and numerical optimization, the projected optimum solution was achieved within the operable analytical design space.The enhanced risk assessment, presented in Fig. 5, adopts a systematic approach to mitigate components with high severity.Both the experimental study and revised risk assessment data indicate that all factors pose moderate to low risk.

Control Strategy
The final stage of QbD implementation is the control strategy.Each component that was found to affect the drug's stability or a crucial process parameter was analyzed, and the acceptable ranges for each were explained.The results and the statistical calculations were used to settle on the proposed range of factors.Scientists are aided in gaging the method's reliability, and repeatability using the data of control Strategy.The control strategy is a critical component of QbD that ensures consistent product quality, reduces variability, facilitates continuous improvement, and meets regulatory requirements.As shown in Table 4, the optimized method with applied control strategies found sensitive and proficient to separate degradation peaks from drug peak with more than 2 resolution in all forced degradation conditions.The stability of the drug and its degradation products were examined using the optimized chromatographic conditions.By utilizing the optimized chromatographic conditions and chromatograms, the drug's stability and degradation were analyzed under all degradation conditions.Lenvatinib was found to degrade during acid hydrolysis, alkaline hydrolysis, peroxide degradation, photolytic degradation, and thermal degradation.Different degradation products (DPs) were identified under various degradation conditions, and their names were based on their retention time.Figure 6 illustrates the chromatogram of Lenvatinib under various degradation conditions, including acid hydrolysis, alkaline hydrolysis, neutral hydrolysis, oxidative hydrolysis, thermal degradation, and photolytic degradation.Figure 6C demonstrates overlay chromatogram for i) pure drug, ii) oxidative hydrolysis, iii) thermal degradation, iv) neutral hydrolysis and v) photolytic degradation.The drug found sensitive toward acidic and alkaline hydrolysis, but it showed comparative stability to neutral hydrolysis, oxidative, thermal, photolytic, and degradation.DP I and IV were observed in acid hydrolysis,  while DP II, III, and V were detected in alkaline hydrolysis as shown in Table 5.

Lenvatinib Degradation Behavior
The optimization of the Lenvatinib method demonstrated its specificity, selectivity, robustness, accuracy, and precision in effectively separating the degradation product peaks from the drug peak.Acidic and alkaline hydrolyses were identified as stress degradation factors that rendered Lenvatinib sensitive.This was evidenced by the appearance of additional peaks in the respective chromatograms and a reduction in the area of Lenvatinib in each condition compared to its initial area.Utilizing the Lenvatinib responses and analyzing all degradation products resulting from stress studies, the mass balance was calculated (Table 5).The study on drug stability uncovered Lenvatinib's susceptibility to hydrolysis, emphasizing the need for thorough monitoring of the liquid dosage stability of the drug.

Analytical Method Validation
According to Tables 6 and 7, the developed SIAM (System Suitability Analysis Method) was subjected to validation in accordance with ICH (International Council for Harmonization) guidelines, specifically Q2 (R1) (2).The results indicate that all parameters exhibited % RSD (Relative Standard Deviation) values below one.The method's linearity was established by a regression coefficient of 0.9983 within the concentration range of 10 to 60 µg/mL.The optimized approach successfully differentiated all potential degradation peaks from the drug peak, as evidenced by peak purity and resolution values ranging from 0.990 to 0.999 (with a minimum requirement of > 2).The LOD (Limit of Detection) and LOQ (Limit of Quantification) values determined were 0.015 and 0.05 µg/mL, respectively.In terms of precision, both Inter-day and Intraday measurements were performed at three different concentrations (10,30, and 50 µg/mL) in triplicate on three consecutive days and on the same day.The resulting RSD values for Inter-day and Intraday precision were 0.366 and 0.301, respectively.The % Assay RSD was estimated to be within the range of (100.45-102.77)± 0.998, indicating good precision in determining the drug content.Similarly, the accuracy % Recovery RSD was estimated to be within the range of (100.45 ± 0.2110-102.77± 0.4396), highlighting the method's reliability in accurately recovering the drug content.

Method Greenness Score
In the AGREE Tool input parameters, based on the 12 principles of SIGNIFICANCE, are assigned varying degrees of importance.These SIGNIFICANCE principles encompass aspects, such as sample type and quantity, device location, sample preparation steps, automation/miniaturization, derivatization, waste management, analysis throughput, energy  7i.Each principle's significance is depicted by the width of its corresponding section, while the success of the procedure in meeting each principle is indicated by an intuitive red-yellow-green color scale.The evaluation process is made quick and easy with the assistance of user-friendly software, which automatically generates the graph and report.In the center of the graph, the overall score is displayed, with a value closer to one and a darker shade of green indicating a more environmentally friendly method.The same developed protocol was studied with another greenness assessment tool GAPI (Green analytical process index) and the result found is shown in Fig. 7ii.The GAPI works on the principle of GAC (Green analytical chemistry) and provide pictogram based on range decided for sample preparation and pre-analysis process.This includes yield, temperature/time, health hazard, instrumentation, energy used, occupational hazard, purity, waste and amount of solvent used.In all the events if 5-6 process scores are achieved, then it is considered as ideal green procedure and developed method found suitable for use.The procedure involves minimal steps for external sample treatment on an HPLC system.The sample is injected into the HPLC for a duration of 20 min, with a flow rate of 0.8 mL/min.The solvent composition for the isocratic elution is ACN: 10 mM ammonium formate (39:61; v/v).The  AGREE tool generates a graph that resembles a clock, displaying the total score and using color to indicate the ecofriendliness of the methodology (Fig. 7i).The calculated score of 0.61 suggests that the assessed method is more environmentally friendly compared to other published methods, as denoted by the dark green color.The color in each section with the corresponding criterion number represents how well the process performed in terms of that evaluation criteria.

Conclusion
Regulatory authorities and pharmaceutical companies are placing increasing emphasis on the quality parameters of drugs, which calls for continuous monitoring of critical parameters throughout the entire product life cycle.This study presents an efficient, sensitive, accurate, and robust analytical method for Lenvatinib using the innovative Analytical Quality by Design (QbD) approach.The method successfully separated five degradation products when Lenvatinib was subjected to various stress conditions.Method validation studies demonstrated that the system is sensitive, accurate, precise, and exhibits high linearity (> 0.99), as well as robustness.Lenvatinib was found to be sensitive under acid and alkaline hydrolytic conditions.A sustainable procedure compatible with LC-MS was developed using QbD principles.The developed stability-indicating method is suitable for bioanalytical studies and enables tracking and monitoring of Lenvatinib stability in its different dosage forms.The primary objective of this initiative is to raise environmental awareness and promote the development of environmentally friendly and cost-effective solutions.The environmentally conscious approach was exemplified using the AGREE & GAPI tools, which demonstrated that the created technique is both eco-friendly and highly sensitive, while also being compatible with LC-MS analysis.

Fig. 5
Fig. 5 Updated risk assessment for Lenvatinib stability method

Table 2
Critical parameters for optimization

Table 3
Response surface design

Table 4
Control strategy for Lenvatinib stability method (SIAM) usage, reagent source, toxicity, and operator safety.Following the Principles of Green Analytical Chemistry, all 12 input factors are standardized on a scale of 0 to 1.The overall evaluation is determined by summing up the scores for each guiding principle.The final result is visualized in the form of a clock-like graph, represented in Fig.

Table 5
Result from stress degradation study of Lenvatinib

Table 6
Summary of validation parameter of SIAM of Lenvatinib

Table 7
System suitability parameters of stability method a Mean of five replicates