Ion-pair RP-HPLC strategy for resolving polarity-mismatched APIs in sustained-release capsules: an AQbD-driven mechanistic and statistical optimization

Ion-pair RP-HPLC strategy for resolving polarity-mismatched APIs in sustainedrelease capsules: an AQbD-driven mechanistic and statistical optimization Leo Anggara1, Satrialdi2, Sophi Damayanti1 1 Department of Pharmacochemistry, School of Pharmacy, Institut Teknologi Bandung, Bandung, 40132, Indonesia 2 Department of Pharmaceutics, School of Pharmacy, Institut Teknologi Bandung, Bandung, 40132, Indonesia Corresponding author: Sophi Damayanti ([email protected]) Received 10 August 2025♦ Accepted 9 September 2025♦ Published 2 October 2025 Citation: Anggara L, Satrialdi, Damayanti S (2025) Ion-pair RP-HPLC strategy for resolving polarity-mismatched APIs in sustained-release capsules: an AQbD-driven mechanistic and statistical optimization. Pharmacia 72: 1–15. https://doi.org/10.3897/pharmacia.72.e168287 Abstract A robust ion-pair reversed-phase HPLC (RP-HPLC) method was developed for the simultaneous separation of pseudoephedrine sulfate (PSE) and loratadine (LOR) in sustained-release capsules. Due to the pronounced polarity mismatch between PSE (hydrophilic, log P 0.9) and LOR (lipophilic, log P 5.20), sodium 1-octanesulfonate was employed as an ion-pairing reagent to modulate retention and enhance selectivity. Method development was guided by an Analytical Quality by Design (AQbD) framework using central composite design (CCD) to evaluate the influence of column temperature, pH, organic solvent ratio, and ion-pair concentration. Optimal separation was achieved at pH 2.6, with PSE and LOR exhibiting kʹ values of 2.42 and 5.8, and resolution exceeding 2.0. The method was validated per ICH Q2(R2), showing excellent specificity, linearity (r² > 0.999), accuracy (98–102%), precision (RSD< 2%), and robustness. Mechanistic interpretation revealed electrostatic–hydrophobic dual retention control, providing insight into polarity-bridging strategies in RP-HPLC. This method advances separation science for challenging analyte combinations in complex pharmaceutical matrices. Keywords analytical quality by design, central composite design, ion-pair chromatography, loratadine, polarity mismatch, pseudoephedrine sulfate, RP-HPLC, sustained-release formulation Introduction Sustained-release (SR) drug formulations offer therapeutic advantages by maintaining consistent plasma drug levels and reducing dosing frequency (Sweetman 2009). These formulations are particularly beneficial in managing chronic or symptomatic conditions such as allergic rhinitis and chronic urticaria, where consistent symptom control and enhanced patient adherence are critical (Sweetman 2009). Among various drug combinations used for allergy relief, pseudoephedrine sulfate (PSE) (Fig. 1a) and loratadine (LOR) (Fig. 1b) stand out due to their complementary pharmacologic effects – PSE as a nasal decongestant and LOR as a second-generation antihistamine (Simons Copyright Anggara L et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Pharmacia 72: 1–15 DOI 10.3897/pharmacia.72.e168287 Research Article Anggara L et al.: AQbD-Optimized Ion-Pair RP-HPLC for APIs in sustained-release capsules2 Estelle 2004; Wexler 2023). While both drugs are widely used, their co-formulation in SR dosage forms introduces significant analytical complexity (Siddique et al. 2010). The fundamental challenge lies in their distinct physicochemical properties. PSE is a hydrophilic compound with a log P of 0.9, whereas LOR is lipophilic with a log P of 5.20 (Moffat et al. 2011). These polarity differences lead to contrasting chromatographic behaviors in reversed-phase systems: PSE exhibits poor retention and elutes early, while LOR strongly interacts with the stationary phase (Leśko et al. 2024). When these drugs are co-formulated in SR matrices, additional complications arise from excipients that modulate the release profile, possibly interfering with analyte recovery or peak shape. Therefore, developing a selective and robust analytical method capable of simultaneously quantifying both APIs in complex SR matrices is essential for ensuring product quality and compliance with regulatory standards. Historically, several analytical approaches have been employed to quantify PSE and LOR, such as UV-spectrophotometry (Mabrouk et al. 2003; Singhvi and Bhatia 2006; Palabiyik and Onur 2007; Culzoni and Goicoechea 2007), high-performance thin-layer chromatography (HPTLC) (Sane et al. 2001), and conventional reversed-phase high-performance liquid chromatography (RP-HPLC) (Abu-Lathou et al. 2005). These techniques, however, are often optimized for simple dosage forms like tablets or syrups (Abu Reid and Gadkariem 2017; Abu Reid 2021) and may not provide sufficient resolution or robustness for complex SR capsules. Most prior methods relied on one-factor-at-a-time (OFAT) strategies, which do not account for interactions among method variables and require extensive trial-and-error experimentation (Jayaraman et al. 2020; Beg et al. 2021). Ion-pair chromatography (IPC) offers a practical solution to this challenge by modifying the retention characteristics of polar analytes (Enmark et al. 2022; Shi et al. 2024). Incorporating an ion-pairing reagent into the mobile phase enables reversible complexation with ionic compounds, enhancing their retention in the hydrophobic stationary phase (Shi et al. 2024). In the case of PSE, which is highly polar and possesses a basic amino group, the addition of sodium 1-octanesulfonate enhances retention by forming ion-pair complexes with the protonated amino group of PSE, promoting greater hydrophobic interaction with the C18 stationary phase, thus aligning its retention time more closely with that of LOR. Despite the theoretical advantages of IPC, few studies have systematically explored its integration with Quality by Design (QbD) principles for method development (Jayaraman et al. 2020). Analytical Quality by Design (AQbD) represents a paradigm shift from empirical optimization toward a scienceand risk-based approach (Singh and Beg 2013; Peraman et al. 2015; Singh and Beg 2015; Singh et al. 2016; Deidda et al. 2018; Tome et al. 2019). AQbD begins with defining the Analytical Target Profile (ATP), followed by initial risk assessment and application of Design of Experiments (DoE) tools such as central composite design (CCD) to model and optimize method variables (Bandopadhyay et al. 2020; Adib et al. 2022). This framework facilitates understanding of parameter interactions and identifies a method operable design region (MODR), a multidimensional space where method parameters (e.g., pH, mobile phase composition) can vary without compromising performance, ensuring robustness (Kim et al. 2023). In this study, we developed and validated a robust ionpair RP-HPLC method for the simultaneous analysis of PSE and LOR in SR capsules, effectively addressing their Figure 1. Chemical structure of PSE and LOR. Pharmacia 72: 1–15 3 polarity mismatch. Guided by AQbD principles, we employed central composite design (CCD) for method optimization. The method demonstrated excellent linearity, accuracy, precision, robustness, and specificity, in accordance with ICH Q2(R2) guidelines. This integrated approach offers a scalable and reliable strategy for the analysis of polarity-mismatched APIs in complex pharmaceutical matrices. Experimental Materials Standards of PSE and LOR were obtained from Embio Limited (Maharashtra, India) and Vasudha Pharma Chem. Limited (Telangana State, India). All solvents and reagents (e.g., methanol HPLC grade, acetonitrile HPLC grade, 85% ortho-phosphoric acid p.a., 37% hydrochloric acid p.a.) were obtained from Merck (Darmstadt, Germany). Sodium 1-octanesulfonic acid sodium salt (pro HPLC) was obtained from HiPerSolv Chromanorm (Leuven, Belgium). HPLC-grade water was used throughout. Placebo and SR capsule samples were provided by XYZ Pharmaceutical Company (Serang, Indonesia). All other reagents were of analytical or HPLC grade. Standard and sample preparation Standard stock solutions were prepared by dissolving 300 mg of PSE standard and 12.5 mg of LOR standard in 5 mL of methanol. The resulting solutions were further diluted with 0.1 N hydrochloric acid to obtain concentrations of 1200 µg/ mL for PSE and 50 µg/mL for LOR. These standard solutions were then diluted with the mobile phase to obtain final concentrations of 96 µg/mL PSE and 4 µg/mL LOR, followed by filtration through a 0.45 µm PTFE membrane filter. To determine the assay of PSE and LOR in a drug product, no fewer than 10 SR capsules were opened. The capsule contents were triturated to homogeneity, transferred quantitatively into a 1 L volumetric flask, and rinsed with methanol to a final volume of 100 mL. Subsequently, 500mL of 0.1 N hydrochloric acid was added, and the mixture was sonicated for 30 minutes. After sonication, the solution was allowed to cool to room temperature and then diluted to volume with 0.1 N hydrochloric acid. Further dilutions were performed to obtain a sample solution containing 96 µg/mL PSE and 4 µg/mL LOR in the mobile phase. The final solution was filtered through a 0.45 µm PTFE membrane filter. Instrumentation and software The HPLC systems consisted of a Waters Alliance iS with an ultraviolet (UV) detector (Waters, USA) and a Waters Alliance e2695 separation module with a 2998 photodiode array detector (PDA) (Waters, Milford, MA, USA). Both systems were equipped with a pump, autosampler, and column compartment. The optimized working conditions were as follows: Phenomenex Luna® 5 µm C18 (2) 100 Å, 250 × 4.6 mm column (Torrance, USA), with a mobile phase consisting of 350 mL acetonitrile, 255 mL methanol, and 395 mL water containing 0.4% sodium 1-octanesulfonate, adjusted to pH 2.6 ± 0.05 with 85% ortho-phosphoric acid, at a flow rate of 1.0 mL/min. The column temperature was maintained at 31.5 °C. The injection volume was 20 µL, and the detection wavelength was set at 210 nm (optimal wavelength from PDA screening 190–400 nm). Chromatogram data were processed using the Empower Chromatography Data System (version 3.8.0) (Waters, Milford, MA, USA). Initial risk assessment and preliminary method development Before the preliminary experiments, an initial risk assessment of the analytical method was performed. A risk assessment matrix was used to identify the critical method parameters that could affect analytical performance. Based on the assessment, high-risk factors were selected as the critical method parameters (CMPs) that should be controlled. To initiate method development, a preliminary experiment was performed to screen the mobile and stationary phases. This study consisted of several OFAT experiments. The concentration of ion-pair reagent, the organic solvent composition, the pH of the mobile phase, and the column temperature were investigated at this stage. The mobile phase without an ion-pair reagent and various concentrations (0.2%, 0.4%, and 0.6%) was tested based on the polarity of the analytes. Three different pH values (2.4, 2.6, and 2.8) were evaluated for the mobile phase, taking into account the pKa of the analytes. Finally, three distinct column temperatures were employed to study the influence of mobile phase velocity. Experimental design and data analysis Minitab 22 software (M/s Minitab Pty Ltd., Sydney, Australia) was used to generate experimental designs for method development and to statistically analyze the chromatographic results. Based on the results of the risk assessment and preliminary study, a central composite design (CCD) was employed with four method parameters – pH, organic ratio, ion-pair concentration, and column temperature – to evaluate their main effects on resolution (Rs), tailing factor (Tf), retention time (RT), and number of theoretical plates (N). Each factor was studied at three levels (−1, 0, +1) with α, resulting in a total of 31 experimental runs, including 7 replicates at the center point to estimate experimental error and assess model robustness. After performing the tests suggested by the experimental design, data analysis was conducted using ANOVA to investigate significant relationships between the method parameters and chromatographic responses. Statistical parameters such as p-value, coefficient of determination (R²), and adjusted R² were used to confirm the fitness and significance of the model. Anggara L et al.: AQbD-Optimized Ion-Pair RP-HPLC for APIs in sustained-release capsules4 MODR and method validation The predictability of the model and robustness of the method were confirmed by verification experiments at the optimal settings and edge points of the MODR. The developed method was validated according to ICH guideline Q2(R2) with respect to specificity, linearity, accuracy, precision, limit of detection (LOD), and limit of quantitation (LOQ). Specificity of the analytical method was evaluated by analyzing interference from the diluent and sample matrices at the RT of PSE and LOR. Peak purity values were also assessed, with results showing that the purity threshold was greater than the purity angle for both the standard and sample solutions. Linearity was evaluated using standard solutions of PSE and LOR at concentrations ranging from 48–144 µg/mL for PSE and 2–6 µg/mL for LOR. Five different concentrations, each injected in triplicate, were analyzed under the chromatographic conditions described above. The concentrations of the solutions were plotted against the corresponding peak area responses for PSE and LOR, and linear regression equations were subsequently calculated. Accuracy was evaluated at three concentration levels of the sample solutions (50%, 100%, and 150%) using nine determinations (three replicates at each concentration). PSE and LOR standards were spiked into the sample matrices. The percentage recovery was calculated by comparing the measured amounts with the amounts added. Precision of the method was assessed through repeatability (intra-day) and intermediate precision (inter-day) by analyzing six replicates of a fixed concentration of the drug. Assay precision was further evaluated across different days and analysts to determine intraand inter-day variability. The results were expressed as relative standard deviation (RSD) of the assay values. The LOD and LOQ were calculated based on the standard deviation of the response (σ) and the mean slope of the calibration curve (S), according to the following equations: LOD = (σ/S) × 3.3 LOQ = (σ/S) × 10 Results and discussion ATP and critical method attributes To establish the analytical method according to the AQbD approach, defining the ATP was a crucial step. Similarly to quality target product profiles (QTPP) as described in ICH Q8, the ATP consisted of objectives and performance requirements for the analytical procedure. In this study, the ATP was defined by the simultaneous quantification of PSE and LOR with the following requirements: (1) sufficient selectivity between PSE and LOR peaks, (2) accuracy in the range of 98–102%, (3) precision expressed as %RSD of less than 2% with an assay range of 90.0–110%, and (4) an analysis time of less than 30 minutes. Based on the ATP, the liquid chromatographic system suitability parameters, including Rs, Tf, RT, and N, were defined as critical method attributes (CMAs). The CMAs are key responses that must be controlled within a tolerable range to ensure the required performance of the analytical method. According to the results of the preliminary experiments, the desired values for each CMA were established as follows: Rs between closely eluting PSE and LOR peaks > 2.0, Tf of PSE and LOR peaks less than 2.0, RT of the last eluting peak less than 30 minutes, and N not less than 2000. Initial risk assessment A risk assessment matrix (Table 1) was employed as a foundational step in the AQbD framework to identify and rank the impact of various CMPs on the CMAs for the chromatographic separation of PSE and LOR. The goal was to prioritize parameters that significantly influence method performance and robustness during the method development phase. Column temperature exhibited a high-risk impact on peak area, Tf, and N. Variations in temperature directly affect solute diffusion, mass transfer kinetics, and analyte– stationary phase interactions. As both analytes show polarity differences, shifts in temperature can result in significant peak broadening or compression, leading to tailing or reduced N. pH changes were identified as having a high impact on RT, Rs, and Tf, particularly due to their effect on the ionization state of PSE (a weak base) and its interaction with the ion-pairing reagent. PSE retention is highly pH-dependent, especially in the presence of an ion-pairing agent, whereas LOR remains largely non-ionized at acidic pH. Optimization at pH (adjusted with orthophosphoric acid) was essential for reproducible retention and selectivity, confirming the need for tight pH control. The proportion of acetonitrile and methanol in the mobile phase had a high impact on RT, Rs, and Tf, reflecting its influence on analyte solubility and elution strength. Increased organic content can reduce retention but may also decrease Rs if not balanced with ion-pairing and pH conditions. A ternary composition of acetonitrile:methanol:water (35:30:35, v/v/v) was selected based on preliminary trials to balance elution strength and Rs. The concentration of sodium 1-octanesulfonate was classified as low risk for peak area but high risk for RT and Rs, particularly for PSE. Although flow rate and injection volume were kept constant in the study (1.0 mL/min and 20 µL, respectively), they were included in the risk matrix for completeness. Injection volume was assigned high risk for peak area and medium risk for tailing, indicating its role in peak broadening if overloaded. Flow rate had a low to medium impact, consistent with expectations in isocratic reversed-phase methods. Overall, column temperature, mobile phase pH, organic composition, and ion-pairing reagent concentration emerged as the CMPs requiring fine-tuning. These parameters were prioritized for further method optimization using DoE. By integrating the AQbD approach early in method development, a more robust and reliable separation strategy tailored to the physicochemical properties of PSE and LOR was ensured. Pharmacia 72: 1–15 5 Preliminary and screening method development The initial phase of method development focused on screening chromatographic parameters to achieve effective separation of PSE, LOR, and matrix components. Parameters investigated included solvent selection, stationary phase, mobile phase composition, elution mode, detection wavelength, column dimensions, column temperature, flow rate, and injection volume. Before applying DoE, a series of preliminary tests were conducted to evaluate the influence of key factors such as column type, mobile phase pH, organic solvent ratio, and ion-pair concentration. Given the substantial polarity difference between PSE and LOR, these variables were critical in reversed-phase HPLC separation. Column selection used a C18 phase (250 × 4.6 mm, 5 µm), while pH adjustments were achieved by adding 0.1 mL of 85% ortho-phosphoric acid to reach an acidic pH. A ternary mobile phase of acetonitrile, methanol, and water in a 35:30:35 (v/v/v) ratio was selected. Comparisons were made between formulations containing 0.3% sodium 1-octanesulfonate as an ion-pairing agent and those without. Detection wavelength optimization was performed using a PDA detector in the range of 190–400 nm (see Suppl. material 1: figs S2, S3). Column temperature was maintained at 30 °C, with flow rate and injection volume fixed at 1.0 mL/min and 20 µL, respectively. In the application of this separation method, the APIs eluted in the following order: PSE and LOR. A major challenge in analytical method development was to achieve adequate separation of PSE and LOR with a short analysis time. Due to its highly polar and hydrophilic nature, PSE exhibited poor retention in the absence of an ion-pairing agent, eluting before the void volume. The introduction of sodium 1-octanesulfonate formed a hydrophobic ion-pair complex with the protonated amine group of PSE, enhancing its retention and enabling effective Rs from both LOR and excipients. This behavior leads to minimal interaction with the non-polar stationary phase of the C18 column. As a result, the analyte co-eluted with unretained matrix components, making quantification and Rs unreliable. By contrast, this anionic surfactant interacts with the positively charged pseudoephedrine molecule to form a more hydrophobic ion-pair complex, thereby enhancing its retention. Upon incorporation of the ion-pairing reagent into the aqueous mobile phase, PSE was retained beyond the void volume and separated effectively from both LOR and other matrices. This confirms the critical role of ion-pairing in enabling selective and reproducible retention of highly polar basic compounds in reversed-phase HPLC. Suppl. material 1: fig. S1 illustrates the effect of ion-pairing agent concentration on the retention behavior of PSE and LOR. In the absence of an ion-pairing reagent (Suppl. material 1: fig. S1a), PSE eluted at approximately 2.286 minutes, even before the column’s void volume, indicating poor retention due to its high polarity and weak interaction with the hydrophobic stationary phase. LOR, by contrast, showed moderate retention under the same conditions (5.662 minutes). The introduction of sodium 1-octanesulfonate as an ion-pairing reagent significantly improved PSE’s retention. As shown in Suppl. material 1: fig. S1b– S1e, increasing the ion-pair concentration from 0.2% to 0.6% led to a progressive increase in RT for both analytes. At 0.6% (Suppl. material 1: fig. S1e), PSE was retained at 4.562 minutes and LOR at 17.252 minutes, with improved Tf and Rs. These results confirm that ion-pairing is essential for achieving effective chromatographic separation of PSE and LOR, particularly due to their contrasting polarity. The ion-pairing reagent significantly enhanced the retention of PSE by forming a transient neutral complex with its protonated amine, thereby increasing hydrophobicity and interaction with the stationary phase. LOR, largely non-ionized at acidic pH, was retained naturally via hydrophobic interactions. Although LOR does not form ion pairs under acidic conditions (pKa ~5.0, remaining largely neutral at acidic pH), the presence of the ion-pairing reagent in the mobile phase still modified the overall chromatographic environment, which in turn affected LOR’s retention behavior. Adding sodium 1-octanesulfonate (an anionic surfactant) to the aqueous phase effectively reduced the overall polarity of the mobile phase. This shift increased the relative hydrophobicity contrast between the mobile and stationary phases (C18), thereby enhancing the retention of hydrophobic analytes like LOR. The sulfonate tail of the ion-pairing reagent may adsorb onto the C18 stationary phase, forming a pseudo-stationary phase or dynamic layer. This modifies the surface polarity of the stationary phase and alters analyte partitioning behavior, even for non-ionizable compounds like LOR. Ion-pairing reagents also interact with solvents and may reduce the elution strength of the mobile phase, especially toward hydrophobic compounds. This requires Table 1. Risk assessment matrix for chromatography. CMPs CMAs Peak Area Retention Time Resolution Tailing Factor Theoretical Plate Column temperature High High Low High High Mobile phase pH Medium High High High Low Organic composition in mobile phase Low High High High Medium Ion pair composition in mobile phase Low High High Low Low Flow rate*Low High Low Low Low Injection volume*High Low Low Medium Low Note: *It is kept constant in this experiment. Anggara L et al.: AQbD-Optimized Ion-Pair RP-HPLC for APIs in sustained-release capsules6 more mobile phase to elute LOR, shifting its retention to longer times. The differential response to ion-pairing allowed simultaneous separation within a single run. During method development, the selection of an appropriate detection wavelength influenced the separation of PSE, LOR, and matrix components from the sample. In addition to optimizing mobile phase composition and ion-pairing conditions, wavelength selection played a crucial role in achieving effective chromatographic separation and reliable quantification of PSE, LOR, and matrix components. Due to differences in the UV absorbance profiles of PSE and LOR, wavelength selection directly affected not only the sensitivity of detection but also the overall selectivity of the method. PSE, a highly polar compound with limited chromophores, exhibits relatively weak absorbance at higher wavelengths, whereas LOR, being more hydrophobic and aromatic, absorbs strongly in the 250–280 nm range. As illustrated in Suppl. material 1: fig. S2, PSE exhibited lower peak responses across the UV range tested, with the strongest signal detected around 200–225 nm. However, at these lower wavelengths, a significant interference peak was also observed near the RT of PSE, which could compromise both quantitation and Rs. Conversely, LOR showed consistently strong absorbance across a broader range (225–325 nm), with relatively stable peak responses. The interference peak, likely originating from matrix constituents, demonstrated a rising trend with increasing wavelength, further complicating the detection of PSE at higher wavelengths. This presented a trade-off: while lower wavelengths enhanced PSE sensitivity, they also introduced matrix interference; higher wavelengths reduced interference but compromised PSE detection. Preliminary trials at commonly used wavelengths such as 210 nm resulted in broad, less defined peaks and overlap with matrix interferences, particularly for PSE. However, selecting such a low detection wavelength necessitates careful consideration of the UV cut-off of the diluent used during sample preparation and injection. The UV cut-off is the lowest wavelength at which the diluent does not absorb significantly. If the diluent absorbs near or above 210 nm, it can produce high background noise, raise the baseline, and mask analyte peaks – particularly problematic for PSE, which already gives a relatively weak signal. Therefore, diluents with low UV absorbance at 210nm, such as methanol, acetonitrile, water, or dilute hydrochloric acid (e.g., 0.1 N HCl), were selected to minimize interference and maintain baseline stability. This consideration was essential not only to achieve optimal peak response and selectivity (as shown in Suppl. material 1: fig. S3) but also to ensure accurate quantification and maintain method robustness during routine analysis. Optimization of analytical method parameters Following the risk assessment, four high-risk CMPs – column temperature, pH modulator (ortho-phosphoric acid) concentration, organic composition (MeOH %), and ion-pair concentration – were selected for optimization using a central composite design (CCD). The central composite design is the most commonly used fractional factorial design in response surface methodology (Bhattacharya 2021). Each parameter was studied at five levels (−α, low, middle, high, +α), as shown in Suppl. material 1: table S1, to investigate both linear and quadratic effects on the CMAs, including Rs, Tf, N, and RT. The CMPs to be optimized were column temperature (20, 25, 30, 35, and 40 °C), volume of phosphoric acid in the mobile phase acting as a pH modulator (0.06, 0.08, 0.10, 0.12, and 0.14 mL), organic ratio of methanol (20, 25, 30, 35, and 40%), and ion-pairing reagent (sodium 1-octanesulfonate) concentration (0.1, 0.2, 0.3, 0.4, and 0.5%). The experimental design is summarized in Table 2. To assess the statistical significance and predictive capability of the fitted models for each critical quality attribute (CQA) – including Rs, Tf, N, and RT – ANOVA was performed for all response models generated by the CCD. ANOVA confirmed that all quadratic models were statistically significant, with p-values < 0.05, indicating that the observed effects were unlikely to be due to random variation. The F-values were substantially greater than 1, suggesting that the variance explained by the model was significantly larger than the residual error. The lack-of-fit was found to be statistically non-significant (p > 0.05) for all models, indicating that the model fit the experimental data well and no significant variation was left unexplained. In summary, the observed p-values were < 0.05, while the p-values for the lack-of-fit were > 0.05, and the R² values were > 0.99, indicating that the model was significant and valid for the responses. The results of ANOVA are presented in Suppl. material 1: table S2. The mathematical models derived from the CCD successfully described the influence of CMPs on the CMAs for simultaneous quantitation of PSE and LOR by HPLC, as shown in Suppl. material 1: table S3. For both PSE and LOR, Rs was influenced by multiple linear, interaction, and quadratic terms. The Rs model for PSE showed no significant CMP effects, while the Rs for LOR was significantly affected by column temperature (A), organic solvent composition (C), and ion-pair concentration (D), with notable interactions such as AC and CD. The model equations suggest that increases in temperature and ion-pair concentration tend to decrease Rs for LOR, indicating the need for optimization to balance selectivity and peak separation. The Tf models revealed differing sensitivities between the analytes. While PSE showed no significant CMPs, LOR was significantly influenced by column temperature (B), pH adjuster (C), and their interaction (CC). The positive coefficient of pH (C) suggests that increased pH can improve peak symmetry for LOR. Moreover, significant quadratic effects suggest the presence of curvature, implying nonlinear behavior in the response surface. N, a measure of column efficiency, was significantly affected by CMPs for both analytes. For PSE, organic solvent volume (B) showed a major effect, while for LOR, temperature (A), organic solvent (C), and their Pharmacia 72: 1–15 7 interaction terms contributed substantially. This implies that mobile phase composition plays a critical role in column efficiency, possibly due to its influence on analyte–matrix interactions and elution strength. RT was influenced by nearly all CMPs for both PSE and LOR. For PSE, temperature (A), solvent volume (B), and ion-pair concentration (D) were significant, as were several interaction terms (e.g., AC, BD). In contrast, LOR showed significant sensitivity to all four CMPs (A, B, C, and D), with prominent interactions (e.g., CC and CD). This suggests that retention of LOR is more sensitive to experimental conditions, likely due to its physicochemical properties and stronger interaction with the mobile or stationary phase. The final phase of method development involved identifying optimal chromatographic conditions using the established response surface models for both PSE and LOR. The optimization targeted simultaneous maximization of Rs and N and minimization of Tf and RT to ensure a robust and efficient separation (Suppl. material 1: table S4). The optimized levels of CMPs were identified through the desirability function approach in Minitab software. The optimum settings were column temperature (A): 31.5 °C, pH of phosphate buffer (B): 0.13 mL, methanol composition (C): 25.5%, and ion-pair concentration (D): 0.4%. These conditions were predicted to deliver the best balance of chromatographic performance attributes for both analytes. While the contour plots (Fig. 2) and surface plots (Fig. 3) comprehensively evaluated interactions between column temperature, ortho-phosphoric acid volume, and organic solvent ratio, the impact of ion-pair concentration on PSE RT was intentionally limited to its Table 2. Design of experiment of AQbd using CCD. Std Order Run Order Input factors Chromatographic responses CMPs CMAs Column temp. Acid adjuster (mL) Org. comp. Ion pair conc. (%) PSE LOR Rs. a Tf bN cRT dRs. a Tf bN cRT d 19 1 30 0.06 30 0.3 4.2 1.0 13786 3.891 3.5 1.0 12470 12.196 23 2 30 0.10 30 0.1 2.0 0.8 13697 3.320 6.3 1.0 13450 8.850 27 3 30 0.10 30 0.3 4.6 1.0 10214 3.800 1.8 1.0 9768 11.109 12 4 35 0.12 25 0.4 1.8 1.0 11437 3.827 2.6 1.0 11145 10.886 11 5 25 0.12 25 0.4 2.1 1.0 10860 4.046 5.2 1.0 10314 12.717 25 6 30 0.10 30 0.3 4.8 1.0 11331 3.784 1.8 1.0 10833 10.959 22 7 30 0.10 40 0.3 0.0 1.0 10801 3.286 2.4 1.0 10721 6.292 6 8 35 0.08 35 0.2 0.0 1.0 12108 3.305 0.0 1.0 11268 7.342 13 9 25 0.08 35 0.4 0.0 1.0 11022 3.744 0.0 1.0 10337 9.401 28 10 30 0.10 30 0.3 0.0 1.0 11413 3.786 0.0 1.0 10895 10.976 5 11 25 0.08 35 0.2 0.0 1.0 11380 3.467 0.0 1.0 10393 8.291 18 12 40 0.10 30 0.3 0.0 1.0 12039 3.592 0.0 1.0 11436 9.508 2 13 35 0.08 25 0.2 0.0 1.0 11604 3.796 1.3 1.0 11925 13.160 14 14 35 0.08 35 0.4 0.0 1.0 11664 3.559 0.0 0.8 10604 8.258 10 15 35 0.08 25 0.4 0.0 1.0 11632 4.180 6.1 1.0 11679 15.367 15 16 25 0.12 35 0.4 0.0 1.0 11365 3.722 0.0 1.0 10779 9.168 24 17 30 0.10 30 0.5 0.0 1.0 11134 4.190 0.0 1.0 10985 13.890 16 18 35 0.12 35 0.4 0.0 1.0 11893 3.536 0.0 1.0 12127 8.022 3 19 25 0.12 25 0.2 0.0 1.0 10859 3.913 1.2 1.1 12165 14.432 21 20 30 0.10 20 0.3 3.7 1.0 15570 4.608 9.3 1.0 15654 24.115 30 21 30 0.10 30 0.3 0.0 1.0 11513 3.792 0.0 1.0 11098 11.036 29 22 30 0.10 30 0.3 0.0 1.0 11491 3.794 0.0 1.0 11064 11.049 1 23 25 0.08 25 0.2 4.3 1.0 15341 4.190 5.8 1.0 14765 17.724 9 24 25 0.08 25 0.4 0.0 1.0 10573 4.439 7.5 1.0 10575 18.206 7 25 25 0.12 35 0.2 0.0 1.0 11050 3.410 0.0 1.0 10298 7.822 20 26 30 0.14 30 0.3 0.0 1.2 6795 3.896 0.0 1.1 7537 12.408 26 27 30 0.10 30 0.3 0.0 1.3 5939 3.746 1.3 1.2 6603 10.712 31 28 30 0.10 30 0.3 0.0 1.3 5778 3.747 1.3 1.2 6660 10.714 17 29 20 0.10 30 0.3 0.0 1.3 5806 3.952 2.4 1.2 5939 12.464 4 30 35 0.12 25 0.2 0.0 1.3 6298 3.729 0.0 1.2 6457 12.601 8 31 35 0.12 35 0.2 0.0 1.2 5708 3.248 0.0 1.4 6790 6.964 a. Rs.: Resolution between main peaks to the narrowest peak b. Tf: Tailing factor of PSE and LOR c. N: Theoretical plate of PSE and LOR d. RT: Retention time of PSE and LOR Anggara L et al.: AQbD-Optimized Ion-Pair RP-HPLC for APIs in sustained-release capsules8 Figure 2. Contour plots (2D) indicating the effects of CMP (particularly the ion-pair concentration by holding other column temperature, pH, and organic composition) on the RT of PSE. synergistic effects with these parameters. This focused approach was adopted because preliminary studies indicated that ion-pair concentration alone exhibited a predictable, near-linear relationship with PSE RT across the tested range (0.1–0.5%), as evidenced by the consistent spacing of RT isobars in Figs 2, 3. The contour plots (Fig. 2) systematically elucidate the relationships between critical chromatographic parameters and the RT of PSE to define the MODR. When examining column temperature and ion-pair concentration (Fig. 2, Plot 1), a clear trend emerges where RT for PSE increases at lower temperatures (<25 °C) and higher ionpair concentrations (>0.4%), with an optimal balance achieved between 30–35 °C and 0.3–0.4% ion-pairing reagent (RT 3.6–3.8 min). This suggests that excessive ion-pair concentrations should be avoided to prevent unnecessarily prolonged analysis times. The interaction between ortho-phosphoric acid volume and ion-pair concentration (Fig. 2, Plot 2) reveals that RT for PSE is particularly sensitive to small changes in ortho-phosphoric acid volume, where values below 0.10 mL significantly increase retention (>4.4 min), while the range of 0.12– 0.13mL provides stable RT (3.8–4.0 min) when combined with 0.3–0.4% ion-pair. Notably, the organic solvent ratio (MeOH%) demonstrates a more predictable effect (Fig. 2, Plot 3), with higher MeOH% (>27%) shortening RT but potentially compromising Rs, whereas the nominal 25.5% MeOH maintains optimal RT (3.6–3.8 min) across the recommended ion-pair range (0.25–0.45%). Collectively, these plots validate the MODR boundaries where all system suitability criteria are met: column temperature (30– 35 °C), ion-pair concentration (0.3–0.4%), ortho-phosphoric acid volume (0.12–0.13 mL), and MeOH% (25.5± 1%). This multivariate approach aligns with QbD principles by identifying robust operational ranges while excluding edge conditions (e.g., <25 °C or >0.5% ion-pair) that introduce undesirable variability in RT or Rs. The 3D surface plots illustrate the combined effects of critical method parameters on PSE RT (Fig. 3). When column temperature and ion-pair concentration were varied while holding ortho-phosphoric acid volume (0.13 mL) and MeOH ratio (25.5%) constant, PSE RT showed a predictable decrease with increasing temperature (4.25 min at 20 °C to 3.50 min at 40 °C) and ion-pair concentration (0.10–0.55%). Similarly, variations in ortho-phosphoric acid volume and ion-pair concentration demonstrated that RT was most stable at intermediate ortho-phosphoric acid volumes (0.10–0.125 mL) and ion-pair concentrations of 0.25–0.40%. The organic solvent ratio plot revealed that RT remained consistent (3.5–4.0 min) across the tested MeOH range (25–40%) when combined with optimal ion-pair concentrations (0.25–0.40%). These results collectively define the MODR, where PSE RT is both stable and reproducible. Pharmacia 72: 1–15 9 A global desirability (D), corresponding to the geometric mean of the desirability for each response, was 0.8823, indicating that the predicted optimal responses were close to the target values (Fig. 4). Even though D = 1 represents an ideal response, D values in the range of 0.6–0.8 are acceptable (Salcedo-Chavez et al. 2002; Reyes-Moreno et al. 2012; Marinkovic 2021). The predicted responses obtained from the model were evaluated by performing the analysis at the optimized variable values. Table 3 shows that the experimental results were similar to the predicted responses, demonstrating the predictability and validity of the optimization model. The chromatogram obtained at the optimized conditions is shown in Fig. 6. MODR and method robustness A design space (DS) is a region of the method parameters where all chromatographic responses fall within the desired ranges. The DS can be generated by overlaying the contour plots of all response functions. DS were constructed by varying ion-pair concentration with each of the following factors: column temperature, pH modulator (ortho-phosphoric acid), and MeOH%, while keeping the remaining parameters constant at their optimized values. All contour plots are shown in Fig. 5. The DS, displayed in white, demonstrated that the optimal solution is within the DS. However, the DS does not consider probability estimation; thus, the risk of uncertainty in model prediction was not evaluated. Therefore, to ensure the robustness of the analytical method, a robust DS (MODR) was experimentally evaluated to confirm that the analytical attributes remained unaffected by small variations in method parameters (Deidda et al. 2018). In all cases, the responses satisfied the criteria with acceptable variation (Suppl. material 1: tables S5, S6). DS optimization focused on CMPs, including ion-pair concentration, organic phase ratio (MeOH%), pH, and column temperature. In contrast, the robustness study within the MODR prioritized parameters most susceptible to operational variability, specifically flow rate (0.8– 1.2mL/min), column temperature (26.5–36.5°C), and pH extremes (2.4–2.8). Ion-pair concentration (fixed at Figure 3. Surface plots (3D) indicating the effects of CMP (particularly the ion-pair concentration by holding other column temperature, pH, and organic composition) on the RT of PSE.