Box–Behnken Design-Based Optimized UHPLC Method for the Analysis of Lipid-Based SNEDDS Ferrying Hydrocortisone and Thymoquinone

Abstract

This study aimed to develop and validate a robust ultrahigh-performance liquid chromatography (UHPLC) method for the simultaneous quantification of hydrocortisone (HCT) and thymoquinone (TMQ) from self-nanoemulsifying drug delivery systems (SNEDDS). A Box–Behnken experimental design was applied to identify the impact of critical parameters, including the column temperature (20–40 °C), flow rate (0.2–0.4 mL/min), and buffer ratio (60–75%), on chromatographic responses. The optimized conditions comprised a column temperature of 20 °C, a flow rate of 0.2 mL/min, and a buffer ratio of 70.7%, achieving excellent peak resolution and asymmetry. The method demonstrated linearity (R² > 0.999) across the concentration range of 1–30 μg/mL for both analytes. Precision studies revealed relative standard deviations below 9.39% and 2.55% for HCT and TMQ, respectively, while accuracy ranged from 96.41% to 102.69% for HCT and from 97.83% to 106.21% for TMQ. The method exhibited high sensitivity with limits of detection of 0.203 and 0.129 μg/mL and limits of quantification of 0.615 and 0.392 μg/mL for HCT and TMQ, respectively. The method was robust, sensitive, and reproducible. The validated method was successfully applied to analyze HCT and TMQ contents with high recovery rates of 96.8 ± 2.53% and 101.5 ± 2.37%, respectively. The retention time for HCT was relatively shorter compared to that for TMQ, which may be attributed to various factors. This difference is more likely related to physicochemical properties such as hydrophobicity, polarity, and H-bonding capacity, together with chromatographic conditions, as both drugs are mainly un-ionized under the acidic mobile phase conditions. The optimized UHPLC method provides a reliable analytical tool for quality control and formulation development of SNEDDS.

1. Introduction

Hydrocortisone (HCT), also known as cortisol, is a steroid hormone and pharmaceutical compound of significant importance in medical practice. Chemically, it is a corticosteroid with the molecular formula C₂₁H₃₀O₅ and a molecular weight of 362.46 g/mol. It has been widely used to treat a diverse range of medical conditions, such as adrenal insufficiency, inflammatory disorders, allergic reactions, and certain types of cancer. However, the clinical application of HCT is limited owing to its reported low aqueous solubility, which negatively impacts its oral bioavailability. Therefore, the incorporation of HCT in pharmaceutical formulations is required to enhance drug bioavailability following oral administration. Self-nanoemulsifying drug delivery systems (SNEDDS) could be utilized to enhance the oral bioavailability of poorly water-soluble drugs. Besides their ability to form nanoemulsion droplets with the aid of peristaltic movement, the integration of bioactive oils could enhance the therapeutic efficacy of loaded drugs. Black seed oil is enriched with a phytochemical compound, namely thymoquinone (TMQ). It has been reported that TMQ has antioxidant, anti-inflammatory, immunomodulatory, and anticancer properties. This could offer potential therapeutic benefits due to its augmented effect and reduce the potential side effects of HCT.

The proposed formulation containing HCT and TMQ necessitates careful dosing and monitoring, underlining the importance of accurate analytical methods for their quantification in pharmaceutical formulations. In the realm of pharmaceutical analysis and drug development, the importance of sensitive and robust ultrahigh-performance liquid chromatography (UHPLC) methods for the simultaneous detection of multiple compounds cannot be overstated. Individual analysis of components from fixed-dose formulation is quite time-consuming and expensive for scientists. Analytical techniques are the backbone for quality control, formulation development, and pharmacokinetic studies in the pharmaceutical industry. The ability to accurately and reliably quantify multiple active pharmaceutical ingredients (APIs) in a single analytical run not only saves time and resources but also provides crucial information about drug interactions, stability, and bioavailability. Therefore, developing a robust UHPLC method capable of simultaneously detecting multiple compounds in SNEDDS formulations is paramount for ensuring the quality, efficacy, and safety of these advanced drug delivery systems.

The traditional optimization method uses a large amount of solvents and consumes a large amount of time due to random changes in method parameters. Consequently, Design of Experiments (DoE) has been used recently not only to reduce the number of experimental runs required but also to provide insights into parameter interactions. Moreover, based on the statistical analysis of suggested runs, it provides the optimum UHPLC conditions for the analysis of drugs.

This study aims to develop a robust and sensitive UHPLC method capable of simultaneously detecting and quantifying thymoquinone and hydrocortisone in proposed SNEDDS formulations. To achieve this purpose, the impact of the mobile phase flow rate, the ratio of the aqueous phase, and the column temperature on the measured response were investigated. After that, the suggested optimized UHPLC method was validated in terms of linearity, accuracy, and precision. Finally, HCT and TMQ contents within the SNEDDS formulation were estimated using the UHPLC method to validate its accuracy in quantifying drug concentrations.

2. Materials and Methods

2.1. Materials

AVONCHEM Ltd. (Cheshire, UK) and Sigma-Aldrich (St. Louis, MO, USA), respectively, supplied hydrocortisone and thymoquinone. Nicole Chemical Co. (Tokyo, Japan) provided hydrogenated castor oil 30. BASF (Ludwigshafen, Germany) provided Imwitor-308. Black seed oil (BSO) was procured from the Wadi Al-Nahil Investment Group (Riyadh, Saudi Arabia). All other reagents were of analytical grade and used without further purification.

2.2. Optimizing HPLC Method Parameters Using Design Expert

Developing an optimal ultrahigh-performance liquid chromatography (UHPLC) method is critical in pharmaceutical analysis and quality control. Design of Experiments software was used to study the influence of independent variables on the measured responses to optimize the UHPLC method. The response surface methodology (RSM) approach, specifically the Box–Behnken design (BBD), was used to achieve this purpose. Table shows the statistical design parameters, including three independent variables (temperature, flow rate, and buffer ratio) with their respective ranges and seven dependent responses (retention time, peak area, and peak asymmetry for both HCT and TMQ, along with their resolution), that were optimized using Box–Behnken experimental design. Moreover, Table presents the suggested 15 experimental runs used in the present study to optimize the UHPLC. The selected mathematical models were validated by evaluating various statistical parameters, such as the p-value and the coefficients of determination (R², adjusted R², and predicted R²). The generated regression equations and 3D surfaces provided valuable insights into the relationships between the factors and responses. The suitability of the models was assessed by using the p-values and F-values. These statistical tools enabled us to identify the optimal UHPLC conditions to yield the desired method performance.

1. Statistical Design of the Independent and Dependent Factors Used to Develop and Optimize the UHPLC Method for HCT and TMQ.

Independent factors	Name	Units	Low (−1)	High (+1)	Dependent factors (responses)
A	Temperature	°C	20	40	Retention time (Y1 and Y5), peak area (Y2 and Y6), peak asymmetry (Y3 and Y7), and resolution (Y4)
B	Flow rate	mL/min	0.2	0.4
C	Aqueous buffer (mobile phase B)	%	60	75

Suggested 15 runs by DOE using Box–Behnken design approach
Std	Run	A: Temp (°C)	B: flow rate (mL/min)	C: buffer (%)
1	1	20	0.2	67.5
9	2	30	0.2	60
8	3	40	0.3	75
12	4	30	0.4	75
2	5	40	0.2	67.5
5	6	20	0.3	60
14	7	30	0.3	67.5
10	8	30	0.4	60
6	9	40	0.3	60
13	10	30	0.3	67.5
7	11	20	0.3	75
11	12	30	0.2	75
3	13	20	0.4	67.5
15	14	30	0.3	67.5
4	15	40	0.4	67.5

2.3. Chromatography Conditions

The quantification of HCT and TMQ was conducted using a Thermo chromatography (DIONEX UltiMate 3000) isocratic quaternary solvent pump system (Thermo Fisher Scientific Inc., Waltham, MA, USA). The UHPLC system also included autosamplers, a column oven, an inline degasser, and a PDA (photodiode array) detector. Chromeleon Client Program Software version 7 (Waltham, MA, USA) was used to program the system and analyze the acquired data. Both HCT and TMQ were quantified using a Phenomenex (50 mm × 2.1 mm, 1.7 μm particle size) reversed-phase C₁₈ analytical column. The eluted mobile phase consisted of a predetermined mixture of mobile phase A (acetonitrile) and mobile phase B (0.1% v/v formic acid in water). During method optimization, the composition was varied by adjusting the aqueous buffer ratio from 60% to 75% v/v. The flow rate was set between 0.2 and 0.4 mL/min under a column temperature range of 20–40 °C. The wavelengths used to detect HCT and TMQ were 245 and 255 nm, respectively. The injection volume was 2 μL for each sample.

2.4. Preparation of Stock, Standard, and Quality Control Samples

Accurately weighed amounts of the drugs (5 mg each) API (HCT and TMQ) were transferred into volumetric flasks (10 mL), and these were separately dissolved using acetonitrile to prepare a stock solution with a final concentration of 500 μg/mL. Standard solutions with concentrations ranging from 1.0 to 30.0 μg/mL were prepared from the stock solutions by appropriate dilution. In addition, quality control (QC) samples, consisting of the lower limit of detection (1.0 μg/mL) as well as low (3.0 μg/mL), intermediate (12.0 μg/mL), and high concentrations (24.0 μg/mL), were also prepared following the same procedure.

2.5. UHPLC Method Validation Parameters

The analytical method was validated according to international guidelines (ICH guidelines) through the evaluation of linearity, accuracy, precision, robustness, and sensitivity parameters.

2.5.1. Linearity

The linearity of the proposed UHPLC method was evaluated across a concentration range of 1–30 μg/mL for both HCT and TMQ. Six independent replicates of freshly prepared solutions were analyzed for each concentration level. The peak areas were recorded, and statistical parameters, including the mean, standard deviation (SD), and relative standard deviation (RSD), were calculated to assess the linear relationship between analyte concentration and detector response.

2.5.2. Accuracy and Precision

The accuracy of the optimized UHPLC method was estimated to determine the closeness of the mean actual concentration to the theoretical concentration. Moreover, precision was estimated to define how much actual drug concentration for each injection is close to the other injections. Four concentration levels were selected to assess method accuracy (% recovery) and precision (% RSD): 1 μg/mL representing the lower limit of quantification (LLOQ), 3 μg/mL as a low-quality control (LQC), 12 μg/mL as a middle-quality control (MQC), and 24 μg/mL as a high-quality control (HQC). Six replicates at each concentration level were analyzed daily for 3 days.

2.5.3. Robustness

The robustness of the UHPLC method was evaluated by deliberately varying critical chromatographic parameters within a realistic range. The performance of the method was assessed under different analytical conditions using a medium-quality control concentration of 12 μg/mL. The evaluation included varying the mobile phase flow rate (0.18, 0.20, and 0.22 mL/min), adjusting the column temperature (18, 20, and 22 °C), and modifying the UV detection wavelength (HCT: 243, 245, and 247 nm; TMQ: 253, 255, and 257 nm) for HCT and TMQ, respectively. The impact of these variations on the chromatographic performance was assessed to ensure method reliability under slightly different analytical conditions, demonstrating the capacity of the method to withstand minor but deliberate variations in procedural parameters while maintaining its reliability and accuracy.

2.5.4. Sensitivity

The method sensitivity was determined by calculating the limit of detection (LOD) and limit of quantification (LOQ) using the following equations:

$$\mathrm{LOD}=(3.3\times \mathrm{SD})/\mathrm{s}$$ 1

$$\mathrm{LOQ}=(10\times \mathrm{SD})/\mathrm{s}$$ 2

where SD represents the standard deviation of the response and s represents the slope of the calibration curve. These parameters demonstrate the capability of the method to reliably detect and quantify low concentrations of the analytes.

2.6. Preparation and Drug Estimation from the Selected SNEDDS Formulation

A hydrocortisone-free SNEDDS formulation was prepared using hydrogenated castor oil 30, Imwitor-308, and black seed oil as a surfactant, cosurfactant, and oil phase in a ratio of 4:3:3, respectively. The components were accurately weighed and mixed thoroughly to achieve a homogeneous mixture. Subsequently, 10 mg of hydrocortisone was incorporated into 1990 mg of the SNEDDS formulation to produce a hydrocortisone-loaded SNEDDS formulation with a drug loading of 5 mg/g.

3. Results and Discussion

3.1. Studying Impact of Independent Factors on UHPLC Method Responses

The Box–Behnken design (BBD) approach was employed to optimize the UHPLC method for the simultaneous quantification of HCT and TMQ. The BBD approach effectively predicts the appropriate model for each response, enabling the visualization of relationships between experimental factors and chromatographic responses. Unlike traditional approaches, BBD facilitates observing linear and nonlinear interactions between independent variables. DoE suggested 15 experimental runs that comprehensively explore the analytical space while maintaining experimental efficiency. This allows for the effective investigation of the impact of selected independent variables (temperature, flow rate, and buffer ratio) on the measured responses (retention time, peak area, and peak asymmetry of HCT and TMQ, along with the resolution between them). Table shows data for the measured responses of the suggested 15 runs. Table shows the statistical summary of the selected model for all measured chromatographic responses (Y₁–Y₇), along with their generated polynomial equations. All responses are quadratic except for Y₃ and Y₇. The generated polynomial equations suggested a significant impact of the explored factors on the set responses. Therefore, these are critical factors taken into consideration while performing method development for reproducible analysis with high accuracy and precision. A method can be considered economic with rapid analysis with short retention time for the tested drugs. Thus, the method can be optimized based on short retention time and high accuracy.

2. Chromatographic Parameters for Simultaneous Determination of HCT and TMQ Using the Box–Behnken Experimental Design.

	HCT				TMQ
Run	Retention time (min)	Peak area (mAU·min)	Peak asymmetry	Resolution between HCT and TMQ peaks	Retention time (min)	Peak area (mAU·min)	Peak asymmetry
1	1.53	8.13	1.12	10.17	6.53	12.64	1.34
2	1.1	7.95	1.33	6.81	3.42	13.09	1.29
3	2.02	5.53	0.98	9.53	6.47	8.56	1.4
4	1.63	4.15	0.99	10.24	5.59	6.67	1.48
5	1.52	8.25	1.18	8.09	5.11	12.69	1.29
6	0.75	5.37	1.4	7.4	2.53	9.22	1.36
7	1.04	5.58	1.22	8.99	3.87	9.04	1.38
8	0.57	3.97	1.47	6.45	1.71	7.15	1.4
9	0.75	5.55	1.49	5.81	2.07	9.34	1.36
10	1.05	5.55	1.21	9.01	3.87	8.99	1.4
11	2.23	5.67	0.94	11.39	8.62	8.75	1.49
12	3.11	8.56	0.92	10.42	11.21	12.23	1.33
13	0.8	4.05	1.18	9.85	3.24	6.96	1.46
14	1.04	5.58	1.23	8.93	3.87	9.08	1.37
15	0.78	4.33	1.36	7.89	2.57	6.99	1.44

3. Statistical Summary and Regression Analysis of Optimization Parameters for Chromatographic Responses (Y₁–Y₇) Using Box–Behnken Design.

Response	p	F	R2	Pred. R2	PRESS	Model
Y1	0.0001	0.2379.4	0.999	0.997	0.0076	Quadratic
Y2	0.0001	734.7	0.995	0.989	0.3722	Quadratic
Y3	0.0001	148.8	0.976	0.951	0.0238	Linear
Y4	0.0001	1495.4	0.998	0.998	0.0043	Quadratic
Y5	0.0001	128600	1.0	0.999	0.0002	Quadratic
Y6	0.0001	6326.7	0.999	0.999	0.0568	Quadratic
Y7	0.0001	34.86	0.905	0.805	0.0105	Linear

	Generated polynomial equations
Y1	= 0.9590 + 0.3264B – 0.4730C – 0.1673BC – 0.0524C2
Y2	= 5.55 – 2.05B + 0.1338C + 0.6266B2
Y3	= 1.20 + 0.0462A + 0.0562B – 0.2325C
Y4	= 3.09 – 0.1571A – 0.0222B + 0.3159C – 0.0952C2
Y5	= 1.35 – 0.1206A – 0.3471B + 0.5921C + 0.0034AB – 0.0216AC + 0.0552B2 + 0.0677C2
Y6	= 9.03 + 0.0012A – 2.86B – 0.3338C – 0.0775AC + 0.0950BC + 0.8017B2 – 0.0508C2
Y7	= 1.34 – 0.02A + 0.0662B + 0.0362C

3.2. Retention Time

The retention time results for HCT (Y₁) and TMQ (Y₅) demonstrated significant variation across the experimental conditions, ranging from 0.57 to 3.11 min and from 1.71 to 11.21 min with mean values of 1.33 and 4.71 min, respectively. One-way ANOVA analysis of the selected three independent factors on the retention time of HCT and TMQ is presented in Supplementary Table T1 and Figure . The data showed that the flow rate and buffer significantly influenced the retention time of HCT and the peak area (Figure A–D), with an insignificant impact of temperature. Similarly, the buffer composition greatly influenced the retention time and the peak area (Figure A–D). Thus, a low buffer ratio can be recommended to achieve the peak earlier for HCT. The impact of temperature, buffer composition, and flow rate on the peak asymmetry for HCT is approximately proportional and linear, as shown Figure E,F. Thus, low temperature of the column, flow rate, and buffer composition may reduce the peak asymmetry of HCT. Increasing the flow rate and temperature significantly reduced the retention time of TMQ, which may be attributed to increased drug solubility at higher temperature. To investigate the peak resolutions of both drugs, these three factors must be taken into account. It is apparent that the temperature and the buffer composition had a relatively pronounced impact on the peak resolution as compared to the flow rate, as depicted in Figure G,H. Similarly, Figure I–L demonstrates the impact of these factors on the retention time and the peak area for TMQ. The temperature was found to be less effective on the peak area than the retention time for TMQ. Thus, optimal levels of buffer composition, column temperature, and flow rate can be recommended operating conditions for the sensitive and reproducible analysis of TMQ for rapid retention and low peak asymmetry (Figure M,N).

1.

(A–N) 3D response plots, illustrating the impact of the factors on the responses Y₁–Y₇ for HCT and TMQ.

The retention time of the eluted drugs is an important parameter during method optimization due to its direct impact on the time and consumption of organic solvents. The observed reduction in HCT and TMQ while increasing the mobile phase flow rate is ascribed to the mobile phase velocity, which increases the speed of the drug elution. Similarly, increased column temperatures reduce the viscosity of the mobile phase, which accelerates TMQ elution with the mobile phase. However, the observed minimal impact of the column temperature on HCT is likely a result of the rapid drug elution as compared to TMQ, which minimizes the influence of temperature on HCT elution. On the other hand, increasing the buffer ratio favors the retention of drugs on a hydrophobic column, which significantly delays the drug elution and increases retention time. ,

3.3. Peak Area

The results of the peak area for HCT (Y₂) and TMQ (Y₆) demonstrated significant variation across the experimental conditions, ranging from 3.97 to 8.56 mAU·min and from 6.67 to 13.09 mAU·min, with mean values of 5.88 and 9.43 mAU·min, respectively. ANOVA analysis of the selected three independent factors on the peak area of HCT and TMQ is presented in Supplementary Table T1 and Figure . The data showed that the flow rate and buffer composition significantly influenced the peak area of both drugs. On the contrary, the temperature did not significantly affect the peak area of both drugs. In conclusion, increasing the flow rate significantly reduced the peak areas of both drugs. On the other hand, increasing buffer composition significantly increased the peak area of both drugs.

The peak area responses for both analytes (Y₂ and Y₆) exhibited notable sensitivity to the experimental conditions, providing crucial information about method detectability and quantification capabilities. The increment in the peak area observed due to the decreasing flow rate could be attributed to the proper interaction between the drugs and columns. This could positively give a chance for optimum drug resolution and augment the detected signal. The observed increment in peak areas with increasing buffer aligns with the extended retention time, which provides adequate time for the drug–column interactions and consequently enhances the detection signal.

3.4. Peak Asymmetry

The results for the peak asymmetry of HCT (Y₃) and TMQ (Y₇) demonstrated significant variation across the experimental conditions, ranging from 0.92 to 1.49 and from 1.29 to 1.49, with mean values of 1.20 and 1.39, respectively. ANOVA analysis of the selected three independent factors on the peak asymmetry of HCT and TMQ is presented in Supplementary Table T1 and Figure . The data showed that the temperature, flow rate, and buffer composition significantly influenced the peak asymmetry of both drugs (p < 0.05). Conclusively, increasing the flow rate and temperature significantly increased the peak asymmetry of both drugs, whereas increasing the buffer composition significantly decreased the peak asymmetry.

Peak asymmetry values (Y₃ and Y₇) are crucial indicators of the chromatographic performance and peak shape quality. They give a precise indication of the drug elution from the column, where the optimum value is close to 1. The impact of the buffer ratio could be ascribed to its effects on the drug ionization and its interaction with the column. On the other hand, increasing both flow rate and temperature resulted in peak asymmetrical distortion, which could be attributed to insufficient time for proper analyte distribution at higher flow rates and modified drug–column interactions at elevated temperatures.

3.5. Resolution

The resolution results for HCT and TMQ (Y₄) demonstrated significant variation across the experimental conditions, ranging from 5.81 to 11.39, with a mean value of 8.73. ANOVA analysis of the selected three independent factors on the resolution of HCT and TMQ is presented in Supplementary Table T1. The data showed a significant impact of temperature, flow rate, and buffer composition on the resolution of both drugs (p < 0.05). Thus, increasing the flow rate and temperature significantly decreased the resolution between drugs. On the other hand, increasing buffer composition significantly increased the resolution between drugs.

The resolution between hydrocortisone and thymoquinone (Y₄) emerged as a critical quality attribute, demonstrating robust separation across all experimental conditions. The resolution between the two drug peaks significantly influences the accuracy of the analysis. The observed increment in resolution while increasing buffer composition could be attributed to the increased retention time, which provides adequate spacing between the peaks. On the other hand, the decrease in resolution with increasing flow rate and temperature could be explained by reduced interaction time between analytes and the stationary phase, leading to insufficient peak separation.

3.6. Optimization of the UHPLC Method

Traditional optimization approaches are impractical and inefficient due to their one-factor-at-a-time methodology. This fails to provide precise response predictions and accurate estimates of factor related interactions. On the other hand, systematic optimization using DoE enables a comprehensive mathematical modeling of multiple factors simultaneously and predicts optimum factors to achieve desirable responses. Without compromising desirability, DoE software suggested the optimized formulation based on the following criteria: low retention time, maximum peak area, peak asymmetry close to 1, and maximum resolution. This reduces the consumption of excess organic solvents and increases the method sensitivity, peak shape, and interference between two peaks. The suggested optimized UHPLC method consisted of a temperature of 20 °C, a flow rate of 0.2 mL/min, and a buffer ratio of 70.7%. The desirability of the optimized conditions was 0.9267 (Figure ), indicating that the suggested response aligns with the suggested criteria.

2.

Individual and overall desirability values for optimization of UHPLC method parameters.

3.7. Confirmation

The optimized UHPLC method was implemented to compare the predicted and observed responses, as shown in Table . Figure shows a chromatogram obtained from the injection of a standard solution containing HCT and TMQ. The observed retention times of HCT and TMQ were 1.542 and 6.647 min, respectively. Moreover, the measured peak areas for injected samples were 8.314 and 12.754 mAU·min, respectively. The peak asymmetry values for HCT and TMQ were 1.113 and 1.343, respectively. In addition, the estimated resolution value between the two peaks was 10.173. It is clear from the results that the mean of the observed responses is close to the predicted values, indicating the validity of the current design.

4. Comparison between Predicted and Observed Chromatographic Responses for HCT and TMQ Using Optimized UHPLC Method Conditions.

Response	Predicted mean	Observed mean
Retention time (HCT)	1.54065	1.542
Peak area (HCT)	8.22824	8.314
Peak asymmetry (HCT)	1.08886	1.113
Resolution between HCT and TMQ	10.1815	10.173
Retention time (TMQ)	6.71971	6.647
Peak area (TMQ)	12.6719	12.754
Peak asymmetry (TMQ)	1.3413	1.343

3.

Chromatogram of a hydrocortisone (HCT) and thymoquinone (TMQ) standard solution (50.0 μg/mL) using optimized UHPLC conditions.

3.8. Validation of UHPLC Method Parameters

3.8.1. Linearity

The validation of the studied UHPLC method for the simultaneous quantification of HCT and TMQ demonstrated excellent linearity over the concentration range of 1–30 μg/mL (Table ). For HCT, the calibration curves exhibited remarkable consistency with slopes ranging from 0.4050 to 0.4090, while TMQ showed a similarly robust performance with slopes between 0.6345 and 0.6400. The method’s reproducibility was confirmed through six independent preparations at each concentration level. Both analytes demonstrated minimal systematic bias, with HCT showing intercept values from −0.0314 to −0.0133 and those of TMQ ranging from −0.0889 to −0.0615. These results, coupled with correlation coefficients (R²) exceeding 0.9999 for both compounds, indicate exceptional linearity across the entire calibration range. The consistency of these fundamental parameters provides strong evidence for the method’s stability and reliability in routine analysis.

5. Linear Regression Analysis of HCT and TMQ via the Developed UHPLC Method .

Parameter	HCT	TMQ
Range (μg/mL)	1–30	1–30
Regression coefficient	0.9999	0.9999
Slope	0.4050-0.4090	0.6345-0.6400
Intercept	from –0.0314 to –0.0133	from –0.0889 to –0.0615
LOD (μg/mL)	0.2030	0.1290
LOQ (μg/mL)	0.6150	0.3920

^aLOD: limit of detection; LOQ: limit of quantification.

3.8.2. Accuracy and Precision

The accuracy and precision of the optimized UHPLC method for the simultaneous quantification of hydrocortisone (HCT) and thymoquinone (TMQ) were comprehensively evaluated through both interday and intraday studies at four concentration levels. Table shows the calculated accuracy and precision for the prepared quality control samples. The results showed that the HCT accuracy range was 96.41–102.69% and 96.43–101.37% for intra- and interday quality control samples, respectively. Moreover, the calculated precision of HCT was 0.37–9.39% RSD and 0.29–9.08% RSD, respectively. Regarding TMQ, the intra- and interday accuracy ranges of quality control samples were 97.83–103.43% and 97.94–106.21%, respectively. In addition, the calculated intra- and interday precisions of TMQ were 0.15–1.02% RSD and 0.44–2.55% RSD, respectively. The present results revealed that optimized UHPLC could estimate HCT and TMQ concentrations in the selected range (1–30 μg/mL).

6. Intra- and Interday Accuracy and Precision for Quality Control Samples of HCT and TMQ.

	Intraday accuracy and precision		Interday accuracy and precision
Quality control sample	Accuracy (%)	Precision (% RSD)	Accuracy (%)	Precision (% RSD)
HCT
1.0 μg/mL	102.69	9.39	101.11	9.08
3.0 μg/mL	101.38	1.30	101.37	1.25
12.0 μg/mL	99.62	1.01	99.57	0.64
24.0 μg/mL	96.41	0.37	96.43	0.29
TMQ
1.0 μg/mL	103.43	1.02	106.21	2.55
3.0 μg/mL	102.08	0.75	102.66	0.91
12.0 μg/mL	100.51	0.52	100.78	0.47
24.0 μg/mL	97.83	0.15	97.94	0.44

3.8.3. Robustness

The robustness of the UHPLC method was evaluated by deliberately varying three critical parameters: UV detection wavelength (243–247 nm for HCT and 253–257 nm for TMQ), flow rate (0.18–0.22 mL/min), and column temperature (18–22 °C) (Supplementary Table T2).

The results showed that changing the UV detection wavelength did not influence the retention time of both drugs, with RSD values of 0.10% and 0.04% for HCT and TMQ, respectively. Moreover, UV wavelength variations had a greater impact on the TMQ peak area (RSD 9.23%) compared with the HCT peak area (RSD 1.33%). The peak asymmetry showed variations with RSD values of 2.85% and 0.67% for HCT and TMQ, respectively, while the resolution between peaks maintained an RSD of 0.52%.

Changing the flow rate from 0.18 to 0.22 mL/min had a remarkable impact on the RSD values for HCT and TMQ, which were 8.26% and 8.71%, respectively. In addition, the flow rate showed a lower effect on the peak area of both drugs with RSD values of 4.99% and 4.47%, respectively. On the other hand, peak asymmetry was not affected by changing the flow rate, indicated by low RSD values, which were 1.02% and 1.08%, respectively. Varying the column temperature from 18 to 22 °C showed that for HCT, the retention time, peak area, and peak asymmetry had RSDs of 0.24%, 2.33%, and 2.66%, respectively. The resolution between the peaks was 10.181 ± 0.180. For TMQ, the retention time, peak area, and peak asymmetry had RSDs of 2.23%, 0.69%, and 1.15%, respectively.

3.8.4. Sensitivity

The method sensitivity for the simultaneous quantification of HCT and TMQ was evaluated by determining the limit of detection (LOD) and limit of quantification (LOQ) using statistical methods based on the calibration data. The calculations utilized the standard deviation of the response (0.025) and slopes from multiple calibration curves according to ICH guidelines.

For HCT, using the average standard deviation of response (0.025) and mean slope (0.406327), the LOD was calculated as 0.203 μg/mL (LOD = 3.3 × 0.025/0.406327). The LOQ was determined to be 0.615 μg/mL (LOQ = 10 × 0.025/0.406327). For TMQ, employing the same standard deviation (0.025) and its mean slope (0.638315), the calculated LOD was 0.129 μg/mL (LOD = 3.3 × 0.025/0.638315), while the LOQ was determined to be 0.392 μg/mL (LOQ = 10 × 0.025/0.638315).

3.9. Preparation and Content Determination of Selected SNEDDS Formulation

The validated UHPLC method was used to determine the actual HCT and TMQ contents within an SNEDDS formulation. Supplementary Figure S1 shows a representative chromatogram obtained from analyzing SNEDDS formulation samples containing HCT and TMQ using the validated UHPLC method. Moreover, the calculated percentages of drug recovery for HCT and TMQ were 96.8 ± 2.53% and 101.5 ± 2.37%, respectively. The precise quantification of both drugs indicates the validity in estimating the drug content of HCT and TMQ in the proposed formulation. Chemically, both HCT and TMQ are weakly acidic, with pK _a values of ∼12 for HCT and ∼5 for TMQ, respectively. Under the acidic mobile phase used, both analytes are largely un-ionized. TMQ is a weakly acidic drug with a pK _a value of 5, which was soluble in a mobile phase possessing acidic pH. Therefore, a neutral mobile phase (pH = 7) will result in drug insolubility and drug degradation in the aqueous system. Thus, the mobile pH was maintained at 4 by the addition of 0.1% formic acid. Conclusively, the mobile phase pH was advised to be on either side of the drug pK _a to maintain retention time consistency while performing analysis.

4. Conclusion

Considering the results obtained, the developed method is quite efficient and economical for the estimation of both drugs from the SNEDDS formulation and standard quality control samples. The studied validation parameters suggested that the adopted analytical method is accurate, precise, sensitive, and reproducible for the simultaneous estimation of TMQ and HCT from nonbiological samples (formulations). Moreover, the identified critical analytical attributes were the column temperature, flow rate, and buffer composition. The temperature showed an inversely proportional impact on the retention time, which may be attributed to the acidic nature of TMQ (pK _a = 5.0) and HCT (pK _a = 12.2). Both drugs exhibited well-resolved peak development in the explored mobile phase at the investigated temperature. Similarly, the retention time was reduced upon the use of an increased flow rate. Thus, a well-resolved peak can be developed by controlling the combined impact of the column temperature, flow rate, and buffer composition for the efficient estimation of both drugs from formulations with high sensitivity and accuracy.

The supplementary data are available in the Supporting Information.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c07999.

• ANOVA analysis data, robustness evaluation, and the HPLC peaks for both drugs estimated from the SNEDDS formulation (PDF)

The authors acknowledge and extend their appreciation to the Ongoing Research Funding program (ORF-2025-524), King Saud University, Riyadh, Saudi Arabia, for funding this study.

The authors declare no competing financial interest.