Development of a QAMS Analysis Method for Industrial Lanolin Alcohol Based on the Concept of Analytical Quality by Design

Abstract

The Analytical Quality by Design (AQbD) concept was adopted to establish a quantitative analysis of multi-components with a single marker (QAMS) method for industrial lanolin alcohol, targeting cholesterol, lanosterol, and 24,25-dihydrolanosterol. The potential critical method parameters (CMPs) were identified as column temperature, flow rate, and gradient. Definitive screening design and statistical modeling were employed to optimize the gradient conditions of the mobile phase, column temperature, and flow rate. The Method Operable Design Region (MODR) was determined using a risk-based quantification approach. The robustness was assessed using a Plackett–Burman experimental design, followed by methodological validation. Optimal analytical conditions were as follows: acetonitrile (B)—water (A) mobile phase system; flow rate of 1.58 mL/min; detection wavelength of 205 nm; injection volume of 10 µL; and column temperature of 37 °C. A gradient elution program was implemented as follows: 0–19.0 min, 90.5% B; 19.0–25.0 min, 90.5–100% B; and 25.0–55.0 min, 100% B. Cholesterol served as an internal standard for quantifying lanosterol and 24,25-dihydrolanosterol, with relative correction factors of 0.4227 and 0.8228, respectively. This analytical method utilized only the cholesterol reference substance as an internal standard to quantify the content of cholesterol, lanosterol, and 24,25-dihydrolanosterol in industrial lanolin alcohol. It reduced the testing costs and enhanced efficiency, making it potentially suitable for widespread adoption in lanolin alcohol processing industries.

1. Introduction

Industrial lanolin alcohol, also known as industrial wool wax alcohol, is derived from lanolin through saponification and various separation processes [1]. Key chemical components of industrial lanolin alcohol include cholesterol (molecular formula C₂₇H₄₆O), lanosterol (molecular formula C₃₀H₅₀O), and 24,25-dihydrolanosterol (molecular formula C₃₀H₅₂O) [2], as depicted in Figure 1. All three feature a tetracyclic structure. Cholesterol is a steroid compound [3], while lanosterol and 24,25-dihydrolanosterol are tetracyclic triterpenoid compounds differing by only one double bond in their side chains [4].

Cholesterol is utilized in the biosynthesis of 7-dehydrocholesterol [3,5], which is a precursor to vitamin D3. Additionally, cholesterol is used in aquaculture feed and in the production of artificial bezoar. Lanosterol plays important physiological roles, such as enhancing cellular protective responses by inducing abnormal proteasome degradation [6], regulating protein homeostasis [7], and reducing protein aggregation within the lens of the eye [8]. It is a significant raw material in the cosmetics, pharmaceuticals, and chemical industries. Recent studies have also highlighted lanosterol’s potential in alleviating cataracts [9,10,11], with subconjunctival injection emerging as a promising non-surgical approach for cataract prevention and treatment [12]. 24,25-Dihydrolanosterol, a substrate of CYP51 [13], exhibits physiological activity in inhibiting cholesterol synthesis.

The composition of industrial lanolin alcohol varies between batches due to differences in the quality of raw lanolin and the methods used for extraction. To strengthen quality control and improve efficiency in the utilization of industrial lanolin alcohols, it is necessary to conduct a quantitative analysis of their chemical composition. Depending on their chemical composition, industrial lanolin alcohols can be tailored for specific downstream applications. For instance, those with a higher lanosterol content may be targeted for high-purity lanosterol extraction, while those rich in cholesterol might undergo processes like molecular distillation for cholesterol extraction. High-performance liquid chromatography (HPLC) is a chromatographic technique that separates compounds based on differences in their distribution coefficients between the stationary phase and mobile phase [14]. It is recognized for its efficiency, rapidity, and sensitivity, which facilitate the accurate analysis of complex samples. Moreover, HPLC is not constrained by the volatility or thermal stability of the sample, making it one of the most widely used analytical methods [15]. However, there were no reported HPLC methods for analyzing industrial lanolin alcohols. Moreover, the high cost of lanosterol and 24,25-dihydrolanosterol reference standards necessitates the development of cost-effective liquid chromatography methods capable of simultaneously quantifying the levels of cholesterol, lanosterol, and 24,25-dihydrolanosterol in industrial lanolin alcohols.

Quality by Design (QbD) is a systematic drug development approach based on extensive scientific knowledge and quality risk management, starting from predefined objectives and emphasizing the understanding and control of the product and process [16]. Extending the concept of QbD to the development of analytical methods is referred to as Analytical Quality by Design (AQbD). The ICH Q14 guideline describes principles of risk-based analytical method change management and introduces AQbD as an enhancement approach for analytical method development [17]. The basic implementation steps of AQbD involve defining the analytical target profile (ATP) and critical quality attributes (CQAs), conducting a risk assessment and prior knowledge evaluation to identify analytical method parameters that may significantly impact method performance, studying relevant parameter ranges through Design of Experiments (DoE), determining the Method Operable Design Region (MODR), and performing method validation [18]. AQbD emphasizes providing expected performance throughout the entire lifecycle, ensuring that analytical methods are easily understandable and robust [19]. Currently, AQbD has been widely applied in the development of analytical methods for traditional Chinese medicine [20,21,22,23,24,25], chemical drugs [26,27,28], biological drugs [29,30,31,32], and food products [33,34,35]. The use of DoE allows for studying relationships among multiple parameters with fewer experiments [36]. Specifically, the definitive screening design (DSD) approach offers advantages such as requiring fewer trials, providing high resolution, and resulting in savings in both time and experimental costs [37], thereby making it particularly suitable for optimizing analytical method parameters.

Quantitative analysis of multi-components with a single marker (QAMS) refers to an analytical method where the content of multiple target components in a sample is determined using a single reference substance [38]. This approach is particularly suitable for components that are difficult to obtain or expensive as reference materials, or which exhibit poor stability [39]. Typically, an inexpensive component structurally similar to the target analytes is employed as the internal standard [40]. Relative correction factors (RCFs) are established between the analytes and the internal standard to calculate the contents of other components concurrently, facilitating the simultaneous determination of multiple components [41].

The AQbD concept was employed to establish a QAMS method for quantifying the cholesterol, lanosterol, and 24,25-dihydrolanosterol in industrial lanolin alcohol. First, the ATP and CMPs were defined. A definitive screening experimental design was employed to optimize the chromatographic conditions. Quantitative models correlating chromatographic responses with method parameters were established. Subsequently, an MODR was developed employing a risk-based quantification approach. A parameter combination was then selected from within the MODR to develop a QAMS method. The method’s robustness was assessed using a Plackett–Burman experimental design. Finally, methodological validation and application of this AQbD-based QAMS method for industrial lanolin alcohol were conducted.

2. Materials and Methods

2.1. Materials and Reagents

Acetonitrile was purchased from Merck (chromatographic purity, Darmstadt, Germany). N-Methyl-2-pyrrolidone was purchased from Macklin Biochemical Co., Ltd. (analytical pure, Shanghai, China). Cholesterol standard was purchased from Aladdin Biochemical Technology Co., Ltd. (purity 99%, Shanghai, China). Ultrapure water was prepared using a Milli-Q water purification system (Millipore, Billerica, MA, USA). Lanosterol standard (purity 100%) was prepared in-laboratory. 24,25-Dihydrolanosterol standard was purchased from Aladdin Biochemical Technology Co., Ltd. (purity 95%, Shanghai, China). Ten batches of industrial lanolin alcohol samples were provided by Nowi Biotechnology Co., Ltd. (Jiangxi, China) or obtained through purchase.

2.2. Sample Preparation and Analysis

Preparation of Test Solution: Approximately 20 mg of industrial lanolin alcohol was accurately weighed into a 10-mL volumetric flask. N-Methyl-2-pyrrolidone was added and dissolved using an ultrasonic processor (KQ2200E, Meimei Ultrasonic Instruments Co., Ltd. Kunshan, China). The solution was then diluted to the mark and centrifuged at 12,000 rpm for 10 min using a mini high-speed centrifuge (AB204-N, Mettler Toledo, Zurich, Switzerland), and the supernatant was then obtained for analysis.

Preparation of Reference Solution: The reference solutions were prepared by dissolving appropriate amounts of cholesterol, lanosterol, and 24,25-dihydrolanosterol in N-methyl-2-pyrrolidone. This resulted in a solution containing 1.76 mg/mL of cholesterol, 1.28 mg/mL of lanosterol, and 1.16 mg/mL of 24,25-dihydrolanostero. The solution was subsequently diluted by factors of 3.333, 8.333, 20.83, 52.08, 130.2, and 325.5 to generate a series of mixed solutions with varying concentrations of the reference compounds.

Liquid Chromatography Analysis: The samples were analyzed using HPLC-UV-Vis (SHIMADZU LC-20AT, Shimadzu Corporation, Kyoto, Japan) with a SunShell C18 column (4.6 mm × 150 mm, 2.6 μm, Chromanik Technologies Inc., Osaka, Japan). The mobile phase consisted of water (A) and acetonitrile (B), and the chromatographic conditions were optimized.

2.3. Determining the Analytical Target Profile and Critical Method Parameters

Based on the AQbD strategy, the development of analytical methods begins with defining the ATP. The ATP comprises a description of the intended purposes of the analytical method, appropriate details of the attributes of the product under test, and performance characteristics alongside relevant performance criteria [42]. The ATP includes the determination requirements for one or multiple quality attributes [17]. Initially, the goal was to achieve complete chromatographic separation of cholesterol, lanosterol, and 24,25-dihydrolanosterol peaks while minimizing the analysis time, based on a preliminary analysis. Key method evaluation indicators were established according to the results of the preliminary experiments. According to the ICH Q14, it is recommended that a risk assessment be conducted and prior knowledge be evaluated to identify the analytical procedure parameters that may impact the performance of the analytical methods before advancing to multi-variate experiments and modeling [17]. The fishbone diagram serves as a valuable visual tool for finding all the analytical parameters. Therefore, a fishbone diagram analysis was performed.

2.4. Definitive Screening Experimental Design

The Design Expert (version 12.0.1.0, Stat-Ease Inc., Minneapolis, MN, USA) software was utilized to generate experimental design tables and conduct the subsequent data statistical analysis. Based on the preliminary experimental results, the critical method parameters of the chromatographic analysis method—column temperature (X₁), flow rate (X₂), and gradient (X₃–X₅)—were selected for the experimental design study. As shown in

Table 1. HPLC gradient condition.

Time/min	B%
0–X4	X3
X4~X5	X3~100
X5~70	100

, the mobile phase gradient for the analytical method was designed with three gradients involving three parameters (X₃–X₅). The levels chosen for each factor are detailed in

Table 2. Factors and levels of definitive screening design.

Level	X1 (Column Temperature)/°C	X2 (Flow Rate) /(mL/min)	X3 (The Initial Ratio of Phase B)/%	X4 (The End Time of Gradient 1)/min	X5 (The End Time of Gradient 2)/min
−1	32.0	1.40	87.0	18.0	24.0
0	35.0	1.50	89.0	20.0	27.0
1	38.0	1.60	91.0	22.0	30.0

. The evaluation criteria consisted of two metrics: the resolution between cholesterol and the unknown peak (Y₁) and the retention time of the last peak (Y₂). Given the multiple factors concurrently studied in this research, a definitive screening design was employed with three repetitions of center points across 15 experiments, as specified in

Table 3. Definitive screening design experimental conditions and results.

X1/°C	X2/(mL/min)	X3/%	X4/min	X5/min	Y1	Y2/min
35.0	1.40	87.0	18.0	24.0	1.356	60.204
32.0	1.40	91.0	20.0	30.0	1.835	64.703
32.0	1.60	87.0	18.0	30.0	1.816	62.462
32.0	1.50	91.0	18.0	24.0	1.766	58.900
38.0	1.60	87.0	20.0	24.0	1.416	54.484
38.0	1.40	89.0	18.0	30.0	1.677	60.920
35.0	1.60	91.0	22.0	30.0	1.888	57.495
38.0	1.50	87.0	22.0	30.0	1.769	60.928
32.0	1.60	89.0	22.0	24.0	1.646	59.028
38.0	1.40	91.0	22.0	24.0	1.644	57.123
32.0	1.40	87.0	22.0	27.0	1.410	67.294
35.0	1.50	89.0	20.0	27.0	1.766	58.917
35.0	1.50	89.0	20.0	27.0	1.758	58.934
35.0	1.50	89.0	20.0	27.0	1.800	59.216
38.0	1.60	91.0	18.0	27.0	1.649	53.398

.

2.5. Data Processing

Quantitative models were established to link various evaluation indicators with method parameters. Formula (1) was employed to construct these models, utilizing Design Expert 12.0.1.0 (Stat-Ease Inc., Minneapolis, MN, USA). The models were simplified through stepwise regression, with a significance level of 0.10 set for adding or removing terms. The data were analyzed using analysis of variance (ANOVA) to investigate the significant relationships between method parameters and chromatographic responses. Statistical parameters such as p-values, the coefficient of determination (R²), and the adjusted coefficient of determination (R²_adj) were employed to assess the fit and significance of the models.

$$Y=a_0+{\sum }_{i=1}^5{a}_i{X}_i+{\sum }_{i=1}^5{a}_{ii}{X}_i^2+{\sum }_{i=1}^4{\sum }_{j=i+1}^5{a}_{ij}{X}_i{X}_j$$

(1)

2.6. Establishment and Validation of MODR

Using MATLAB software (R2022b, MathWorks Inc., Natick, MA, USA), custom scripts developed in our laboratory were employed to compute the Method Operational Design Regions (MODR) process [43]. This study utilized an exhaustive Monte Carlo-based risk quantification approach to calculate MODR, with a significance level set at 0.050. The step sizes were 0.050 for X₁, 0.002 for X₂, 0.040 for X₃, 0.040 for X₄, and 0.040 for X₅. The maximum allowable risk for method failure was set at 0.10, and simulations were conducted 500 times.

2.7. Establishment and Validation of QAMS Method

2.7.1. Determination of Internal Standard Reference Material for QAMS

Internal standard reference materials must meet three criteria: (1) abundant content in the sample; (2) stability; and (3) ease of accessibility [39]. Cholesterol, due to its stable chemical properties and abundant presence in samples as a major active ingredient, was identified as suitable for use as an internal standard reference material in QAMS. Additionally, cholesterol is readily accessible and cost-effective as a reference material, making it the preferred choice.

2.7.2. Determination of Relative Retention Time and Relative Correction Factors

Cholesterol, lanosterol, and 24,25-dihydrolanosterol reference standards were precisely weighed and combined with N-methyl-2-pyrrolidone to prepare a mixed standard solution. This solution was injected into a liquid chromatograph to measure the peak areas and retention times. The relative correction factors and relative retention times were calculated using the standard curve method [44]. Equation (2) represents the calculation formula for relative correction factors, while Equation (3) outlines the formula for relative retention times, where $f$ is relative correction factor, $RRT$ is relative retention time, $A_s$ represents the peak area of internal standard, $C_s$ is its concentration, $A_i$ is the peak area of the target analyte, $C_i$ is its concentration, $R_s$ is the retention time of the internal standard, and $R_i$ is the retention time of the target analyte.

$$f={\displaystyle \frac{f_s}{f_i}}={\displaystyle \frac{\raisebox{1ex}{$A_s$}\!\left/ \!\raisebox{-1ex}{$C_s$}\right.}{\raisebox{1ex}{$A_i$}\!\left/ \!\raisebox{-1ex}{$C_i$}\right.}}$$

(2)

$$RRT=R_i/R_s$$

(3)

2.7.3. Robustness Testing

The robustness of an analytical method is the ability to consistently meet expected performance requirements during normal operation, which can be evaluated by varying the analytical parameters. In the study of robustness, a Plackett–Burman experimental design was employed to investigate the effects on chromatographic response, as well as on the relative retention times and relative correction factors of lanosterol and 24,25-dihydrolanosterol, when fluctuations occur in column temperature, flow rate, gradient changes, and injection volume within optimized ranges. The aim was to assess the robustness of QAMS. A total of 12 experiments were conducted, as detailed in

Table 4. Plackett–Burman experimental conditions and results.

	X1/°C	X2/(mL/min)	X3/%	X4/min	X5/min	X6/μL	Y1	Y2/min	Y3	Y4	Y5	Y6
1	38	1.56	91.0	19.5	25.5	5.0	1.957	52.90	1.095	0.4033	1.339	0.7950
2	36	1.56	90.0	18.5	24.5	5.0	1.538	53.45	1.069	0.3956	1.303	0.8084
3	36	1.56	91.0	18.5	25.5	15	1.700	53.39	1.089	0.4032	1.339	0.7805
4	38	1.60	90.0	18.5	24.5	15	1.559	52.70	1.070	0.4266	1.300	0.8544
5	38	1.60	91.0	18.5	24.5	5.0	1.757	52.26	1.084	0.4033	1.331	0.8019
6	36	1.60	90.0	19.5	25.5	5.0	2.057	53.80	1.073	0.4029	1.301	0.8068
7	38	1.56	91.0	19.5	24.5	15	1.633	53.69	1.078	0.4146	1.324	0.8135
8	36	1.60	91.0	19.5	24.5	5.0	2.085	52.61	1.083	0.4131	1.328	0.8185
9	38	1.60	90.0	19.5	25.5	15	1.586	54.61	1.077	0.4282	1.310	0.8483
10	38	1.56	90.0	18.5	25.5	5.0	1.724	54.92	1.080	0.4304	1.318	0.8556
11	36	1.56	90.0	19.5	24.5	15	1.504	54.22	1.093	0.4249	1.331	0.8282
12	36	1.60	91.0	18.5	25.5	15	1.735	53.04	1.090	0.4242	1.341	0.7978
RSD (%)									0.8108	2.966	1.160	2.996

Notes: X₁: column temperature, X₂: flow rate, X₃: the initial ratio of phase B, X₄: the end time of gradient 1, X₅: the end time of gradient 2, X₆: Injection volume, Y₁: the resolution between cholesterol and the unknown peak, Y₂: the retention time of the last peak, Y₃: lanosterol relative retention time, Y₄: lanosterol relative correction factor, Y₅: 24,25-dihydrolanosterol relative retention time, Y₆: 24,25-dihydrolanosterol relative correction factor.

. The parameters and their set ranges were as follows: column temperature (X₁): 37.0 ± 1.0 °C, flow rate (X₂): 1.58 ± 0.20 mL/min, the initial ratio of phase B (X₃): 90.5 ± 0.5%, the end time of gradient 1 (X₄): 19.0 ± 0.5 min, the end time of gradient 2 (X₅): 25.0 ± 0.5 min, and injection volume (X₆): 10.0 ± 5.0 μL.

2.8. Analytical Method Validation

Chromatographic conditions: The analytical method included a SunShell C18 column (4.6 mm × 150 mm, 2.6 μm) with a mobile phase of acetonitrile (B) and water (A). The flow rate was 1.58 mL/min, with detection at 205 nm. A 10 µL sample was injected at a column temperature of 37 °C. Gradient elution conditions were applied as follows: 0 to 19.0 min, 90.5% B; 19.0 to 25.0 min, 90.5% to 100% B; and 25.0 to 55.0 min, 100% B.

Linear assessment: A range of different concentrations of control solution mixtures were injected in a volume of 10 µL each for analysis. The peak areas of each component were plotted against their concentrations to construct standard curves and establish linear regression equations within the analytical range.

Injection precision: Precision was tested by injecting the same sample solution six times consecutively, calculating the relative standard deviation (RSD) values for peak areas and retention times.

Method repeatability: Repeatability was assessed by analyzing six parallel-prepared sample solutions separately, calculating the RSD values for the content of each component.

Sample stability: The stability of the sample was tested by injecting the same sample solution at 0, 3, 6, 9, 12, 15, 18, 21, and 24 h, calculating the RSD values for the peak areas of each component.

Recovery test: Nine portions of sample solutions with known concentrations were prepared and divided into three groups. These groups represented low, medium, and high concentration levels, with spiked control additions aimed at achieving ratios of approximately 0.8:1.0, 1.0:1.0, and 1.2:1.0 relative to the target analyte levels in the sample. Each concentration level was independently prepared in triplicate for subsequent analysis.

2.9. Method Applications

Ten samples of industrial lanolin alcohol from different brands and batches were analyzed using a developed QAMS method via liquid chromatography. Cholesterol, lanosterol, and 24,25-dihydrolanosterol content were quantified using both QAMS and external standard methods. The relative deviation between the results obtained from the external standard method and QAMS was calculated.

3. Results

3.1. Determination of Analytical Target Profile and Critical Method Parameters

In the development of this analytical method, the ATP was defined as the simultaneous determination of cholesterol, lanosterol, and 24,25-dihydrolanosterol in industrial lanolin alcohol, under the following conditions: (1) chromatographic peaks of analytes exhibit high resolution; (2) analysis time is minimized; (3) precision, repeatability, and stability of injection are expressed as RSD less than 5%; and (4) recovery rate of spiked samples falls within 95–105% with RSD less than 5%. Based on ATP, the resolution and retention time are defined as CQAs. According to the preliminary results, it is challenging to separate cholesterol from nearby unknown peaks, whereas lanosterol and 24,25-dihydrolanosterol peaks are more distinguishable. Thus, the key method evaluation indicators were defined as the resolution between cholesterol and the unknown peak (Y₁) and the retention time of the last peak (Y₂).

Through a literature review and brainstorming, a fishbone diagram was constructed to outline potential CMPs, as depicted in Figure 2. The method parameters were categorized into five groups: mobile phase, detection conditions, column, gradient, and sample. Based on the preliminary experimental findings, the gradient, column temperature, and flow rate were selected as potential critical method parameters for the experimental design and investigation.

3.2. Experimental Data Modeling

The results of the definitive screening experiments are shown in Table 3. Quadratic mathematical models were developed. Regression coefficients for each model equation and the results of the variance analysis are presented in

Table 5. Regression coefficients and analysis of variance for each model.

		Y1		Y2
Term		Coefficient	p Value	Coefficient	p Value
Constant term	Constant	1.78	0	59.04	0
Linear term	X1	−0.0318	0.0060	−2.55	<0.0001
	X2	0.0493	0.0009	−2.34	<0.0001
	X3	0.1015	<0.0001	−1.38	<0.0001
	X4	0.0093	0.2397	0.5984	<0.0001
	X5	0.1157	<0.0001	1.68	<0.0001
Quadratic term	X12	-	-	1.04	<0.0001
	X22	−0.1524	<0.0001	-	-
	X42	-	-	0.2932	0.0281
	X52	-	-	−0.4593	0.0041
Interaction term	X1X2	−0.0384	0.0093	-	-
	X2X3	−0.0355	0.0074	-	-
	X3X4	0.0238	0.0670	-	-
Model	R2	0.9936		0.9991
	p value	<0.0001		<0.0001

, with all the models showing a highly significant level (p < 0.0001), thus confirming their statistical significance. The R² values for the two models were 0.9936 and 0.9991, indicating an excellent model fit and the ability to explain a significant portion of the data variability.

3.3. Influence of the Parameters

Contour plots illustrating different responses were derived from the established mathematical models, with examples presented in Figure 3. As the column temperature (X₁) increased, the resolution between cholesterol and the unknown peak (Y₁) decreased. With an increase in the flow rate (X₂), the resolution initially increased and then decreased. As the initial ratio of phase B (X₃), the end time of gradient 1 (X₄), and the end time of gradient 2 (X₅) increased, the resolution between cholesterol and the unknown peak also increased. As both column temperature and flow rate increased, the retention time of the last peak (Y₂) decreased. An increase in the initial ratio of phase B led to a decrease in the retention time of the last peak. A longer end time of gradient 1 and 2 resulted in a longer retention time for the last peak.

3.4. Results of the Establishment and Validation of MODR

This study utilized an exhaustive Monte Carlo-based risk quantification approach to calculate MODR. To meet the quantitative requirements, a minimum resolution of 1.550 between the unknown peak and cholesterol was set. Additionally, considering the need for shorter analysis times, an upper limit of 55.00 min was set for the retention time of the last peak. To effectively demonstrate the MODR, two parameters were held constant. The result of the MODR is shown in Figure 4. Parameter combinations that do not pose a risk greater than 10% of failing to meet the optimization objectives were included within the MODR.

Three sets of method parameters were chosen within and outside the MODR for validation experiments. The experimental conditions and results for these validation methods are detailed in

Table 6. Conditions and results of the MODR validation experiment.

	X1 (°C)	X2 (mL/min)	X3 (%)	X4 (min)	X5 (min)	Y1	Y2 (min)	Whether Meets Requirements
In	37.0	1.58	90.5	19.0	25.0	1.831	51.864	Yes
	38.0	1.56	91.0	19.5	25.5	1.957	52.903	Yes
	36.0	1.60	90.0	19.5	25.5	2.057	53.795	Yes
Out	34.0	88.0	1.40	19.0	25.0	0.982	64.522	No
	33.0	90.0	1.45	21.0	25.0	1.371	62.297	No
	37.0	90.5	1.42	22.0	30.0	1.600	60.844	No

. Within the MODR, all the indicators met the specified range requirements. However, for points outside the MODR, Y₁ and Y₂ did not meet the range requirements. This demonstrated the reliability of the established MODR.

3.5. Results of the Establishment and Validation of QAMS Method

3.5.1. Results of the Determination of Relative Retention Time and Relative Correction Factor

The calculation of the relative correction factor and relative retention time using the standard curve method is presented in

Table 7. The calculation of the relative correction factor and relative retention time.

Component	Linear Regression Equation	Relative Retention Time	Relative Correction Factor
Cholesterol	Y= 4.08 × 103 X	1.000	1.000
Lanosterol	Y= 9.65 × 103 X	1.087	0.4227
24,25-Dihydrolanosterol	Y= 4.96 × 103 X	1.323	0.8228

. Cholesterol was used as the internal standard; thus, the relative retention time for lanosterol was 1.087 with a relative correction factor of 0.4227, while the relative retention time for 24,25-dihydrolanosterol was 1.323 with a relative correction factor of 0.8228.

3.5.2. Results of the Robustness Testing

The Plackett–Burman experimental design was employed to assess the ability of the analytical method to meet the expected performance requirements when the operating parameters were at the edge of their optimized ranges. The study evaluated fluctuations in chromatographic responses, as well as in the relative retention times and relative correction factors of lanosterol and 24,25-dihydrolanosterol. The detailed results from the Plackett–Burman experiments are presented in Table 4. All 12 experiments showed a resolution greater than 1.5 between cholesterol and the unknown peak, with the retention time of the last peak being consistently below 55 min.

These findings indicated that the obtained method evaluation indicators met the analytical requirements when parameters varied within their optimized operational range. Using cholesterol as an internal standard, minimal fluctuations were observed in the relative retention times and relative correction factors of lanosterol and 24,25-dihydrolanosterol, all showing an RSD below 3%. This confirmed the robustness of the established single-standard multi-test analysis method. Therefore, the following robust MODR was recommended: column temperature (X₁): 37.0 ± 1.0 °C, flow rate (X₂): 1.58 ± 0.20 mL/min, the initial ratio of phase B (X₃): 90.5 ± 0.5% gradient 1 end time (X₄): 19.0 ± 0.5 min, gradient 2 end time (X₅): 25.0 ± 0.5 min, and injection volume (X₆): 10.0 ± 5.0 μL.

3.6. Results of the Analytical Method Validation

The chromatogram of the mixed reference standard and industrial lanolin alcohol obtained under the chromatographic conditions described in Section 2.8 is shown in Figure 5.

The linear regression equations and linear ranges for cholesterol, lanosterol, and 24,25-dihydrolanosterol are presented in

Table 8. Standard curves and linear ranges of cholesterol, lanosterol, and 24,25-dihydrolanosterol.

Component	Linear Regression Equation	R2	Linear Range (μg·mL−1)
Cholesterol	Y= 4.08 × 103 X	0.9997	5.42–529
Lanosterol	Y= 9.65 × 103 X	1.000	3.93–384
24,25-Dihydrolanosterol	Y= 4.96 × 103 X	1.000	3.56–348

. The results indicated that cholesterol exhibited strong linearity within the range of 5.42–529 μg·mL⁻¹, lanosterol within the range of 3.93–384 μg·mL⁻¹, and 24,25-dihydrolanosterol within the range of 3.56–348 μg·mL⁻¹.

The results of the injection precision, repeatability, and stability tests are presented in

Table 9. The results of tne injection precision, method repeatability, and sample stability tests.

Component	Injection Precision RSD (%)	Method Repeatability RSD (%)	Sample Stability RSD (%)
Cholesterol	1.629	1.855	1.721
Lanosterol	0.7341	1.125	0.8294
24,25-Dihydrolanosterol	1.715	1.911	1.807

. The RSD values for precision, repeatability, and stability were all less than 5%, meeting the requirements of the analytical method.

The results of the recovery experiments are presented in

Table 10. Results of the recovery experiments.

Concentration Level	Cholesterol	Lanosterol	24,25-Dihydrolanosterol
Low level recovery (%)	100.1	100.9	106.1
	99.10	100.3	101.2
	100.1	102.4	103.9
Medium level recovery (%)	101.5	104.1	98.40
	98.95	99.82	98.37
	95.21	97.69	100.3
High level recovery (%)	98.98	98.98	101.8
	101.5	101.1	102.3
	101.9	103.5	105.2
Average recovery (%)	99.70	101.0	101.8
RSD (%)	2.044	2.064	2.571

, where the average recovery rates for each component met the specified requirements with RSD values all below 5%. This demonstrates that the optimized method is accurate and reliable for determining the contents of cholesterol, lanosterol, and 24,25-dihydrolanosterol in industrial lanolin alcohol samples.

3.7. Application of the Analytical Method

The results of the cholesterol, lanosterol, and 24,25-dihydrolanosterol content determination in industrial lanolin alcohol samples from different batches are presented in

Table 11. Ten batches of industrial lanolin alcohol content determination results.

Manufacturer	Batch	Content Determined by External Standard Method%			Content Determined by QAMS Method%		ARD in Lanosterol Content Measured by Two Methods%	ARD in 24,25-Dihydrolanosterol Content Measured by Two Methods%
		Cholesterol	Lanosterol	24,25-Dihydrolanosterol	Lanosterol	24,25-Dihydrolanosterol
A	NK230912	5.54	9.89	6.26	10.1	6.45	2.10	2.99
A	NK240402	5.33	9.90	6.24	10.1	6.43	2.00	3.00
B	202403141	3.80	6.37	3.71	6.52	3.82	2.33	2.92
B	202403142	3.67	6.05	3.51	6.19	3.62	2.29	3.09
B	202403143	3.79	6.23	3.59	6.38	3.70	2.38	3.02
C	202211002	7.02	13.4	7.07	13.7	7.28	2.21	2.93
C	202207002	6.18	14.1	7.36	14.5	7.58	2.80	2.95
C	202211003	7.09	13.7	7.20	14.0	7.41	2.90	2.87
D	202301	24.1	12.2	5.69	12.4	5.87	1.63	3.11
E	202308	24.8	13.3	6.84	13.6	7.05	2.23	3.02

. The average relative deviations (ARD) between the results obtained using the QAMS method and the external standard method were less than 5%, indicating no significant differences between the two methods. The cholesterol content in industrial lanolin alcohol samples from five manufacturers across ten batches ranged from 3.67% to 24.8%, the lanosterol content ranged from 6.05% to 14.1%, and the 24,25-dihydrolanosterol content ranged from 3.51% to 7.36%. Together, these compounds accounted for a total content ranging from 13.23% to 44.94% in industrial lanolin alcohol, highlighting substantial variations in the cholesterol content among samples from different manufacturers.

4. Conclusions

By leveraging the cost-effective and readily available cholesterol as the reference substance, we developed a QAMS HPLC method for simultaneously determining the contents of cholesterol, lanosterol, and 24,25-dihydrolanosterol in industrial lanolin alcohol. This strategy minimized the expenditure on reference standards, thereby facilitating quality control during the production of industrial lanolin alcohol. Based on AQbD principles, a parameter combination within the MODR was selected as the HPLC analysis method for industrial lanolin alcohol, with specific parameters as follows: acetonitrile (B)-water (A) mobile phase system, flow rate of 1.58 mL/min, detection wavelength of 205 nm, injection volume of 10 µL, and column temperature of 37 °C. A gradient elution program was adopted: 0–19.0 min, 90.5% B; 19.0–25.0 min, 90.5–100% B; and 25.0–55.0 min, 100% B. Cholesterol serves as an internal standard for quantifying lanosterol and 24,25-dihydrolanosterol, with relative correction factors of 0.4227 and 0.8228, respectively. The proposed AQbD-based QAMS method not only significantly reduces analysis costs but also enhances efficiency, addressing current gaps in methods for determining the contents of these three components in industrial lanolin alcohol.