Analytical Quality by Design‐Guided Optimisation and Validation of a Short‐Run Stability‐Indicating Reverse‐Phase Ultra‐Fast Liquid Chromatography (RP‐UFLC) Method for the Quantitation of Nonivamide

TL;DR

This paper presents a new, efficient, and eco-friendly method for accurately measuring nonivamide in pharmaceutical samples using liquid chromatography.

Contribution

The study introduces a validated RP-UFLC method optimized via analytical quality by design principles for quantifying nonivamide.

Findings

The optimized RP-UFLC method achieved a resolution of 13 and %RSD < 5% under specific conditions.

The method showed good greenness with an AGREE score of 0.72 and met ICH validation criteria.

Nonivamide was stable under most stress conditions except alkaline and oxidative stress.

Abstract

Nonivamide (NON), a capsaicin analogue with similar pharmacological effects, is used in pain management, yet limited information exists on its accurate quantification by reverse‐phase liquid chromatography. A cost‐effective, efficient and precise RP‐HPLC method was developed, optimised using response surface methodology (central composite design), validated and assessed for greenness. Naproxen served as the internal standard. Acetonitrile (ACN) with a potassium phosphate buffer achieved separation, with detection at 285 nm. Critical analytical attributes included retention times, resolution and solvent composition. Optimised conditions were 41.0% v/v of ACN, a flow rate of 1.5 mL/min and a buffer of pH 4. Under these conditions, NON eluted at 6.8 min with a resolution of 13 and %RSD < 5%, aligning with model predictions, confirming robustness and system suitability. Greenness evaluation (AGREE) yielded a score of 0.72 (good–very good). Method validation followed the ICH guidelines: linearity of 2–200 μg/mL, LOD of 0.67 μg/mL and LOQ of 2 μg/mL. Precision and accuracy were within acceptable limits (< 5%). Stress studies revealed NON stability under most conditions, except alkaline and oxidative stress, whereas specificity was confirmed by detection in the presence of degradants. Overall, the developed method is robust, reproducible, reliable and environmentally considerate, enabling accurate NON quantification from pharmaceutical bulk.

Figures

Chemical structures of NON (1) and CAP (2).

Chemical structures of diclofenac and naproxen.

Results of the AGREE assessment of the developed RP‐UFLC–PDA method for the quantitation of NON.

Typical calibration curve for NON over the concentration range 2–200 μg/mL (n = 3).

3D response surface plot depicting the impact of (A) flow rate and (B) organic solvent concentration on retention time of NON.

3D response surface plot depicting the impact of (A) flow rate and pH and (B) organic solvent concentration and pH on retention time of IS.

3D surface plot representing the effect of pH and organic solvent concentration on the resolution factor.

3D surface plot representing the effect of flow rate and organic solvent concentration on the amount of organic solvent used.

Chromatograms of the forced degradation studies: (A) untreated NON, (B) acidic degradation, (C) alkali degradation, (D) oxidative degradation, (E) neutral degradation, (F) temperature stress, (G) photostability, (H) dry heat and (I) analyte stability.

Tables

TABLE 1. Summary of CCD experiments and associated outcomes.

Std	Run	pH	Flow rate (mL/min)	Org. solvent (%)	Ret. time (NON) (min)	Ret. time IS (min)	Res. factor	Org. solv. used (mL)
10	1	5.5	1.7	45.0	4.201	1.885	14.715	9.6413
7	2	7.0	1.0	50.0	4.805	1.502	19.179	7.2075
8	3	7.0	1.5	50.0	3.271	1.016	17.357	7.3598
20	4	5.5	1.3	45.0	5.454	2.523	15.261	9.5718
11	5	5.5	1.3	36.6	13.228	4.009	26.611	18.5718
13	6	3.0	1.3	45.0	5.293	3.236	9.894	9.2892
18	7	5.5	1.3	45.0	5.431	2.440	15.428	9.5314
5	8	7.0	1.0	40.0	11.202	1.666	28.837	13.4424
14	9	8.0	1.3	45.0	5.209	1.046	14.499	9.1418
4	10	4.0	1.5	50.0	3.239	2.167	7.159	7.2878
16	11	5.5	1.3	45.0	5.407	2.433	15.476	9.4893
3	12	4.0	1.0	50.0	4.823	3.233	8.080	7.2345
17	13	5.5	1.3	45.0	5.410	2.425	15.631	9.4946
19	14	5.5	1.3	45.0	5.407	2.425	15.604	9.4893
6	15	7.0	1.5	40.0	7.611	1.145	28.178	13.700
9	16	5.5	0.8	45.0	8.530	3.888	16.879	9.2124
15	17	5.5	1.3	45.0	5.402	2.421	15.650	9.4805
12	18	5.5	1.3	53.4	3.050	1.825	9.080	6.3519
2	19	4.0	1.5	40.0	7.532	3.942	13.796	13.5576
1	20	4.0	1.0	40.0	11.143	5.843	14.697	13.3716

TABLE 2. Summary of degradation studies performed under various conditions.

	Degradation condition
	Acid	Alkali	Oxidative	Hydrolytic	Temperature stress	Dry heat	Photostability	Analyte stability
IC (μg/mL)	100	100	100	100	100	100	100	100
MC (μg/mL)	85.44	47.16	45.96	98.96	97.18	97.60	99.06	90.24
%Degradation	14.56	52.85	54.04	1.04	2.82	2.40	0.40	9.76
%RSD	1.69	3.42	3.86	3.41	0.54	0.51	0.29	0.36

Full text

Introduction

1

Nonivamide (N‐(4‐hydroxy‐3‐methoxybenzyl)nonanamide) is a semi‐synthetic derivative of capsaicin (CAP) often used as a substitute with a similar chemical structure and pharmacological effects. NON and CAP have a very short half‐life because of their high degree of first‐pass metabolism. Because of structural and biological similarity to CAP, NON is considered an inexpensive alternative to CAP (Cao et al. 2014). It is a less pungent analogue of CAP, and it is also the direct structural analogue. CAP possesses a carbon chain with one additional methyl group and double bond than NON, and the binding affinity of NON to transient receptor potential 1 (TRPV1) is significantly lower (Rohm et al. 2015). NON consists of a benzene ring, a hydrophobic lipid tail and a polar amide group (Wang et al. 2024). With a molecular weight of 293.4 g/mol, NON is water insoluble but soluble in alcohol and ethers. Problems with low solubility can cause limited bioavailability, which can lead to less‐than‐ideal drug delivery (Kalepu and Nekkanti 2015). The chemical structures of NON and CAP are depicted in Figure 1.

Chemical structures of NON (1) and CAP (2).

It is a crucial compound in the pharmaceutical sector because it is widely used in medicine to treat pain and, more recently, has been shown to be effective against cancer‐related pain (Wojnarowska et al. 2011). An analytical method of a pharmaceutical product guarantees quality control through identification, safety, purity and effectiveness of that product, and a successful method development for NON would expedite product development and delivery to patients living with chronic pain (Ravisankar et al. 2014).

Nonivamide has been studied in combination with nicoboxil in the treatment of lower back pain and for its anti‐inflammatory properties (Gaubitz et al. 2016; Walker et al. 2017). Boehringer Ingelheim has developed Finalgon Cream, a topical formulation comprising nicoboxil 1.08% w/w and nonivamide 0.17% w/w, to relieve musculoskeletal pain. In a clinical study, Blahova et al. (2016) found Finalgon Cream to be safe and efficient in the treatment of acute non‐specific low back pain.

Nonivamide has been analysed together with CAP and dihydrocapsaicin using LC–MS/MS and GC–MS (Kim and Yoon 2021; Reilly et al. 2002). High‐performance liquid chromatography analysis of NON in Korean hot peppers has been reported, and the results indicated that nonivamide elutes at 96.7 min (Choi 2006), and in another HPLC study, the elution run time of NON was 27 min (Yang et al. 2023). These results indicate that a method that significantly reduces retention time to approximately under 10 min is needed, and this will improve the throughput, which is cost‐effective. Literature reports methods with long retention times; this means more organic solvent is used, and this can be expensive.

An evaluation of the greenness of analytical procedures is crucial, as not all approaches exhibit the same degree of environmental sustainability. The environmental friendliness of the proposed technique is assessed using the green analytical procedure index (GAPI) (Płotka‐Wasylka 2018), analytical method greenness score (AMGS) (Hicks et al. 2019), analytical Eco‐Scale (Gałuszka et al. 2012) and Analytical GREEnness (AGREE) metrics (Pena‐Pereira et al. 2020).

AGREE is a software program designed for estimating the greenness profile (Pena‐Pereira et al. 2020). The input conditions in AGREE represent the 12 essential principles of green analytical chemistry and are assigned varying weights that allow for reliable flexibility. A scale ranging from 0 to 1 was developed, incorporating each of the 12 principles of green analytical chemistry. The findings of AGREE relate to all 12 principles of green analytical chemistry, with the overall result being the cumulative effect of each principle. A clockwise diagram is created, with the centre of the chart representing the overall scores, accompanied by a colour that reflects the greenness profile. The clockwise diagram displays a spontaneous red–yellow–green colour scale that indicates the procedure related to the 12 principles. In contrast, the weight of each principle corresponds to the width of its respective segment. The analytical technique is considered more environmentally friendly if the total score at the centre of the clockwise diagram approaches 1, with the colour indicating a dark green hue. The colour indicates the performance of the procedure for each assessment criterion in the section, with the number corresponding to each criterion (Pena‐Pereira et al. 2020).

Response surface methodology (RSM) is a set of statistical methods for defining the relationships between variables and enabling effective optimisation of processes that rely on several variables. The primary advantage of RSM is that it efficiently explores the response surface with equivalent precision and significantly reduces the number of tests necessary for assessment, analysis and optimisation (Shishir and Chen 2017). The purpose of the RSM approach is to give researchers an understanding of the structure of the response surface they are studying by enabling them to estimate interactions. Central composite design (CCD) and Box–Behnken design (BBD) are the two most utilised designs. The BBD is regarded as an effective choice and a perfect substitute for CCD (Hanrahan et al. 2005). Although BBDs are more economical in terms of the number of experimental runs, CCDs are better suited for this type of study because they include both factorial and axial points, allowing for a more comprehensive exploration of the design space. This makes CCDs especially advantageous when evaluating potential curvature effects and when predictions near the extremes of the variable range are important.

In RSM, the CCD is often used to construct a second‐order polynomial for the response variables without utilising a full factorial design of tests. At least three levels of each factor must be present in the experimental design in order to determine the coefficients of a polynomial with quadratic terms (Sahoo and Barman 2012). The CCD model is the key component of RSM. This kind of optimisation model's greatest benefit is that it is more accurate and does not require a three‐level factorial experiment to create a second‐order quadratic model (Bhattacharya 2021). The independent factors were selected: pH, flow rate and organic solvent concentration (%) to improve the chromatographic separation, and the dependent variables were selected: retention time, resolution, tailing factor and organic solvent used (mL) to evaluate the effectiveness of the method.

This study aimed to develop a green, low‐cost, effective and precise analytical method to quantify NON in pharmaceutical bulk. The RP‐UFLC method was developed and optimised using CCD‐assisted RSM. The optimised method was then assessed for greenness using the AGREE criteria and subsequently validated to quantify NON from the pharmaceutical bulk.

Materials and Methods

2

Chemicals and Reagents

2.1

Nonivamide (N‐vanillylnonanamide) and naproxen were purchased from DB Fine Chemicals (Pty) Ltd (Johannesburg, South Africa). HPLC‐grade acetonitrile and phosphoric acid were purchased from Fisher Scientific (Loughborough, UK). Potassium phosphate monobasic and sodium hydroxide pellets were purchased from Merck (Johannesburg, South Africa). HPLC‐grade water was collected from a Direct‐Q Ɛt Direct‐Q UV water purification system with a resistivity of 18.2 MΩ·cm at 25°C (Merck KGaA, Darmstadt, Germany).

Instrument Specifications

2.2

An ultra‐fast liquid chromatographic (RP‐UFLC) system from Shimadzu equipped with an SIL‐20AC autosampler, an SPD‐M20A photodiode array (PDA) detector and an LC‐20ad solvent delivery module (Kyoto, Japan). A Kinetex 5‐μm C18 (150 × 4.6 mm) 100‐Å LC column (Phenomenex, Torrance, CA, USA) was used for the separation. Data acquisition, processing and reporting were achieved using the Shimadzu LabSolutions CS 6.81 software (Kyoto, Japan). The PDA detector was operated at 285 nm with the injection volume set to 10 μL. All analyses were conducted at ambient temperature for both the sample and column and performed in triplicate (n = 3).

Internal Standard (IS) Selection

2.3

ISs are primarily used to adjust the variations in dilutions, degradation, recovery, derivatisation, injection and detection, in addition to variations in the amount of the analyte present in the sample. An IS should therefore possess the same or very similar physicochemical properties as the analyte, meaning that the analyte has comparable molecular weight and synthesis pathways as the IS (Tan et al. 2011).

The IS for this study was selected based on structural similarities. Diclofenac and naproxen were evaluated for structural similarities to NON, and literature revealed that naproxen (MW = 230.62 g/mol) has an aromatic ring and a methoxy group but lacks a hydroxyl and long alkyl chain (Valentovic 2007), and in contrast, diclofenac (MW = 296.15 g/mol) has a phenylacetic group and an aromatic ring with two chlorine atoms (Ulubay et al. 2018). Even though the molecular weight of NON is more comparable to diclofenac, naproxen was picked because it is more structurally related to NON, as both have an aromatic ring and a methoxy group. The chemical structures of diclofenac and naproxen are provided in Figure 2.

Chemical structures of diclofenac and naproxen.

Sample Preparation

2.4

Standard stock solutions of NON (1000 μg/mL) and NAP (1000 μg/mL) were prepared by accurately weighing 100 mg of each API into 100‐mL A‐grade volumetric flasks, using a RADWAG AS 220.R2 PLUS Analytical Balance (Torunska 5, Radom, Poland) and diluting with a small volume of acetonitrile. The stock solutions were sonicated for 10 and 40 min, respectively, using a Biobase UC‐100A Ultrasonic Cleaner (Jinan Biobase Medical Co. Ltd, Shandong, China) until a clear solution was observed, after which the solutions were made to volume with acetonitrile. Calibration standards of NON over the concentration range of 2–200 μg/mL were prepared by serial dilution of the standard stock solution on the day of analysis using acetonitrile as the diluent. A concentration of 100‐μg/mL NAP was added to all calibration standards and test samples prior to analysis.

Buffer Preparation

2.5

The phosphate buffer solution (50 mM) was prepared by accurately weighing 6.8 g of potassium phosphate monobasic into a 1‐L Schott Duran bottle (Schott Duran GmbH, Wertheim) and filling up to 500 mL with HPLC‐grade water. The 500‐mL solution was then sonicated until a clear solution was observed, and then the solution was made to volume with HPLC‐grade water. The pH of the buffers was monitored at 25°C using a Mettler Toledo FiveEasy Plus pH Meter (Johannesburg, South Africa) and was adjusted using H_3_PO_4_ and NaOH to get the desired pH per experiment. Degassing under vacuum with the aid of a KNF Neuberger LABOPORT Diaphragm Vacuum Pump N (KNF Neuberger Inc, Trenton, NJ, USA) and filtering through a 0.45‐μm HVLP Durapore Membrane Filter (Millipore Corporation, Bedford, MA, USA) was done prior to injection.

Experimental Design

2.6

The experimental design used RSM. A CCD including three components and 20 experimental runs was employed in the optimisation study. This design comprised three components across five distinct levels (−α, −1, 0, +1 and +α), requiring 20 runs, five centre points and a two‐step replication. The centre point repetitions are employed to ensure repeatability, enhance the robustness of the experimental design and ascertain the pure error. Table S1 describes the design summary and the conducted experiments, including the coded levels and their corresponding real values. A summary of the experiments performed is provided in Table S1.

Numerical Optimisation

2.6.1

Numerical optimisation approaches are employed to establish optimal methodological circumstances based on the defined aims and constraints of each answer. The present study employed Derringer's desirability function to optimise four responses with different objectives. The models were optimised using Design‐Expert statistical software to produce overall solutions for chromatographic conditions. The recommended solution with 93.8% desirability was run in triplicate (n = 3). A summary of the optimisation targets, conditions and predicted outputs is provided in Table S2.

Determination of Optimised Method Greenness

2.6.2

Following optimisation, we input our findings into the AGREE calculator (Version 0.52020) (Pena‐Pereira et al. 2020). AGREE is a tool for assessing the environmental and occupational risks linked to a certain analytical technique, grounded in the 12 principles of green analytical chemistry. The assessment's outcome is represented in a comprehensible graph that includes an overall score and indicates the extent to which the reviewed technique adheres to each of the 12 principles (Pena‐Pereira et al. 2020).

The evaluation criteria are derived from the 12 principles of green analytical chemistry (SIGNIFICANCE) and are converted into a standardised 0–1 scale. The final score is determined according to the criteria of SIGNIFICANCE (Pena‐Pereira et al. 2020).

The greenness of the developed RP‐UFLC–PDA method for nonivamide with an IS was assessed using the SIGNIFICANCE mnemonic (Gałuszka et al. 2013) and weightings of 1–4.

• S—‘Select direct analytical technique’ was assigned a score of 1, as RP‐UFLC requires sample withdrawal and chromatographic separation, so direct in‐process measurement is not feasible.
• I—‘Integrate analytical processes and operations’ received a weighting of 2, reflecting limited integration beyond PDA detection, though autosampler automation partially streamlines operations.
• G—‘Generate as little waste as possible and treat it properly’ was critical (4), because UFLC reduces solvent consumption and minimises hazardous waste compared with conventional HPLC.
• N—‘Never waste energy’ was rated 2; UFLC shortens run times and reduces energy use, but no additional energy‐saving innovations are employed.
• I—‘Implement automation and miniaturisation of methods’ was scored 3, as the method employs autosamplers and low‐volume injections, improving reproducibility and reducing waste.
• F—‘Favour reagents obtained from renewable sources’ received a score of 2; although solvents like ethanol could substitute acetonitrile, most reagents (standards and IS) are synthetic.
• I—‘Carry out in situ measurements’ was low (1), because RP‐UFLC requires sample removal and preparation.
• C—‘Avoid derivatisation’ was rated 3, as the method avoids unnecessary chemical modifications, reducing reagent use and complexity.
• A—‘Note that the sample number and size should be minimal’ was critical (4), because UFLC allows microlitre‐scale injections, reducing sample consumption and waste.
• N—‘Choose multianalyte or multi‐parameter method’ scored 2; although the method quantifies nonivamide alongside an IS, further multi‐parameter integration is limited.
• C—‘Implement online or replace toxic reagents’ was given 3, reflecting the potential for greener solvents and the overall aim to minimise hazardous chemical use.
• E—‘Ensure operator safety’ was critical (4), because handling toxic organic solvents requires proper precautions and safe disposal.

The summary of the mnemonic and associated weightings is provided in Table S3.

Method Validation

2.7

The UFLC method developed in this study was validated according to the ICH Q2(R2) guidelines to confirm its suitability for the quantitative analysis of NON. Validation parameters assessed include linearity, precision, accuracy, detection limits and specificity. Linearity was established across a defined concentration range, showing a strong correlation between peak area and analyte and NON concentration. Accuracy was confirmed through recovery studies, whereas precision was evaluated by assessing repeatability and intermediate precision with results expressed as %RSD. Specificity was demonstrated by the method's ability to clearly distinguish the NON from degradation products (European Medicines Agency: Committee for Medicinal Products for Human Use 2022).

Linearity

2.7.1

The linearity of NON was evaluated by analysing the peak area ratio of the analyte and IS from nine independent levels of concentrations, 2 μg/mL being the lowest and 200 μg/mL being the highest. The calibration curve was obtained, and the line of regression equation and correlation coefficient (R ^2^) were established.

Precision

2.7.2

Repeatability (intra‐day precision) and intermediate precision (interday precision) were the two levels at which precision was assessed. The relative standard deviation (%RSD) of triplicates of NON quality control concentrations (2, 10, 15, 30, 40, 50, 100, 150 and 200 μg/mL) on the same day and three consecutive days was used to determine intra‐day and interday precision. The %RSD was calculated using Equation (1).

$$[eqn]$$

Accuracy

2.7.3

Accuracy was assessed according to the ICH guidelines using three concentration levels within the specified calibration range. Three concentrations of NON were prepared (8, 25 and 125 μg/mL) and analysed in triplicate (n = 3). The results are reported as %Recovery, %RSD and %Bias. A resultant %RSD of < 5% was accepted in this study. The %Bias was calculated using Equation (2).

$$[eqn]$$

Limit of Quantification (LOQ) and Limit of Detection (LOD)

2.7.4

With a precision of < 5%RSD, the LOQ was established for this approach, and the LOD was calculated as 30% of the LOQ.

Specificity and Forced Degradation Studies

2.7.5

Stress studies were conducted by exposing NON to acidic, alkaline, neutral, hydrogen peroxide, light and heat conditions. These studies were performed in solution except when the drug was exposed to dry heat and UV light, in which case the powder form of NON was used. Drug material degradation of 5%–20% has been acknowledged as appropriate for chromatographic test validation (Blessy et al. 2014). The degradation limit for this study was set at 5%.

Acidic, Alkali and Oxidative Degradation

2.7.5.1

Approximately 100 mL of 1000‐μg/mL NON solutions was added to 100 mL of 0.1‐M HCl for acid degradation, 0.1‐M NaOH for alkali degradation and 3% v/v of H_2_O_2_ for oxidative degradation. The solutions were refluxed at 100°C on a Heidolph Hei‐PLATE Mix ‘n’ Heat core hot plate (Heidolph Scientific Products GmbH, Schwabach, Germany) for 8 h. After 8 h, 100 μg/mL was prepared from the solutions for analysis.

Neutral Degradation

2.7.5.2

A 100‐mL NON solution with a concentration of 200 μg/mL was added to 100‐mL HPLC‐grade water. The solution was then refluxed at 100°C for 8 h. The solution was allowed to cool to ambient temperature before analysis.

Temperature Stress

2.7.5.3

NON (100 μg/mL) was exposed to heat and maintained at 60°C, 70°C, 80°C and 90°C for 8 h using a Labcon shaking water bath (Labcon, Krugersdorp, South Africa) and allowed to cool to 25°C prior to analysis using the validated method.

Photostability

2.7.5.4

Dry NON powder was exposed to UV light under the CAMAG UV Cabinet 4 (CAMAG AG & Co. GmbH, Berlin, Germany) for 8 h at 366 nm, as the ICH Q1B Option 2 guideline recommends that photostability testing be done under a light source with an output similar to the D65/ID65 emission standard or under a UV lamp with a spectral distribution of 320–400 nm. From the treated powder, a 100‐μg/mL solution was prepared and analysed.

Dry Heat

2.7.5.5

Dry NON powder was exposed to heat in a Scientific Digital Oven 276‐80I (Scientific Engineering (Pty), Florida, South Africa) set to 45°C for 8 h. From the treated powder, a 100‐μg/mL solution was prepared and analysed.

Analyte Stability

2.7.5.6

Approximately 100 μg/mL of 10‐mL NON was stored in a 4°C fridge for 72 h, and then the solution was analysed.

Results

3

Method Optimisation

3.1

A CCD space consisting of 20 experiments was generated, and the maximum and minimum values of the numerical factor were set. The pH values were set at 4 minimum and 8 maximum, based on the stability of both NON and NAP. The responses from the dependent factors were recorded as summarised in Table 1.

Evaluation of Model Adequacy for Retention Time of NON

3.1.1

The retention time of NON was characterised by a transformed quadratic model, which exhibited the lowest PRESS in comparison to linear, two‐factor interaction (2FI) and cubic models. The optimal mathematical model was determined through the assessment of statistical parameters such as R ^2^, adjusted R ^2^ and PRESS. The predicted R ^2^ was in close alignment with the adjusted R ^2^, differing by less than 2%, which suggests that the model is suitable for investigating the design space. The model fit summary for NON retention time demonstrated excellent predictability, with a standard deviation of 0.0074, a mean of 0.4237, a coefficient of variation of 1.74%, an R ^2^ of 0.9933, an adjusted R ^2^ of 0.9920, a predicted R ^2^ of 0.9877 and an adequate precision value of 89.

The data were transformed using the inverse square root, and after transformation, the λ was found in the parabola's optimal region, confirming that the data matched the model adequately. The Box–Cox plots prior to and after transformation are displayed in Figures S1 and S2, respectively.

The ANOVA results for the quadratic retention time model indicate that the model F value of 5821.44 proved that the model is significant, and there is only a 0.01% probability that an F value this large could occur because of noise. The p values of A, B, AB, A ^2^, B ^2^ and C ^2^ were less than 0.0500, which indicate that the model terms are significant. The lack‐of‐fit F value of 6.84 implies that the lack of fit is significant, with a probability of 2.74% that a lack‐of‐fit F value this large could occur because of noise. A significant lack of fit means there is a statistically significant mismatch between the predicted and observed values. Despite the significant lack of fit, the high F values for flow rate and organic solvent composition, as well as the significant quadratic terms, confirm that the model is robust in explaining the variation in retention time.

Evaluation of Model Adequacy for Retention Time of IS

3.1.2

The retention time of the IS was examined using a 2FI model. This model was selected because of its statistical adequacy in elucidating the variability in the dataset relative to higher order models.

The model demonstrated strong significance, with a model F value of 30.45 (p < 0.0001), suggesting only a 0.01% likelihood that such a high F value is attributable to random variation. Flow rate (F = 29.18, p = 0.0001), organic solvent composition (F = 37.20, p < 0.0001) and pH (F = 99.97, p < 0.0001) were identified as significant factors. Among the interaction terms, AC (F = 4.82, p = 0.0470) and * bc

• (F = 15.01, p = 0.0019) were significant, whereas AB was not (p = 0.4515). The lack‐of‐fit test was significant (F = 147.96, p < 0.0001), indicating a systematic deviation between predicted and observed values, but the overall model still captured the key sources of variation in IS retention time effectively.

Evaluation of Model Adequacy for Peak Resolution

3.1.3

The peak resolution between NON and NAP was investigated, and the resulting model was statistically significant with a p value of < 0.0001. The predicted R ^2^ of 0.7251 was found to be in reasonable agreement with the adjusted R ^2^ of 0.8197 with the difference of less than 0.2. The adequate precision of 17.282 was measured by the model, indicating an adequate signal and that this model could be used to navigate the design space.

The ANOVA for the linear model of peak resolution indicated that the model was significant (F = 29.79, p < 0.0001), with organic solvent composition (F = 46.07, p < 0.0001) and pH (F = 42.29, p < 0.0001) identified as the primary factors, although flow rate was not significant (p = 0.3328). The fit statistics corroborated the adequacy of the model, demonstrating an R ^2^ of 0.8481, an adjusted R ^2^ of 0.8197, a predicted R ^2^ of 0.7251 and a precision value of 17.2821. The coefficient of variation was low (5.81%), and the standard deviation of 0.0685, in relation to a mean response of 1.18, indicated strong repeatability of the model.

Evaluation of Model Adequacy for Organic Solvent Utilised

3.1.4

The amount of organic solvent used per triplicate of injections is a good measure of how green an analytical method is. In this case, the amount of organic solvent used per triplicate of injections was evaluated, and the model was found to be significant. The model terms A, B, B ^2^ and C ^2^ were statistically significant contributors (p < 0.05). Organic solvent demonstrated the most significant with an associated F value of 21,686.68 and a p value of < 0.0001. This suggests that variations in the ratio of organic solvent significantly affected the greenness of the method.

The lack of fit was statistically significant (p = 0.0211), which is often observed in highly precise models when the pure error is extremely low. However, the magnitude of residuals and the very high model fit statistics compensate for this limitation.

The model fit statistics further validated the robustness of the quadratic model. The coefficient of determination (R ^2^ = 0.9996) signifies that 99.96% of the variability in the response is elucidated by the model. The adjusted R ^2^ (0.9992), which accounts for the number of predictors, closely approximated the R ^2^ value, indicating no overfitting. The predicted R ^2^ (0.9968) demonstrated strong concordance with the adjusted R ^2^, affirming the model's predictive dependability. The adequate precision ratio of 189.84 is significantly higher than the threshold of 4, signifying an unusually robust signal‐to‐noise ratio, hence confirming the reliability of the model for exploring and optimising the design space.

Model Optimisation

3.2

Under the optimised chromatographic conditions, distinct, symmetrical and well‐resolved peaks were obtained, confirming the method's ability to effectively separate NON and NAP. The retention times of NON and the IS were highly reproducible across triplicate injections, with %RSD values of 0.14% and 0.13%, respectively, both well below the laboratory threshold of 5%. The resolution factor (R _ f _) also demonstrated consistency (%RSD = 0.42%), and the organic solvent composition showed minimal variation (%RSD = 0.14%), confirming system stability. Compared with the predicted retention time, NON exhibited a prediction error of only 1.89%, reflecting the robustness of the mathematical modelling approach. These results highlight the excellent predictive ability of RSM, validating its suitability as a tool for chromatographic process optimisation. Furthermore, the excellent predictive ability of RSM is shown, indicating its effectiveness as a suitable tool for process optimisation (Makoni et al. 2018). A typical chromatogram of the separation is depicted in Figure S3.

Greenness of the Optimised Method

3.2.1

The implementation of a 12‐criterion green analytics evaluation on our RP‐UFLC–PDA approach resulted in an overall greenness score of 0.72 (72% compliance). The majority of criteria received a green rating, signifying robust conformity with GAC. Moderate (yellow/amber) ratings emerged because of the method's significant consumption of solvent and electrical power, whereas one red grade indicated dependence on non‐renewable chemicals (ACN). The score aligns with a short‐run UFLC methodology employing dilute‐and‐inject sample preparation, minimal injection volumes, a standard bench‐top UFLC–PDA and conventional acetonitrile‐buffer mobile phases at around 1.5 mL/min. The greenness score is provided in Figure 3.

Results of the AGREE assessment of the developed RP‐UFLC–PDA method for the quantitation of NON.

Method Validation

3.3

Linearity

3.3.1

The linearity of the method was measured across the calibration range at three distinct NON concentrations (low, medium and high). The NON concentrations (2–200 μg/mL) were spiked with 100‐μg/mL NAP (IS). The peak area ratio (NON/NAP) was calculated, and the calibration curve was generated. The linear regression equation was found to be y = 0.0073x + 0.0243 with a correlation coefficient of 0.9973, as depicted in Figure 4. The calibration was established over the concentration range of 2–200 μg/mL (9 points), demonstrating excellent linearity between concentration and peak area ratio. According to these results, the method demonstrated linearity with the studied concentration range.

Typical calibration curve for NON over the concentration range 2–200 μg/mL (n = 3).

Precision

3.3.2

Repeatability (Intra‐Day)

3.3.2.1

Three analyses (n = 3) were conducted across the calibration range concentrations to establish repeatability. Table S4 summarises the repeatability data produced after analysis. It shows that the %RSD values are < 5% in every analysis, suggesting that the method's intra‐day precision is sufficient.

Intermediate Precision (Interday)

3.3.2.2

Results obtained from intermediate precision indicated that the %RSD for all days is within range, < 5%, therefore indicating that the method can be used to quantify NON for three consecutive days. The summary of the intermediate precision is presented in Table S5.

Accuracy and Bias

3.3.3

Accuracy was measured at three concentration levels within the calibration curve (8, 25 and 125 μg/mL), and the %Bias was calculated using Equation (4), and the results indicate that the method is accurate for the analysis of NON, with the %RSD and %Bias being < 5.

The accuracy of the method was confirmed across the tested concentration range, with mean recoveries consistently within acceptable limits. At 8 μg/mL, the measured concentration was 7.86 μg/mL, corresponding to a %Bias of 1.75% and a recovery of 98.25% (%RSD = 0.71%). At 25 μg/mL, the method yielded a measured concentration of 24.5 μg/mL, with a %Bias of 2.00% and a recovery of 98.00% (%RSD = 2.22%). At 125 μg/mL, the measured concentration was 121.5 μg/mL, giving a %Bias of 2.80% and a recovery of 97.20% (%RSD = 0.73%). Collectively, these results demonstrate that the method is accurate and reliable for quantifying NON within the evaluated concentration range.

LOQ and LOD

3.3.4

The evaluation of the limit of quantitation (LOQ) for NON was conducted across a range of low concentrations. No peaks were observed at concentrations of 0.10, 0.15, 0.20, 0.25 and 0.50 μg/mL, suggesting that these levels fall below the method's quantifiable range. At a concentration of 1 μg/mL, a peak was noted (peak ratio = 0.005297); however, the %RSD was measured at 7.93%, surpassing the acceptable limit of 5% for dependable quantitation. At a concentration of 2 μg/mL, the method exhibited satisfactory precision, indicated by a peak ratio of 0.018528, a standard deviation of 0.000371 and a %RSD of 2.00%. The findings indicate that the LOQ of the method was set at 2 μg/mL and the LOD was calculated and found to be 0.67 μg/mL.

Specificity and Force Degradation Studies

3.3.5

Forced degradation is the breakdown of drug substances and drug products under severe conditions. It is used to indicate that a stability‐indicating method is specific. It also helps to clarify the structure of the degradation products and offers insights into the drug substance degradation pathway. Drug substance degradation of 5%–20% has been acknowledged as a practical threshold for chromatographic test validation (Blessy et al. 2014).

NON was analysed under accelerated conditions to assess its stability, and an untreated analyte was used as a reference.

Discussion

4

Evaluation of Model Adequacy for Retention Time of NON

4.1

The Box–Cox plot was used to transform the data to make the statistical test more applicable. Data with skewed distributed outcomes can be transformed using the Box–Cox transformation approach. It uses a variety of power transformations to enhance the effectiveness of variance equalisation and normalisation for both positively and negatively skewed data (Marimuthu et al. 2022). Figure S1 shows the Box–Cox plot before transformation, where the current λ of the model is represented by the blue line, the best λ is shown by the green line, and the confidence interval borders for λ (power of the response) are shown by the red lines. With the λ value of −0.5, the lowest point of the curve indicates that this is the ideal value for power transformation. The confidence interval for the optimal λ value roughly falls between −0.8 and −0.1, as shown by the vertical red lines on the plot. Upon analysis, the Box–Cox plot suggested applying a power transformation using the inverse square root, because λ was not found within the confidence interval (Aly et al. 2025).

The 3D surface (Figure 5) demonstrates the relationship between flow rate (A) and organic solvent concentration (B). A significant decrease in retention time is observed when both flow rate and organic solvent concentration are at their highest. The polarity of the mobile phase decreases as the concentration of ACN rises, and the hydrophobic interactions between the ligands and NON also decrease, which lowers the retention time (Nguyen 2022). It is also observed that retention time decreases as flow rate increases, regardless of pH (C).

3D response surface plot depicting the impact of (A) flow rate and (B) organic solvent concentration on retention time of NON.

There is little effect of pH on retention time in the tested range. It has been reported that certain functional groups on drugs lack acid–base characteristics, indicating that they are unable to donate or accept protons. These functional groups are referred to as neutral. No matter how much the pH is adjusted, all neutral functional groups in aqueous media stay constant because they do not have an ionisable hydrogen atom or the chemical characteristics necessary to take it on (Roche 2007). NON is largely non‐polar and neutral across the typical pH range (4–7). It does not have strongly acidic or basic functional groups that can ionise significantly within this pH range. The relationship between retention time and independent variables is demonstrated by Equation (3), which suggests that increasing the flow rate will reduce the retention time more noticeably. It also suggests that organic solvent concentration also shortens retention time but with a smaller effect than flow rate; pH has the smallest effect on retention time at the studied range.

$$[eqn]$$

Evaluation of Model Adequacy for Retention Time of IS

4.2

Flow rate (A), organic solvent content (B) and pH (C) exhibited statistically significant impacts on retention time (p < 0.05). The impact of pH (C) was the most significant, evidenced by the highest F value (99.97) and the lowest p value (1.80 × 10^−7^), indicating that pH is the primary determinant influencing IS retention behaviour within the tested range. The flow rate and organic solvent content were significant factors, exhibiting F values of 29.18 and 37.20, respectively.

The interaction effects AC (flow rate × pH) and * bc

• (organic solvent × pH) were statistically significant (p = 0.0469 and p = 0.0019, respectively), demonstrating that pH influences the effects of both flow rate and organic solvent. The interaction between flow rate and solvent (AB) was not significant (p = 0.4515), indicating that these two parameters operate mostly separately. These effects are depicted in Figure 6.

3D response surface plot depicting the impact of (A) flow rate and pH and (B) organic solvent concentration and pH on retention time of IS.

The lack of fit was significant (F = 147.96, p < 0.0001), indicating a statistically significant divergence between the anticipated and actual values. Although a substantial lack of fit is typically unfavourable, in this instance, it is probably due to the model's high precision combined with minimal pure error values, which can amplify the severity of the lack of fit.

The findings indicate that the retention time of IS is predominantly influenced by pH, followed by organic solvent concentration and flow rate, with synergistic interactions between pH and the other two variables. The data indicate that adjusting the pH of the mobile phase is essential for manipulating IS retention time, whereas flow rate and organic solvent have secondary but significant impacts.

Evaluation of Model Adequacy for Peak Resolution

4.3

The Box–Cox plot was used to transform the data to make the statistical test more applicable. Following analysis, the Box–Cox plot suggested applying a power transformation using the log, because λ was not found within the confidence interval (Aly et al. 2025). The Box–Cox plot following transformation is depicted in Figure S3.

The resolution between the peaks of NON and NAP was significantly influenced by the concentration of ACN and pH, as shown in Figure 7.

3D surface plot representing the effect of pH and organic solvent concentration on the resolution factor.

It is suggested by the 3D surface plot that an increase in the concentration of the organic solvent has a strong negative effect on resolution in that the resolution between the peaks reduces significantly with an increase in organic solvent concentration. It is noted from the previous outcome that an increase in ACN concentration dramatically influences retention and selectivity, which narrows the separation window and lowers resolution. ACN weakens the interaction between hydrophobic NON and the non‐polar stationary phase, causing faster elution and reduced separation time between adjacent peaks (Nguyen 2022). At higher ACN concentrations, the selectivity between NON and NAP may diminish because they differ in ionisation states that are pH dependent, therefore affecting resolution (Kazakevich and LoBrutto 2007).

The pH of the mobile phase also exerts a significant effect on the resolution. NAP is an NSAID (weak acid) with a pK _ a _ of 4.15 (Farque et al. 2025). NAP is unionised at lower pH and has a stronger attraction to the column, resulting in elution times closer to those of NON, reducing the resolution between the two peaks. At higher pH (above pK _ a _), NAP is ionised and elutes faster, resulting in better resolution of peaks.

The relationship of the independent variables and resolution further corroborates this relationship and is represented by Equation (4).

$$[eqn]$$

Evaluation of Model Adequacy for Organic Solvent Utilised

4.4

The relationship between the organic solvent and flow rate and organic solvent concentration is demonstrated by the 3D surface plot (Figure 8), where the volume of organic solvent used for three injections decreases as there is an increase in flow rate and organic solvent concentration.

3D surface plot representing the effect of flow rate and organic solvent concentration on the amount of organic solvent used.

Specificity and Force Degradation Studies

4.5

The forced degradation study revealed variable stability of NON (Figure 2); the compound showed moderate degradation under acidic hydrolysis with a measured degradation of 14.56%. This is likely due to the protonation of the amide functional group. In contrast, alkaline hydrolysis resulted in severe degradation of 52.85%, indicating that NON is highly sensitive to basic conditions. This can be attributed to the strong nucleophilic action of hydroxide ions, which readily attack the amide bond, leading to significant structural breakdown. Similarly, oxidative stress caused 54.04% degradation, suggesting the presence of oxidation‐prone moieties, in this case, the amide group. These groups are vulnerable to attack by H_2_O_2_ (Gabrič et al. 2022; Venkatesh and Kumar 2022; Zelesky et al. 2023). NON was highly stable under hydrolytic conditions at neutral pH, with only 1.04% degradation observed. This indicates that NON does not undergo significant hydrolysis in the absence of acid or base catalysis.

According to ICH Q1B, photostability testing evaluates the vulnerability of the active pharmaceutical ingredient (API) to UV and visible light, which can cause photolytic degradation by bond cleavage or radical production, potentially changing potency and safety (Janga et al. 2018). Accelerated temperature stress at elevated conditions increases the degradation rate following Arrhenius kinetics, offering predictive insights into the shelf life and temperature‐dependent degradation pathways of the API (Blessy et al. 2014).

The results under thermal stress conditions showed minimal degradation of 2.82%, indicating that NON is largely stable under elevated temperature and humidity. A similar trend was observed under dry heat exposure and photostability with degradation of 2.40% and 0.40%, respectively. Analyte stability testing at 4°C revealed degradation of 9.76%, which is within acceptable limits per ICH guidelines. The summary of the degradation observations is represented by Table 2, with corresponding chromatograms presented in Figure 9.

Chromatograms of the forced degradation studies: (A) untreated NON, (B) acidic degradation, (C) alkali degradation, (D) oxidative degradation, (E) neutral degradation, (F) temperature stress, (G) photostability, (H) dry heat and (I) analyte stability.

Across all conditions, the method demonstrated good precision, as evidenced by the %RSD values < 5%. Overall, NON is relatively stable under most stress conditions except for alkaline, oxidative and acidic stress, where significant degradation was observed. These stress studies did not result in a total loss of NON, meaning that NON can still be detected and separated from degradants.

Conclusion

5

A reverse‐phase UFLC was successfully developed and validated for the quantification of nonivamide. Method optimisation was guided by RSM, which helped establish ideal chromatographic conditions for the effective separation of NON. Changes in flow rate and organic solvent concentration play a significant role in the retention of NON, and pH plays a significant role in resolution. A strong linear relationship between NON concentration and peak ratio was observed, and statistical analysis confirmed the method's reliability and reproducibility for use in raw pharmaceutical bulk.

The newly developed RP‐UFLC–PDA method has several unique strengths. It is extremely fast: Nonivamide elutes at ~6.8 min, and the total run time can be shortened to ≤ 7.5 min, considerably shorter than conventional HPLC assays (Barbero et al. 2008). The chromatographic resolution is excellent, allowing clean quantitation of nonivamide and separation from all degradation products. Despite the speed, the method maintains high performance: It is accurate and precise (repeatability RSD within pharmacopoeial limits) and fully linear from 2 to 200 μg/mL. The LOQ is 2 μg/mL (LOD of 0.67 μg/mL), which is adequate for typical topical product levels and greatly exceeds pharmacopoeial requirements. The method was validated according to the ICH Q2(R2) guidelines (specificity, accuracy, precision, linearity and robustness) and was demonstrated to be stability‐indicating. The use of an IS further improves quantitative reliability. Importantly, environmental impact was assessed with the method's greenness score of 0.72 (out of 1.0), reflecting low solvent consumption and waste generation relative to older methods.

Nonetheless, the method has some limitations. It relies on acetonitrile as the organic phase, which is toxic and less green; future work could substitute a greener solvent (e.g., ethanol or isopropanol) or a more aqueous mobile phase to improve eco‐friendliness. Also, because of the lack of commercial nonivamide‐containing products, the method has not yet been applied to real pharmaceutical formulations (e.g., topical creams or rubefacients). It would be valuable to apply and further validate the assay on spiked or clinical samples and to extend it to matrices such as plant extracts or cosmetic creams.

In summary, the new RP‐UFLC–PDA assay offers a rapid, accurate and relatively green approach for nonivamide quantification. Its combination of speed, resolution and full validation makes it highly suitable for pharmaceutical analysis and quality control of capsaicinoid‐containing formulations. This method should facilitate routine QC and stability testing of topical pain‐relief products or pepper‐based extracts by providing fast turnaround without compromising analytical performance.

Summary

6

An AQbD‐guided RP‐UFLC–PDA method was optimised to quantify nonivamide rapidly and reliably using naproxen as an IS. The final conditions delivered a ≤ 7.5‐min run with nonivamide eluting at ~6.8 min, high resolution and consistent system suitability performance. Validation confirmed linearity (2–200 μg/mL), acceptable precision/accuracy and sensitivity (LOQ of 2 μg/mL), whereas forced degradation demonstrated specificity and stability‐indicating capability. The method also showed a favourable greenness profile (AGREE 0.72), supporting routine QC and stability testing of nonivamide.

Author Contributions

Phindile Mahlangu: writing – original draft, investigation, formal analysis, visualization. Madan S. Poka: supervision, writing – review and editing. Pedzisai A. Makoni: supervision, methodology, writing – review and editing. Bwalya A. Witika: conceptualization, supervision, formal analysis, funding acquisition, resources, methodology, writing – review and editing, writing – original draft.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Table S1: Design summary and the conducted experiments. Table S2: Summary of the optimisation targets, conditions and predicted outputs. Table S3: Summary of the mnemonic and associated weightings for the AGREE approach for greenness. Table S4: Summary of repeatability data. Table S5: Summary of intermediate precision data calculated for 3 days. Figure S1: Box‐Cox plot for power transformation of retention time data for NON. Figure S2: Box‐Cox plot for power transformation of 1/square root retention time data for NON. Figure S3: A typical chromatogram of the optimised conditions at both IS and NON at 100 μg/mL.