Introduction

Multimodal analgesia using drugs with complementary mechanisms has gained momentum as a safer and more effective approach to pain management1. The fixed-dose combination of etoricoxib (Fig. 1), a selective COX-2 inhibitor, and tramadol (Fig. 1), a centrally acting opioid analgesic, represents a promising example of this strategy2.

Fig. 1
Fig. 1
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Chemical structures of ETO and TRA.

Etoricoxib (ETO), chemically 5-chloro-2-(6-methylpyridin-3-yl)-3-[4(methylsulfonyl) phenyl]pyridine, is a second-generation selective cyclooxygenase-2 (COX-2) inhibitor developed for the treatment of inflammatory disorders such as rheumatoid arthritis, osteoarthritis, acute gout, and for the relief of acute and chronic pain. It offers significant anti-inflammatory and analgesic effects while producing fewer gastrointestinal side effects compared with conventional nonsteroidal anti-inflammatory drugs. ETO has the empirical formula C₁₈H₁₅ClN₂O₂S and a molecular weight of 358.84 g·mol⁻¹. It appears as a white to off-white powder, relatively insoluble in water but soluble in methanol and acetone, and freely soluble in alkaline aqueous solutions3.

Tramadol hydrochloride (TRA), chemically (±)-cis-2-[(dimethylamino)methyl]-1-(3-methoxyphenyl)cyclohexanol hydrochloride, has the molecular formula C₁₆H₂₅NO₂·HCl and molecular mass 299.84 g·mol⁻¹. It is a white to off-white, crystalline, odorless powder with a melting point in the range of 180–184 °C. TRA exerts dual analgesic actions through weak µ-opioid receptor agonism combined with inhibition of norepinephrine and serotonin reuptake, providing both peripheral and central analgesic effects. Clinically, TRA is indicated for the management of moderate to severe pain in adults, particularly when treatment with non-opioid analgesics alone proves inadequate4.

ETRAL-TR®, a dispersible granule formulation combining 90 mg ETO and 50 mg TRA, exemplifies a modern trend toward opioid-sparing, multimodal options5. Its ease of administration and rapid onset make it suitable for the management of acute and musculoskeletal pain6. Despite its therapeutic advantages, there is currently no validated spectrophotometric method available for the concurrent quantification of ETO and TRA in such formulations. Although reverse-phase high-performance liquid chromatography has been utilized for their simultaneous estimation in synthetic mixtures7,8, these methods often entail high operational costs, extended analysis times, and complex instrumentation9. UV-visible spectrophotometry, by contrast, offers a cost-effective, rapid, and accessible alternative for routine pharmaceutical analysis. However, direct UV analysis of ETO and TRA is complicated by their overlapping absorption spectra arising from structural similarities in their chromophore systems. ETO exhibits a strong absorption maximum at 279 nm due to its bipyridine and sulfonyl phenyl moieties, while tramadol shows a broad absorption band centered around 217 nm, attributed to its aromatic methoxy group and tertiary amine functionality. Both drugs absorb strongly within the 200–300 nm range, resulting in significant spectral interference, particularly between 230 and 270 nm, where their absorbance curves intersect. This overlap produces non-selective signals that hinder accurate quantification using conventional zero-order spectrophotometry. Consequently, mathematical and derivative spectrophotometric methods were employed to resolve the spectral interference and enable simultaneous determination of both analytes with high precision and selectivity.

In response to this limitation, the present study aims to develop and validate UV spectrophotometric approaches for the simultaneous determination of ETO and TRA in pharmaceutical formulation. Specifically, simultaneous equation10 and first derivative11,12,13,14 spectrophotometric methods were applied to resolve spectral overlap and achieve accurate quantification. These methods were validated in accordance with ICH Q2(R1) guidelines, confirming their selectivity, linearity, and precision in both synthetic mixtures and pharmaceutical formulation. Additionally, the environmental sustainability of the proposed analytical procedures was assessed by Analytical GREEnness (AGREE)15 tool. The evaluation results demonstrated that the developed methods comply with several principles of green analytical chemistry, including minimal solvent consumption, reduced waste generation, use of low-toxicity reagents, and low energy requirements, thereby ensuring both analytical reliability and environmental sustainability.

Experimental

Materials and Instrumentation

Reference-grade etoricoxib (ETO) was kindly supplied by SIGMA Pharmaceutical Industries (Cairo, Egypt), and tramadol (TRA) was obtained from Pharmakeda Health Company (Cairo, Egypt). The fixed-dose dispersible granule formulation ETRAL-TR® (containing 90 mg ETO and 50 mg TRA per sachet), Laboratorios Silanes (Mexico City, Mexico). HPLC-grade methanol was purchased from Sigma-Aldrich (Darmstadt, Germany). The choice of solvent plays a critical role in spectrophotometric analysis because it directly influences solubility, spectral characteristics, and baseline stability of the analytes. In the present study, several solvents including water, ethanol, and methanol were evaluated for their suitability. Methanol was ultimately selected as the analytical solvent because it provided complete solubility for both etoricoxib and tramadol, yielded well-defined absorption spectra with sharp peaks and minimal baseline noise, and exhibited no spectral interference within the selected wavelength range (200–400 nm).

All spectrophotometric measurements were performed using a Shimadzu UV–Visible dual-beam spectrophotometer (model UV-1800, Shimadzu Inc., Japan), bandwidth 1 nm, equipped with 1 cm quartz cells. Instrument control and data acquisition were performed using UV-Probe Software for UV-Visible Spectrophotometers (Version 2.43, Shimadzu Corporation, Kyoto, Japan; https://www.shimadzu.com ).

Standard solutions

Accurately weighed portions of ETO and TRA, each equivalent to 10 mg, were transferred into separate 100 mL volumetric flasks and dissolved in methanol. The solutions were diluted to volume with methanol to yield 100 µg/mL stock solutions for each analyte.

Calibration graphs

A series of working solutions were prepared by transferring appropriate aliquots of the stock solutions into 10 mL volumetric flasks and diluting to volume with methanol. The final concentration ranges were 2–23 µg/mL for ETO and 3–40 µg/mL for TRA. The absorption spectra of each set were recorded in the range of 200–400 nm, using methanol as a blank.

Simultaneous equation method

Absorbance values were recorded at 279 nm (λmax of ETO) and 217 nm (λmax of TRA). The concentrations of ETO (C1) and TRA (C2) in binary mixtures were calculated using the following equations:

$$\:{\text{C}}_{1}=({\text{A}}_{2}{\text{a}}_{\text{y}1}-{\text{A}}_{1}{\text{a}}_{\text{y}2})/({\text{a}}_{\text{x}2}{\text{a}}_{\text{y}1}-{\text{a}}_{\text{x}1}{\text{a}}_{\text{y}2})\:\&\:{\text{C}}_{2}=({\text{A}}_{1}{\text{a}}_{\text{x}2}-{\text{A}}_{2}{\text{a}}_{\text{x}1})/({\text{a}}_{\text{x}2}{\text{a}}_{\text{y}1}-{\text{a}}_{\text{x}1}{\text{a}}_{\text{y}2})$$

Where: A₁ and A₂ are the measured absorbances at 279 nm and 217 nm, respectively. ax1 and ax2 are the absorptivity coefficients of ETO at 279 nm and 217 nm, respectively. ay1 and ay2 are the absorptivity coefficients of TRA at 279 nm and 217 nm, respectively.

First derivative method

The zero-order spectra of each drug were transformed to first-derivative spectra using a scaling factor of 100 and Δλ = 4 nm. ETO was quantified by measuring the derivative amplitude at 302 nm, the zero-crossing point of TRA. Conversely, TRA was determined at 283 nm, the zero-crossing point of ETO. Calibration plots of derivative amplitude versus concentration were constructed for both analytes.

Analysis of synthetic mixtures

Synthetic binary mixtures of ETO and TRA were prepared in the pharmaceutical ratio 1.8: 1.0 by combining appropriate volumes of the standard solutions in 10 mL volumetric flasks and diluting with methanol. The mixtures were analyzed following the calibration procedures, and the concentrations of each drug were calculated from the regression equations.

Analysis of pharmaceutical formulation

The contents of five ETRAL-TR® sachets were combined and homogenized. A portion of the powder equivalent to the content of one sachet was transferred to a 100 mL volumetric flask containing approximately 60 mL methanol. The mixture was shaken vigorously for 20 min, filtered, and the filtrate was diluted to volume with methanol. Subsequent dilutions were prepared to yield five sample solutions of varying concentrations. These were analyzed using the established calibration methods, and the ETO and TRA concentrations were determined.

Results and discussion

Spectral characteristics

The UV absorption spectra of ETO and TRA displayed significant spectral overlap (Fig. 2), which hindered direct and simultaneous quantification using conventional zero-order spectrophotometry. In such situations, spectral resolution techniques such as mathematical manipulation of absorbance data or transformation into derivative spectra are essential to enable accurate quantification of individual components in a mixture.

Fig. 2
Fig. 2
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Absorption spectra of ETO (20 µg/mL) and TRA (35 µg/mL).

In this study, two approaches were adopted to address spectral interference: the simultaneous equation method and the first derivative spectrophotometric method. The simultaneous equation and first derivative spectrophotometric methods were selected for their simplicity, rapidity, and suitability for routine quality control applications. Both techniques effectively resolve spectral overlap between etoricoxib and tramadol without requiring complex statistical modeling or multivariate calibration approaches such as PLS, CLS, or PCR. These classical mathematical methods offer excellent accuracy and precision using standard UV–Visible spectrophotometric instrumentation, ensuring cost-effectiveness, environmental compatibility, and practical applicability in pharmaceutical laboratories.

Simultaneous equation method

The simultaneous equation method relies on the principle that each drug exhibits measurable absorbance at the λmax of the other component. In this case, the absorbances of the mixtures were recorded at 279 nm (λmax of ETO) and 217 nm (λmax of TRA), producing values A₁ and A₂, respectively. These measurements were substituted into the following equations to calculate the concentrations of ETO (C1) and TRA (C2):

$$\:{\text{C}}_{1}=({\text{A}}_{2}{\text{a}}_{\text{y}1}-{\text{A}}_{1}{\text{a}}_{\text{y}2})/({\text{a}}_{\text{x}2}{\text{a}}_{\text{y}1}-{\text{a}}_{\text{x}1}{\text{a}}_{\text{y}2})\:\&\:{\text{C}}_{2}=({\text{A}}_{1}{\text{a}}_{\text{x}2}-{\text{A}}_{2}{\text{a}}_{\text{x}1})/({\text{a}}_{\text{x}2}{\text{a}}_{\text{y}1}-{\text{a}}_{\text{x}1}{\text{a}}_{\text{y}2})$$

Where: aₓ₁ and aₓ₂ = absorptivity coefficients of ETO at 279 nm and 217 nm, respectively. aγ₁ and aγ₂ = absorptivity coefficients of TRA at 279 nm and 217 nm, respectively.

The absorptivity values were determined by averaging the absorbance/concentration ratios for each drug at the selected wavelengths from eight independent measurements covering the established linearity ranges of 2–23 µg/mL for ETO and 3–40 µg/mL for TRA. This approach enabled direct calculation of each drug’s concentration in the binary mixture without prior separation.

First derivative method

To further enhance selectivity, the zero-order spectra of ETO and TRA were transformed into first-derivative spectra using a Δλ of 4 nm and a scaling factor of 100. During method development, the influence of the derivative parameters on spectral quality was systematically examined. Variation of the Δλ between 2 and 8 nm revealed that smaller intervals increased spectral noise, while larger ones reduced resolution between overlapping peaks. The chosen value of Δλ = 4 nm provided optimal signal smoothness and well-resolved zero-crossing points for both analytes. Similarly, the scaling factor of 100 enhanced signal definition without amplifying background fluctuations. These optimized conditions ensured reproducible derivative spectra and improved selectivity in quantitative analysis. Analysis of the derivative spectra revealed specific zero-crossing wavelengths at which one drug could be measured without interference from the other; ETO was quantified at 302 nm, corresponding to the zero-crossing point of TRA, while TRA was determined at 283 nm, the zero-crossing point of ETO. At these wavelengths, the derivative amplitudes corresponded exclusively to the analyte of interest, ensuring high selectivity, as illustrated in Fig. 3. Calibration curves were then constructed by plotting the derivative amplitudes against the respective concentrations (2–23 µg/mL for ETO and 3–40 µg/mL for TRA), and the resulting regression equations were applied to accurately determine the concentrations of ETO and TRA in mixed solutions.

Fig. 3
Fig. 3
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First derivative spectra of ETO (20 µg/mL) and TRA (35 µg/mL) showing distinct zero-crossing points sed for quantitative estimation at 302 nm for ETO and 283 nm for TRA.

Method validation

The proposed spectrophotometric methods were validated in accordance with the ICH Q2(R1) guidelines for analytical procedures, assessing linearity and range, detection and quantification limits, accuracy, precision, and selectivity.

Linearity and Range

Linearity was established across eight calibration points in triplicate covering the concentration ranges of 2–23 µg/mL for ETO and 3–40 µg/mL for TRA. For the simultaneous equation method, calibration graphs were constructed by plotting absorbance values at 279 nm (λmax of ETO) and 217 nm (λmax of TRA) against the respective concentrations. In the first derivative method, derivative amplitudes were measured at 302 nm (zero-crossing of TRA, for ETO determination) and 283 nm (zero-crossing of ETO, for TRA determination). Both methods demonstrated excellent linearity with coefficient of determination (r²) of 0.9998 for each analyte, confirming the suitability of the methods for quantitative determination (Table 1).

Table 1 Regression and validation data for quantitative analysis of ETO and TRA by the proposed methods.
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Limits of Detection and Quantification

The sensitivity of the proposed methods was assessed by calculating the limits of detection (LOD) and quantification (LOQ) using the standard equations LOD = 3.3σ/S and LOQ = 10σ/S, where σ represents the standard deviation of the residuals and S is the slope of the calibration curve. The results indicated high sensitivity for both drugs. For ETO, the LOD and LOQ were 0.362 and 1.096 µg/mL, respectively, using the simultaneous equation method, and 0.326 and 0.988 µg/mL by the first derivative method. For TRA, the simultaneous equation method gave LOD and LOQ values of 0.674 and 2.043 µg/mL, respectively, while the derivative method gave LOD and LOQ values of 0.602 and 1.826 µg/mL (Table 1).

Accuracy

Accuracy was assessed using the mean percentage recovery obtained from three replicate determinations of four different synthetic mixtures. The recovery results (Table 2) ranged between 98.52% and 100.65% for ETO, and 98.89% to 100.98% for TRA using the simultaneous equation method. For the first derivative method, recoveries ranged from 99.09% to 100.39% for ETO, and 99.34% to 100.84% for TRA. These values confirm the accuracy of the developed procedures for quantifying both drugs in combined formulations.

Table 2 Results of accuracy and precision evaluation for ETO and TRA determination.
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Precision

The precision of the proposed methods was evaluated in terms of repeatability (intra-day) and intermediate precision (inter-day), expressed as relative standard deviation (RSD%). Repeatability was determined by three replicate analyses of four synthetic mixtures within the same day, while intermediate precision was assessed over three consecutive days. Both methods exhibited RSD values below 2% for both analytes (Table 2), demonstrating excellent precision and reproducibility.

Selectivity

Selectivity was confirmed by analyzing synthetic mixtures and the commercial formulation ETRAL-TR®. No interference was observed from excipients or the co-formulated drug, as shown by the accuracy and precision results (Tables 2 and 3). Standard addition experiments further verified the absence of matrix interference, with recovery values close to 100%. Statistical comparison of the proposed methods with a reported reference method7 revealed no significant difference, as indicated by Student’s t-test and F-test values within the accepted limits (Table 3).

Table 3 Application of the developed methods for the determination of ETO and TRA in pharmaceutical formulations and statistical evaluation against a reported method.
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Comparative Evaluation and Greenness Assessment

Both the simultaneous equation and first-derivative spectrophotometric methods proved reliable for the concurrent quantification of ETO and TRA in binary mixtures and pharmaceutical formulations. The simultaneous equation method offers operational simplicity and rapid execution, requiring minimal mathematical computation, making it ideal for routine quality control. However, because it depends on absorptivity coefficients, it is slightly more susceptible to baseline fluctuations and spectral overlap. In contrast, the first-derivative method provides enhanced selectivity and sensitivity, as it utilizes zero-crossing points to effectively eliminate spectral interference. Although it requires optimization of instrumental parameters (Δλ and scaling factor), once standardized, it exhibited excellent reproducibility and stability. A quantitative comparison with the reported HPLC-UV method (Table 4) demonstrated that both proposed UV-based approaches yield comparable accuracy and precision, with recovery values within the acceptable range (98–101%) and statistically equivalent results confirmed by t- and F-tests. The LOD values for the derivative method (0.326 µg/mL for ETO and 0.602 µg/mL for TRA) were slightly lower than those of the simultaneous equation approach (0.362 µg/mL and 0.674 µg/mL, respectively), indicating higher analytical sensitivity, though still marginally higher than those obtained by HPLC. In terms of cost and solvent consumption, the proposed UV methods offer substantial advantages. Each analysis requires only a few milliliters of methanol, compared with the acetonitrile–phosphate buffer mixtures used in HPLC, which consume 20–30 mL per run and generate significantly more waste. This not only reduces operational expenses but also supports green analytical chemistry principles16,17,18.

Table 4 Compartive evaluation of the proposed method with the reported method.
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The AGREE greenness evaluation yielded a score of 0.65, indicating a favorable environmental profile. Compared to chromatographic methods, the proposed spectrophotometric approaches are eco-friendlier, cost-efficient, and less labor-intensive, while maintaining equivalent analytical performance. Overall, the comparative assessment highlights that both methods are accurate, precise, and environmentally sustainable. The simultaneous equation method is well-suited for rapid, routine analyses, whereas the first-derivative method is preferred when higher selectivity is required. Together, these methods represent robust and green alternatives to HPLC for the simultaneous estimation of ETO and TRA in pharmaceutical formulations.

Conclusion

Two validated spectrophotometric approaches have been introduced for the quantification of etoricoxib and tramadol in combined formulations. Both methods met validation standards, showing excellent linearity, accuracy, precision, and selectivity. The simultaneous equation method offers speed and simplicity, while the derivative method provides greater selectivity and slightly lower detection limits. When compared with a reported RP-HPLC procedure, the spectrophotometric methods delivered statistically equivalent results, but with the advantages of reduced cost, shorter analysis time, and minimal solvent use. Their favorable AGREE score further confirms their environmental compatibility. Although the proposed spectrophotometric methods demonstrated excellent accuracy, precision, and compliance with green analytical chemistry principles, certain limitations should be acknowledged. These UV-based methods exhibit lower sensitivity compared to chromatographic techniques and are not suitable for detecting degradation products or impurities. Additionally, minor matrix interference may occur in more complex pharmaceutical preparations due to overlapping excipient absorbance. Despite these limitations, the developed procedures remain highly practical for routine quality control and environmentally sustainable analysis of etoricoxib and tramadol in combined formulation.