Spectral residual augmented classical least squares for simultaneous green determination of cetirizine, fexofenadine and loratadine by UV spectrophotometry in pharmaceuticals and environmental samples

Abstract

Second-generation antihistamines—cetirizine, fexofenadine, and loratadine—require simultaneous determination methods for pharmaceutical quality control including cleaning validation and cross-contamination monitoring in multi-product manufacturing facilities, yet their severely overlapping UV spectra preclude direct spectrophotometric quantification. This study developed a novel, sustainable UV-spectrophotometric method employing spectral residual augmented classical least squares (SRACLS) chemometrics to mathematically resolve spectral overlap and enable simultaneous quantification. Calibration (25 mixtures, partial factorial design) and validation sets (20 mixtures, central composite design) spanned 4–12 µg/mL concentration ranges. Comparative evaluation revealed that SRACLS demonstrated superior performance versus concentration residual augmented classical least squares (CRACLS), achieving 40–70% lower prediction errors (RRMSEP: 1.745, 2.605, 1.736 versus 3.011, 3.960, 2.674) and tighter residual distributions (± 3–5 versus ± 5–6 units). Subsequently, ICH Q2(R2) validation confirmed excellent analytical performance: recoveries 98.06–101.95% across the full working range, intra-day precision ≤ 1.522% RSD, inter-day precision ≤ 1.986% RSD, LOD values of 0.379–0.560 µg/mL, LOQ values of 1.149–1.697 µg/mL, and robust selectivity against pharmaceutical excipients and environmental co-contaminants (96.05–103.38% recovery). Application to commercial tablets yielded results statistically equivalent to reported HPLC methods (t-test, F-test: p > 0.05), whereas analysis of tap water samples spiked at concentrations relevant to pharmaceutical manufacturing facility effluents following salting-out assisted liquid-liquid extraction achieved 95.43–103.85% recovery. Moreover, comprehensive sustainability assessment demonstrated excellent performance: MoGAPI 76, CaFRI 85, AGSA 70.83, BAGI 77.5, CACI 66, and AMRI 68, attributed to eliminated organic solvent consumption, minimal energy usage, low waste generation, and high throughput (> 30 samples/hour). Overall, this work represents the first SRACLS application to antihistamine analysis, providing a practical green alternative to chromatographic methods for pharmaceutical quality control and manufacturing effluent monitoring applications.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-56246-6.

Introduction

Second-generation antihistamines represent a major therapeutic class characterized by selective peripheral H1-receptor inverse agonism with minimal central nervous system penetration, effectively managing allergic rhinitis, chronic urticaria, and related allergic conditions without sedative effects^1–3. Cetirizine, fexofenadine, and loratadine—among the most widely prescribed antihistamines globally—exhibit rapid onset (1–2 h), once-daily dosing convenience, and extensive clinical validation, leading to widespread over-the-counter availability and generic market penetration⁴. In pharmaceutical manufacturing, multi-product facilities producing multiple antihistamine formulations face critical quality control challenges including cleaning validation, cross-contamination monitoring, and simultaneous multi-component analysis requirements. Beyond pharmaceutical applications, these antihistamines constitute emerging environmental contaminants. While trace concentrations are detected in wastewater treatment plant effluents (80–220 ng/L) and surface waters (4–11 ng/L), pharmaceutical manufacturing facility discharges exhibit substantially elevated levels, with cetirizine reaching 2.1 mg/L—concentrations several orders of magnitude higher requiring routine monitoring and discharge control^5,6. This dual context—pharmaceutical quality control and manufacturing effluent monitoring—necessitates analytical methods capable of simultaneous determination across varied matrices while maintaining sensitivity, selectivity, and sustainability.

Existing analytical methods for antihistamine determination predominantly rely on chromatographic separation. High-performance liquid chromatography with UV or fluorescence detection represents the most widely reported approach, achieving detection limits of 0.10–1.75 µg/mL and analysis times of 3–15 min^7,8. However, HPLC methods require substantial organic solvent consumption (acetonitrile, methanol-based mobile phases), expensive instrumentation, specialized maintenance, and trained personnel⁹. Liquid chromatography-tandem mass spectrometry (LC-MS/MS) offers superior sensitivity with lower limits of quantification (0.52-1.0 ng/mL in plasma) and structural confirmation capabilities for pharmacokinetic studies^10–12. Nevertheless, LC-MS/MS demands high capital investment, specialized expertise, complex sample preparation, high operational costs, and remains inaccessible to many routine quality control laboratories¹³. Spectrofluorimetric methods utilizing native fluorescence or derivatization reactions achieve enhanced sensitivity with nanomolar detection limits^14–16, yet require pH optimization, complexation reagents, time-consuming derivatization procedures, and suffer from matrix interference limitations. Electrochemical methods employing modified carbon electrodes—carbon nanotubes, boron-doped diamond—enable rapid analysis with minimal sample preparation^17,18. However, electrode modification procedures, variable reproducibility, and limited selectivity for multi-component mixtures without prior separation restrict practical applicability. These limitations underscore the need for simpler, cost-effective, environmentally sustainable alternatives capable of simultaneous multi-component determination without chromatographic separation.

Conventional UV spectrophotometry offers simplicity, cost-effectiveness, and widespread availability for pharmaceutical analysis¹⁹. However, direct spectrophotometric determination of cetirizine, fexofenadine, and loratadine presents significant challenges due to severe spectral overlap resulting from their similar chromophoric structures—aromatic rings and conjugated systems—which produce overlapping absorption bands in the 220–280 nm region. This spectral overlap prevents simultaneous quantification without mathematical resolution techniques. Derivative spectrophotometry has been applied to resolve binary mixtures of antihistamines with pseudoephedrine using zero-crossing measurements²⁰, yet this approach remains limited to simpler binary systems and requires tedious optimization of derivative orders and wavelength intervals²¹. On the other hand, chemometric methods provide powerful solutions by applying mathematical and statistical techniques to extract chemical information from multivariate spectral data²². Multivariate calibration enables simultaneous use of multiple wavelengths to resolve spectral overlap, transforming UV spectrophotometry from a single-component to a multi-component analytical technique²³. Classical least squares (CLS) represents the first multivariate approach, directly relating absorbance to concentration through Beer’s Law matrix formulation²⁴. CLS generates physically meaningful pure component spectra, providing qualitative information and model interpretability absent in inverse methods²⁵. However, conventional CLS fails when unmodeled interferents—pharmaceutical excipients or environmental co-contaminants—contribute spectral variance not explicitly included in calibration²⁶. Augmented CLS variants address this limitation through residual incorporation strategies. Spectral residual augmented CLS (SRACLS) augments calibration with dominant spectral residual patterns, enabling modeling of unmodeled interferents without recalibration²⁷. Concentration residual augmented CLS (CRACLS) iteratively refines predictions by incorporating concentration residuals during the prediction phase, providing adaptive capability for varying matrix compositions²⁸. Both methods retain CLS qualitative advantages—pure component spectral recovery and model transparency—while achieving prediction performance comparable to partial least squares (PLS) regression^29,30. Notably, SRACLS excels for systems where spectral overlap dominates and matrix composition remains relatively constant, making it particularly suitable for antihistamine analysis in pharmaceutical formulations and tap water samples³¹.

Green analytical chemistry emphasizes the development of environmentally sustainable analytical methods that minimize waste generation, reduce hazardous reagent consumption, enhance operator safety, and lower energy requirements throughout the analytical process³². The twelve principles of green analytical chemistry provide a framework for designing eco-friendly methods, prioritizing prevention over remediation, atom economy, and use of safer solvents³³. Assessment tools such as the Analytical GREEnness metric (AGREE), Blue Applicability Grade Index (BAGI), Modified Green Analytical Procedure Index (MoGAPI), and Carbon Footprint Reduction Index (CaFRI) enable comprehensive, multi-dimensional evaluation of method sustainability from greenness, practical applicability and carbon footprint perspectives^34–38. UV spectrophotometry coupled with chemometric modeling represents an inherently green alternative to chromatographic methods for pharmaceutical quality control and environmental monitoring³⁹. The proposed approach eliminates organic solvent consumption entirely—no mobile phase solvents, extraction solvents, or derivatization reagents—relying solely on aqueous buffer systems⁴⁰. Compared to HPLC methods requiring acetonitrile-based mobile phases, UV-chemometric methods generate minimal chemical waste, significantly reduce operational costs, and eliminate hazardous solvent disposal requirements. Also, lower energy consumption results from simplified instrumentation without pumps, thermostated column compartments, or degassing systems. Additionally, the rapid analysis time (< 5 min per sample) and elimination of chromatographic separation further enhance throughput and sustainability. These advantages align with growing regulatory and industrial demands for green analytical practices in pharmaceutical manufacturing and environmental laboratories.

The primary objective of this study was to develop and validate a novel, sustainable UV-spectrophotometric method for simultaneous determination of cetirizine, fexofenadine, and loratadine using augmented classical least squares chemometric approaches. This research conducted a comprehensive comparative evaluation of spectral residual augmented classical least squares (SRACLS) and concentration residual augmented classical least squares (CRACLS) algorithms, systematically assessing prediction accuracy, model robustness, and practical applicability. Calibration and validation sets were constructed using experimental design principles—a 25-mixture partial factorial design for calibration and a 20-mixture central composite design for validation—ensuring comprehensive coverage of the ternary concentration space (4–12 µg/mL per analyte). Method validation followed ICH Q2(R2) guidelines, encompassing linearity, accuracy, precision and selectivity assessments. Practical applicability was demonstrated through analysis of commercial pharmaceutical formulations and tap water samples, representing quality control and environmental monitoring applications, respectively. This work represents the first application of SRACLS and CRACLS algorithms to this specific antihistamine combination, addressing a significant gap in the chemometric literature. The method provides a green alternative to conventional chromatographic approaches, eliminating organic solvent consumption while maintaining analytical performance comparable to HPLC methods. Furthermore, the dual application scope—pharmaceutical quality control and environmental screening—demonstrates practical versatility for both manufacturing facilities conducting cleaning validation and water quality laboratories monitoring pharmaceutical contamination. Comprehensive sustainability assessment using recent tools provides quantitative evidence of the method’s environmental advantages from multiple complementary dimensions including greenness principles, carbon footprint reduction, practical applicability and reliability. This study contributes to the growing body of green analytical chemistry by demonstrating that chemometric-assisted UV spectrophotometry can successfully replace chromatographic methods for complex multi-component pharmaceutical analysis without compromising analytical quality.

Experimental

Materials

Reference standards of cetirizine dihydrochloride (99.5%), fexofenadine hydrochloride (99.2%), and loratadine (99.8%) were procured from the Egyptian Drug Authority (EDA), Cairo, Egypt. Commercial pharmaceutical tablet formulations were obtained from local pharmacies in Cairo, Egypt. The analyzed formulations included Zyrtec^® tablets (cetirizine dihydrochloride, 10 mg per tablet), Allegra^® tablets (fexofenadine hydrochloride, 120 mg per tablet), and Claritine^® tablets (loratadine, 10 mg per tablet). HPLC-grade ethanol, supplied by Sigma-Aldrich (St. Louis, MO, USA), served as the solvent for stock solution preparation. Distilled water, used as the diluent solvent for spectrophotometric measurements and sample preparation, was obtained from a laboratory water distillation unit. Tap water samples for environmental analysis were collected from laboratory water supply taps and filtered through 0.45 μm membrane filters (Millipore, Bedford, MA, USA) prior to analysis to remove particulate matter. All chemicals and reagents were used as received without further purification.

Instrumentation and Software

Ultraviolet-visible spectrophotometric measurements were conducted using a Shimadzu UV-1800 double-beam spectrophotometer fitted with 10 mm path length matched quartz cuvettes. Spectral acquisition parameters were set as follows: wavelength range 200–400 nm, data interval 1 nm, scan rate 2800 nm/min, and spectral bandwidth 1 nm. Spectral data collection and preliminary processing were executed using UV Probe software version 2.43 (Shimadzu Corporation, Kyoto, Japan).

Experimental design construction for calibration and validation sets was performed using Design Expert^® software version 11 (Stat-Ease Inc., Minneapolis, MN, USA), which facilitated the generation of partial factorial and central composite designs. Chemometric modeling, including SRACLS and CRACLS algorithm implementation, was accomplished using MATLAB^® R2016a (version 9.0.0.341360, MathWorks Inc., Natick, MA, USA). Custom MATLAB scripts were developed to execute the augmented classical least squares algorithms, encompassing calibration matrix construction, spectral and concentration residual calculations, model optimization, cross-validation procedures, and prediction of unknown samples.

Construction of experimental space

Calibration and validation sets were systematically designed using experimental design principles to ensure comprehensive coverage of the ternary concentration space while maintaining statistical rigor. Individual stock solutions of cetirizine dihydrochloride, fexofenadine hydrochloride, and loratadine were prepared by dissolving appropriate quantities in HPLC-grade ethanol to yield final concentrations of 100 µg/mL for each analyte. Working standard solutions were prepared by sequential dilution of stock solutions with distilled water.

The calibration set consisted of 25 ternary mixtures constructed according to a five-level partial factorial experimental design (Table S1). Five concentration levels were established for each analyte: 4, 6, 8, 10, and 12 µg/mL, systematically varied to provide non-collinear concentration patterns across the design space. This design approach was selected to provide systematic exploration of the concentration domain while ensuring adequate model degrees of freedom. Concentration ranges for the calibration set were established as 4–12 µg/mL for each of the three antihistamines, selected based on their molar absorptivities in the UV region and analytical sensitivity requirements.

Calibration mixtures were prepared using the following procedure: accurate volumes of each working standard solution were transferred into 10 mL volumetric flasks using calibrated micropipettes to achieve the target concentrations specified in Table S1. The flasks were then diluted to volume with distilled water and mixed thoroughly by inversion. UV absorption spectra were recorded for each calibration mixture across 200–400 nm and compiled into an absorbance data matrix for chemometric model development.

An independent validation set comprising 20 ternary mixtures was designed using a central composite design approach with concentration levels of 5, 7, 8, 9, and 11 µg/mL for each analyte (Table S2). This design incorporated three distinct components: factorial point combinations at 7 and 9 µg/mL exploring intermediate concentration ranges, axial points at extreme levels of 5 and 11 µg/mL with α = 3, and six replicate center points at 8 µg/mL for all analytes to evaluate measurement precision and model repeatability. Validation mixtures were prepared following the same pipetting procedure as the calibration set. The central composite design structure enables comprehensive assessment of model predictive capability across the entire experimental domain, including evaluation of interpolation accuracy and modest extrapolation performance. UV spectra for validation samples were acquired under identical instrumental conditions and utilized for independent verification of chemometric model performance and prediction accuracy.

Augmented least squares modelling and method validation

Two augmented classical least squares algorithms were developed and compared for simultaneous quantification of the three antihistamines based on the Beer’s Law matrix relationship:

where A is the absorbance matrix, C is the concentration matrix, K represents pure component spectra, and E denotes spectral residuals.

The spectral residual augmented classical least squares (SRACLS) method was implemented by first constructing an initial CLS calibration model from the absorbance spectra and known concentrations of the calibration set. Spectral residuals, calculated as the difference between measured and CLS-predicted spectra, were subjected to principal component analysis to identify dominant patterns of unmodeled spectral variation. The K-matrix (pure component spectra matrix) was then augmented with the most significant spectral residual loading vectors, and the calibration model was reconstructed. The optimal number of principal components for augmentation was determined through leave-one-out cross-validation by monitoring the root mean square error of cross-validation (RMSECV) and selecting the minimum that yielded statistically insignificant improvement upon addition of further components.

The concentration residual augmented classical least squares (CRACLS) algorithm operated through an iterative prediction refinement process. Initial CLS predictions were obtained for each calibration sample, and concentration residuals (differences between actual and predicted concentrations) were calculated. These residuals, representing contributions from unmodeled components, were iteratively incorporated into the calibration matrix during subsequent prediction steps until convergence was achieved. The optimal number of iterations was determined by cross-validation, selecting the point where concentration residuals stabilized and prediction errors minimized.

Model performance was evaluated using multiple statistical metrics including coefficient of determination (R²), slope and intercept from predicted versus actual concentration plots, relative root mean square error of calibration (RRMSEC), relative root mean square error of prediction (RRMSEP), and relative bias-corrected mean square error of prediction (RBCMSEP). Method validation followed ICH Q2(R2) guidelines, encompassing assessment of accuracy (recovery studies at three concentration levels in triplicate), precision (intra-day and inter-day repeatability expressed as relative standard deviation), and selectivity (interference studies with common pharmaceutical excipients and environmental co-contaminants). All chemometric calculations and statistical analyses were performed using custom MATLAB scripts as described in Sect.  2.2.

Application to pharmaceutical formulations and environmental samples

Pharmaceutical formulations

For pharmaceutical tablet analysis, ten tablets of each formulation (Zyrtec^®, Allegra^®, and Claritine^®) were accurately weighed and finely powdered using a mortar and pestle. A portion of the powder equivalent to 10 mg of the active ingredient was transferred into a 100 mL volumetric flask and dissolved in 50 mL of HPLC-grade ethanol with sonication for 15 min to ensure complete extraction of the active ingredients. The solution was cooled to room temperature, diluted to volume with ethanol, and filtered through Whatman No. 42 filter paper to remove insoluble excipients. An appropriate aliquot of the filtrate was transferred to a 10 mL volumetric flask and diluted to volume with distilled water to achieve a final concentration within the calibration range (4–12 µg/mL). UV spectra were recorded and analyzed using the developed SRACLS model. Recoveries were calculated by comparing predicted concentrations with label claims, and results were statistically compared with reported HPLC methods^7,8 using Student’s t-test and F-test at 95% confidence level.

Environmental samples (Tap Water)

Tap water samples were subjected to salting-out assisted liquid-liquid extraction (SALLE) prior to analysis to minimize matrix interference and remove dissolved inorganic salts and natural organic matter. A 5 mL aliquot of tap water was spiked with known concentrations of the three antihistamines (4, 6, 8, and 10 µg/mL) and transferred to a glass centrifuge tube. Sodium chloride (1 g) was added as the salting-out agent, followed by addition of 3 mL of HPLC-grade acetonitrile as the extraction solvent. The mixture was vortexed vigorously for 3 min and centrifuged at 4000 rpm for 5 min to achieve phase separation. The upper acetonitrile-rich layer was carefully collected using a micropipette. The acetonitrile extract was evaporated to dryness under a gentle stream of nitrogen at 40 °C. The residue was reconstituted in 5 mL of distilled water, and UV spectra were acquired for SRACLS analysis. Recovery percentages were calculated by comparing predicted concentrations with spiked amounts.

Greenness, practicality, carbon footprint, and reliability evaluation

The environmental sustainability, practical applicability, and carbon footprint of the developed method were comprehensively assessed using six complementary evaluation tools. The Modified Green Analytical Procedure Index (MoGAPI) (https://bit.ly/MoGAPI) assessed method greenness through fifteen categories organized into five procedural stages, providing both visual pentagram representation and a quantitative total score (0-100 scale)⁴¹. The Carbon Footprint Reduction Index (CaFRI) (https://bit.ly/CaFRI) specifically evaluated greenhouse gas emissions through assessment of energy consumption, CO2 production, sample transportation, waste management, and recycling initiatives, presenting results as a footprint-shaped pictogram (0-100 scale) with color-coding indicating carbon footprint levels³⁶. The Analytical Green Star Area (AGSA) (bit.ly/AGSA2025) was applied to provide quantitative greenness assessment explicitly structured around the twelve principles of green analytical chemistry, offering built-in scoring and resistance to user bias through a star-shaped compass pictogram (0-100 scale), where larger green areas indicate superior environmental performance⁴². The Blue Applicability Grade Index (BAGI) (https://mostwiedzy.pl/BAGI) assessed practical applicability across ten criteria including analytical performance, robustness, cost-effectiveness, and throughput, presenting results as a blue star-shaped pictogram (0-100 scale)³⁷. The Click Analytical Chemistry Index (CACI) (bit.ly/CACI2025) was additionally applied as a complementary practicality assessment tool, specifically addressing method affordability, analytical scope, portability, automation, sensitivity, and analysis time — dimensions not fully captured within the BAGI framework. CACI evaluates seven criteria presenting results as a circular color-coded pictogram (0-100 scale)⁴³. The Analytical Method Reliability Index (AMRI) (bit.ly/AMRI2026) was employed to provide standardized quantitative assessment of method reliability beyond binary validation acceptance criteria, evaluating ten validation parameters including linearity, range, accuracy, precision, LOD, LOQ, selectivity, robustness, stability, and application to real samples, rewarding methods that exceed minimum ICH and FDA requirements through a hand-shaped color-coded pictogram (0-100 scale)⁴⁴.

Results and discussion

UV spectral characteristics

The chemical structures of cetirizine, fexofenadine, and loratadine (Fig. S1) contain multiple aromatic rings, heteroatoms, and electron-withdrawing chlorine substituents that produce characteristic ultraviolet absorption profiles. The UV absorption spectra recorded in distilled water at 8 µg/mL concentration across the 200–350 nm range (Fig. 1) demonstrate distinct absorption characteristics for each antihistamine while revealing severe spectral overlap that precludes direct simultaneous quantification. All three compounds exhibit intense absorption in the short-wavelength UV region, attributed primarily to π→π* electronic transitions of the aromatic chromophores. Cetirizine displays dual absorption maxima at 205 nm and 230 nm, with absorption intensity declining rapidly beyond 250 nm and reaching baseline levels by 270 nm (Fig. 1). Fexofenadine exhibits an absorption maximum at 210 nm and maintains detectable absorption extending to approximately 280 nm (Fig. 1). Loratadine demonstrates the most extended absorption profile with high absorbance in the short-wavelength region (205 nm) and a characteristic broad absorption band spanning 220–300 nm with maximum intensity around 246 nm (Fig. 1). The spectral profiles reveal severe overlap throughout the critical 205–280 nm region, with no wavelength exhibiting selective absorption by a single component. This extensive spectral superposition—resulting from structurally similar chromophoric systems and overlapping π→π* transition energies—renders direct spectrophotometric quantification impossible without mathematical deconvolution. Hence, chemometric methods such as spectral residual augmented classical least squares (SRACLS) and concentration residual augmented classical least squares (CRACLS) were employed to mathematically resolve the overlapping spectral contributions and enable simultaneous quantification of the three antihistamines without chromatographic separation.

Fig. 1.

UV absorption spectra of cetirizine, fexofenadine, and loratadine recorded in distilled water at 8 µg/mL concentration across 205–350 nm wavelength range.

Experimental design and concentration space

Systematic construction of calibration and validation sets through experimental design principles ensures comprehensive coverage of the ternary concentration space while maintaining statistical independence between model training and testing datasets. The calibration set comprised 25 ternary mixtures designed according to a five-level partial factorial experimental design (Table S1), with cetirizine, fexofenadine, and loratadine concentrations independently varied across 4, 6, 8, 10, and 12 µg/mL levels. The three-dimensional visualization of the calibration space (Fig. 2, blue spheres) demonstrates uniform distribution of mixture compositions throughout the experimental region, with samples distributed at boundary extremes (4 µg/mL and 12 µg/mL), intermediate levels (6 µg/mL and 10 µg/mL), and central concentrations (8 µg/mL). The partial factorial design ensures that each component varies independently across its concentration range, avoiding systematic correlation between component concentrations that would compromise model performance. The concentration range of 4–12 µg/mL was established based on preliminary Beer–Lambert law linearity assessment, accounting for the additive nature of absorbance in ternary mixture systems. The combined absorbance contributions of all three analytes were maintained within the optimal detector response window across this range, ensuring chemometric model integrity and prediction reliability.

Fig. 2.

Three-dimensional visualization of experimental design space showing calibration set distribution (blue spheres, 25 mixtures from partial factorial design) and validation set distribution (green spheres, 20 mixtures from central composite design) across cetirizine, fexofenadine, and loratadine concentration ranges (4–12 µg/mL).

The validation set consisted of 20 ternary mixtures constructed using a central composite design (Table S2), incorporating concentration levels of 5, 7, 8, 9, and 11 µg/mL to provide independent assessment of model predictive capability. The central composite design comprises factorial points at intermediate levels (7 and 9 µg/mL), axial points at 5 and 11 µg/mL positioned at α = 3 distance from the design center, and six replicate center points at 8 µg/mL for all three analytes to evaluate measurement precision. The three-dimensional distribution of validation samples (Fig. 2, green spheres) demonstrates positioning within the interior of the calibration space, ensuring that validation predictions represent interpolation rather than extrapolation. The two-dimensional projections (Figs. S2-S4) illustrate orthogonal relationships between component pairs, with calibration samples (blue circles) distributed across all concentration combinations and validation samples (orange triangles) concentrated near the central region for interpolation testing. The concentration range of 4–12 µg/mL was selected based on Beer’s Law linearity for the three antihistamines in the UV region and pharmaceutical relevance for tablet formulation analysis after appropriate dilution to bring analyte concentrations within the analytical working range.

Chemometric model development and comparative performance

Both SRACLS and CRACLS algorithms were developed and optimized to resolve the severely overlapping UV spectra and enable simultaneous quantification of the three antihistamines. For SRACLS, the optimal number of principal components (PCs) for spectral residual augmentation was determined through leave-one-out cross-validation by monitoring the relative root mean square error of cross-validation (RRMSECV) as a function of PC number (Fig. 3A). The RRMSECV curves for all three analytes exhibited rapid initial decline followed by plateau behavior, indicating that additional PCs beyond the optimal number provided negligible improvement while risking overfitting. Cetirizine achieved minimum RRMSECV at 3 PCs (green star marker), fexofenadine at 4 PCs, and loratadine at 2 PCs, suggesting that the complexity of unmodeled spectral variance differs among the three compounds. For CRACLS, the optimal number of iterations for concentration residual incorporation was similarly determined by cross-validation (Fig. 3B). The iterative refinement process showed convergence after 5 iterations for cetirizine, 5 iterations for fexofenadine, and 3 iterations for loratadine (green star markers), beyond which further iterations did not significantly reduce prediction errors and introduced computational inefficiency. Notably, CRACLS required more optimization parameters (5 iterations) compared to SRACLS (2–4 PCs) for comparable performance, indicating greater model complexity and computational demand in the iterative concentration residual approach versus the one-time spectral residual augmentation employed in SRACLS.

Fig. 3.

Optimization of chemometric models through cross-validation. (A) SRACLS optimization curves showing relative root mean square error of cross-validation (RRMSECV) as a function of principal component number for cetirizine, fexofenadine, and loratadine, with optimal values indicated by green star markers at 3, 4, and 2 PCs, respectively. (B) CRACLS optimization curves showing RRMSECV as a function of iteration number, with optimal values at 5, 5, and 3 iterations indicated by green star markers.

The calibration and validation performance of both algorithms was assessed using multiple statistical metrics (Table 1). SRACLS demonstrated superior performance across all three analytes, achieving coefficients of determination (R²) of 0.999 for cetirizine, 0.997 for fexofenadine, and 0.998 for loratadine for the calibration set, with corresponding relative root mean square errors of calibration (RRMSEC) of 1.471, 2.080, and 1.613 for cetirizine, fexofenadine, and loratadine, respectively. The slopes from predicted versus actual concentration plots approached unity (1.011, 0.997, 0.993) with near-zero intercepts (-0.124, 0.032, 0.037), confirming linearity and absence of systematic bias. These slope values additionally serve as sensitivity indicators, confirming proportional and unbiased analyte responses across the working concentration range. In comparison, CRACLS yielded slightly lower calibration R² values of 0.997, 0.992, and 0.995 for the three analytes, with higher RRMSEC values of 2.090, 3.525, and 3.015, indicating reduced fitting accuracy during model training. For the independent validation set, SRACLS achieved relative root mean square errors of prediction (RRMSEP) of 1.745, 2.605, and 1.736, while CRACLS exhibited higher RRMSEP values of 3.011, 3.960, and 2.674, corresponding to 40–70% higher prediction errors. The relative bias-corrected mean square error of prediction (RBCMSEP) values—which isolate random prediction error from systematic bias—followed similar trends, with SRACLS achieving values of 0.244, 0.543, and 0.241 compared to CRACLS values of 0.725, 1.255, and 0.572, confirming superior precision for the spectral residual augmentation approach.

Table 1.

Validation results for SRACLS and CRACLS models showing calibration and prediction performance metrics.

Method	Drug	Slope a	Intercept a	R 2 a	RRMSEC	RRMSEP	RBCMSEP
SRACLS	Cetirizine	1.011	-0.124	0.999	1.471	1.745	0.244
	Fexofenadine	0.997	0.032	0.997	2.080	2.605	0.543
	Loratadine	0.993	0.037	0.998	1.613	1.736	0.241
CRACLS	Cetirizine	1.011	-0.022	0.997	2.090	3.011	0.725
	Fexofenadine	1.005	0.086	0.992	3.525	3.960	1.255
	Loratadine	0.960	0.301	0.995	3.015	2.674	0.572

^a Data obtained by plotting the actual versus the predicted values for the calibration data.

The recovery residual plots (Fig. 4) provide direct visual comparison of prediction error patterns between the two algorithms. SRACLS residuals (Fig. 4A) distributed randomly around zero for both calibration and validation samples, with cetirizine and loratadine residuals confined within approximately ± 3 units and fexofenadine within ± 5 units, indicating absence of systematic bias and homoscedastic error variance. CRACLS residuals (Fig. 4B) exhibited substantially larger scatter ranges, with cetirizine extending to ± 5 units, fexofenadine to ± 6 units, and loratadine to ± 6 units for validation samples, demonstrating reduced model robustness and increased prediction uncertainty. The increased scatter in CRACLS predictions, particularly evident for validation samples, confirms the statistical metrics from Table 1 and illustrates the practical consequences of higher RRMSEP values. The predicted versus actual concentration plots (Fig. 5) reinforce these observations, with SRACLS predictions (Fig. 5A) exhibiting excellent correlation (R² values of 0.9969, 0.9934, and 0.9965 for cetirizine, fexofenadine, and loratadine) with tight clustering around the ideal diagonal line, while CRACLS predictions (Fig. 5B) showed increased scatter, particularly for fexofenadine (R² = 0.9832) and loratadine (R² = 0.9911). The superior performance of SRACLS can be attributed to its effective handling of unmodeled spectral variance through one-time principal component augmentation during calibration, which captures consistent interferent patterns without introducing iterative computational complexity. For spectrally overlapping antihistamines in relatively consistent pharmaceutical and environmental matrices, SRACLS provides optimal balance between accuracy, precision, and computational efficiency, justifying its selection for subsequent applications.

Fig. 4.

Recovery residual plots comparing prediction error patterns between (A) SRACLS and (B) CRACLS algorithms. Each panel displays residuals for cetirizine (top), fexofenadine (middle), and loratadine (bottom) across calibration samples (blue circles) and validation samples (orange triangles).

Fig. 5.

Predicted versus actual concentration plots for (A) SRACLS and (B) CRACLS algorithms. The diagonal line represents perfect prediction (slope = 1, intercept = 0). SRACLS demonstrates superior linearity compared to CRACLS for the three analytes.

Method validation

The developed SRACLS method was validated in accordance with ICH Q2(R2) guidelines, encompassing accuracy, precision, limits of detection and quantification, and selectivity assessments. Accuracy was evaluated through recovery studies conducted at three concentration levels spanning the full working range: a low level of 5 µg/mL, a middle level of 8 µg/mL, and a high level of 11 µg/mL, in triplicate. For cetirizine, mean recoveries ranged from 98.51% to 101.79% with standard deviations between 1.111 and 1.462, confirming absence of proportional or constant errors across the full working range. Fexofenadine yielded mean recoveries of 99.67% to 101.95% with standard deviations between 1.165 and 1.551, while loratadine recoveries ranged from 98.06% to 99.78% with standard deviations between 1.349 and 1.486 (Table S3). The consistently high recoveries across low, middle, and high concentration levels confirm the absence of concentration-dependent bias across the full 4–12 µg/mL working range, in full compliance with ICH Q2(R2) guidelines.

Precision was assessed through both intra-day and inter-day studies. Intra-day precision, evaluated through six replicates within a single analytical session, yielded %RSD values of 1.128–1.522% across all analytes and concentration levels. Inter-day precision, assessed over three consecutive days, produced slightly higher but equally acceptable %RSD values of 1.363–1.986% (Table S3). These values fall well within the ICH Q2(R2) acceptance criterion of ≤ 2% RSD, confirming consistent quantitative results independent of day-to-day instrumental variations or minor environmental fluctuations.

Limits of detection and quantification were determined for the SRACLS model according to ICH Q2(R2) guidelines using the standard deviation of residuals from the calibration regression line, according to LOD = 3.3σ/S and LOQ = 10σ/S, where σ represents the standard deviation of calibration residuals and S represents the slope of the calibration curve. LOD values of 0.379, 0.560, and 0.431 µg/mL and LOQ values of 1.149, 1.697, and 1.305 µg/mL were obtained for cetirizine, fexofenadine, and loratadine respectively, with all LOQ values falling well below the lower limit of the claimed working range (4 µg/mL), confirming adequate method sensitivity across the full calibration range.

Selectivity was comprehensively evaluated by analyzing spiked mixtures containing eight common pharmaceutical excipients and four environmental interferents at concentrations relevant to real sample matrices (Table S4). Pharmaceutical excipients including lactose monohydrate, microcrystalline cellulose, magnesium stearate, povidone, croscarmellose sodium, starch, titanium dioxide, and talc yielded recoveries of 96.53–103.38% with %RSD values below 1.8%. Environmental interferents including humic acid, sodium dodecyl sulfate, ibuprofen, and paracetamol produced recoveries of 96.05–103.38%, demonstrating that co-occurring matrix components do not compromise quantification accuracy. The robust selectivity performance across diverse interferents demonstrates a key advantage of the SRACLS approach, whereby spectral residual augmentation captures consistent interferent spectral variance patterns during calibration and incorporates them into the augmented K-matrix as pseudo-components, mathematically compensating for their contributions without requiring their explicit concentration values in the calibration design standards.

Application to pharmaceutical formulations and environmental samples

Pharmaceutical formulations

The validated SRACLS method was applied to quantify cetirizine, fexofenadine, and loratadine in commercial pharmaceutical tablets (Zyrtec^®, Allegra^®, and Claritine^®) to assess practical applicability for quality control purposes (Table 2). Mean recovery values from five replicate determinations were 100.63 ± 2.079% for cetirizine, 99.02 ± 1.295% for fexofenadine, and 100.84 ± 1.421% for loratadine, demonstrating excellent agreement with label claims and confirming method accuracy in complex pharmaceutical matrices containing multiple excipients. Statistical comparison with reported HPLC methods^7,8 using Student’s t-test and F-test at 95% confidence level revealed no significant differences in accuracy or precision. The calculated t-values (0.680, 0.569, and 1.048 for cetirizine, fexofenadine, and loratadine, respectively) were all below the critical value of 2.306, indicating comparable accuracy between methods. Similarly, F-values (3.11, 3.509, and 1.613) remained below the critical value of 6.338, confirming equivalent precision. These statistical results validate that the proposed SRACLS method provides quantitative performance comparable to established chromatographic approaches while offering significant advantages in terms of reduced analysis time, eliminated organic solvent consumption, and simplified sample preparation requiring only tablet extraction and dilution.

Table 2.

Quantitative analysis of commercial pharmaceutical preparations by the proposed SRACLS method and statistical comparison with reported HPLC methods.

Formulation	Drug	Method		Mean a		SD		Variance		t-test (2.306) b		P value		F-value (6.338) b		P value
Zyrtec®	Cetirizine	SRACLS		100.63		2.079		4.320		0.680		0.521		3.11		0.298
		Reported method		99.91		1.179		1.389
Allegra®	Fexofenadine	SRACLS		99.02		1.295		1.676		0.569		0.59		3.509		0.252
		Reported method		99.72		2.424		5.876
Claritine®	Loratadine	SRACLS		100.84		1.421		2.019		1.048		0.327		1.613		0.655
		Reported method		99.764		1.805		3.256

^a Average of five determinations.

^b The values in parenthesis are tabulated values of “t “and “F”.

Environmental samples (Tap Water)

The applicability of the SRACLS method for environmental monitoring was evaluated by analyzing tap water samples spiked with the three antihistamines at four concentration levels (4, 6, 8, and 10 µg/mL) following salting-out assisted liquid-liquid extraction (SALLE) pretreatment (Table 3). Recovery values ranged from 95.91% to 102.81% for cetirizine, 95.43% to 103.85% for fexofenadine, and 97.92% to 102.79% for loratadine, with relative standard deviations between 1.946% and 3.717% across all concentration levels. The consistently high recoveries across the concentration range confirm effective extraction and matrix cleanup through the SALLE procedure, which successfully removed suspended particulates and minimized interference from dissolved inorganic salts and natural organic matter present in tap water. The slightly higher %RSD values compared to standard solutions (Table S3) reflect the additional variability introduced by the extraction step and natural matrix complexity, yet remain acceptable for environmental screening applications. It is acknowledged that the spiking concentrations employed (4–10 µg/mL) exceed trace antihistamine concentrations typically detected in natural water samples and wastewater treatment plant effluents. The method is therefore specifically intended for monitoring pharmaceutical manufacturing facility effluents, where antihistamine discharge concentrations can reach higher levels. This application scope represents a practically relevant and analytically justified environmental monitoring context distinct from trace-level natural water monitoring. Modification of the reconstitution step following SALLE extraction, through reconstitution in a smaller volume than the original sample, could provide genuine pre-concentration capability extending method applicability to lower concentration environmental matrices in future research. Hence, these results demonstrate that the SRACLS method coupled with simple SALLE pretreatment provides a practical analytical tool for monitoring pharmaceutical contamination in water supplies, with particular relevance for screening manufacturing facility effluents where antihistamine concentrations can reach mg/L levels requiring routine surveillance.

Table 3.

Recovery data for tap water analysis using SRACLS method following salting-out assisted liquid-liquid extraction (SALLE) pretreatment.

Amount added (µg/mL)	Cetirizine Recovery ± RSD (%)	Fexofenadine Recovery ± RSD (%)	Loratadine Recovery ± RSD (%)
4	95.91 ± 2.357	95.43 ± 3.242	97.92 ± 3.692
6	102.81 ± 3.278	103.47 ± 3.717	102.79 ± 1.973
8	102.71 ± 2.556	103.85 ± 2.759	99.31 ± 3.378
10	97.13 ± 2.367	101.22 ± 2.65	102.22 ± 1.946

Greenness, practicality, carbon footprint, and reliability evaluation

The environmental sustainability, practical applicability, and carbon footprint of the developed SRACLS method were comprehensively evaluated using six complementary assessment tools, providing multidimensional insight into method greenness, practicality, and reliability from analytical performance, environmental impact, practical efficiency, and climate change perspectives (Fig. 6).

Fig. 6.

Comprehensive greenness, practicality, carbon footprint, and reliability assessment of the developed SRACLS method. (A) MoGAPI pentagram showing greenness assessment across five procedural stages with total score of 76 out of 100, with segments color-coded (green, yellow, red) based on performance. (B) CaFRI footprint pictogram illustrating carbon footprint reduction assessment with score of 85 out of 100, displaying green sections for energy, waste, and reagent categories. (C) AGSA compass-shaped pictogram displaying quantitative greenness assessment structured around the twelve principles of green analytical chemistry with overall score of 70.83. (D) BAGI asteroid-shaped pictogram showing practical applicability assessment with score of 77.5 out of 100. (E) CACI circular color-coded pictogram showing practical usability assessment with score of 66, where colored segments indicate excellent performance, gray signifies intermediate performance, and black denotes poor performance. (F) AMRI hand-shaped color-coded pictogram showing method reliability assessment with score of 68, with green sections indicating good compliance, yellow indicating intermediate performance, and red indicating parameters requiring attention.

The Modified Green Analytical Procedure Index (MoGAPI) provided a total score of 76 out of 100 (Fig. 6A), combining visual pentagram representation with quantitative assessment across 15 categories organized into five procedural stages. The pentagram display shows predominantly green and yellow sectors with limited red areas, indicating good overall greenness. Green sectors reflect use of green solvents (distilled water as primary diluent with minimal ethanol for stock solutions), hermetic sealing ensuring operator safety, low energy consumption (≤ 0.1 kWh per sample), and quantitative analytical capability. Yellow sectors represent off-line sample collection, macro-scale extraction via SALLE procedure, and moderate waste generation (1–10 mL per sample), while red sectors indicate requirements for sample transport and chemical preservation. The Carbon Footprint Reduction Index (CaFRI) yielded a score of 85 (Fig. 6B), demonstrating excellent performance in carbon emission reduction with the footprint pictogram displaying predominantly green sections. Key contributors to the high CaFRI score included minimal electrical power consumption (< 0.1 kW), low CO2 emission factor (< 0.1 kg CO2/kWh), high sample throughput (> 30 samples/hour), normal temperature storage eliminating refrigeration energy demands, minimal waste generation (< 10 mL per sample), and low reagent consumption (≤ 3 hazard pictograms, < 5 mL organic solvents per sample). The yellow section represents transportation logistics typical of laboratory operations. The AGSA evaluation yielded a score of 70.83 (Fig. 6C), indicating good overall greenness through its star-shaped compass pictogram structured explicitly around the twelve principles of green analytical chemistry. High scores were achieved for principles reflecting elimination of chemical derivatization, minimal energy consumption (< 0.1 kW per sample), simultaneous multi-analyte determination, low reagent toxicity, and adequate operator safety through standard laboratory precautions. Moderate scores were assigned for principles addressing sample treatment, in-situ measurement capability, and waste management, reflecting the requirement for tablet extraction and SALLE pretreatment for environmental samples. The AGSA score confirms the method’s strong alignment with green analytical chemistry principles while providing an objective, bias-resistant quantitative evaluation.

The Blue Applicability Grade Index (BAGI) assessed practical implementation, yielding a score of 77.5 that exceeds the 60-point threshold for practical methods (Fig. 6D). The asteroid-shaped pictogram displays predominantly medium to dark blue sectors, indicating good practical applicability across multiple dimensions. The method achieved high ratings for quantitative multi-analyte analysis (three antihistamines simultaneously), simple commercially available instrumentation (UV-Vis spectrophotometer), high simultaneous sample preparation capacity (> 95 samples), simple low-cost sample preparation procedures, high throughput (> 10 samples/hour), and use of common commercially available reagents. Lighter blue sectors reflect the requirement for manual operation without automation and the need for matrix cleanup via SALLE for environmental tap water samples. Complementing the BAGI assessment, the CACI evaluation yielded a score of 66, confirming acceptable practical performance (Fig. 6E). The CACI pictogram demonstrated high scores for feasibility, reflecting the use of commercially available reagents and standard UV-Vis instrumentation with analysis costs below $10 per sample, and for applicability, reflecting simultaneous quantification of three analytes across two sample matrices. Moderate scores were assigned for sample preparation, reflecting the minimal ethanol-based extraction required for tablet analysis and SALLE pretreatment for tap water samples. Lower scores for portability and automation reflect the laboratory-based, manually operated nature of the method, consistent with its intended application in pharmaceutical quality control and environmental screening rather than field deployment. Together, BAGI and CACI scores confirm that the developed method achieves good practical applicability across affordability, scope, and operational efficiency dimensions.

The AMRI evaluation yielded a score of 68, indicating acceptable method reliability (Fig. 6F). The hand-shaped color-coded pictogram displayed green sections for accuracy, precision, and selectivity parameters, reflecting the excellent validation performance demonstrated throughout this study. Recovery values of 98.06–101.95% and %RSD values well below the ICH Q2(R2) acceptance criterion of ≤ 2% contributed positively to the accuracy and precision scores, respectively. Selectivity assessment against twelve interferents including eight pharmaceutical excipients and four environmental co-contaminants further strengthened the reliability score. Yellow sections reflected the absence of robustness and stability-indicating assessments, representing areas for potential future method development. The AMRI score confirms that the developed SRACLS method delivers reliable, trustworthy analytical performance that not only meets but substantially exceeds minimum ICH validation requirements across the most critical analytical parameters.

Collectively, these six complementary assessments demonstrate that the SRACLS UV-spectrophotometric method achieves a balanced sustainability profile, reconciling high analytical performance with excellent environmental friendliness, practical applicability, and method reliability, positioning it as a viable green alternative to conventional HPLC methods for simultaneous antihistamine determination in pharmaceutical and environmental matrices.

Conclusions

This study successfully developed and validated a novel, sustainable UV-spectrophotometric method for simultaneous determination of cetirizine, fexofenadine, and loratadine using spectral residual augmented classical least squares (SRACLS) chemometric modeling, addressing critical analytical challenges in pharmaceutical quality control, cleaning validation, and cross-contamination monitoring in multi-product manufacturing facilities. Comprehensive comparative evaluation demonstrated that SRACLS outperformed concentration residual augmented classical least squares (CRACLS) across all performance metrics, achieving superior prediction accuracy (RRMSEP values 40–70% lower), tighter residual distributions (± 3–5 units versus ± 5–6 units), and higher coefficients of determination (R² > 0.993 versus 0.983–0.991 for validation sets) while requiring fewer optimization parameters (2–4 principal components versus 3–5 iterations). The SRACLS superiority stems from one-time spectral residual augmentation during calibration that captures consistent interferent spectral variance patterns and incorporates them into the augmented K-matrix as pseudo-components, making it particularly suited for spectrally overlapping compounds in relatively stable matrix compositions. Rigorous validation according to ICH Q2(R2) guidelines confirmed excellent analytical performance with recoveries of 98.06–101.95% across the full working range, intra-day precision ≤ 1.522% RSD, inter-day precision ≤ 1.986% RSD, LOD values of 0.379–0.560 µg/mL, LOQ values of 1.149–1.697 µg/mL, and robust selectivity against eight pharmaceutical excipients and four environmental co-contaminants (96.05–103.38% recovery). Successful application to commercial pharmaceutical formulations yielded results statistically equivalent to reported HPLC methods (t-test and F-test, p > 0.05), while analysis of tap water samples spiked at concentrations relevant to pharmaceutical manufacturing facility effluents following SALLE pretreatment achieved 95.43–103.85% recovery across the 4–10 µg/mL concentration range, demonstrating practical versatility for both quality control and manufacturing effluent screening applications.

The method achieves excellent sustainability scores across six complementary assessment dimensions: MoGAPI score of 76 indicating good procedural greenness, CaFRI score of 85 demonstrating excellent carbon footprint reduction, AGSA score of 70.83 confirming good alignment with the twelve principles of green analytical chemistry, BAGI score of 77.5 confirming practical applicability, CACI score of 66 indicating acceptable method affordability and analytical scope, and AMRI score of 68 reflecting acceptable method reliability. The method eliminates organic solvent mobile phases entirely, consumes minimal energy (< 0.1 kW), generates minimal waste (< 10 mL per sample), achieves high throughput (> 30 samples/hour), and requires only simple, widely available UV-Vis instrumentation, positioning it as a viable green alternative to conventional HPLC methods without compromising analytical quality. This work represents the first application of SRACLS and CRACLS algorithms to simultaneous antihistamine determination, contributing novel chemometric methodology to pharmaceutical analysis while advancing green analytical chemistry principles.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Ali Alqahtani (Investigation, Methodology, Funding acquisition, Formal analysis, Writing – original draft, Writing – review & editing). Taha Alqahtani (Formal analysis, Investigation, Resources, Validation, Writing – review & editing). Adil Alshehri (Formal analysis, Investigation, Resources, Validation, Writing – review & editing). Sumaiah Alrubiaan (Formal analysis, Investigation, Resources, Validation, Writing – review & editing). Ahmed A. Almrasy (Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing - Review & Editing).

Funding

This research was funded by Deanship of Research and Graduate Studies at King Khalid University, KSA, through (General Research Project under grant number (GRP/48/46).

Data availability

The data presented in this study are available on request from the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.