Chemometric-assisted UV-Vis spectrophotometric method for the simultaneous quantification of triple anthelmintics in veterinary pharmaceuticals

Abstract

Effective control of parasitic diseases in veterinary medicine relies heavily on anthelmintic drugs, particularly combinations targeting both nematodes and cestodes. However, simultaneous quantification of multi-component anthelmintic formulations presents significant analytical challenges, especially with cost-effective UV-Vis spectrophotometry due to inherent spectral overlap. This study introduces a novel, rapid, and environmentally conscious UV-Vis spectrophotometric method, leveraging advanced chemometrics, for the simultaneous determination of Fenbendazole (FN), Pyrantel embonate (PN), and Praziquantel (PZ) in veterinary pharmaceuticals. A novel Adaptive Plateau-based Successive Projections Algorithm coupled with Automated Tuning Support Vector Regression (AP-SPA/AT-SVR) approach was developed. AP-SPA strategically selected optimal wavelengths, mitigating collinearity, while AT-SVR, employing hybrid hyperparameter optimization, robustly modeled complex spectral-concentration relationships. The AP-SPA/AT-SVR method demonstrably outperformed traditional Partial Least Squares Regression (PLSR), achieving significantly enhanced predictive accuracy, evidenced by reduced Mean Squared Error (MSE) and elevated coefficients of determination (R²). Rigorous validation, adhering to the accuracy profile approach, confirmed method accuracy across the relevant concentration range. Furthermore, comprehensive greenness and whiteness assessments unequivocally established the method superior sustainability profile. This innovative chemometric-assisted UV-Vis spectrophotometric method provides a valuable, rapid, accurate, and environmentally responsible tool for quality control in veterinary pharmaceutical analysis, offering a compelling alternative to conventional HPLC.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-31003-3.

Introduction

The global landscape of veterinary medicine is increasingly concerned with parasitic diseases, posing significant threats to animal health and welfare. Furthermore, the zoonotic nature of many parasites underscores the critical intersection between animal and human health, demanding robust strategies for disease management and control¹. Pharmaceutical intervention, employing a diverse arsenal of antiparasitic agents, remains the cornerstone of therapeutic and prophylactic measures in veterinary practice.Within this context, anthelmintic drugs, specifically those effective against both nematodes and cestodes, are indispensable for comprehensive parasite control. Infections caused by these helminths can lead to a spectrum of debilitating systemic complications in companion animals². The inherent limitations in the anthelmintic efficacy of many individual active pharmaceutical ingredients often necessitate the use of multi-drug combinations in veterinary formulations to achieve broad-spectrum parasite coverage and synergistic therapeutic effects^3,4. This trend towards combination therapies presents a significant analytical challenge, requiring robust and efficient methods for the simultaneous quantification of multiple active compounds within complex pharmaceutical matrices. Fenbendazole, a benzimidazole derivative (FN, Supplementary Fig S1-A), exerts its anthelmintic action by disrupting microtubule polymerization, thereby impeding essential parasite metabolic pathways including glucose transport and fumarate reductase activity⁵. Pyrantel embonate, a tetrahydropyrimidine derivative (BN, Supplementary Fig S1-B), functions as a cholinergic antagonist, inducing neuromuscular paralysis in nematodes through depolarization of neuromuscular junctions, facilitating parasite expulsion⁶. Praziquantel, a pyrazinisoquinolone derivative (PZ, Supplementary Fig S1-C), exhibits rapid absorption and targets cestodes by disrupting tegumental membranes, leading to parasite paralysis and death. This mechanism is attributed to increased membrane permeability, resulting in impaired glucose uptake and subsequent metabolic collapse within the parasite⁷. The synergistic pharmacological profiles of FN, PN, and PZ in combination provide a comprehensive anthelmintic effect, effectively combating a broad spectrum of gastrointestinal parasites, including Toxocara canis, Ancylostoma caninum, and Echinococcus species^3,4. Accurate and reliable quantification of these three analytes in combination formulations is therefore paramount for quality control and ensuring therapeutic efficacy.

High-Performance Liquid Chromatography (HPLC) has historically served as the gold standard for the quantitative analysis of anthelmintic drugs in pharmaceutical preparations⁴. However, conventional HPLC methodologies are often encumbered by limitations, including the requirement for sophisticated and costly instrumentation, high operational expenditures, and significant consumption of organic solvents. These factors raise substantial environmental and economic concerns, particularly in resource-constrained analytical settings. In contrast, UV-Vis spectrophotometry presents itself as an alternative, offering inherent advantages in terms of cost-effectiveness, ease of operation, and reduced environmental impact, aligning with the principles of green analytical chemistry. Despite these benefits, the simultaneous spectrophotometric determination of FN, PN, and PZ is inherently challenging due to the spectral overlap exhibited by these compounds in the UV-Vis region. This spectral interference complicates their individual quantification when employing traditional univariate spectrophotometric techniques^8,9.

The application of UV-Vis spectrophotometry for the simultaneous quantification of FN, PN, and PZ has not been reported, primarily due to the aforementioned spectral overlap hindering selective and accurate determination. To overcome this analytical bottleneck, this study introduces a novel chemometric approach employing the Successive Projections Algorithm (SPA) for wavelength selection, coupled with Support Vector Regression (SVR) for robust quantitative modeling. SPA is particularly well-suited for addressing spectral collinearity and redundancy, effectively identifying the most informative and non-redundant wavelengths within the complex spectral data¹⁰. Its deterministic nature ensures method robustness and reproducibility, while its computational efficiency, rooted in projection operations, surpasses exhaustive search methods¹¹. Furthermore, SPA compatibility with various preprocessing techniques enhances its capacity to extract relevant analytical signals from complex spectral datasets¹². Complementing SPA, Support Vector Regression (SVR) is chosen for its performance in handling both linear and non-linear relationships between spectral data and analyte concentrations. SVR demonstrates robust predictive capabilities even in the presence of complex spectral features and matrix effects, making it ideally suited for quantitative analysis in challenging matrices¹³. The synergistic integration of SPA and SVR, specifically through an innovative Adaptive Plateau-based SPA coupled with Automated Tuning SVR (AP-SPA/AT-SVR) strategy, offers a transformative solution to the limitations of conventional UV-Vis spectrophotometry for multi-analyte determination in the presence of significant spectral overlap, eliminating the subjectivity associated with manual peak selection and enhancing method reliability.

In the context of escalating global awareness regarding environmental sustainability, the analytical chemistry community is increasingly focused on minimizing the use of hazardous solvents and reducing analytical waste generation. This paradigm shift has spurred the development and adoption of various green analytical chemistry assessment tools, including the Green Solvent Selection Tool (GSST), National Environmental Methods Index (NEMI), Green Certificate Modified Eco-Scale, and the Modified Green Analytical Procedure Index (MoGAPI)^14–18. Furthermore, metrics such as whiteness, quantified using the Red-Green-Blue 12 (RGB 12) algorithm, provide additional quantitative insights into the holistic sustainability profile of analytical methodologies¹⁹. The development of environmentally conscious analytical methods is not merely an ethical imperative but also a strategic necessity for ensuring long-term analytical viability and minimizing laboratory environmental footprint.

Therefore, the primary objective of this research is to develop and validate a rapid, cost-effective, and environmentally benign UV-Vis spectrophotometric method for the simultaneous quantification of FN, PN, and PZ in complex veterinary pharmaceutical formulations. The proposed methodology incorporates data preprocessing steps, including variance thresholding for noise reduction, followed by an adaptive SPA-based wavelength selection employing a plateau-based stopping criterion for optimal feature subset identification. Subsequently, SVR model hyperparameters are optimized through a hybrid approach combining random and targeted grid search strategies to maximize predictive accuracy and model robustness. This innovative AP-SPA/AT-SVR approach, coupled with a comprehensive validation strategy, provides a compelling and sustainable analytical solution, directly addressing the inherent limitations of conventional UV-Vis spectrophotometry for multi-component analysis and facilitating enhanced quality control in the analysis of veterinary pharmaceuticals, while aligning with the growing demands for greener analytical practices.

Experimental

Instrumentation

Spectral characterization and quantitative measurements were performed using a Specord 210 Plus spectrophotometer (Analytik Jena, Germany). The UV-Vis spectra were acquired across a wavelength range of 200 to 400 nm to encompass the characteristic absorption bands of the analytes. All measurements were conducted using matched quartz cuvettes with a 1 cm optical path length. Instrument operation and data acquisition were managed through Aspect UV software (version 1.2.3). An absolute ethanol blank was used as the reference for all spectral acquisitions, allowing for automatic baseline correction by the instrument software.

To provide a comparative analytical benchmark and to assess the accuracy of the proposed spectrophotometric method, an HPLC method was employed⁴. The chromatographic separations were executed on a Dionex UltiMate 3000 HPLC system (ThermoScientific) using isocratic elution. A Phenomenex Luna phenyl-hexyl column (150 mm × 4.6 mm, 3 μm particle size) was selected. The mobile phase consisted of a mixture of acetonitrile and 0.5% triethylamine (TEA) aqueous solution, adjusted to pH 9.0 in a ratio of 45:55 (v/v). A flow rate of 1.0 mL/min was maintained throughout the analysis. Spectrophotometric detection was performed at 290 nm for FN and PN, and 220 nm for PZ. Data acquisition and instrument control were managed using Chromeleon^® 7 software. System suitability parameters, including tailing factor (< 2), theoretical plates (>2000), and injection precision (< 2.0% RSD), were monitored and found to be well within acceptable limits throughout the analysis.

Materials and reagents

Reference standards of fenbendazole (FN, Assay: 98.81% ± 0.58%), pyrantel embonate (PN, Assay: 98.86% ± 0.76%), and praziquantel (PZ, Assay: 98.93% ± 0.79%) were sourced from the Egyptian Drug Authority (EDA), ensuring traceability and compliance with pharmacopeial standards. The commercially available formulation, Cestal plus chewable tablets (Lavet Pharmaceuticals Ltd, Kistarcsa, Hungary), with labeled contents of 200 mg FN, 144 mg PN, and 50 mg PZ per tablet, served as the veterinary dosage form. Absolute ethanol of analytical grade, obtained from Merck (Darmstadt, Germany), was employed as the solvent for standard and sample preparation.

Experimental design and models evaluation

A multifactor multilevel calibration design, as described by Brereton²⁰, was strategically implemented to construct a robust calibration set for the spectrophotometric method. This design involved the systematic variation of three factors – the concentrations of FN, PN, and PZ – each at four distinct levels (detailed in Supplementary Table S1). The concentration ranges were carefully selected to encompass the anticipated analyte concentrations in the target veterinary pharmaceutical formulations, ensuring method applicability across the relevant concentration domain. For rigorous independent validation of the proposed chemometric model, a test set comprising ten samples was generated using a Latin Hypercube Design (LHD; Supplementary Table S2). LHD was chosen for its efficiency in sampling the experimental space, providing a representative and unbiased assessment of the model predictive performance.

The performance of AP-SPA/AT-SVR model, utilized for spectral data analysis, was quantitatively evaluated using established statistical metrics: the Mean Squared Error (MSE) and the coefficient of determination (R²). MSE, representing the average squared prediction error, provides a measure of the model overall prediction accuracy. R², ranging from 0 to 1, quantifies the proportion of variance in the analyte concentrations explained by the model, with values closer to 1 indicating superior model fit and predictive capability. These metrics were calculated according to the equations:

Where n denotes the number of data points, Y_i represents the actual value of the target variable for the i^th data point, Ŷ_i is the predicted value of the target variable for the i^th data point, RSS is the sum of squares of the residuals, and TSS is the total sum of squares.

It is important to note that no mathematical smoothing or further baseline corrections were applied. Prior to model development, a variance threshold of 0.1 was applied to the spectral data to enhance signal quality and model robustness. This threshold was selected to filter out non-informative variables—particularly in the high-noise region below 205 nm due to solvent absorbance—while retaining important analytical signals. To optimize model complexity and computational efficiency, a plateau threshold of 0.0001, defined as the relative change in MSE between successive iterations of SPA, was implemented as a stopping criterion. This criterion ensures that the variable selection process terminates when minimal improvement in model performance is achieved, preventing overfitting and enhancing model generalizability. Both thresholds were selected based on a rigorous sensitivity analysis.

Preparation of standard solutions

Stock solutions of FN, PN, and PZ were prepared at concentrations of 50 µg mL⁻¹, 36 µg mL⁻¹, and 12.5 µg mL⁻¹, respectively. Accurately weighed reference standards were dissolved in absolute ethanol. Calibration standards were subsequently generated through serial volumetric dilutions of the stock solutions using absolute ethanol. For method validation, independent validation standards were prepared at concentrations of 2.5, 7.5, and 17.5 µg mL⁻¹ for FN; 1.8, 5.4, and 12.5 µg mL⁻¹ for PN; and 0.6, 1.9, and 4.4 µg mL⁻¹ for PZ. These validation standards were chosen to represent concentrations across the calibration range and were analyzed in quintuplicate over three consecutive days. All prepared solutions were stored in amber volumetric flasks.

Method validation using accuracy profile approach

Method validation was conducted following the accuracy profile approach^21–25. This validation strategy ensures the reliability and fitness-for-purpose of the analytical method. Trueness, reflecting the closeness of agreement between the average value obtained from a large series of test results and an accepted reference value, was assessed by calculating the relative bias (%), with acceptance criteria set at ± 5%. Precision, encompassing both repeatability (within-day precision) and intermediate precision (between-day precision), was evaluated and expressed as relative standard deviations (RSD%), with acceptance criteria stringently set at ≤ 5%. Accuracy, representing the overall closeness of agreement between test results and the true value, was determined using β-expectation tolerance intervals with β set at 95%. This ensures a 95% probability that future results will fall within the acceptance limits, which were defined as ± 10% for the total error. The full statistical procedure for this approach is detailed in the cited SFSTP guidelines^26–29. Uncertainty was quantified as the relative expanded uncertainty (%) using a coverage factor of k = 2, providing a 95% confidence level. Acceptance limits for uncertainty were set at ≤ 10%, reflecting acceptable levels of measurement variability. Linearity was assessed by fitting a linear regression model to the back-calculated concentrations against the nominal concentrations of the FN, PN, and PZ validation standards. The parameters of this regression (slope, intercept, R²) were used exclusively to confirm the linear relationship of the results³⁰.

Software and packages

Model development and implementation of the AP-SPA/AT-SVR and PLSR algorithms were performed within a Google Colaboratory environment using Python (version 3.12.12). The analysis leveraged the functionalities of the scikit-learn (version 1.6.1) library for machine learning, NumPy (version 2.0.2) for numerical computations, and Pandas (version 2.2.2) for data manipulation and analysis. Accuracy profiles, for visual representation of method accuracy, were constructed using Microsoft Excel 2010.

Application to veterinary dosage form analysis

The proposed spectrophotometric method was applied to the analysis of Cestal plus chewable tablets. Five tablets were pulverized to homogeneity, and a representative portion of the powdered sample, accurately weighed to correspond to 50 mg of FN, 36 mg of PN, and 12.5 mg of PZ, was transferred to a beaker. The sample was sonicated with 75 mL of absolute ethanol for 30 min. The resulting extract was then filtered through a filter paper into a 100 mL volumetric flask. The filtrate was subsequently diluted to volume with absolute ethanol. Further dilutions were prepared to ensure the concentrations of FN, PN, and PZ in the final solutions fell within the working range of the proposed spectrophotometric method.

Results and discussion

The simultaneous quantification of FN, PN, and PZ is of significant importance in veterinary medicine, as this combination offers broad-spectrum anthelmintic efficacy, simplifying treatment regimens and improving animal health. However, as illustrated in Fig. 1, the UV-Vis absorption spectra of FN, PN, and PZ in absolute ethanol exhibit substantial spectral overlap across a considerable wavelength range (200–300 nm). The broad and closely positioned absorption maxima of these analytes complicate their simultaneous determination using conventional UV-Vis spectrophotometric techniques. The spectrum of a ternary mixture (Fig. 1) further underscores this challenge, representing the additive spectral contributions of each component and highlighting the complexity of deconvoluting individual analyte concentrations. A 3D plot of the entire spectral dataset is provided in Supplementary Fig S2, which further illustrates the severe spectral overlap. To overcome these limitations and enable accurate simultaneous quantification, we developed a novel approach integrating AP-SPA for optimal wavelength selection with AT-SVR for model development.

Fig. 1.

Absorption spectra of Fenbendazole (FN, 2.5 µg mL⁻¹), Pyrantel embonate (PN, 5.4 µg mL⁻¹), and Praziquantel (PZ, 4.4 µg mL⁻¹), along with their ternary mixture (FN: 2.5 µg mL⁻¹, PN: 9.0 µg mL⁻¹, PZ: 4.4 µg mL⁻¹).

Experimental design (Calibration and test Sets)

Developing robust and generalizable chemometric models for quantitative spectral analysis necessitates a carefully designed calibration set. An inadequately constructed calibration set can compromise model accuracy and limit its predictive capability for new, unknown samples³¹. To account for potential spectral interactions between FN, PN, and PZ, a multilevel experimental design was implemented to generate a calibration set comprising 16 mixtures (Supplementary Table S1). This design ensures that the concentrations of FN, PN, and PZ are varied independently, minimizing correlations between analyte concentrations and facilitating a more accurate assessment of their individual and combined spectral contributions. While the sample size is modest, this systematic design is highly efficient for capturing complex relationships in multivariate systems. For independent model validation, a test set of 10 samples was generated using a LHD, a space-filling technique chosen for its ability to provide representative coverage of the experimental domain with a minimal number of points²⁴. The robust performance of the model on this external test set validates the sufficiency of our design. Figure 2 presents the scatter matrix plot visualizing the distribution of both calibration and test set samples within the three-dimensional concentration space of FN, PN, and PZ. This plot visually confirms the space-filling characteristics of both designs, demonstrating adequate representation of the experimental domain.

Fig. 2.

Scatter matrix plot for the calibration set (multifactor multilevel design) and test set (space filling Latin hypercube design).

Optimization of chemometric model parameters

The predictive performance of the chemometric model is highly dependent on the selection of key parameters. To ensure the robustness and accuracy of our proposed method, a sensitivity analysis was conducted to optimize the variance threshold for data preprocessing and the plateau threshold for the AP-SPA stopping criterion. The effect of the variance threshold on the model predictive MSE is presented in Supplementary Fig S3. While the absolute minimum MSE for each analyte occurs at slightly different thresholds, a value of 0.1 was selected as it represents the best overall compromise, yielding consistently low prediction errors across all three analytes simultaneously (Supplementary Fig S3-A). This ensures that spectral noise is effectively filtered without removing crucial analytical information for any of the components.

The optimization of the AP-SPA plateau threshold is shown in Supplementary Fig S3-B. The results clearly indicate that a threshold of 0.0001 corresponds to the minimum achievable MSE for all three analytes. A less strict threshold results in higher error, while stricter thresholds show a trend of increasing error. Therefore, 0.0001 was confirmed as the optimal stopping criterion and used for all subsequent model development.

Adaptive Plateau-based successive projections algorithm (AP-SPA) for wavelength selection

To address the challenge posed by the significant spectral overlap, the AP-SPA was employed for optimal wavelength selection³². Unlike traditional SPA, which typically selects a pre-defined number of variables, AP-SPA incorporates an adaptive stopping criterion based on a plateau threshold (0.0001). This adaptive approach monitors the reduction in MSE during successive SPA iterations. The algorithm terminates when the improvement in MSE falls below this threshold, effectively preventing the inclusion of irrelevant or redundant wavelengths and mitigating the risk of model overfitting. Application of AP-SPA to the UV-Vis spectral data of FN, PN, and PZ mixtures resulted in a parsimonious selection of seven highly informative wavelengths. The specific wavelengths selected for the final model were [224, 262, and 343 nm] for FN, [208 and 328 nm] for PN, and [207 and 238 nm] for PZ. Supplementary Fig S4 visualizes these selected wavelengths, superimposed on the individual UV-Vis spectra of each analyte, highlighting their correspondence to regions of maximum absorbance and/or spectral differentiation. This targeted wavelength selection minimizes data redundancy and collinearity, leading to a more robust and computationally efficient calibration model. AP-SPA demonstrated enhanced computational efficiency compared to traditional SPA and exhaustive search methods, significantly accelerating the subsequent model building and validation steps by adaptively stopping the selection process and reducing data dimensionality.

Automated tuning support vector regression (AT-SVR) for quantitative modeling

To effectively model the potentially non-linear relationships between the UV-Vis spectra and the concentrations of FN, PN, and PZ, SVR with a Radial Basis Function (RBF) kernel was integrated with SPA. While traditional SPA often utilizes PLSR, PLSR linear nature can limit its performance when dealing with complex datasets exhibiting non-linearity³². To optimize the SVR model performance, a dual-stage hyperparameter tuning strategy was implemented exclusively on the calibration set using an internal 5-fold cross-validation (CV) procedure. This strategy combined a randomized search for broad exploration of the parameter space with a subsequent grid search for precise refinement. The performance of each hyperparameter combination was assessed based on its average cross-validated MSE across the five folds. Once the optimal hyperparameters were identified, a final model was trained on the entire calibration set and then evaluated a single time against the strictly external test set to ensure an unbiased assessment of its generalizability. Randomized search efficiently identified promising regions within the hyperparameter space, while grid search systematically evaluated all hyperparameter combinations within these refined regions to pinpoint the optimal parameter set. Supplementary Fig S5 illustrates this two-stage optimization, demonstrating the rapid identification of low-MSE regions by randomized search (upper panel) and the precise location of the global MSE minimum by grid search (lower panel). Table 1 compares the performance of the AP-SPA/AT-SVR method to PLSR for the simultaneous quantification of FN, PN, and PZ, based on MSE and R² for both calibration and test sets. Table 1 compares the performance of the AP-SPA/AT-SVR method to the traditional PLSR model. While the PLSR model showed a slightly lower calibration MSE for FN, the AP-SPA/AT-SVR model demonstrated superior predictive capability on the independent test set for all three analytes, as evidenced by lower MSE and higher R² values. This superior generalizability is the most crucial indicator of a model’s real-world utility. The advantage of our proposed method is particularly evident for PZ, where AP-SPA/AT-SVR significantly reduced the test set MSE from 0.09 (PLSR) to 0.02 and increased the R² from 0.941 to 0.972. These results demonstrate the superior predictive capability of the AP-SPA/AT-SVR approach, highlighting the synergistic benefits of adaptive feature selection and automated SVR modeling for complex spectral data analysis. Furthermore, to ensure the model was not overfitted, a residuals analysis was performed on the external test set (Supplementary Fig. 6). The plots show a random, non-systematic distribution of Studentized residuals around zero, confirming that the model is robust and generalizes well to new data.

Table 1.

Comparison the performance of adaptive Plateau-based successive projections algorithm with automated tuning support vector regression (AP-SPA / AT-SVR) and partial least squares regression (PLSR) for Fenbendazole (FN), pyrantel embonate (PN), and praziquantel (PZ).

Algorithm	Analyte	Set	MSE	R2
			Value	Value
PLSR	FN	Calibration	0.10	0.999
		Test	0.05	0.989
	PN	Calibration	0.09	0.992
		Test	0.05	0.993
	PZ	Calibration	0.05	0.961
		Test	0.09	0.941
AP-SPA / AT-SVR	FN	Calibration	0.11	0.997
		Test	0.03	0.999
	PN	Calibration	0.10	0.994
		Test	0.04	0.998
	PZ	Calibration	0.01	0.979
		Test	0.02	0.972

Method validation using accuracy profile approach

The proposed spectrophotometric method was validated for accuracy, precision, trueness, and linearity for the simultaneous quantification of FN, PN, and PZ, following the accuracy profile approach as outlined in the SFSTP guidelines^26–29. The comprehensive validation results are summarized in Table 2. The relative bias values for all three analytes, consistently within ± 5% across the tested concentration ranges (Table 2), indicate excellent trueness of the method. Similarly, the repeatability and intermediate precision, expressed as Relative Standard Deviation (RSD), were consistently below the acceptance criterion of ≤ 5% across all concentrations (Table 2), demonstrating satisfactory precision both within-day and between-days. The accuracy profiles, visualized in Fig. 3, confirm that the β-expectation tolerance intervals fall well within the acceptance limits of ± 10% for all analytes across their validated concentration ranges. The relative expanded uncertainties were also within the acceptance criterion of ≤ 10% (Table 2). It is important to note that the measurement uncertainty was calculated using a “top-down” approach, which is directly integrated with the accuracy profile methodology^33,34. This approach computes the total uncertainty by combining the variance from the intermediate precision—which empirically captures multiple random error sources from the validation design—with the uncertainty associated with the measurement bias. This provides a holistic and practical estimate of the uncertainty based on the method’s observed performance, as detailed in the cited literature^35,36. The low risk values (all < 5%, Table 2) further substantiate the method reliability. Linearity, assessed over the concentration ranges detailed in Table 2, was excellent, with regression analysis yielding R² close to unity, slopes near 1, and intercepts approaching zero for all three analytes. For a direct graphical assessment of the model linearity and lack of bias, predicted versus actual concentration plots are provided in Supplementary Fig S7. In accordance with the total error approach, the validated quantification range of the method is empirically defined by the accuracy profiles (Fig. 3). The Lower Limit of Quantification (LLOQ) is established as the lowest concentration for which the method total error (encompassed by the β-expectation tolerance interval) is confirmed to be within the acceptance limits. Based on this criterion, the LLOQs for FN, PN, and PZ were determined to be 2.5 µg mL^{− 1}, 1.8 µg mL^{− 1}, and 0.6 µg mL^{− 1}, respectively.

Table 2.

Summary of validation parameters for the determination of Fenbendazole (FN), pyrantel embonate (PN), and praziquantel (PZ) using the proposed spectrophotometric method.

Introduced concentration (µg mL− 1)		FN			PN			PZ
		2.5	7.5	17.5	1.80	5.40	12.50	0.60	1.90	4.40
Trueness	Relative bias (%)	0.52	-0.08	-2.75	-1.89	1.42	0.50	0.52	0.63	0.52
Precision	Repeatability RSD (%) / Intermediate precision RSD (%)	2.59/2.64	3.72/3.72	3.25/3.30	3.47/3.51	3.74/3.74	3.54/3.54	3.86/3.86	3.91/3.91	4.14/4.14
Accuracy	Relative β-expectation upper limit (%) /Relative β-expectation upper limit (%)	-5.37/6.41	-8.33/8.17	-9.93/4.43	-9.57/5.78	-7.00/9.83	-7.41/8.41	-8.09/9.13	-8.12/9.37	-8.73/9.76
Uncertainty	Relative expanded uncertainty (%)a	6.09	8.50	8.33	8.80	6.49	5.87	8.92	6.48	9.76
Risk (%)		0.28%	2.11%	2.56%	2.44%	2.71%	1.71%	2.62%	2.83%	3.61%
Linearity	Slope	0.98			1.01			1.01
	Intercept	0.16			-0.01			0.00
	R2	0.99			1.00			0.99

^aThe expanded uncertainty was computed using a coverage factor of 2.

Fig. 3.

Accuracy profiles obtained with Adaptive Plateau-based Successive Projections Algorithm with Automated Tuning Support Vector Regression (AP-SPA / AT-SVR for A) fenbendazole (FN), (B) Pyrantel embonate (PN), and (C) Praziquantel (PZ). Relative bias (red line), ± 10% acceptance limits (---), 95% β-expectation tolerance limits (blue line), and relative back-calculated concentrations (•).

Application to veterinary dosage form analysis

To evaluate its practical applicability, the developed AP-SPA/AT-SVR UV-spectrophotometric method was applied to determine the content of FN, PN, and PZ in commercially available Cestal Plus veterinary chewable tablets. The results obtained with the proposed spectrophotometric method were statistically compared to those from a reported HPLC reference method⁴ using both t-tests and F-tests. Representative chromatograms confirming adequate separation and peak shape for the reference method are provided in Supplementary Fig S8. The statistical evaluation (Table 3) revealed no statistically significant difference (p >0.05) between the two methods, demonstrating excellent agreement. This strong concordance confirms that potential interference from excipients was negligible under the established sample preparation and dilution protocol. This confirms the accuracy and reliability of the proposed UV method for routine analysis of Cestal Plus tablets and highlights its potential to replace more complex, time-consuming, and costly chromatographic techniques for quality control purposes.

Table 3.

Statistical comparison of the results obtained by the reported HPLC method and the proposed spectrophotometric method and for the determination of Fenbendazole (FN), pyrantel embonate (PN), and praziquantel (PZ) in Сestal plus tablets.

Parameter	FN		PN		PZ
	HPLC a	Spectrophotometric	HPLC a	Spectrophotometric	HPLC a	Spectrophotometric
Mean	100.31	99.48	99.39	99.01	99.33	100.03
SD	0.77	1.39	0.74	1.14	0.63	1.30
n	5		5		5
Student’s t-test (2.31) b	1.16		0.62		1.15
F-test (6.39)a	0.31		0.42		0.24

^aHPLC analysis was performed on a Phenomenex Luna 3 μm phenyl–hexyl column (150 mm × 4.6 mm) using a mobile phase consisting of acetonitrile and 0.5% triethylamine at pH 9.0 in a ratio of 45:55 (v/v) at a flow rate of 1.0 ml min. The UV detection was performed at 290 nm for FN and PN and at 220 nm for PZ.

^bValues in parentheses represent the tabulated values of t and F at P = 0.05.

Greenness and whiteness assessment

This multi-tool approach to sustainability is consistent with the current state-of-the-art in green analytical chemistry, where a holistic view is essential for a true assessment of a method’s environmental impact. Recent studies have demonstrated the power of combining greenness, blueness, and whiteness metrics to provide a comprehensive sustainability profile for complex pharmaceutical analyses^37,38. Our work builds on this paradigm by applying these principles to a novel chemometric model for veterinary pharmaceuticals, confirming that high analytical performance can be achieved in concert with significant environmental benefits. The GSST assigned a high greenness score to ethanol, the solvent used in this method, indicating its environmentally benign nature compared too many organic solvents commonly employed in HPLC methods (Supplementary Fig S9). The NEMI pictogram assessment yielded a fully green profile, signifying adherence to NEMI sustainability criteria. This favorable NEMI profile is primarily attributed to the use of ethanol, the absence of hazardous reagents, and the inherently low waste generation of UV spectrophotometry (Table 4). The modified Eco-Scale assigned a score of 84 (out of 100), reflecting the minimal use of hazardous substances and low waste production (Table 4 and Supplementary Table S3). The MoGAPI tool yielded a high score of 81, attributed to the simple and solvent-efficient sample preparation and the inherent greenness of UV spectrophotometry, which avoids extensive chromatographic separation and associated solvent consumption (Table 4 and Supplementary Table S4).

Table 4.

Summary of greenness and whiteness assessment of the reported HPLC and proposed spectrophotometric methods using various metrics.

Metric	LC/MS 3	HPLC 4	Spectrophotometric
National Environmental Methods Index (NEMI)
Green Certificate Modified Eco-Scale
Modified GAPI (MoGAPI)
Red-Green-Blue 12 (RGB 12) algorithm

Furthermore, to provide a more holistic evaluation, a whiteness assessment was conducted based on the principles of White Analytical Chemistry (WAC). WAC complements greenness by balancing analytical performance (Red), eco-friendliness (Green), and practical/economic efficiency (Blue) into a single, unified metric^39,40. We employed the Red-Green-Blue 12 (RGB12) algorithm for this purpose, as it provides a quantitative measure of a method’s overall sustainability and practicality⁴¹. The RGB12 algorithm yielded a high score of 91.9 for the proposed method, reflecting its excellent simplicity, directness, and use of a safe, readily available solvent (Table 4 and Supplementary Tables S5-S7). In contrast, typical HPLC methods for similar multi-analyte determinations often require significant volumes of hazardous organic solvents, generate substantial waste, and involve more complex sample preparation steps, resulting in lower whiteness scores. Therefore, the proposed spectrophotometric method presents a significantly greener and more sustainable analytical alternative, aligning with the growing emphasis on environmentally responsible analytical practices. Therefore, the proposed spectrophotometric method presents a significantly greener and more sustainable analytical alternative, aligning with the growing emphasis on environmentally responsible analytical practices. While the proposed AP-SPA/AT-SVR method offers significant advantages in terms of speed, cost-effectiveness, and environmental sustainability compared to HPLC, certain limitations must be acknowledged. First, UV-Vis spectrophotometry generally exhibits lower sensitivity than HPLC-MS/MS, making it less suitable for detecting trace-level impurities or metabolites in biological fluids. Second, the success of the chemometric model is heavily dependent on the design of the calibration set; any significant variation in the matrix excipients not accounted for in the calibration model could affect prediction accuracy. Finally, unlike HPLC, which physically separates components, this method relies on mathematical resolution, requiring specialized software and statistical expertise for model maintenance.

Conclusion

This research demonstrably establishes the viability of a robust and efficient UV-Vis spectrophotometric method, empowered by advanced chemometric data processing, for the simultaneous quantification of FN, PN, and PZ in complex veterinary pharmaceutical formulations. The innovative AP-SPA/AT-SVR approach developed herein unequivocally surpasses the performance of traditional PLSR, achieving significantly enhanced predictive accuracy, as evidenced by lower MSE and superior R², particularly crucial for challenging samples exhibiting pronounced spectral overlap. This underscores the power of synergistically combining adaptive feature selection with automated hyperparameter optimization to attain exceptional analytical robustness and accuracy in multi-component spectrophotometric assays. Successful deployment of this method for routine quality control or real-time process analytical technology (PAT) would require addressing practical challenges. These include establishing protocols for managing long-term instrument drift, standardizing procedures to minimize operator variability, and ensuring compatibility with automated systems. While beyond the scope of this study, these steps are crucial for translating the validated method into a real-world industrial tool. While initial model development necessitates computational investment, the resulting validated method offers a compelling analytical solution characterized by its rapidity, cost-effectiveness, and inherent environmental benignity, presenting a strategically advantageous and greener alternative to HPLC. Looking ahead, future investigations will strategically explore the integration of deep learning methodologies, specifically convolutional neural networks (CNNs), to further augment prediction accuracy and method robustness, potentially revolutionizing PAT and quality control within veterinary pharmaceutical manufacturing. The prospect of deploying this advanced analytical strategy with portable UV-Vis spectrophotometers holds transformative potential, enabling decentralized, on-site analysis capabilities and facilitating rapid, data-driven decision-making throughout the pharmaceutical supply chain, ultimately contributing to enhanced veterinary pharmaceutical quality and accessibility.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Badriah Saad Al-Farhan contributed to the data analysis, the computation and investigated and approved the final draft of the paper. Ghada M.G. Eldin contributed to the supervision, conceptualization, methodology, and the initial draft of the paper writing. All authors read and approved the final version.

Funding

Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).

Data availability

All data generated or analyzed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.