Eclet. Quim. 49 | e-1515, 2024 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 ISSN 1678-4618 page 1/19 1Sana’a University, Faculty of Science, Sana’a, Yemen. +Corresponding author: Fares Abdullah Alarbagi, Phone: +967773698413, Email address: f.ghaleb@su.edu.ye Original Article Development and validation of a green spectrophotometric method for simultaneous determination of combined pharmaceutical dosage form (paracetamol and caffeine) using chemometrics technique in comparison with HPLC Bushra Alattab1 , Fares Abdullah Alarbagi1+ , Maher Ali Almaqtari1 , Entesar Alhuraishi1 , Hussein Al-Maydama1 Abstract A green analytical method, a simple, fast, and cost-effective simultaneous spectrophotometric method using two chemometric techniques, the partial least square regression (PLS) and principal component regression (PCR), for determining a combination of paracetamol and caffeine in pharmaceutical formulations was developed. Pretreatment and separation steps are not required in the proposed method. For model construction and validation, various drug concentrations and instrumental spectra of 25 mixed solutions of paracetamol and caffeine were analyzed. The UV analysis of the prepared mixtures was recorded for a selected solvent blank in the wavelength range of 210-300 nm. The digitized absorbance was sampled at 0.2-nm intervals. R2 values of 0.9993 and 0.9994 assigned for the PLS of paracetamol and caffeine and 0.9995 and 0.9991 for the PCR of paracetamol and caffeine, respectively, exhibited greater prediction efficiencies. The obtained results were statistically compared with the results of the HPLC reference method. Concerning accuracy and precision, the statistical comparison revealed no significant differences between the suggested and reference HPLC approaches. Article History Received September 06, 2023 Accepted June 11, 2024 Published September 17, 2024 Keywords 1. paracetamol; 2. caffeine; 3. green method; 4. validation; 5. spectrophotometric method. Section Editor María Natalia Besil Arismendi Highlights Development and validation of a new eco-friendly chemometric spectrophotometric. The proposed methods are statistically compared with reported HPLC method. Can be used for the routine quality control of paracetamol and caffeine analysis. https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://ror.org/04hcvaf32 mailto:f.ghaleb@su.edu.ye https://orcid.org/0000-0001-6979-5452 https://orcid.org/0000-0003-1282-8174 https://orcid.org/0000-0002-2512-2325 https://orcid.org/0000-0001-7177-6568 https://orcid.org/0000-0002-0455-8074 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 2/19 1. Introduction The combination of paracetamol and caffeine is commonly used as a pain reliever and antipyretic agent in pharmaceutical formulations (Uddin et al., 2019). Chemically, paracetamol is (N-(4-hydroxyphenyl) acetamide (Scheme 1a). Paracetamol, also known as paracetamol, is one of the most popular medications commonly used to treat fever (antipyretic) and mild to moderate pain (analgesic agent) (Drugbank, 2005a; Glavanović et al., 2016; Yehia and Mohamed, 2016). Caffeine is 1,3,7-Trimethyl-3,7-dihydro-1H-purine-2,6-dione and its chemical structure (Scheme 1b). It is one of the drugs mostly used worldwide as a Central Nervous System (CNS) stimulant of the methylxanthine class (Drugbank, 2005b; Uddin et al., 2019). 1,3,7-Trimethylpurine-2,6-dione Caffeine a) n-(4-hydroxyphenyl)acetamide paracetamol b) Scheme 1. Chemical structure of paracetamol (a) and caffeine (b). Source: Adapted from Drugbank (2005a; b). The field of chemometrics has had a significant impact on analytical chemistry, particularly in the area of spectral analysis, which is important in the quality control of mixed drugs and pharmaceutical formulations involving two or more medications of overlapping spectra (Eticha et al., 2018; Glavanović et al., 2016; K. Patel et al., 2013a). Chemometric methods depend on multivariate analysis, which means considering more than one variable at a time in UV Spectrophotometry techniques (Riddhi and Rajashree, 2019). Many wavelengths are taken as variables, and the absorbance at each wavelength is considered (Gandhi et al., 2017; Riddhi and Rajashree, 2019). The most important chemometric methods used in multivariate analysis are Principal Component Regression (PCR) and Partial Least Squares (PLS). These methods use multivariate calibration using spectrophotometric data along with statistical tools, mathematical models, and software for the determination of combined drugs in pharmaceutical formulations (Riddhi and Rajashree, 2019). These methods also rely on the calibration of the mathematical model by using absorbance data of calibration standards with known concentrations and then predicting the concentration of unknown samples from their absorbance data (Gandhi et al., 2017; Riddhi and Rajashree, 2019). Chemometrics has multiple applications in spectroscopy, including UV-visible spectrophotometry (Ashour et al., 2015; Attia et al., 2018; Belal et al., 2018; Darbandi et al., 2020; Elfatatry et al., 2016; Gholse et al., 2022; Manouchehri et al., 2016; Mattar and Sobhy, 2022; Moussa et al., 2021; M. Patel et al., 2013b; Phechkrajang et al., 2015; Putri et al., 2021; Sebaiy et al., 2020; V. D. Singh and V. K. Singh, 2021; Vichare et al., 2010), fluorescence spectroscopy (Manouchehri et al., 2016; Salem et al., 2019; Shinde and Divya, 2015; Walash et al., 2011; Zhu et al., 2016), NIR spectroscopy (Manouchehri et al., 2016; Moroni et al., 2022; Muntean et al., 2021; Muntean et al., 2017; Rahman et al., 2020; Sun et al., 2021), and FTIR spectroscopy (Rahman et al., 2020). In addition, chromatography techniques such as Liquid Chromatography (Aminu et al., 2019; Mohammed et al., 2021; Tsvetkova et al., 2012; Vu Dang et al., 2020) as well as a variety of other analytical chemistry techniques, such as flow-injection analysis (Ortega-Barrales et al., 2002; Silva et al., 2011). Uddin et al. (2019) reported that the classic UV spectral assay could not be used to determine most analytes of interest because they are accompanied in their dose forms by other substances that absorb in the same spectral area. Traditional procedures, such as extraction, are difficult to employ because they require a lot of solvent, which comes with hazards of analyte loss or contamination, as well as the likelihood of incomplete separation, which is costly and time-consuming. However, when paired with chemometric methods for determining a combined mixture in pharmaceutical quality control, spectrophotometry as a simple, precise, rapid, and low-cost method may be a great option. They provide benefits when the quality monitoring of pharmaceutical products demands reliable, accurate, and fast analytical procedures. This process avoids prior separation processes and is fast, accurate, and easy to use. One of the tools used to assess the greenness of analytical procedures is the analytical Greenness Calculator, which is based on the 12 principles of Green Analytical Chemistry. It is a tool for assessing the environmental and occupational risks connected with a certain analytical technique applied in this study (Gałuszka et al., 2013), as shown in Scheme 2. The criteria scores and the Analytical Greenness score are linked to a “traffic lights” red-yellow-green sequential color map, with red assigned to the lowest values and green to the highest values, and its value ranges from 0.0 (the lowest score) to 1.0 (perfect score) (Tobiszewski et al., 2017), as shown in Scheme 3. To the best of our knowledge, no published work has been conducted on developing and validating spectrophotometric methods for the examination of some combined pharmacological compounds using a chemometrics approach in the Yemeni market (The Republic of Yemen). Therefore, the present study aims to develop and validate an adequate and green simultaneous spectrophotometric assay method for the determination of paracetamol and caffeine in a combined pharmaceutical formulation-assisted chemometric technique. https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 3/19 Scheme 2. Annotated result of the generic assessment. Scheme 3. The span of the colour map used in the graph and the corresponding values. 2. Materials and methods 2.1. Materials and reagents The reference standard paracetamol and caffeine were obtained from Global Pharma Company, Sana’a, Yemen. All reagents and chemicals used for the spectrophotometric methods were of analytical grade, and HPLC grade was used for the HPLC method. Deionized water (with a specific conductance of 0.05 µS cm–1) was in-house produced and used for the preparation of all sample solutions. Hydrochloric acid, sodium hydroxide, and benzoic acid were obtained from Shiba’a Pharma Company, Sana’a, Yemen. Preparation of standard stock solution: Stock solutions of 1000 μg mL–1 of paracetamol and 130 μg mL–1 of caffeine were individually prepared in a 100 mL volumetric flask by dissolving 100 mg paracetamol and 13 mg caffeine separately in water. Preparation of hydrochloric acid solution: it was prepared by diluting appropriate amounts of reagent in deionized water to make 0.1 mol L–1. Preparation of sodium hydroxide solution: This solution was prepared by dissolving 4.00 g of NaOH pellet into a 1000 mL volumetric flask in deionized water to obtain a final concentration of 0.1 mol L–1. Preparation of the benzoic acid solution: it was prepared by dissolving appropriate amounts of benzoic acid in methanol. 2.2. Instrumentation A double beam UV-Vis spectrophotometer (analytik jena), Model (SPECORD 200) at Sana’a University-Faculty of Science was used for the absorbance measurements. The HPLC system was from JASCO and included a UV detector (UV-2070 Plus), pump (PU-2089), autosampler (AS-2055 Plus), column oven (CO- 2067 Plus), and a C18 column (10 cm × 4.6 mm, 5 μm). Electronic balance (AA-160), Denver Instrument. Electronic balance (GH- 252), AND. Electronic balance (GR-120), AND. pH meter (3520), Jenway. A centrifuge (Z326 K) and Hermle were also used. 2.3. Development procedures To develop accurate, precise, and reliable simultaneous spectrophotometric methods assisted with the chemometrics technique, analytical methods were established and developed to obtain the intended results for quantifying the targeted components. The suitability of the proposed and developed method was decided based on the results of the validation method. This method was studied and experimented for the paracetamol determination with caffeine in marketed pharmaceutical formulations. They were compared to the results of the reference method. 2.3.1. Selection of the solvent The effect of the solvent on solubility was studied to choose a suitable solvent. Solubility was checked in water, methanol, 0.1 mol L–1 NaOH, and 0.1 mol L–1 HCl. The targeted combined active pharmaceutical ingredients in this study were dissolved in volumetric flasks by adding appropriate amounts of selected solvents for the dissolution of the desired active pharmaceutical components without excipients. 2.3.2. Selection of the spectral zone analysis After the solvent selection step and before pre-processing the data, the individual pure and mixture absorbance spectra of the targeted pharmaceutical components in an appropriately selected solvent were recorded in the range of 200–400 nm with 0.2 nm intervals. UV spectra of the mixtures analysis were selected among a suitable wavelength range against a solvent blank, providing the greatest amount of information about the two components (Shah and Jasani, 2017). 2.3.3. Construction of the training set Twenty-five different concentrations of paracetamol and caffeine binary mixtures were prepared as the training set (calibration set) to construct the model. The absorbencies of these mixtures were measured between 200 and 400 nm at 0.2-nm intervals against a blank. 2.4. Validation of the chemometric analysis 2.4.1. Construction of the chemometric models The two multivariate calibration models; the partial least square (PLS) and principal component regression (PCR), were developed as follows: • The absorbencies of binary mixtures were measured against a blank, and the spectra were saved and extracted into MS Excel for model generation and merit figures to evaluate the obtained results; • The PCR and PLS models were developed using absorption data at selected spectral zones for analysis at intervals of 0.2 nm using the Minitab 17 program; • The leave-one-out (LOO) cross-validation method was used to obtain the necessary number of latent variables (optimum number of the principal factors); • The calibration samples, constant, and coefficients at each wavelength were calculated to obtain the predicted concentrations; https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 4/19 • Finally, the predicted concentrations of the components were compared with the actual concentrations in each sample and the binary mixture was calculated for each sample; • To determine the precision and accuracy of predictions for the models, the root mean square error of cross-validation (RMSECV), which must be as low as possible for a particular model, was calculated for each method using the following Eq. 1 (Shah and Jasani, 2017): RMSECV = √ ∑(𝑪act−𝑪pre)𝟐 𝑰c (1) where: RMSECV = Root means square error of cross-validation C act = Actual concentration of the calibration set C pre = predicted concentration of the calibration set I c = Total number of samples in the calibration set 2.4.2. Validation method and construction of the validation set To validate and evaluate the performance of the proposed and developed spectrophotometric methods assisted by chemometric models, these methods were applied to the validation set. In addition, the performance criteria of the developed methods, including linearity, accuracy, precision (repeatability), and specificity, were validated as per the recommendations of International Conference Harmonization (ICH) and hence determined. 2.5. Analytical method procedures 2.5.1. Construction of the calibration (training) set Several 25 binary mixtures of paracetamol and caffeine were prepared by transferring different aliquots of their standard stock solutions into a series of 50 mL volumetric flasks (Table 1). The absorbencies of these mixtures were measured between 200 and 400 nm at 0.2 nm intervals against water as a blank. 2.5.2. Construction of the validation set A set of 12 binary mixtures of paracetamol and caffeine was prepared by transferring different volumes into 50 mL volumetric flasks, and the procedure for the construction of the training set was repeated (Table 2). 2.5.3. Preparation of the test sample Approximately 20 tablets of a commercial pharmaceutical formulation tablet containing 500/65 mg of paracetamol/caffeine, respectively, were analysed using the proposed chemometric methods. The sample 500/65 were weighed and finely powdered in a mortar. A quantity of powdered tablets equivalent to 100 mg of paracetamol and 13 mg of caffeine was accurately weighed and transferred into a 100 mL volumetric flask containing 50 ml of water. The mixture was shaken for 5 min, and with frequent shaking, the volume was completed to 100 mL with the selected solvent. The solution was then filtered through 0.45 μm filter paper. 0.8 mL of the filtrate was transferred into a 50 mL volumetric flask and then diluted by completion to 50 mL with water. The absorbance was measured between 200 and 400 nm at 0.2-nm intervals against water as a blank. 2.5.4. Preparation of spiked samples Powdered tablets of 100 mg paracetamol and 13 mg caffeine in triplicates were accurately weighed and transferred to a 100 mL volumetric flask. Then, 50 mL of water was added, and the calculated amount of paracetamol and caffeine from standard solutions was spiked into the sample solution. The mixture was shaken for 5 min, and with frequent shaking the volume completion to 100 mL with the selected solvent was carried out. The solution was then filtered. A total of 0.8 mL of the filtrate was transferred into a 50 mL volumetric flask and then diluted with water up to 50 mL. The absorbance was then measured. 2.5.5. Analysis of the marketed formulations The developed method was applied to the measurement of three commercially available samples. It was performed using the marketed formulation with a concentration of 500 mg paracetamol and 65 mg caffeine. The tablet solution prepared in the sample preparation section was diluted with water to prepare solutions with a concentration of 16 μg mL–1 paracetamol and 2.08 μg mL–1 caffeine. The spectra of the prepared solutions were recorded, and then the developed multivariate models PCR and PLS were applied to determine the concentrations of paracetamol and caffeine. 2.6. Comparing the suggested method with the reference method Comparison was carried out with the recovery results of the newly developed methods and that of reference method for each of paracetamol with caffeine according to the United States Pharmacopeia (USP, 43). 100 μg mL–1 paracetamol with 13 μg mL–1 caffeine and 360 μg mL–1 of benzoic acid as internal standard solution were prepared by dissolving 100 mg paracetamol with 13 mg caffeine in methanol: glacial acetic acid (95:5) in a 100 mL volumetric flask as standard stock solution. The internal standard solution was prepared in a 100 mL volumetric flask by dissolving 600 mg of benzoic acid in methanol. 5 mL of paracetamol with the caffeine of the standard stock solution and 3 mL of internal standard solution were transferred in methanol: glacial acetic acid (95:5) in a 50 mL volumetric flask. A test sample was prepared by transferring a portion of the powder equivalent to 250 mg paracetamol with 32.5 mg caffeine from NLT 20 finely powdered tablets to a 100 mL volumetric flask. 75 mL of methanol: glacial acetic acid (95:5) as solvent was added as solvent and the solution was shaken for 30 min and then diluted with solvent. Two milliliters of this solution and 3 mL of internal standard solution were transferred into 50 mL volumetric flask and diluted with solvent. The standard and test samples of paracetamol with caffeine were injected through an HPLC system with a mixture of methanol: glacial acetic acid: and water (28: 3: 69) as the mobile phase at a flow rate of 2 mL/min. UV detection of paracetamol and caffeine was then carried out at 275 nm (United States Pharmacopeia and the National Formulary (USP 43 - NF 38). The United States Pharmacopeial Convention; 2020). https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 5/19 Table 1. Composition of the calibration set. Mixture No. Paracetamol (μg mL–1) Caffeine (μg mL–1) Mixture No. Paracetamol (μg mL–1) Caffeine (μg mL–1) 1 10 1.3 14 16 2.34 2 10 1.82 15 16 2.6 3 10 2.08 16 18 1.3 4 10 2.34 17 18 1.82 5 10 2.6 18 18 2.08 6 14 1.3 19 18 2.34 7 14 1.82 20 18 2.6 8 14 2.08 21 20 1.3 9 14 2.34 22 20 1.82 10 14 2.6 23 20 2.08 11 16 1.3 24 20 2.34 12 16 1.82 25 20 2.6 13 16 2.08 -- -- -- Table 2. Results of the predicted concent vrations with the recovery of paracetamol and caffeine in the binary mixture in each sample for the PLS model. Name Paracetamol Caffeine Constant -0.20039 -0.02079 Mixture NO. Actual Conc. (μg mL–1) Predicted Conc. (μg mL–1) %Recovery Actual Conc. (μg mL–1) Predicted Conc. (μg mL–1) %Recovery 1 10 10.07 100.70 1.3 1.30 100.00 2 10 10.01 100.10 1.82 1.82 100.00 3 10 9.84 98.40 2.08 2.08 100.00 4 10 10.09 100.90 2.34 2.35 100.43 5 10 9.92 99.20 2.6 2.60 100.00 6 14 14.02 100.14 1.3 1.30 100.00 7 14 13.96 99.71 1.82 1.80 98.90 8 14 14.02 100.14 2.08 2.08 100.00 9 14 13.98 99.86 2.34 2.35 100.43 10 14 14.04 100.29 2.6 2.59 99.62 11 16 15.98 99.88 1.3 1.29 99.23 12 16 15.90 99.38 1.82 1.81 99.45 13 16 16.05 100.31 2.08 2.09 100.48 14 16 15.91 99.44 2.34 2.33 99.57 15 16 16.15 100.94 2.6 2.61 100.38 16 18 18.01 100.06 1.3 1.30 100.00 17 18 18.11 100.61 1.82 1.80 98.90 18 18 18.00 100.00 2.08 2.08 100.00 19 18 18.06 100.33 2.34 2.34 100.00 20 18 18.19 101.06 2.6 2.59 99.62 21 20 20.09 100.45 1.3 1.33 102.31 22 20 19.82 99.10 1.82 1.81 99.45 23 20 20.00 100.00 2.08 2.10 100.96 24 20 19.87 99.35 2.34 2.34 100.00 25 20 19.89 99.45 2.6 2.60 100.00 Mean% 99.99 Mean% 99.99 RSD% 0.64 RSD% 0.68 RMSECV 0.093 RMSECV 0.011 3. Results and Discussion 3.1. Development procedures for paracetamol and caffeine determination 3.1.1. Selection of the solvent To choose a suitable solvent, solubility was checked in water, methanol, 0.1 mol L–1 NaOH, and 0.1 mol L–1 HCl. The drug was found to be soluble in methanol, water, 0.1 mol L–1 NaOH, and 0.1 mol L–1 HCl. Therefore, water was selected as a diluent that has striking advantages such as being easily available, easy to handle, cheap, and environmentally friendly for implementing the spectrophotometric method, and Fig. 1 shows the spectra of paracetamol and caffeine in water. Figure 1. UV Absorbance spectra of pure and mixed samples of paracetamol and caffeine in water solvent. 0 1 2 3 4 5 6 200 220 240 260 280 300 320 340 360 380 A b so rb an ce λ (nm) Para+ Caff https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 6/19 3.1.2. Selection of the spectral zones for analysis To determine the overlap spectral zones, the absorbance spectra of the pure paracetamol and caffeine samples and that of the sample of the mixed paracetamol with caffeine in water were recorded in the range of 200–400 nm with 0.2 nm intervals. For the analysis, the UV spectra of the mixtures were selected for a suitable wavelength range (210-300 nm) against the water blank. This range provided a great amount of information about the two components, as shown in the paracetamol and caffeine spectra (Fig. 1). 3.1.3. Construction of the training set To determine the linear range from measuring the absorbance at different concentrations for paracetamol with caffeine, the response was found to be linear in the range of 10–20 μg mL–1 for paracetamol and 1.3–2.6 μg mL–1 for caffeine using 25 different concentrations of paracetamol and caffeine mixtures, as shown in Table 1. 3.2. Validation of the chemometric analysis for paracetamol and caffeine determination 3.2.1. Construction of chemometric models The spectra were saved and extracted into MS Excel for model generation. The PCR and PLS models were developed using the absorption data for the selected spectral zones using the Minitab 17 software. After the PCR and PLS models were constructed, the optimum number of principal components of paracetamol and caffeine were obtained and given in Table S1–S4 (Supplementary Material). 3.2.1.1. Determination of the optimum number of principal components of paracetamol and caffeine for PLS Choosing the proper number of principal components for the development of the model was necessary to obtain good predictions. The leave-one-out (LOO) cross-validation method was used to obtain the necessary optimum number of principal factors for the PLS model. It was found that the optimum number of principal components was three for paracetamol and four for caffeine, as mentioned above and given in Tables S1 and S2. 3.2.1.2. Determination of constants and coefficients obtained at each wavelength of paracetamol and caffeine for PLS models The constant and coefficients at each wavelength were calculated using the Minitab 17 program, as illustrated in Table S3. 3.2.1.3. Determination of predicted concentrations and recovery of paracetamol and caffeine in PLS models The predicted or calculated concentrations in μg mL–1 of the paracetamol and caffeine were calculated from the multiple regression Eq. 2. The predicted or calculated concentrations of the components were compared with the actual concentrations, and the assay of the binary mixture was performed. The root mean square error of cross-validation (RMSECV) was calculated and found to be low. The low values of RMSECV in Table 2indicate that both the precision and accuracy of the PLS model for paracetamol and caffeine were very high, and the R2 values in Fig. 2 were also of high linearity. The linearity of the developed method of the PLS model was tested by constructing a cross-validation of the data in Table 2. The results obtained in Fig. 2 indicate that the developed method possessed high linearity with R2 = 0.9993 within the method linear range (10–20 μg mL–1) for paracetamol and R2 = 0.9994 within the method linear range (1.3–2.6 μg mL–1) for caffeine. In comparison, Uddin et al. (2019) revealed less linearity with R2 values of 0.9928 and 0.9933 assigned for the PLSR of paracetamol and caffeine in methanol solvent, respectively. In contrast, the other study (Aktaş and Kitiş, 2014) that was carried out in 0.1 mol L–1 HCl revealed linearity almost similar to our eco-friendly developed method. Predicted (Calculated) = Constant + ∑ (Coefficient × Absorbance) (2) Figure 2. PLS cross-validation for the calibration set of the actual vs. predicted concentration. y = 0.9993x + 0.0102 R² = 0.9993 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Predicted (Conc.) (μg mL-1) (a) Paracetamol Actual concentration (μg mL-1) y = 0.9994x + 0.0009 R² = 0.9994 0 1 2 3 0 1 2 3 Predicted (Conc.) (μg mL-1) (b) Caffeine Actual concentration (μg mL-1) https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 7/19 3.2.1.4. Determination of the optimum number of principals components and their coefficients of paracetamol and caffeine for PCR The PCR was computed using six principal components (PCs) and a regression analysis of these PCs with a concentration was performed to determine the PC coefficients of paracetamol and caffeine for the PCR model, as shown in Table S4. From the treatment of the principal component’s coefficients in (Table S4) using the Minitab 17 program. Regression equations for paracetamol and caffeine were obtained and used to calculate the predicted concentrations, as shown below. Response variable (Predicted concentration) of paracetamol -0.177 + 1.23301 Z1 + 1.1417 Z2 + 3.102 Z3 + 0.81 Z4 + 2.94 Z5 + 16.91 Z6 Response variable (Predicted concentration) of caffeine 0.0284 + 0.01374 Z1 + 1.5390 Z2 + 3.531 Z3 + 1.016 Z4 + 1.491 Z5 + 1.30 Z6 where: Z is the principal component coefficients. 3.2.1.5. Determination of the predicted concentrations and recovery of paracetamol and caffeine in the PCR models The predicted or calculated concentrations in μg mL–1 of the paracetamol and caffeine were calculated from the above regression equations. The predicted or calculated concentrations of paracetamol and caffeine were compared with the actual concentrations, and the assay for binary mixture was performed for each sample. The root mean square error of cross-validation (RMSECV) was calculated and found to be minimal. The small RMSECV values in Table 3 indicate that both the precision and accuracy of the PCR model for paracetamol and caffeine were very great, with the R2 values in Fig. 3 showing very strong linearity. 3.2.2 Validation procedures and construction of the validation set for paracetamol and caffeine determination 3.2.2.1 Linearity method The linearity of the developed methods for both the PLS and PCR models was tested by constructing a cross-validation of the data, as shown in Table 4. The results obtained (Figs. 4 and 5) indicated that the developed method possessed high linearity: R2 = 0.9989 and 0.9988 for the PLS and PCR models, respectively, within the method linear range (10 – 20 μg mL–1) of paracetamol. Whereas R2 = 0.9989 and 0.9987 for the PLS and PCR models, respectively, within the method linear range (1.3–2.6 μg mL–1) of caffeine. The linearity of the developed method was better than that of the method in Uddin et al. (2019). In addition, another study by Alam et al. (2022) showed less linearity with R2 values of 0.9970 and 0.9928 assigned for the linear regression analysis of paracetamol and caffeine using the greener normal-phase HPTLC technique, respectively, and with R2 values of 0.9966 and 0.9976 assigned for the linear regression analysis of paracetamol and caffeine using the greener reversed-phase HPTLC technique, respectively. 3.2.2.2. Construction of validation set The results of the prediction and the percentage recoveries are presented in Table 4. The predictive abilities of the models were evaluated by plotting the actual known concentrations against the predicted concentrations shown in Figs. 4 and 5. A tremendous agreement between the predicted (calculated) and actual paracetamol and caffeine concentrations for the PLS and PCR models can be observed in Figs. 4 and 5. Figure 3. PCR cross-validation for the calibration set of the actual vs. predicted concentrations. y = 0.9992x + 0.0123 R² = 0.9995 0 5 10 15 20 25 0 10 20 30 Predicted (Conc.) (μg mL-1) (a) Paracetamol Actual concentration (μg mL-1) y = 1.0001x + 0.0002 R² = 0.9991 0 1 2 3 0 1 2 3 Predicted (Conc.) (μg mL-1) (b) Caffeine Actual concentration (μg mL-1) (3) (4) https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 8/19 Table 3. Results of the predicted concentrations with the recovery of paracetamol and caffeine in the binary mixture in each sample for the PCR models. Name Paracetamol Caffeine Constant -0.177 0.0284 Mixture NO. Actual Conc. (μg mL–1) Predicted Conc. (μg mL–1) %Recovery Actual Conc. (μg mL–1) Predicted Conc. (μg mL–1) %Recovery 1 10 10.09 100.90 1.3 1.30 100.00 2 10 10.04 100.40 1.82 1.82 100.00 3 10 9.85 98.50 2.08 2.08 100.00 4 10 10.10 101.00 2.34 2.35 100.43 5 10 9.93 99.30 2.6 2.60 100.00 6 14 13.97 99.79 1.3 1.31 100.77 7 14 13.94 99.57 1.82 1.80 98.90 8 14 14.02 100.14 2.08 2.09 100.48 9 14 13.99 99.93 2.34 2.35 100.43 10 14 14.07 100.50 2.6 2.59 99.62 11 16 15.99 99.94 1.3 1.30 100.00 12 16 15.88 99.25 1.82 1.81 99.45 13 16 16.05 100.31 2.08 2.10 100.96 14 16 15.90 99.38 2.34 2.32 99.15 15 16 16.15 100.94 2.6 2.61 100.38 16 18 18.01 100.06 1.3 1.30 100.00 17 18 18.05 100.28 1.82 1.78 97.80 18 18 17.91 99.50 2.08 2.08 100.00 19 18 18.04 100.22 2.34 2.34 100.00 20 18 18.11 100.61 2.6 2.59 99.62 21 20 20.08 100.40 1.3 1.32 101.54 22 20 20.00 100.00 1.82 1.81 99.45 23 20 19.98 99.90 2.08 2.10 100.96 24 20 19.87 99.35 2.34 2.35 100.43 25 20 19.96 99.80 2.6 2.61 100.38 Mean% 100.00 Mean% 100.03 RSD% 0.60 RSD % 0.75 RMSECV 0.079 RMSECV 0.014 Table 4. Results of the validation set of paracetamol and caffeine for the PLS and PCR models. NO. METHOD PLS PCR Para. Caff. Para. Caff. Para. Caff. Actual (μg mL–1) Predicted (μg mL–1) %R Predicted (μg mL–1) %R Predicted (μg mL–1) %R Predicted (μg mL–1) %R 1 10 2.34 10.178 101.78 2.344 100.17 10.247 102.47 2.312 98.80 2 10 2.60 10.030 100.30 2.610 100.38 10.096 100.96 2.573 98.96 3 16 1.82 15.912 99.45 1.800 98.90 15.900 99.38 1.784 98.02 4 16 2.08 15.876 99.23 2.056 98.85 15.896 99.35 2.040 98.08 5 20 1.30 19.798 98.99 1.257 96.69 19.746 98.73 1.248 96.00 6 20 2.60 19.905 99.53 2.575 99.04 19.893 99.47 2.545 97.88 7 12 2.808 11.806 98.38 2.864 101.99 11.852 98.77 2.837 101.03 8 12 3.12 11.802 98.35 3.155 101.12 11.829 98.58 3.136 100.51 9 19.2 2.184 18.847 98.16 2.181 99.86 18.812 97.98 2.162 98.99 10 19.2 2.496 19.445 101.28 2.470 98.96 19.431 101.20 2.444 97.92 11 24 1.56 23.865 99.44 1.530 98.08 23.795 99.15 1.514 97.05 12 24 3.12 23.946 99.78 3.129 100.29 23.895 99.56 3.094 99.17 Mean% 99.55 -- 99.53 Mean% 99.63 -- 98.54 RSD% 1.12 -- 1.42 RSD% 1.29 -- 1.40 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 9/19 Figure 4. PLS cross-validation for the validation set of the actual vs. predicted concentrations. Figure 5. PCR cross-validation for the validation set of the actual vs. predicted concentrations. 3.2.2.3. Precision (Repeatability) The repeatability (intraday precision) of the developed method was determined by determining the binary mixture at three different concentrations for paracetamol and caffeine in bulk using three different concentrations (i.e., 10/1.3, 16/1.82 and 20/2.6 μg mL–1 of paracetamol/caffeine, respectively) sequentially in triplicates. The results are reported as percentage RSD. The low values of percentage RSD indicated the high precision of the method. The %RSD values of the developed method were within the acceptable limit as suggested by the USP pharmacopeia, and the results are presented in Table 5. 3.2.2.4. Accuracy The accuracy of the method was investigated using the standard addition method for three different percentage levels (i.e., 80, 100, and 120%) by recovery experiments. Known amounts of standard solutions containing paracetamol and caffeine were added to sample solutions under investigation to make up solutions of 80%, 100%, and 120% levels in triplicate and scanned in the range 200–400 nm. The quantity of drugs recovered at each percentage level was determined using the developed PCR and PLS models. The mean percentage recovery for each percentage level showed low values of percentage RSD, and the percentage recovery was within the acceptable limit (90–110%) as suggested by the USP pharmacopeia. This indicates a high accuracy method at all three levels, and the accuracy data are given in Tables 6 and 7. 3.2.2.5. Specificity (spiking method) The specificity of the method was checked by adding a certain amount of paracetamol and caffeine standard into a known amount of the marketed sample solution, as described earlier (i.e., Methodology). Specificity data are shown in Tables 8 and 9. As can be seen from these data, recovery for paracetamol and caffeine using the developed PCR and PLS models are within the acceptable limit (90-110%). This suggests that the methods are free from interference due to the excipients used in the commercial formulation. The above validation indicates the method is simple, rapid, economical, precise, and accurate in addition to being eco-friendly. Therefore, it can be used for routine analysis in the quality control of mixtures and commercial products containing paracetamol and caffeine. y = 0.9932x + 0.0319 R² = 0.9989 0 5 10 15 20 25 30 0 10 20 30 Predicted (Conc.) (μg mL-1) (a) Paracetamol Actual concentration (μg mL-1) y = 1.0377x - 0.0928 R² = 0.9989 0 0,5 1 1,5 2 2,5 3 3,5 0 1 2 3 4 Predicted (Conc.) (μg mL-1) (b) Caffeine Actual concentration (μg mL-1) y = 0.9843x + 0.1814 R² = 0.9988 0 5 10 15 20 25 30 0 10 20 30 Predicted (Conc.) (μg mL-1) (a) Paracetamol Actual concentration (μg mL-1) y = 1.0267x - 0.0906 R² = 0.9987 0 1 2 3 4 0 1 2 3 4 Predicted (Conc.) (μg mL-1) (b) Caffeine Actual concentration (μg mL-1) https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 10/19 Table 5. Results of repeatability and Intraday precision using the developed PLS and PCR models. Amount taken (Actual Conc.) μg/ml Predicted Conc. μg mL–1 % Recovery Acceptable % RSD NMT 2% Para. Caff. PLS PCR PLS PCR PLS PCR Para. Caff. Para. Caff. Para. Caff. Para. Caff. Para. Caff. Para. Caff. 10 1.3 9.973 1.291 10.059 1.281 99.73 99.31 100.59 98.54 0.12 0.32 0.08 0.28 10 1.3 9.984 1.299 10.048 1.286 99.84 99.92 100.48 98.92 10 1.3 9.996 1.297 10.063 1.288 99.96 99.77 100.63 99.08 16 1.82 16.382 1.912 16.358 1.91 102.39 105.05 102.24 104.95 0.08 0.28 0.04 0.30 16 1.82 16.396 1.914 16.357 1.91 102.48 105.16 102.23 104.95 16 1.82 16.370 1.904 16.347 1.90 102.31 104.62 102.17 104.40 20 2.6 20.365 2.721 20.282 2.715 101.83 104.65 101.41 104.42 0.16 0.41 0.11 0.50 20 2.6 20.387 2.707 20.275 2.714 101.94 104.12 101.38 104.38 20 2.6 20.324 2.699 20.239 2.691 101.62 103.81 101.20 103.50 Note: % Recovery = Predicted Conc. (μg/ml) / Actual Conc. (μg/ml) ×100. Table 6. Accuracy data for paracetamol by PCR and PLS models. %Level Sample Conc. μg mL–1 Amount of standard paracetamol μg mL–1 Total Conc. μg mL–1 Predicted Conc. μg mL–1 % Recovery % RSD PLS PCR PLS PCR PLS PCR 80% 10 8 18 18.427 18.549 102.37 103.05 0.16 0.12 18.464 18.547 102.58 103.04 18.487 18.586 102.71 103.26 100% 10 10 20 20.291 20.302 101.46 101.51 0.21 0.17 20.367 20.361 101.84 101.81 20.362 20.366 101.81 101.83 120% 10 12 22 22.465 22.416 102.11 101.89 0.08 0.14 22.429 22.403 101.95 101.83 22.445 22.358 102.02 101.63 Table 7. Accuracy data for caffeine by PCR and PLS models. %Level Sample Conc. μg mL–1 Amount of standard caffeine μg mL–1 Total Conc. μg mL–1 Predicted Conc. μg mL–1 % Recovery % RSD PLS PCR PLS PCR PLS PCR 80% 1.3 1.04 2.34 2.377 2.333 101.58 99.70 0.49 0.68 2.395 2.355 102.35 100.64 100% 1.3 1.3 2.6 2.399 2.364 102.52 101.03 0.37 0.52 2.690 2.670 103.46 102.69 2.692 2.683 103.54 103.19 2.708 2.698 104.15 103.77 120% 1.3 1.56 2.86 2.981 2.970 104.23 103.85 0.26 0.28 2.966 2.965 103.71 103.67 2.971 2.981 103.88 104.23 Table 8. Results of specificity for paracetamol using the developed PCR and PLS models. Name of the marketed sample Sample Conc. μg mL–1 Amount added μg mL–1 Total Conc. μg mL–1 Predicted Conc. μg mL–1 % Recovery % RSD PLS PCR PLS PCR PLS PCR Panadol 16 16 32 31.590 31.524 98.72 98.51 1.64 1.5 32.329 32.206 101.03 100.64 Ramol 16 16 32 32.478 32.451 101.49 101.41 1.85 2.0 31.639 31.532 98.87 98.54 Amol 16 16 32 31.625 31.514 98.83 98.48 1.58 1.8 32.339 32.332 101.06 101.04 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 11/19 Table 9. Results of specificity for caffeine using the developed PCR and PLS models. Name of the marketed sample Sample Conc. μg mL–1 Amount added μg mL–1 Total Conc. μg mL–1 Predicted Conc. μg mL–1 % Recovery % RSD PLS PCR PLS PCR PLS PCR Panadol 2.08 2.08 4.16 4.125 4.044 99.16 97.21 1.17 0.21 4.194 4.056 100.82 97.50 Ramol 2.08 2.08 4.16 4.130 4.039 99.28 97.09 0.20 0.47 4.142 4.066 99.57 97.74 Amol 2.08 2.08 4.16 4.171 4.091 100.26 98.34 0.73 0.36 4.214 4.112 101.30 98.85 3.3. Analysis of the marketed formulations The applicability of the developed methods for the quantification of paracetamol and caffeine in marketed formulations was evaluated using the marketed formulation of 500 mg paracetamol with 65 mg caffeine concentration collected from the local pharmacies in the capital Sana’a. Tables 10 and 11 summarize the data obtained for paracetamol and caffeine in the analyzed marketed formulations. As can be seen from these data, the paracetamol and caffeine concentrations were within the acceptable limit (90-110%) according to the United States Pharmacopeia (USP). 3.4. Comparison with the reference method A comparison was carried out with the aid of the SPSS program using F-Test to ensure a non-significant difference between the recovery results of the newly developed methods and that of the reference method for both paracetamol and caffeine. The significance level indicated that the null hypothesis was acceptable because the P-value was greater than the significance level (Table 12). As for reference methods, paracetamol and caffeine were determined according to the United States Pharmacopeia (USP), as described earlier in the methodology. In addition, the chromatograms in Fig. 6 show the results of the analysis for the reference method for the determination of paracetamol and caffeine. Table 10. Assay results for paracetamol and caffeine in tablets (marketed sample) using the proposed PLS method. Name of the marketed sample METHOD PLS Para. Caff. Para. Caff. Actual (μg mL–1) Predicted (μg mL–1) % Recovery % RSD Predicted (μg mL–1) % Recovery % RSD Panadol 16 2.08 16.135 100.84 1.30 2.088 100.38 2 16 2.08 16.434 102.71 2.023 97.26 Amol 16 2.08 15.654 97.84 0.03 2.053 98.70 0 16 2.08 15.660 97.88 2.053 98.70 Ramol 16 2.08 15.597 97.48 2 2.039 98.03 2 16 2.08 16.132 100.83 2.098 100.87 Table 11. Assay results for paracetamol and caffeine in tablets (Marketed Sample) by the PCR proposed method. Name of the marketed sample METHOD PCR Para. Caff. Para. Caff. Actual (μg mL–1) Predicted (μg mL–1) % Recovery % RSD Predicted (μg mL–1) % Recovery % RSD Panadol 16 2.08 16.253 101.58 0.93 2.007 96.49 1.21 16 2.08 16.469 102.93 1.973 94.86 Amol 16 2.08 15.653 97.83 0.01 2.024 97.31 0.03 16 2.08 15.656 97.85 2.025 97.36 Ramol 16 2.08 15.620 97.63 2.6 1.996 95.96 1.40 16 2.08 16.215 101.34 2.036 97.88 Table 12. Results of statistical comparison between the newly developed and reference methods. Name of the marketed sample Components paracetamol Caffeine Methods Reference method (HPLC) PLS PCR Reference method (HPLC) PLS PCR Panadol Mean% 102.12 100.84 101.58 99.27 100.38 96.49 101.67 102.71 102.93 99.32 97.26 94.86 101.90 101.78 102.26 99.30 98.82 95.68 Significance level 0.912 0.663 -- 0.790 0.047 Ramol Mean% 100.08 97.48 97.63 97.75 98.03 95.96 100.02 100.83 101.34 97.35 100.87 97.88 100.05 99.16 99.49 97.55 99.45 96.92 Significance level (α) 0.647 0.789 -- 0.316 0.586 Note: p-value = 0.01. https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 12/19 Figure 6. Chromatogram of paracetamol and caffeine standard with Benzoic acid as the internal standard and commercial samples. (a) Standard paracetamol and caffeine with benzoic acid as the internal standard; (b) Panadol Extra Sample (commercial); (c) Ramol Extra Sample (commercial). 3.5. Greenness evaluation of the developed methods Modern analytical chemistry provides various methods and tools for identifying a specific analyte in various samples. The main objectives of greening analytical methods are to minimize energy consumption, eliminate or reduce the use of chemical substances (solvents, reagents, preservatives, additives for pH adjustment, and others), and properly manage analytical waste while increasing operator safety. Most of these problems demand reductions, e.g., sample number, reagents, energy, waste, risk, and hazard (Gałuszka et al., 2013). This study introduces green analytical methods in the field of pharmaceutical analysis. In this study, water was used as a solvent to prepare the stock solution of one of the analytes and further dilutions to determine paracetamol with caffeine. Water is a safe solvent for health, safety, and environmental hazards. The instrument used was a spectrophotometer; hence, the energy used by these methods is safe. The proposed method in this study generates only a small volume of waste compared with the reference HPLC method. Another important issue is that the toxicity of waste was negligible. In general, AGREE considers UV-chemometrics methods to be the greenest methods compared to HPLC methods. According to the AGREE scale, the UV-chemometrics method shows a very intense greenness of 0.87. However, the HPLC method is less green and shows a very weak intense greenness, 0.45. This comparison is based on the 12 green analytical chemistry principles as follows: A comparison of the results obtained by UV chemometrics and those obtained by HPLC methods for the AGREE program scale is shown in Fig. 7. Figure 7. Generic result of assessment (left) and the corresponding color scale for reference for the comparison of the developed UV- chemometrics and reference HPLC methods of paracetamol with caffeine according to the 12 principles of green analytical chemistry, performed using the AGREE program. 1. Sample treatment; 2. Sample amount; 3. Device Positioning; 4. Sample pre. Stages; 5. Automation, miniaturization; 6. Derivization; 7. Waste; 8. Analysis throughput; 9. Energy consumption; 10. Source of the reagents; 11. Toxicity; 12. Operator’s safety; https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 13/19 4. Conclusions The use of dangerous chemicals has been discouraged using green analytical chemistry. To determine the combined amounts of caffeine and paracetamol in pharmaceutical formulations, a green spectrophotometric method for simultaneous determination-assisted chemometrics that is simple, quick, and cost-effective has been developed. The proposed chemometric models (PLS and PCR) can be used to simultaneously determine paracetamol and caffeine in binary mixtures in pharmaceutical dosage forms without excipient interference or from each other, and there is no need for prior physical separation of the two drugs. Multivariate calibration models were generated using spectral and concentration matrices. Validation of the two models and their application to a commercial pharmaceutical dosage form gave excellent results. As a result, the suggested techniques can be applied to regular quality control of the specified medications in their combination dosage form in standard laboratories. Authors’ contributions Conceptualization: Bushra Alattab; Fares Abdullah Alarbagi; Data curation: Maher Ali Almaqtari; Entesar Alhuraishi; Formal Analysis: Bushra Alattab; Fares Abdullah Alarbagi; Funding acquisition: Not applicable; Investigation: Bushra Alattab; Fares Abdullah Alarbagi; Methodology: Fares Abdullah Alarbagi; Project administration: Bushra Alattab; Fares Abdullah Alarbagi; Resources: Not applicable; Software: Entesar Alhuraishi; Hussein Al-Maydama; Supervision: Bushra Alattab; Fares Abdullah Alarbagi; Validation: Bushra Alattab; Fares Abdullah Alarbagi; Maher Ali Almaqtari; Visualization: Fares Abdullah Alarbagi; Writing – original draft: Fares Abdullah Alarbagi; Writing – review & editing: Hussein Al-Maydama. Data availability statement All data sets were generated or analyzed in the current study. Funding Not applicable. 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Synchronous fluorescence spectrofluorimetric method for the simultaneous https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.1016/j.bioorg.2016.07.014 https://doi.org/10.21203/rs.3.rs-1262160/v1 https://doi.org/10.21203/rs.3.rs-1262160/v1 https://doi.org/10.52711/0974-360X.2021.00825 https://doi.org/10.1016/j.saa.2021.120354 https://doi.org/10.1016/j.saa.2021.119763 https://doi.org/10.1155/2017/7160675 https://doi.org/10.37897/RJPhP.2021.2.2 https://doi.org/10.2116/analsci.18.1241 https://doi.org/10.22037/ijps.v9.40870 https://doi.org/10.31838/ijpr/2021.13.01.075 https://doi.org/10.5530/jyp.2020.12s.46 https://doi.org/10.31080/ASPS.2019.03.0359 https://doi.org/10.1016/j.saa.2018.11.054 https://doi.org/10.1016/j.saa.2019.117429 https://doi.org/10.12973/ejac.2017.00164a https://doi.org/10.1002/elan.201100512 https://doi.org/10.1016/j.saa.2020.119383 https://doi.org/10.1016/j.saa.2020.119346 https://doi.org/10.1039/C7GC03108D https://doi.org/10.3329/bjsir.v54i3.42673 https://doi.org/10.1155/2020/8107571 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. 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Method Components to evaluate Number of components evaluated Number of components selected Cross-validation (Leave-one-out) Set 10 3 Model selection and validation for paracetamol Components X Variance Error R-sq Press R-sq (Pred) 1 0.966084 14.5473 0.95085 17.0743 0.942316 2 0.990946 0.4642 0.99843 0.6627 0.997761 3 0.999871 0.2161 0.99927 0.3068 0.998964 4 -- 0.0555 0.99981 0.3730 0.998740 5 -- 0.0308 0.99990 0.3141 0.998939 6 -- 0.0126 0.99996 0.3219 0.998913 7 -- 0.0032 0.99999 0.3245 0.998904 8 -- 0.0007 1.00000 0.3327 0.998876 9 -- 0.0002 1.00000 0.3332 0.998874 10 -- 0.0000 1.00000 0.3298 0.998886 Table S2. Results of the optimum number of principal factors of caffeine for PLS models. Method Components to evaluate Number of components evaluated Number of components selected Cross-validation (Leave-one-out) Set 10 4 Model selection and validation for caffeine Components X Variance Error R-sq Press R-sq (Pred) 1 0.952542 4.50078 0.10028 4.98888 0.002703 2 0.990880 0.14035 0.97194 0.18389 0.963240 3 0.999871 0.00689 0.99862 0.00937 0.998128 4 0.999899 0.00334 0.99933 0.00779 0.998442 5 -- 0.00097 0.99981 0.00858 0.998285 6 -- 0.00029 0.99994 0.00821 0.998359 7 -- 0.00012 0.99998 0.00840 0.998320 8 -- 0.00002 1.00000 0.00834 0.998332 9 -- 0.00001 1.00000 0.00848 0.998304 10 -- 0.00000 1.00000 0.00846 0.998310 Table S3. The constant and coefficients at each wavelength of paracetamol and caffeine for PLS models. Paracetamol Caffeine Constant -0.20039 Constant -0.02079 Wavelength (nm) Coefficients Wavelength (nm) Coefficients Wavelength (nm) Coefficients Wavelength (nm) Coefficients 300 -3.17198 254.8 0.11817 300 -2.54573 254.8 -0.06339 299.8 -2.62108 254.6 0.11705 299.8 -0.88698 254.6 -0.06383 299.6 -2.39074 254.4 0.11657 299.6 -2.97845 254.4 -0.05558 299.4 -1.71683 254.2 0.11665 299.4 5.04438 254.2 -0.05372 299.2 -1.9243 254 0.11566 299.2 -0.38125 254 -0.06811 299 -1.97862 253.8 0.11516 299 -4.09387 253.8 -0.05123 298.8 -1.58562 253.6 0.11491 298.8 -3.29 253.6 -0.05448 298.6 -1.20244 253.4 0.11407 298.6 0.94618 253.4 -0.07226 298.4 -1.25856 253.2 0.11396 298.4 1.81124 253.2 -0.06115 298.2 -1.0679 253 0.11314 298.2 -0.54598 253 -0.05667 298 -0.98847 252.8 0.11242 298 -2.58962 252.8 -0.057 297.8 -0.77672 252.6 0.1115 297.8 -1.24952 252.6 -0.05138 297.6 -0.77833 252.4 0.1115 297.6 -2.48049 252.4 -0.05338 297.4 -0.55081 252.2 0.11087 297.4 -0.1358 252.2 -0.05592 297.2 -0.51919 252 0.11071 297.2 -0.67162 252 -0.05017 297 -0.51479 251.8 0.10941 297 -1.30059 251.8 -0.06055 296.8 -0.47054 251.6 0.10994 296.8 -0.95739 251.6 -0.06112 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.1186/1752-153X-5-70 https://doi.org/10.1186/1752-153X-5-70 https://doi.org/10.1016/j.saa.2015.07.101 https://doi.org/10.1039/C6AY00821F Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 16/19 296.6 -0.30712 251.4 0.10891 296.6 -1.44424 251.4 -0.04166 296.4 -0.27819 251.2 0.10796 296.4 -0.45932 251.2 -0.06577 296.2 -0.29218 251 0.1086 296.2 -0.49553 251 -0.04374 296 -0.06107 250.8 0.10768 296 0.76776 250.8 -0.04445 295.8 -0.29063 250.6 0.10673 295.8 -0.9825 250.6 -0.05228 295.6 -0.2163 250.4 0.1067 295.6 -0.64288 250.4 -0.04955 295.4 -0.18514 250.2 0.10583 295.4 -0.70114 250.2 -0.05665 295.2 -0.19596 250 0.10582 295.2 -0.68644 250 -0.05365 295 -0.09683 249.8 0.10498 295 -0.74669 249.8 -0.04801 294.8 -0.12287 249.6 0.10461 294.8 -1.46849 249.6 -0.05607 294.6 -0.04307 249.4 0.10457 294.6 -1.12768 249.4 -0.04357 294.4 -0.13292 249.2 0.10466 294.4 -1.62163 249.2 -0.04086 294.2 -0.11608 249 0.10343 294.2 0.36611 249 -0.04269 294 -0.02925 248.8 0.10342 294 0.5644 248.8 -0.04174 293.8 -0.05058 248.6 0.10329 293.8 -0.12767 248.6 -0.0353 293.6 -0.09462 248.4 0.10269 293.6 -0.13326 248.4 -0.05478 293.4 -0.01126 248.2 0.1022 293.4 -0.80982 248.2 -0.04107 293.2 -0.03762 248 0.1018 293.2 0.19936 248 -0.03153 293 -0.0456 247.8 0.10148 293 -0.32957 247.8 -0.03954 292.8 -0.06734 247.6 0.10127 292.8 -0.09365 247.6 -0.04458 292.6 -0.08343 247.4 0.10153 292.6 -0.31811 247.4 -0.05439 292.4 -0.07732 247.2 0.10077 292.4 0.18434 247.2 -0.06205 292.2 -0.07333 247 0.09953 292.2 0.08145 247 -0.04007 292 -0.0856 246.8 0.10028 292 -0.59123 246.8 -0.04153 291.8 -0.06925 246.6 0.09982 291.8 -0.50905 246.6 -0.03187 291.6 -0.08663 246.4 0.09978 291.6 0.40509 246.4 -0.04485 291.4 -0.0139 246.2 0.09973 291.4 0.41079 246.2 -0.03161 291.2 -0.05657 246 0.09897 291.2 -0.09501 246 -0.04129 291 -0.09089 245.8 0.09884 291 -0.18023 245.8 -0.0361 290.8 -0.11682 245.6 0.09866 290.8 0.12179 245.6 -0.02679 290.6 -0.11116 245.4 0.09886 290.6 -0.19209 245.4 -0.03814 290.4 -0.12019 245.2 0.09797 290.4 0.1637 245.2 -0.04417 290.2 -0.10109 245 0.09785 290.2 0.13566 245 -0.04607 290 -0.13797 244.8 0.09808 290 -0.13265 244.8 -0.04249 289.8 -0.13573 244.6 0.09791 289.8 -0.12967 244.6 -0.03722 289.6 -0.13253 244.4 0.0977 289.6 0.02555 244.4 -0.02913 289.4 -0.15148 244.2 0.0972 289.4 -0.21064 244.2 -0.03327 289.2 -0.16285 244 0.09755 289.2 -0.41242 244 -0.03707 289 -0.14923 243.8 0.0974 289 -0.25736 243.8 -0.03062 288.8 -0.14669 243.6 0.09711 288.8 0.24968 243.6 -0.02654 288.6 -0.158 243.4 0.09708 288.6 0.12284 243.4 -0.03557 288.4 -0.17086 243.2 0.09676 288.4 0.1785 243.2 -0.02865 288.2 -0.1695 243 0.09642 288.2 0.19158 243 -0.03372 288 -0.17493 242.8 0.09652 288 0.10924 242.8 -0.03226 287.8 -0.15086 242.6 0.09603 287.8 0.37266 242.6 -0.0202 287.6 -0.18811 242.4 0.09645 287.6 -0.04277 242.4 -0.03252 287.4 -0.1742 242.2 0.09654 287.4 0.21131 242.2 -0.03506 287.2 -0.17609 242 0.09626 287.2 0.24657 242 -0.02784 287 -0.17017 241.8 0.09619 287 0.12559 241.8 -0.02424 286.8 -0.20714 241.6 0.09668 286.8 0.0962 241.6 -0.02498 286.6 -0.18553 241.4 0.0959 286.6 0.3877 241.4 -0.03212 286.4 -0.18549 241.2 0.0963 286.4 0.42973 241.2 -0.02749 286.2 -0.19396 241 0.09613 286.2 0.42634 241 -0.0204 286 -0.18352 240.8 0.09632 286 0.2337 240.8 -0.02946 285.8 -0.20782 240.6 0.09636 285.8 0.40371 240.6 -0.01848 285.6 -0.19629 240.4 0.09577 285.6 0.27051 240.4 -0.02891 285.4 -0.19592 240.2 0.09586 285.4 0.40861 240.2 -0.02316 285.2 -0.19647 240 0.09622 285.2 0.2303 240 -0.02554 285 -0.20083 239.8 0.0961 285 0.45941 239.8 -0.02212 284.8 -0.1987 239.6 0.09582 284.8 0.49869 239.6 -0.02385 284.6 -0.18508 239.4 0.09597 284.6 0.43238 239.4 -0.02365 284.4 -0.19714 239.2 0.09633 284.4 0.3339 239.2 -0.02832 284.2 -0.20147 239 0.09659 284.2 0.36469 239 -0.0268 284 -0.20639 238.8 0.09663 284 0.38612 238.8 -0.01485 283.8 -0.20381 238.6 0.09651 283.8 0.34181 238.6 -0.01829 283.6 -0.19359 238.4 0.09665 283.6 0.38542 238.4 -0.01225 283.4 -0.21951 238.2 0.09657 283.4 0.16936 238.2 -0.01526 283.2 -0.19123 238 0.09689 283.2 0.40077 238 -0.02151 283 -0.2012 237.8 0.09708 283 0.56637 237.8 -0.01965 282.8 -0.19456 237.6 0.097 282.8 0.32709 237.6 -0.02355 282.6 -0.21331 237.4 0.09702 282.6 0.18173 237.4 -0.01789 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 17/19 282.4 -0.20475 237.2 0.09722 282.4 0.20358 237.2 -0.01263 282.2 -0.20026 237 0.09784 282.2 0.36444 237 -0.00706 282 -0.20709 236.8 0.0974 282 0.37242 236.8 -0.02062 281.8 -0.20313 236.6 0.09773 281.8 0.19249 236.6 -0.02412 281.6 -0.20848 236.4 0.098 281.6 0.22699 236.4 -0.00733 281.4 -0.2103 236.2 0.09772 281.4 0.2773 236.2 -0.01646 281.2 -0.19703 236 0.09784 281.2 0.32308 236 -0.01026 281 -0.20881 235.8 0.09841 281 0.22468 235.8 -0.0138 280.8 -0.19285 235.6 0.0985 280.8 0.16909 235.6 -0.01194 280.6 -0.19189 235.4 0.09848 280.6 0.30375 235.4 -0.0138 280.4 -0.20417 235.2 0.09878 280.4 0.15414 235.2 -0.01678 280.2 -0.19544 235 0.09894 280.2 0.26435 235 -0.02103 280 -0.1989 234.8 0.09934 280 0.23919 234.8 -0.01126 279.8 -0.19093 234.6 0.099 279.8 0.29626 234.6 -0.00774 279.6 -0.17525 234.4 0.09917 279.6 0.51439 234.4 -0.00784 279.4 -0.18638 234.2 0.09925 279.4 0.29315 234.2 -0.00805 279.2 -0.18813 234 0.10003 279.2 0.21955 234 -0.01253 279 -0.18442 233.8 0.09998 279 0.30854 233.8 -0.01755 278.8 -0.18587 233.6 0.10022 278.8 0.30478 233.6 -0.01027 278.6 -0.19019 233.4 0.10092 278.6 0.23387 233.4 -0.0081 278.4 -0.18618 233.2 0.10075 278.4 0.35055 233.2 -0.00561 278.2 -0.18654 233 0.10136 278.2 0.29053 233 0.00352 278 -0.18201 232.8 0.10152 278 0.4192 232.8 -0.00622 277.8 -0.18923 232.6 0.10141 277.8 0.26233 232.6 -0.00823 277.6 -0.17961 232.4 0.1018 277.6 0.31118 232.4 -0.00879 277.4 -0.17806 232.2 0.10175 277.4 0.36514 232.2 -0.00428 277.2 -0.17741 232 0.10261 277.2 0.31819 232 -0.00043 277 -0.16926 231.8 0.10291 277 0.3386 231.8 -0.00164 276.8 -0.17351 231.6 0.10292 276.8 0.30991 231.6 -0.00177 276.6 -0.17669 231.4 0.10296 276.6 0.33439 231.4 0.0056 276.4 -0.17355 231.2 0.10333 276.4 0.33753 231.2 -0.00369 276.2 -0.17091 231 0.10374 276.2 0.34312 231 0.00428 276 -0.16386 230.8 0.10418 276 0.37346 230.8 0.0035 275.8 -0.1659 230.6 0.10479 275.8 0.21794 230.6 -0.00563 275.6 -0.16337 230.4 0.10472 275.6 0.35442 230.4 0.00489 275.4 -0.16673 230.2 0.10542 275.4 0.24724 230.2 -0.00581 275.2 -0.15572 230 0.10552 275.2 0.27426 230 0.00595 275 -0.15385 229.8 0.10596 275 0.33961 229.8 0.0065 274.8 -0.15432 229.6 0.10618 274.8 0.27547 229.6 0.00228 274.6 -0.15271 229.4 0.10638 274.6 0.28833 229.4 -0.00461 274.4 -0.14574 229.2 0.10656 274.4 0.33196 229.2 -0.00303 274.2 -0.14712 229 0.10721 274.2 0.18674 229 -0.00132 274 -0.1453 228.8 0.10755 274 0.26149 228.8 0.00793 273.8 -0.13354 228.6 0.10785 273.8 0.27242 228.6 0.01306 273.6 -0.12801 228.4 0.10842 273.6 0.32901 228.4 0.00594 273.4 -0.12673 228.2 0.10859 273.4 0.27983 228.2 0.00814 273.2 -0.11965 228 0.10872 273.2 0.29935 228 0.0032 273 -0.11852 227.8 0.10924 273 0.25227 227.8 0.0105 272.8 -0.1106 227.6 0.10905 272.8 0.31885 227.6 0.00853 272.6 -0.10752 227.4 0.1093 272.6 0.21985 227.4 0.00929 272.4 -0.10465 227.2 0.10985 272.4 0.24164 227.2 0.00172 272.2 -0.09522 227 0.11046 272.2 0.25001 227 0.01777 272 -0.09216 226.8 0.1106 272 0.26687 226.8 0.01083 271.8 -0.08578 226.6 0.11071 271.8 0.24861 226.6 0.00384 271.6 -0.08373 226.4 0.1115 271.6 0.21936 226.4 0.00374 271.4 -0.0755 226.2 0.11167 271.4 0.26732 226.2 -0.00048 271.2 -0.07275 226 0.11182 271.2 0.19673 226 0.01165 271 -0.0614 225.8 0.11199 271 0.16119 225.8 0.00911 270.8 -0.06158 225.6 0.11254 270.8 0.18653 225.6 0.00852 270.6 -0.05443 225.4 0.11265 270.6 0.14512 225.4 0.01667 270.4 -0.05089 225.2 0.11323 270.4 0.14119 225.2 0.01592 270.2 -0.04055 225 0.11303 270.2 0.17367 225 0.0127 270 -0.03647 224.8 0.11357 270 0.20174 224.8 0.02353 269.8 -0.03366 224.6 0.11363 269.8 0.09564 224.6 0.00963 269.6 -0.03094 224.4 0.11357 269.6 0.17085 224.4 0.01553 269.4 -0.02401 224.2 0.11429 269.4 0.15675 224.2 0.00863 269.2 -0.01523 224 0.11355 269.2 0.1152 224 0.01504 269 -0.00982 223.8 0.11403 269 0.12943 223.8 0.0105 268.8 -0.00526 223.6 0.11424 268.8 0.102 223.6 0.02661 268.6 -0.00312 223.4 0.11402 268.6 0.06177 223.4 0.01975 268.4 0.00565 223.2 0.11427 268.4 0.06742 223.2 0.0261 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 18/19 268.2 0.01076 223 0.11387 268.2 0.04745 223 0.03155 268 0.01655 222.8 0.11357 268 0.03964 222.8 0.02794 267.8 0.02367 222.6 0.1138 267.8 0.02999 222.6 0.02827 267.6 0.02674 222.4 0.11355 267.6 0.04151 222.4 0.0255 267.4 0.03211 222.2 0.11266 267.4 0.06309 222.2 0.03409 267.2 0.03769 222 0.11243 267.2 0.00752 222 0.03115 267 0.04393 221.8 0.11142 267 0.02221 221.8 0.03609 266.8 0.04813 221.6 0.11134 266.8 0.02363 221.6 0.02762 266.6 0.0536 221.4 0.11087 266.6 0.03962 221.4 0.03691 266.4 0.05645 221.2 0.1096 266.4 0.01931 221.2 0.04239 266.2 0.06129 221 0.10846 266.2 -0.01085 221 0.04582 266 0.06514 220.8 0.10765 266 0.02409 220.8 0.04515 265.8 0.06951 220.6 0.10606 265.8 -0.00922 220.6 0.03088 265.6 0.07342 220.4 0.10516 265.6 0.00656 220.4 0.04215 265.4 0.07518 220.2 0.1038 265.4 -0.05403 220.2 0.05323 265.2 0.07984 220 0.10136 265.2 0.00241 220 0.05013 265 0.0856 219.8 0.10028 265 -0.03753 219.8 0.05219 264.8 0.08882 219.6 0.09751 264.8 0.02459 219.6 0.04387 264.6 0.09165 219.4 0.09576 264.6 -0.02507 219.4 0.04725 264.4 0.09424 219.2 0.09329 264.4 -0.03678 219.2 0.04766 264.2 0.09598 219 0.09091 264.2 -0.0252 219 0.04726 264 0.09936 218.8 0.08817 264 -0.04011 218.8 0.0572 263.8 0.10157 218.6 0.08536 263.8 -0.02593 218.6 0.0517 263.6 0.10486 218.4 0.08192 263.6 -0.03444 218.4 0.06626 263.4 0.10778 218.2 0.08004 263.4 -0.02858 218.2 0.05415 263.2 0.10915 218 0.07485 263.2 -0.03984 218 0.05407 263 0.11181 217.8 0.07177 263 -0.05378 217.8 0.07554 262.8 0.1132 217.6 0.06893 262.8 -0.05115 217.6 0.06741 262.6 0.11405 217.4 0.06297 262.6 -0.06987 217.4 0.0635 262.4 0.11492 217.2 0.05933 262.4 -0.06584 217.2 0.06013 262.2 0.11651 217 0.05469 262.2 -0.05916 217 0.05869 262 0.11885 216.8 0.05017 262 -0.05737 216.8 0.06929 261.8 0.11934 216.6 0.04544 261.8 -0.04062 216.6 0.06265 261.6 0.12013 216.4 0.04113 261.6 -0.06852 216.4 0.06484 261.4 0.12107 216.2 0.03564 261.4 -0.07011 216.2 0.06679 261.2 0.12092 216 0.03101 261.2 -0.07297 216 0.07003 261 0.1224 215.8 0.02575 261 -0.07327 215.8 0.06925 260.8 0.12341 215.6 0.02124 260.8 -0.04862 215.6 0.06546 260.6 0.12328 215.4 0.01721 260.6 -0.06958 215.4 0.07782 260.4 0.12459 215.2 0.01193 260.4 -0.07804 215.2 0.06201 260.2 0.12375 215 0.00741 260.2 -0.07093 215 0.05706 260 0.12403 214.8 0.00206 260 -0.07518 214.8 0.05957 259.8 0.12459 214.6 -0.00082 259.8 -0.07188 214.6 0.05726 259.6 0.12496 214.4 -0.00438 259.6 -0.09861 214.4 0.05672 259.4 0.12614 214.2 -0.00753 259.4 -0.04769 214.2 0.05022 259.2 0.12568 214 -0.01116 259.2 -0.08026 214 0.04857 259 0.12558 213.8 -0.01397 259 -0.07046 213.8 0.03835 258.8 0.12502 213.6 -0.01572 258.8 -0.05786 213.6 0.05278 258.6 0.12489 213.4 -0.01956 258.6 -0.06397 213.4 0.0418 258.4 0.12508 213.2 -0.02124 258.4 -0.08428 213.2 0.03143 258.2 0.1246 213 -0.02194 258.2 -0.07583 213 0.02191 258 0.12487 212.8 -0.02278 258 -0.06488 212.8 0.03108 257.8 0.12414 212.6 -0.02329 257.8 -0.07595 212.6 0.0144 257.6 0.12361 212.4 -0.02442 257.6 -0.07015 212.4 0.00553 257.4 0.12398 212.2 -0.02323 257.4 -0.06395 212.2 0.01013 257.2 0.12308 212 -0.02229 257.2 -0.06097 212 -0.0053 257 0.12292 211.8 -0.02257 257 -0.06829 211.8 0.00233 256.8 0.12224 211.6 -0.02102 256.8 -0.07187 211.6 -0.01371 256.6 0.12199 211.4 -0.01973 256.6 -0.07402 211.4 -0.01745 256.4 0.12101 211.2 -0.01759 256.4 -0.07965 211.2 -0.02744 256.2 0.12101 211 -0.01646 256.2 -0.06801 211 -0.0351 256 0.12132 210.8 -0.01478 256 -0.07327 210.8 -0.03423 255.8 0.12035 210.6 -0.01303 255.8 -0.06154 210.6 -0.03908 255.6 0.11904 210.4 -0.00943 255.6 -0.06224 210.4 -0.06083 255.4 0.11973 210.2 -0.00852 255.4 -0.05225 210.2 -0.04575 255.2 0.1186 210 -0.00525 255.2 -0.0549 210 -0.02839 255 0.11763 255 -0.06462 Table S4. Results of the principal components coefficients of paracetamol and caffeine for the PCR model. https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Original Article https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 Eclet. Quim. 49 | e-1515, 2024 ISSN 1678-4618 page 19/19 Mixture No. Paracetamol (μg mL–1) Caffeine (μg mL–1) Z1 Z2 Z3 Z4 Z5 Z6 1 10 1.3 9.146716 0.922621 0.11385 0.218591 0.064549 -0.00164 2 10 1.82 9.338489 1.227304 0.100951 0.223531 0.066993 -0.00205 3 10 2.08 9.354737 1.388513 0.100658 0.224171 0.060107 -0.00185 4 10 2.34 9.754932 1.57956 0.107429 0.220398 0.058897 -0.0019 5 10 2.6 9.74823 1.72816 0.099278 0.214642 0.059679 -0.0013 6 14 1.3 12.40446 0.933764 0.141302 0.260088 0.057792 0.001265 7 14 1.82 12.64458 1.256145 0.142028 0.25596 0.062195 -0.00074 8 14 2.08 12.89527 1.456187 0.143263 0.240196 0.066623 -0.00077 9 14 2.34 13.23925 1.710256 0.17538 0.204584 0.056079 -0.00052 10 14 2.6 13.279 1.804253 0.149894 0.224501 0.067227 -0.0009 11 16 1.3 14.17486 0.998982 0.167127 0.211254 0.059428 8.95E-05 12 16 1.82 14.41187 1.337918 0.166771 0.208607 0.064014 0.00127 13 16 2.08 14.67569 1.505969 0.163074 0.221245 0.063982 0.000802 14 16 2.34 14.5841 1.607437 0.143083 0.228941 0.070436 0.001214 15 16 2.6 14.91319 1.774835 0.141138 0.240823 0.070132 7.25E-05 16 18 1.3 15.72434 0.95616 0.156724 0.231376 0.065447 0.000162 17 18 1.82 15.91465 1.176127 0.109593 0.212343 0.065423 0.004414 18 18 2.08 15.9445 1.334762 0.10192 0.225312 0.058374 0.005089 19 18 2.34 16.1327 1.493542 0.099248 0.231075 0.058385 0.001423 20 18 2.6 16.36708 1.642257 0.095751 0.233073 0.055706 0.004384 21 20 1.3 17.24382 0.860645 0.108718 0.209636 0.062819 0.002135 22 20 1.82 17.25686 1.14882 0.104635 0.221209 0.063474 -0.01031 23 20 2.08 17.59386 1.363286 0.105134 0.217987 0.079396 0.003633 24 20 2.34 17.55533 1.472502 0.08927 0.228363 0.06883 0.001512 25 20 2.6 17.82869 1.683043 0.114235 0.230266 0.062232 -0.00376 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515 https://doi.org/10.26850/1678-4618.eq.v49.2024.e1515