Determination of Cefoperazone Sodium in Presence of Related Impurities by Improved Classical Least Squares Chemometric Methods : A Comparative Study

1Pharmaceutical Chemistry Department, Faculty of Pharmacy, University of Tabuk, Tabuk 71491, Saudi Arabia 2Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Beni-Suef University, Alshaheed Shehata Ahmad Hegazy Street, Beni-Suef 62514, Egypt 3Department of Pharmaceutical Chemistry, College of Pharmacy, King Saud University, P.O. Box 2457, Riyadh 11451, Saudi Arabia 4Analytical Chemistry Department, Faculty of Pharmacy, Cairo University, Kasr El-Aini Street, Cairo 11562, Egypt

A literature review showed a group of analytical methods for CEF quantification in its drug products including spectrophotometry [5,6], NIR [7], and derivative UV-spectrophotometry for determination of CEF in binary mixtures with sulbactam [8].Chromatographic methods were utilized for assay of CEF [9], CEF and sulbactam [10,11]; besides HPLC methodology using -cyclodextrin stationary phase for assay of ternary mixture of CEF, ampicillin, and sulbactam was described [12].Furthermore, LC-MS/MS method was described for assay of CEF and sulbactam binary mixture in plasma [13].Moreover, electrochemical and voltammetric assay of CEF were stated [14,15].CEF and its two mentioned impurities were analyzed by HPLC and HPTLC chromatographic methods [16] and chemometric methods [17].
There are two main aims for the presented work.First, we aim to establish a comparison among 4 chemometric models depending on classical least squares (CLS) approach, namely, spectral residual augmented CLS (SRACLS), net analyte processing CLS (NAP-CLS), orthogonal signal correction CLS (OSC-CLS), and direct orthogonal signal correction CLS (DOSC-CLS).The last 3 models are preprocessing techniques implemented to increase the predictive capabilities of CLS model.The proposed improvement could offer CLS model wider applications for quantitative analysis, yet keeping the advantage of its built-in qualitative properties.The comparison shows the underlying algorithm for each model and compares the analysis results of different mixtures of CEF, 7-ACA, and 5-MER, as a case study, to indicate which of the 4 models is best to improve CLS prediction ability.Second, the presented models show the ability of chemometrics to analyze selectively CEF in ternary mixtures with its two reported impurities utilizing inexpensive and available instruments like UV-spectrophotometer, with suggested routine application of the models for quality control analysis of the pharmaceutical dosage form.The selected models offer comparable accuracy and precision for the quantitation of CEF in pharmaceutical formulation compared to the official HPLC method [9].

Materials and Methods
Full description of instrument, materials, chemical reagents, pharmaceutical formulations, stock, and working preparations applied in the presented study is mentioned in our previous published work [17].
2.1.Linearity.UV spectra for different samples of CEF ranging from 1 to 70 g mL −1 were recorded from 210 to 300 nm.CEF showed linearity between 5 and 50 g mL −1 at its  max at 229 nm.The superimposed spectra of 10 g mL −1 of CEF, 7-ACA, and 5-MER are shown in Figure 2.

Experimental Design
2.2.1.Calibration Set.Four-level, three-factor experimental design was accomplished utilizing four concentration levels coded as +2, +1, −1, and −2, where −1 is the central level for CEF and its impurities (7-ACA and 5-MER).The aim of the current design is to cover the mixture space in a proper way, ending up with a training set composed of 16 mixtures [18].Twenty g mL −1 of CEF was chosen as a central level for the design and the proposed concentrations for each level for CEF were dependent on its calibration range.Concerning impurities, their concentration levels were based on the fact that we include them in up to 3% of CEF calculated on molar basis.The concentration design matrix was represented in Table 1.The two-dimensional (2D) scores plot for the first two PCs of the concentration matrix was constructed to check the orthogonality, symmetry, and rotatability for the mixtures of the training set (presented as circles) as shown in Figure 3.
The best preprocessing procedure that gives the optimum results was mean centering one.

Test Set.
To assess the validity and the predictability of the compared chemometric models, the test set mixtures  were attained by preparing nine independent mixtures other than the training set mixtures but within the concentration space of the adopted design as indicated in Table 1.The well positioning of the mixtures of both training set (circles) and test set mixtures (stars) is indicated in Figure 3.

Analysis of Cefobid Vial.
Working solution of CEF (100 g mL −1 ) was prepared using methanol as solvent.Lastly, two mL of this working solution was completed to ten mL with methanol.The mean of three spectra was measured.This experiment was repeated six times and the attained spectra were analyzed by the suggested models.
The new predicted concentration will be calculated according to the following equation: where Ĉnew is the new predicted concentration after necessary augmentation of K and Knew is the augmented pure component contribution which takes into account residual errors, contribution of impurities, and contribution of interfering pure component spectra.The optimum number of loadings used for augmentation of K matrix was selected through running leave-one-out cross-validation (LOO-CV) [22].

Improved
Signal-CLS Models.CLS, as a direct calibration model, is the simplest developed chemometric technique.CLS method necessitates that all the components in the training set should be well recognized.Contrasting CLS, PCR (principal component regression) and PLS (partial least squares) methods can be applied for determination of the components under inspection even in the presence of unknown interfering component that offered the two models an advantage over CLS [23].Predictive power of CLS model can be improved greatly by using preprocessing techniques such as the methods proposed in this paper, like net analyte preprocessing (NAP), orthogonal signal correction (OSC), and direct orthogonal signal correction (DOSC).Preprocessing of the data prior to calibration step may be applied to minimize systematic variations influence that is unrelated to the interesting parameters [24].

Net Analyte Preprocessing (NAP).
Net analyte signal (NAS) calculation is the basis of NAP.NAS gave rise to numerous new calibration models, based on the same concept, extracting portion of the signal, which is directly correlated to the concentration of analyte and thus beneficial for prediction purposes [25].Additionally, NAS was applied for calculation of analytical figures of merit and for developing sensor selection technique [25].The fundamental principle of NAS-based calibration models is to distinguish between two kinds of contributions in the training data matrix X; one originates from the analyte of interest while the second originates from other sources of variability.The full details of NAP are mentioned by Goicoechea and Olivieri [25].

Orthogonal Signal Correction (OSC) and Direct Orthogonal Signal Correction (DOSC).
Numerous algorithms for applying OSC, as a filtering mechanism to data matrix X, were described in detail in literature [24,26,27].In the presented work, we refer to the OSC algorithm discussed by Fearn [27], as it is the most easily interpreted and can be compared to NAP methodology.These algorithms are employed to get rid of parts of the spectra that are orthogonal to the concentration.Fearn's algorithm spans the same space as PLS or PCR models on the unprocessed data and extracts components that are strictly orthogonal to the concentration.The first step is a projection of  onto the subspace that is orthogonal to     to obtain the variation in  that is correlated to   (where   is concentration of  analyte).Fearn's algorithm removed almost the drawbacks that were seen in the other OSC algorithms such as lack of orthogonality, leading to removal of useful information, or adding useless data in the corrected matrix.
DOSC approach introduced by Westerhuis et al. [28] is based only on least squares steps.It finds components, which are orthogonal to , which label the main variation of  to be removed from corrected .For implementation of DOSC, firstly  is decomposed into two orthogonal parts: Ŷ (the projection of  onto ) and  (the residual part, i.e., orthogonal to ).Secondly,  is decomposed into two orthogonal parts, one part that is of the same range as Ŷ and the other part that is orthogonal to it.Finally principal component analysis (PCA) is applied on the part of  orthogonal to  to remove it from  giving rise to corrected .
Mathematically, DOSC can be described by the following steps.
Step 1 is as follows: Step 2.
Step 2 is as follows: Step 3.
Step 3 is as follows: where  is score vector and  is loading vector.
The three models (NAP-CLS, OSC-CLS, and DOSC-CLS) are simpler when compared with other methods such as PLS.This simplicity originates from the utilization of orthogonal projections concepts, followed by the well-established classical least squares fitting.
(1) Optimization of Number of Factors for the NAP-CLS, OSC-CLS, and DOSC-CLS Models.Leave-one-out cross-validation (LOO-CV) is adopted in the current work for optimization of factors number for construction of the proposed models [23], by building the model using  − 1 samples' set (15 mixtures from training or calibration set) to predict the one sample left (validation sample).The root mean square error of crossvalidation (RMSECV) is computed as follows: where  is the number of objects in the calibration set,   is the known concentration for sample , and ĉ  CV is the predicted concentration of sample  using  components.Mean centering was applied to the calibration set each time successive samples were left out.

Results and Discussion
The current work was designed to accomplish a number of goals.First goal is to develop simple, selective, and precise chemometric models for assaying CEF in presence of its impurities in pure form and dosage form.Second goal is to demonstrate the quantitative power as well as qualitative power of the suggested models and compare their inherent characteristics using the analyzed mixtures as a case study.Additionally, we aim to display the influence of various preprocessing steps, such as NAP, OSC, and DOSC, on the performance of CLS in quantitative analysis.Optimization of methods' parameters was the first step to run models properly.For the SRACLS model, the optimum number of loadings  new used for augmentation of K matrix was selected through running LOO-CV and found to be 4.
For appropriate building of NAP-CLS, OSC-CLS, and DOSC-CLS methods, number of projection matrix factors (for NAP-CLS) and number of extracted factors (for OSC-CLS and DOSC-CLS) were adjusted.For this purpose, LOO-CV was applied where log PRESS (predicted residual error sum of squares) values were computed.The optimum number of factors was chosen in accordance with Haaland and Thomas approach [29].In all improved CLS models, two factors were essential for constructing the models except in DOSC-CLS model, where three factors were required.This information demonstrates that DOSC, as a preprocessing technique, is more complex than NAP and OSC procedures.
After parameters' optimization and training procedure, all proposed methods, together with ordinary CLS, were applied successfully for estimation of CEF in training set and test set as indicated in Tables 2 and 3, respectively.Recovery percentages, mean recoveries, standard deviation, and RMSEC and RMSEP values are anticipated in Tables 2  and 3.
RMSEC (for training set) and RMSEP (for test set) were computed in a similar way according to the following equation: where  is the number of samples in the test set (in case of RMSEP) and  − 1 is for training set (in case of RMSEC),   is the known concentration for sample , and ĉ  is the estimated concentration of sample  using  components.There was no significant difference among the models using one-way ANOVA (-test), where  tabulated is 3.098 at  < 0.05.The small values of the RMSEP indicate the minor error of prediction and the high predictive ability of the developed models.Figure 4 shows the RMSEP comparative plot for the prediction of test set samples by the proposed models, where all of the four proposed models are performing better than CLS and best results are given by OSC-CLS and DOSC-CLS models.
The described models were then applied with a great success for the analysis of the available dosage form (Table 4).This fact was further confirmed by the statistical comparison of the suggested models to the official HPLC method [9] (Table 4) where the calculated  and  values are less than the tabulated ones, indicating that there is no significant difference between our models and the reference method regarding both accuracy and precision.All the models were additionally compared by one-way ANOVA (Table 5), where the calculated -value was less than the tabulated one as well, showing that there is no significant difference among all models regarding precision.The obtained results suggest the validity of proposed models to be used for routine quality control analysis of CEF in pure form and pharmaceutical product.

Conclusion
In the presented paper, different chemometric models were applied for the analysis of CEF in presence of its related impurities.The proposed models are CLS, SRACLS, NAP-CLS, OSC-CLS, and DOSC-CLS.The developed models combine advantages of rapidity and easiness of traditional spectrometric methods in addition to their quantitative power (prediction of concentrations of CEF in its mixtures).The traditional CLS model gave the worst results for prediction of independent test set samples, while, among the proposed models, OSC-CLS and DOSC-CLS were the most powerful ones that increase the quantitative power of CLS method based on the analyzed case study.All the suggested models were optimized and validated by prediction of test set samples.The methods can be applied for routine quality control analysis of Cefobid Vials without prior separation or interference from commonly encountered additives.

Figure 3 :
Figure 3: Two-dimensional scores plot for the mean centered 16 training set samples (circles) and the 9 test set samples (stars) of concentration matrices of the 4-level 3-factor experimental design, with % variance of 99.7% for first PC and 0.28% for second PC.

Table 2 :
Analysis results for the prediction of training set (autoprediction) of CEF by the proposed chemometric models.d(g mL −1 ) % F o und(g mL −1 ) % F o un d(g mL −1 ) % F o un d(g mL −1

Table 1 :
Four-level three-factor experimental design of the training set (16 mixtures) and test set (9 mixtures) shown as concentrations of the mixture components in g mL −1 .

Table 3 :
Analysis results for the prediction of test set of CEF and its impurities by the proposed chemometric models.

Table 4 :
Statistical comparison of the results obtained by the proposed methods and the reported HPLC method for determination of CEF in pharmaceutical formulation (Cefobid5 Vial).

Table 5 :
One-way ANOVA parameters for the different proposed models used for the determination of CEF in Cefobid Vial.