untitled European Journal of Chemistry 5 (2) (2014) 311‐320 European Journal of Chemistry ISSN 2153‐2249 (Print) / ISSN 2153‐2257 (Online)  2014 Eurjchem Publishing ‐ Printed in the USA http://dx.doi.org/10.5155/eurjchem.5.2.311‐320.951 European Journal of Chemistry Journal homepage: www.eurjchem.com Stability‐indicating methods for the determination of olanzapine in presence of its degradation products Lobna Abd El Aziz Hussien a, Maha Farouk Abdel Ghani a, Amal Mahmoud Abo El Alamein b and Ekram Hany Mohamed c,* a Analytical Chemistry Department, Faculty of Pharmacy, Ain Shams University, Abbassia, Cairo, 11381, Egypt b Analytical Chemistry Department, Faculty of Pharmacy, Cairo University, Cairo, 12613, Egypt c Analytical Chemistry Department, Faculty of Pharmacy, British University in Egypt, Sherouk, 11837, Egypt *Corresponding author at: Analytical Chemistry Department, Faculty of Pharmacy, British University in Egypt, Sherouk, 11837, Egypt. Tel.: +20.2.01093725602. Fax: +20.2.687.5879. E‐mail address: ekram.hany@bue.edu.eg (E.H. Mohamed). ARTICLE INFORMATION ABSTRACT DOI: 10.5155/eurjchem.5.2.311‐320.951 Received: 22 October 2013 Received in revised form: 06 December 2013 Accepted: 25 December 2013 Online: 30 June 2014 KEYWORDS Simple, sensitive and precise spectrophotometric and chemometric stability indicating techniques were adopted for Olanzapine (OLA) determination in presence of its degradation products over a concentration range of 0.002‐0.02 mg/mL. The spectrophotometric technique involves six methods; first method is first derivative (D1) spectrophotometric one, which allows the determination of OLA in presence of its acidic and alkaline degradation products at 261.2 and 260.6 nm with mean percentage recoveries of 99.90±0.48 and 99.95±0.67, respectively. While second derivative spectrophotometry (D2) was used for determination of drug in presence of alkaline degradation products. Second method is first‐ derivative of the ratio spectra (DR1) for determination of OLA in presence of its acidic and alkaline degradation products at 267.9 and 251.6 nm, respectively with mean percentage recoveries of 99.81±0.64 and 100.53±1.11, respectively. The third method is pH‐induced difference method for determination of OLA in presence of its acidic and alkaline degradation products; with mean percentage recoveries 100.09±0.06 and 99.77±0.78, respectively. Fourth method is the Q‐analysis (absorption ratio) method, which involves the formation of absorbance equation at 296.3 nm (isosbestic point) and 271 nm (λmax of OLA) for the determination of OLA in presence of its acidic degradation products. The mean percentage recovery is 100.07±1.51. Fifth method based on dual wavelength selection was developed for the determination of OLA in presence of its acidic degradation products with mean percentage recovery of 100.36±0.69. Sixth method based on simple mathematic algorithm by the bivariate calibration was also used for the determination of OLA with the mean percentage recovery of 101.72±1.10. The second technique is chemometrics, which includes determination of OLA in presence of its acidic degradation products using multivariate calibration methods (the classical least squares (CLS), principle component regression (PCR) and partial least squares (PLS)) using the information contained in the absorption spectra. Olanzapine Q‐absorbance Chemometrics Dual wavelength Bivariate calibration Derivative spectrophotometer 1. Introduction Olanzapine; 2‐methyl‐4‐(4‐methyl‐1‐piperazinyl)‐10H‐ thieno[2,3‐b][1,5]benzodiazepine (Figure 1) is a second‐gene‐ ration antipsychotic drug, used in treatment of schizophrenia and prescribed mainly for patients with prominent agitation and insomnia [1]. OLA also may help with weight gain in anorexia nervosa [1]. The exact mechanism by which OLA exerts its antipsychotic effect is unknown. However, this effect may be mediated through a combination of dopamine and serotonin antagonism [1]. Olanzapine is metabolized primarily through oxidation mediated by cytochrome P450 (CYP) enzymes and by direct glucuronidation. The two major metabolites, 10‐N‐glucuronide and 4´‐N‐desmethyl olanzapine, are not pharmacologically active at the plasma levels achieved [1]. OLA could be determined by several analytical techniques, titrimetric methods [2‐4], spectroscopic methods including colorimetric [5‐15], U.V. spectrophotometric [16‐18], and fluorimetric [18] methods. OLA can also be determined by electrochemical methods [17,18], capillary electrophoresis [19], and thin layer chromatography [20‐24]. High performance liquid chromatographic [HPLC] methods were widely used for analysis of OLA in pure form [25‐57]. OLA was also successfully determined using gas chromatography [58]. Chemometrics was applied for simultaneous determination of OLA and Fluoxetine [59]. Figure 1. Chemical structure of intact olanzapine. 312 Hussien et al. / European Journal of Chemistry 5 (2) (2014) 311‐320 2. Experimental 2.1. Instrumentation A double beam UV‐VIS spectrophotometer (UV‐1800, Japan) connected to IBM compatible computer. The bundled software is UV probe software version 2.32 (Shimadzu) and the spectral bandwidth was 0.1 nm. The absorption spectra were carried out using 1 cm quartz cells. The chemometric calculations were performed in Matlab for Windows‐version 7 Mathworks Inc.2004. The PLS procedure was taken from PLS Toolbox 2.1, Eigenvector Research Inc. 2001 created by B.M. Wise, N.B. Gallagher for use with Matlab. 2.2. Materials and reagents All chemicals were of analytical grade, the solvents were of spectroscopic grade. OLA was kindly supplied by Egyptian International Pharmaceutical Industries Company (Eipico) 10th of Ramadan City, Egypt. Its purity was 100.45±0.30% (n = 5) according to the reported method [16]. Olanza®5mg tablets, labeled to contain 5 mg of OLA per tablet manufactured by Egyptian International Pharmaceutical Industries Company (Eipico) 10th of Ramadan City, Batch No.1821O07 and purchased from the local market. Sodium hydroxide, hydrochloric acid (Adwic‐Cairo, Egypt), methanol (Analar‐Germany). 2.3. Standard solutions of the intact OLA Stock solution: A standard stock solution of OLA was prepared by accurately transferring 100 mg of pure drug into a 100 mL volumetric flask, dissolving in 20 mL methanol and then the volume was completed to the mark with the same solvent to provide standard stock solution containing 1.00 mg/mL. Working solution: OLA working solution (0.02 mg/mL) was prepared by transferring 2 mL of the standard stock solution into 100 mL volumetric flask and then the volume was completed to the mark with methanol. 2.4. Preparation of standard solution of acidic and alkaline degraded OLA 50 mg of OLA was mixed with 25 mL of 2 M hydrochloric acid one time and 4 M sodium hydroxide another time and refluxed for 6 hours. The solutions were cooled, neutralized with 2 M aqueous sodium hydroxide and 4 M aqueous hydrochloric acid respectively, till pH = 7, transferred to 50 mL volumetric flasks and diluted to the mark with methanol (1.00 mg/mL). Aliquot portions of these solutions were diluted with methanol to prepare working standard solutions of 0.02 mg/mL. Complete degradation was confirmed was confirmed by the reported HPLC method, using inertsil C18 column (5 μm, 150 mm × 4.6 mm i.d). The mobile phase was a mixture of 9.5 mM sodium dihydrogen phosphate (pH adjusted to 6.8±0.1 with triethylamine), acetonitrile and methanol (40:30:30, by volumes) and UV detection at 225 nm [46]. The previously prepared solutions were evaporated to dryness. Then the degradation products were extracted with multiple fraction of methanol (3 × 10 mL). Then the extract was evaporated at room temperature and the degradation products were collected. The degradation products powder was elucidated by IR and mass spectrometry. 2.5. Procedures 2.5.1. Construction of calibration curves for D1 and D2 spectrophotometric method Accurately measured volumes of intact OLA working solution (0.02 mg/mL) were transferred into a series of 10 mL volumetric flasks and diluted to the mark with methanol to obtain concentrations from 0.002 to 0.02 mg/mL. The D1 and D2 spectra of each solution was recorded using Δλ = 8 and scaling factor = 100. For determination of OLA in presence of its acidic degradation products a calibration curve was obtained by plotting the peak amplitudes of D1 at 261.2 nm versus the corresponding drug concentrations. While for OLA determination in presence of its alkaline degradation products the peak amplitudes of D1 and D2 at 260.6 and 239.9 nm were recorded, respectively (corresponding to zero‐crossing of the degradation product) versus the corresponding concentrations of drug, and regression equations were computed. 2.5.2. Construction of calibration curves of (DD1) spectrophotometric method Different aliquots of intact OLA working solution (0.02 mg/mL) were accurately transferred into a series of 10 mL volumetric flasks and diluted to the mark with methanol to obtain concentrations from 0.002 to 0.02 mg/mL. The DD1 curves were recorded at Δλ = 8 and scaling factor = 10. The absorption spectra of these solutions were divided by the absorption spectrum of 0.004 mg/mL of the acidic and alkaline degradation products separately (as divisors). The obtained ratio spectra were then differentiated with respect to wavelength. The peak amplitudes at 267.9 and 251.6 nm were recorded for the determination of OLA in presence of its acidic and alkaline degradation products, respectively. The calibration curves representing the relationship between the measured amplitudes and the corresponding concentrations of the drug were constructed and the regression equations were computed. 2.5.3. Construction of calibration curves for pH‐induced difference method Accurately measured volumes of intact OLA working solution (0.02 mg/mL) were transferred into two sets of 10 mL volumetric flasks, diluting the first set to the mark with 0.1 M NaOH and the second set with 0.1 M HCl to obtain concentration range from 0.002 to 0.02 mg/mL. The Zero‐order spectrum of each dilution was recorded against its corresponding blank. The previous spectra of each dilution were computed, to give (ΔA) spectra. The peak amplitudes of (ΔA) spectra were recorded at 240 and 247.9 nm for determination of ((OLA) in presence of its acidic and alkaline degradation products respectively (Corresponding to zero‐ crossing of the degradation products) and plotted against the corresponding concentrations of OLA. The regression equations were then computed. 2.5.4. Construction of calibration curves for Q‐analysis (absorption ratio) method Accurately measured volumes of intact OLA and its acidic degradation products working solutions were transferred separately into a series of 10 mL volumetric flasks and diluted to the mark with methanol to obtain concentrations from 0.002 to 0.02 mg/mL. The Zero‐order spectrum of each dilution was recorded against methanol as a blank. The absorbance of OLA and its acidic degradates were measured at 296.3 and 271 nm for each dilution separately. Then the absorbance at the selected wavelengths was plotted against the corresponding concentrations and the regression equations were then computed. Absorptivity coefficients of OLA and its acidic degradation products were determined at both selected wavelengths; the absorption equation was then formed. The concentration of the drug of interest is calculated from the equation. Hussien et al. / European Journal of Chemistry 5 (2) (2014) 311‐320 313 2.5.5. Construction of calibration curve for dual wave length method Accurately measured volumes of intact OLA working solution (0.02 mg/mL) were transferred into a series of 10 mL volumetric flasks and diluted to the mark with methanol to obtain concentrations from 0.002 to 0.02 mg/mL. The Zero‐ order spectrum of each dilution was recorded against methanol as blank. The absorbance of OLA was measured at 270 and 246.3 nm for each dilution separately. Then the difference between the absorbance at the selected wavelengths was calculated, plotted against the corresponding concentrations of the drug and the regression equation was then computed. 2.5.6. Construction of calibration curve for bivariate spectrophotometric method Accurately measured volumes of OLA and its acidic degradation products working solutions were transferred separately into a series of 10 mL volumetric flasks and diluted to the mark with methanol to obtain concentrations from 0.002 to 0.02 mg/mL for both OLA and its acidic degrades. The Zero‐ order spectrum of each dilution was recorded against methanol as blank. The absorbance of OLA and its acidic degradation products were measured at 229 and 245 nm for each dilution separately. Then the absorbance values at the selected wavelengths were plotted against the corresponding concentrations and the regression equations were then computed. 2.5.7. Multivariate calibration technique (Chemometric) (a) Construction of training set‐Different mixtures of OLA and its acidic degradation products were prepared by diluting different volumes of their working standard solutions into 10 mL volumetric flask and completing to the final volume with methanol. The absorbance of these mixtures was measured between 240‐370 nm at 1 nm interval with respect to a blank of methanol. The composition of the samples was randomly designed according to five level calibration design [60] in order to obtain non correlated concentration profiles and this calibration design prepared to obey Beer’s law. (b) Constructing the models‐To build the CLS model, feed the computer with absorbance and concentration matrices for training set. Carry out the calculations to obtain the “K” matrix. For the PCR and PLS models, use the training set absorbance and concentration matrices together with PLS‐Toolbox 2.0 software for the calculations. (c) Construction of the validation set. Prepare different nine mixtures of OLA and its acidic degradation products by transferring different volumes of their working standard solutions into a series of 10 mL volumetric flasks and complete to volume with methanol. Apply the developed models to predict the concentration of OLA in each mixture. 2.5.8. Laboratory prepared mixtures Solutions containing different ratios of OLA and up to 60% of its acidic and 60% of its alkaline degradation products were prepared to obtain mixture solutions of intact drug and both its degradation products separately. 2.5.9. Application to pharmaceutical preparation Ten tablets were accurately weighed and finely powdered. A portion equivalent to 50 mg of OLA was weighed, sonicated in 20 mL methanol and filtered into 50 mL volumetric flask. The residue was washed three times each with 8 mL methanol and completed to the mark with the same solvent. Aliquots (according to linearity) was transferred to 10 mL volumetric flasks and diluted with methanol. The general procedures were followed and the concentration of OLA was calculated from its corresponding regression equation. 3. Results and discussion The International Conference on Harmonization (ICH) guideline entitled “stability testing of new drugs substances and products” requires the stress testing of new substances and products, also requires the stress testing to be carried out to elucidate the inherent stability, characteristics of the active substance [61]. An ideal stability indicating method is one that quantifies the standard drug alone and also resolves its degradation products. The structures of the intact drug, acidic and alkaline degradation products were elucidated by IR and mass spectrometry. The major acidic degradation product suggested in acidic conditions is 2‐[(2‐aminophenyl)amino]‐N‐ethenyl‐ N,5‐dimethylthiophene‐3‐carboxamide as presented in (Figure 2). While in case of alkaline conditions, 2‐[(2‐aminophenyl) amino]‐5‐methylthiophene‐3‐carboxylic acid (I) and 4‐methyl piperazin‐1‐amine (II) are suggested to be the major degradation product (Figure 3). Figure 2. Scheme for acidic degradation of OLA. Figure 3. Scheme for alkaline degradation of OLA. The IR spectrum of OLA showed a characteristic band at 3217.7 cm‐1 indicating the presence of NH group, and a band at 2932.9 cm‐1 indicating the presence of Alkane C‐H bonds. While IR spectrum of the acidic degradates showed a characteristic broad band at 3541.5 cm‐1, indicating the presence of OH group and another two characteristic bands at 3483.8 and 3398.2 cm‐ 1 indicating the presence NH2 group while the appearance of a band at 1639.2 cm‐1 suggest the presence of C=O group. The IR spectrum of the alkaline degradation products showed charac‐ teristic broad band at 3439.1 cm‐1, indicating the presence of OH group and a band at 2360.6 cm‐1 suggesting the presence of C≡N group, and a band at 1634.0 cm‐1 suggest the presence of C=O group. While the mass spectrum showed characteristic peaks at m/z 287.11 and 45 in case of acidic degradation and at 248.06 and 115.11 in case of alkaline degradation. The major acidic degradation product suggested is 2‐[(2‐ aminophenyl)amino]‐N‐ethenyl‐N,5‐methylthiophene‐3‐carbox amide (I) and dimethylamine (II). While in case of alkaline degradation, 2‐[(2‐aminophenyl)amino]‐5‐methylthio‐phene‐ 3‐carboxylic acid (I) and 4‐methylpiperazin‐1‐amine (II) are suggested to be the major degradation product . The focus of the present work was to develop accurate, specific, reproducible and sensitive stability indicating methods for the determination of OLA in pure form and in 314 Hussien et al. / European Journal of Chemistry 5 (2) (2014) 311‐320 pharmaceutical formulation in the presence of acidic and alkaline degradation products. The zero‐order absorption spectrum of OLA and its acidic and alkaline degradation products showed sever overlapping (Figure 4 and 5) which interfere with the direct determination of OLA. Figure 4. Zero order spectra of OLA (___) and acidic degradation products (…) (10 ug/mL each) using methanol as a solvent. Figure 5. Zero order spectra of OLA (___) and of alkaline degradation products (‐‐‐) (10 ug/mL each) using methanol as a solvent. 3.1. Derivative spectrophotometry A rapid, simple and low cost spectrophotometric methods based on measuring the peak amplitude of D1 at 261.2 nm (Figure 6) and 260.6 nm (Figure 7) for determination of OLA in presence of its acidic and alkaline degradation products respectively and also measuring the peak amplitude of D2 at 239.9 nm (Figure 8) for determination of OLA in presence of its alkaline degradation products (corresponding to zero crossing of the degradation products) were developed with good selectivity without interference of its acidic and alkaline degradation products over concentration range from 2‐20 ug/mL. In order to optimize D1 and D2 methods, different smoothing and scaling factors were tested, where a smoothing factor Δλ = 8 and scaling factor = 100 showed a suitable signal to noise ratio and the spectra showed good resolutions. The proposed methods are valid for the determination of OLA in presence of its acidic and alkaline degradation products in different laboratory prepared mixtures. 3.2. DR1 method In order to improve the selectivity of the analysis of OLA in presence of its acidic and alkaline degradation products DR1 method was established. Figure 6. First derivative absorption spectra of 10 ug/mL of OLA (__) and 10 ug/mL of acidic degradation products (….) using methanol as a solvent. Figure 7. First derivative absorption spectra of 10 ug/mL of OLA (___) and 10 ug/mL of alkaline degradation products (…) using methanol as a solvent. Figure 8. Second derivative absorption spectra of 10 ug/mL of OLA (___) and 10 ug/mL of its alkaline degradation products (…) using methanol as a solvent. The main advantage of the method is that the whole spectrum of interfering substance is cancelled [62]. Accordingly, the choice of the wavelength selected for calibration is not critical as in D1 or D2 derivative method. In order to optimize DR1 method for determination of OLA in presence of its degradation products, it is necessary to test the influence of the variables: divisor concentration, smoothing and scaling factors. Several divisor concentrations of the acidic and alkaline degradates were tried, the best results was obtained when using 0.004 mg/mL of both degradation products as divisors. Different smoothing and scaling factors were also tested where a smoothing factor Δλ = 8 nm, and scaling factor = 10 were suitable to enlarge the signals of OLA to facilitate its measurement and to diminish error in reading the signal. Hussien et al. / European Journal of Chemistry 5 (2) (2014) 311‐320 315 DR1 values showed good linearity and reproducibility at 267.9 and 251.6 nm without interference from its acidic and alkaline degradation products respectively (Figure 9 and 10). Linearity of the peak amplitudes of the DR1 curves at both wavelengths was obtained in range (0.002‐0.02 mg/mL). The method was checked by analysis of laboratory prepared mixtures of OLA and its acidic and alkaline degradation products in different ratios. Figure 9. First derivative ratio spectra of different concentrations of OLA (2‐ 20 ug/mL) using 4 ug/mL acidic degradation products as a divisor in methanol. Figure 10. First derivative ratio spectra of different concentrations of OLA (2‐20 ug/mL) using 4 ug/mL alkaline degradation products as a divisor in methanol. 3.3. pH‐Induced difference (ΔA) technique The most basic nitrogen atoms of OLA located in the piperazine ring are easily protonated resulting in considerable increase in the angle between planes of OLA aromatic rings (benzene and thiophene). Rotation of the piperazine ring and change in its conformation from twist to boat leads to change in the spectral characteristics of OLA upon protonation [63]. Owing to this property, OLA was determined in presence of its acidic and alkaline degradation products, in raw materials and in pharmaceutical formulation, using pH‐induced difference technique. The absorption spectra of OLA in 0.1 M sodium hydroxide and in 0.1 M hydrochloric acid are presented in (Figure 11). OLA could be quantitatively determined at 240 nm and 247.9 nm in presence of its acidic and alkaline degradation products, respectively (zero crossing point) without interference from its degradation products, (Figure 12 and 13). 3.4. Q‐analysis (absorption ratio) method Absorbance ratio method uses the ratio of absorbances at two selected wavelengths [64], one of which is an isosbestic point and other being the λ‐max of OLA. From the overlain spectrum of the drug and its degradation products, 296.3 nm (isoabsorptive point) and 271 nm (λmax of OLA) were selected for the determination of OLA in presence of its acidic degradation products. Linear calibration curves were obtained in the range (2‐20 ug/mL) for both intact OLA and its acidic degradation products relating the absorbances at the two selected wavelengths 296.3 and 271 nm to the corresponding concentrations of OLA and its acidic degradation products and the regression equations were computed. Absorptivity coefficients of both OLA and its acidic degradation products were determined as shown in Table 1. Figure 11. Zero‐order absorption spectra of OLA (10 ug/mL), (a) in 0.1 M HCl (…), (b) in 0.1 M NaOH (‐ ‐ ‐), (c) ΔA spectra (__). Figure 12. ΔA spectra of OLA (___) and its acidic degradation products (…), in 0.1 M (Hydrochloric acid and sodium hydroxide) (each, 10 ug/mL). Figure 13. ΔA spectra of OLA (__) and its alkaline degradation products (…), in 0.1 M (hydrochloric acid and sodium hydroxide) (each, 10 ug/mL). The concentration of OLA was determined by substituting the absorbance and absorptivity coefficients in the following equation [65]. 316 Hussien et al. / European Journal of Chemistry 5 (2) (2014) 311‐320 Table 1. Absorptivity coefficient values of Olanzapine and acidic degradation products at 296.3 (isosbestic point) and 271.0 nm (λmax of OLA). Sample no Absorptivity at 296.3 nm Absorptivity at 271.0 nm Olanzapine Acidic deg. Olanzapine Acidic deg. 1 22.0 22.0 60.5 41.0 2 22.5 21.5 60.7 40.5 3 21.8 21.8 60.1 41.0 4 22.1 21.8 60.2 41.0 5 22.2 22.2 60.7 41.3 6 21.7 21.9 60.0 41.0 Mean 22.05 21.86 60.36 40.96 Table 2. Application of the method of Kaiser for the selection of the wavelength set for the determination of olanzapine. λ1/λ2 215 nm 229 nm 245 nm 262 nm 271 nm 300 nm 215 nm 0 5.72 2.81 1.00 2.57 4.91 229 nm 0 7.37 3.79 2.49 6.57 245 nm 0 3.15 4.54 3.09 262 nm 0 1.27 4.39 271 nm 0 5.09 300 nm 0 (1) Where A1 and A2 are the absorbances of mixture at 296.3 and 271 nm respectively. and are the absorptivity coefficients of OLA at 296.3 and 271 nm, respectively. While and are the absorptivity coefficients of acidic degradation products at 296.3 and 271 nm, respectively. Qm =A2/A1, Qy= / and Qx= / . 3.5. Dual wavelength method The overlain spectrum of OLA and its acidic degradation products suggested that dual wavelength method is a suitable method for the simultaneous determination of OLA in presence of its degradation products [66]. From the overlain spectra, 270 and 246.3 nm were selected for the determination of OLA, where the acidic degradation products shows the same absorbances. A linear Calibration curve was obtained in the range (0.002‐0.02 mg/mL) relating the difference between the absorbances at the two selected wavelengths 270.0 and 246.3 nm to the corresponding drug concentrations in presence of acidic degradation products. 3.6. Bivariate calibration method OLA was also determined and resolved from its acidic degradation products by using bivariate calibration spectrophotometric method [67]. This method is based on a simple mathematical algorithm, in which the data is used derives from four linear regression calibration equations, two calibrations for each component at two wavelengths selected using the method of Kaiser [68]. The method has been successfully applied to resolve different binary mixtures [69]. The advantage of bivariate calibration method is simplicity and the fact that derivatization procedure is not necessary. Unlike other chemometric techniques, there is no need for full spectrum information and no data processing is required. The linear calibration regression function for the spectrophotometric determination of an analyte (A) at a selected wavelength (i) is given by AAi= mAi CA + eAi where mAi is the slope of linear regression, CA is the concentration of analyte A and eAi is the intercept value. If the measurement of the binary mixture (AB) are performed at two selected wavelengths (λ1, λ2) we have two equations set [67] AAB1=mA1CA+mB1CB+eAB1 (2) AAB2=mA2CA+mB2CB+eAB2 (3) The resolution of such equations set allows the evaluation of CB (concentration of OLA) and CA (concentration of acidic degradation products) from the following equations: (4) (5) These simple mathematical algorithms allows the resolution of the two components by measuring the absorbance of OLA and degradation products, each at two wavelengths and using the parameters of the linear regression functions evaluated individually for each component at the same wavelengths. The method of Kaiser [68] was used for the selection of optimum wavelength set which assured the best sensitivity for the quantitative determination of the studied drug. In order to apply this method, the signals of the two components located at six wavelengths: 215, 229, 245, 262, 271, and 300 nm were selected. The calibration curve equations and their respective linear regression coefficient were obtained directly with the aim of ensuring the linearity between the signal and the concentrations. The slope values of the linear regression were estimated for both the drug and its acidic degradation products at the selected wavelengths and used for the determination of the sensitivity matrices K, which proposed by Kaiser’s method [68]. A series of sensitivity matrices, K, were created for every pair of pre‐selected wavelengths. (6) A = Acidic degradate, B = Olanzapine where mA1,2 and mB1,2 are the sensitivity parameters (slope) of the regression equation of A and B at the two selected wavelengths (λ1 and λ2) . The determinants of these matrices were calculated as shown in Table 2. The wavelength set was selected for which the highest matrix determinant value was obtained. For bivariate determination of OLA in presence of its acidic degradation products, 229 and 245 nm wavelengths were used. Table 3 showed the linear regression calibration formula used for bivariate algorithm. The laboratory prepared mixtures were analyzed by the proposed method for determination of intact OLA in presence of its acidic degradation products using the following equation (7) Hussien et al. / European Journal of Chemistry 5 (2) (2014) 311‐320 317 Table 3. Linear regression calibration formulas used for the bivariate algorithm. Component Calibration equations * λ 1=229 nm λ 1=245 nm Olanzapine A=0.0703C+0.0064 r = 0.9998 A=0.0503C‐0.0032 r = 0.9999 Acidic deg. A=0.0439C‐0.0035 r = 0.9997 A=0.0419C‐0.0035 r = 0.9997 * A = Absorbance at the selected wavelength, C = Concentration in ug/mL; r = Correlation coefficient. Table 4. The concentration of mixtures of OLA, and its acidic degradate in the training set. Sample no Olanzapine (ug/mL) Acidic degradation products (ug/mL) 1 6 6 2 6 2 3 2 10 4 10 4 5 10 6 6 6 4 7 4 8 8 8 10 9 8 6 10 6 10 11 10 2 12 2 8 13 2 6 14 6 8 15 8 4 16 2 4 Table 5. The concentration of mixtures of OLA and its acidic degradation products in the validation set. Sample no Olanzapine (ug/mL) Acidic deg. (ug/mL) 1 2 2 2 4 10 3 4 4 4 10 8 5 10 10 6 8 2 7 8 8 8 4 2 9 4 6 where eAB1, eAB2 are the sum of intercepts of the linear calibrations at the two wavelengths (eAB1 = eA1 + eB1), 1, 2 are the wavelengths 229 and 245 nm, mA, mB are the slopes of the linear regressions and C is the concentration of OLA. 3.7. Multivariate method In this section, different chemometric approaches were applied for the determination of OLA in presence of its acidic degradation products, including CLS, PCR, PLS. These multivariate calibrations were useful in spectral analysis because the simultaneous inclusion of many spectral wavelengths instead of single wavelength greatly improved the precision and predictive ability [60]. The first step in the simultaneous determination of two components by multivariate calibration methods involves constructing the calibration matrix for binary mixture. The calibration set was obtained by using the absorption spectra of a set of 16 mixtures of OLA and its acidic degradation products with different ratios of each component and their concentrations are given in Table 4. The model selected was that with the smallest number of factors such that RMSECV for the model was not significantly greater than RMSECV from the model with additional factor. As the difference between the minimum RMSECV and other RMSECV values became smaller, the probability that each additional factor was significant became smaller. Two factors were found to be suitable for both PLS and PCR methods. The UV spectra of the prepared solutions were recorded over the range 240‐370 nm. Wavelengths (200‐239 nm) dominated by noise and non‐informative spectral region after 370 nm are not included. Spectra were digitized each at 0.1nm interval, and the experimental data points were exposed to MATLAB version 7.0 for calculations. To build the CLS model, feed the computer with absorbance and concentration matrices for training set. Carry out the calculations to obtain the “K” matrix. For the PCR and PLS models, use the training set absorbance and concentration matrices together with PLS‐Toolbox 2.0 software for the calculations. The selection of the optimum number of factors for the PLS technique was a very important step before constructing the models because if the number of factors retained was more than the required, more noise will be added to the data. On the other hand, if the number retained was too small meaningful data that could be necessary for the calibration might be discarded. In this study the leave one out cross validation method was used [70,71]. The root mean square error of prediction (RMSEP) was calculated as diagnostic tool for examining the errors in the predicted concentrations. It indicated both the precision and accuracy of predictions as it played the same role of standard deviation in indicating the spread of the concentration errors. As the difference between the minimum RMSECV and other RMSECV values became smaller, the probability that each additional factor was significant became smaller. After the PCR and PLS models have been constructed, it was found that the optimum number of latent variables described by the developed models was two factors for PCR and PLS models. Calibration graphs were constructed by plotting the predicted concentrations for OLA by each of the developed models versus the true concentrations. The statistical parameters of the linear relationship between the calculated and the true concentration of OLA in the calibration set were presented. In order to assess the predictive ability of each of the developed models, it was applied on an external validation set for determination of OLA. Table 5 shows different concentrations of OLA and its acidic degradation products used in the validation set. 318 Hussien et al. / European Journal of Chemistry 5 (2) (2014) 311‐320 Table 6. Validation parameters for the proposed stability‐indicating spectrophotometric methods. Validation parameters Dn DR1 ΔA D1 261.2 nm D1 260.6 nm D2 239.9 nm 267.9 nm 251.6 nm 240 nm 247.9 nm Linearity (µg/mL) 2‐20 2‐20 2‐20 2‐20 2‐20 2‐20 2‐20 Slope 0.0559 0.0538 0.0206 0.0972 0.0600 0.1256 0.1108 Intercept ‐0.0006 0.0006 0.0001 0.0205 ‐0.0040 0.0024 0.0022 Correlation coefficient (r) 0.9999 0.9999 0.9999 1 0.9999 0.9999 0.9999 LOD (μg/mL) 0.08 0.09 0.11 0.25 0.34 0.229 0.259 LOQ (μg/mL) 0.25 0.29 0.35 0.75 1.05 0.695 0.785 Precision Intra‐day a 1.27 0.15 0.13 0.16 0.06 0.92 0.84 Inter‐day b 1.04 0.29 0.21 0.26 0.31 0.61 0.50 Validation parameters Q‐Analysis method Dual wave length method Bivariate calibration method 296.3 nm 271 nm 247.9 nm 229 nm 245 nm Linearity (µg/mL) 2‐20 2‐20 2‐20 2‐20 2‐20 Slope 0.2196 0.0602 0.0102 0.0703 0.0502 Intercept 0.00053 0.0010 ‐0.0022 0.0064 ‐0.0032 Correlation coefficient (r) 0.9998 0.9999 0.9998 0.9998 0.9999 LOD (μg/mL) 0.369 0.158 0.277 0.4642 0.2557 LOQ (μg/mL) 1.119 0.481 0.839 1.4066 0.7749 Precision Intra‐day a 1.19 0.12 0.46 Inter‐day b 0.98 0.67 0.62 a The intraday (n = 3) average of three concentrations (6, 10, and 14) repeated three times within day. b The interday (n = 9) average of three concentrations repeated three times in three successive days. Table 7. Results of assay validation obtained by applying the proposed chemometric methods for the determination of Olanzapine in presence of its acidic‐ degradation products. Validation parameters CLS PCR PLS Predicted versus actual concentration plot Slope 0.9995 1.0051 0.9995 Intercept 0.0023 0.0194 0.0024 Correlation coefficient (r) 1.0000 0.9999 1.0000 RMSEP 0.0035 0.0318 0.0036 Table 8. Determination of the studied drug in the laboratory prepared (L.P.) mixtures with its degradation products and in tablets by the proposed methods . Sample Dn ‐method a DR1 ‐method a ΔA‐method a D1 261.2 nm D1 260.6 nm D2 239.9 nm 267.9 nm 251.6 nm 240 nm 247.9 nm L.P.‐mixtures (n = 5) b 100.49±0.32 100.93±0.63 100.93±0.63 99.86±0.09 100.80±0.38 99.86±0.17 99.53±0.38 Up to 60% degradation Olanza tablets 5 mg, B.N.1821O07 100.50±1.41 99.90±0.48 99.96±0.32 99.98±0.30 100.65±0.60 100.73±0.65 99.64±0.89 Sample Q‐Analysis method a Dual wave length method a Bivariate calibration method a CLS a PCR a PLS a L.P.‐mixtures (n = 5) b 99.96±0.13 101.47±0.67 100.97±0.13 99.98±0.08 100.10±0.32 100.01±0.08 Up to 60% degradation Up to 50% degradation Olanza tablets 5 mg, B.N.1821O07 100.64±1.08 99.72±1.06 100.87±1.38 99.96±0.32 99.90±0.48 100.50±1.41 a Recovery±RSD. b Sets each of 3 replicates. Table 9. Application of the standard addition technique to the analysis of the studied drug by the proposed methods. Pharmaceutical preparation Authentic added (ug/mL) Standard addition, Recovery% ** D1 D2 DR1 ΔA 261.20 nm 260.60 nm 239.90 nm 267.9 nm 251.6 nm 240 nm 247.9 nm Olanza®tablets* 5mg B.N. 1821O07 2 99.47 98.54 98.57 100.41 101.49 99.69 100.61 4 102.95 99.89 99.35 100.20 101.08 101.25 99.94 6 99.64 99.83 99.93 99.79 100.11 101.34 99.12 8 100.22 100.58 100.58 99.71 100.24 100.58 98.37 10 100.21 99.83 100.37 99.77 100.33 100.77 100.17 Mean 100.50 99.90 99.96 99.98 100.65 100.73 99.64 SD 1.41 0.48 0.32 0.30 0.60 0.65 0.89 Authentic added (ug/mL) Q‐Analysis method Dual wave length method Bivariate calibration method CLS PCR PLS 2 99.46 101.50 102.09 99.47 99.54 98.57 4 100.78 98.71 102.29 102.95 99.89 99.35 6 99.64 99.77 99.01 99.64 99.83 99.93 8 102.03 99.42 100.91 100.22 100.58 100.58 10 101.28 99.19 100.06 100.21 99.83 100.37 Mean 100.64 99.72 100.87 100.50 99.90 99.96 SD 1.08 1.06 1.38 1.41 0.48 0.32 * Equivalent to 10 ug/mL of OLA. ** Average of at least 3 separate determinations. Hussien et al. / European Journal of Chemistry 5 (2) (2014) 311‐320 319 Table 10. Statistical comparison of the results obtained by the proposed methods and the reported method for the determination of Olanzapine in pharmaceutical preparation. Items D1 D2 DR1 ΔA 261.20 nm 260.60 nm 239.90 nm 267.9 nm 251.6 nm 240 nm 247.9 nm Mean 100.46 100.47 100.36 99.54 99.27 100.10 99.99 SD 0.291 0.301 0. 32 0.315 0.194 0.521 0.510 RSD% 0.289 0.300 0.32 0.315 0.194 0.521 0.510 n 5 5 5 5 5 5 5 Variance 0.084 0.091 0.102 0.099 0.038 0.271 0.260 Student’s t‐test (2.306) 0.04 0.06 0.49 0.915 1.060 1.29 1.72 F‐test (6.388) 1.07 1.00 1.37 1.090 2.39 2.97 2.85 Items Q‐analysis method Dual wave length method Bivariate calibration method CLS PCR PLS Reported method * Mean 100.70 100.38 100.71 99.96 100.02 99.97 100.45 SD 0.492 0.231 0.350 0.360 0.371 0.362 0.302 RSD% 0.489 0.230 0.347 0.360 0.371 0.362 0.300 n 5 5 5 5 5 5 5 Variance 0.242 0.056 0.123 0.129 0.137 0.131 0.091 Student’s t‐test (2.306) 0.95 0.116 1.22 2.29 2.03 2.29 F‐test (6.388) 2.70 1.63 1.35 1.41 1.50 1.43 The values between parenthesis are the theoretical values of t‐test and F‐test at p = 0.05. * Direct derivative Spectrophotometric method where the first derivative values were measured at 222 nm in methanol [16]. To validate the prediction ability of the suggested models, they were used to predict the concentration of OLA in laboratory prepared mixtures containing different ratios of them. Results of assay validation obtained by applying the proposed spectrophotometric and chemometric methods for the determination of Olanzapine in presence of its degradation products are presented in Tables 6 and 7, respectively. The proposed methods were applied successfully to analysis of OLA in pharmaceutical formulation, and the results obtained were listed in Table 8. Standard addition technique was successfully applied for the analysis of the studied drug by the proposed methods and results are presented in Table 9. Table 10 represents statistical comparison of the results obtained by the proposed methods and the reported method for the determination of OLA in pharmaceutical preparation. 4. 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