Two- and three-way chemometrics methods applied for spectrophotometric determination of lorazepam in pharmaceutical formulations and biological fluids

Analytica Chimica Acta 533 (2005) 169–177

Two- and three-way chemometrics methods applied for spectrophotometric determination of lorazepam in pharmaceutical formulations and biological fluids Jahanbakhsh Ghasemi ∗ , Ali Niazi Department of Chemistry, Faculty of Sciences, Razi University, Kermanshah, Iran Received 5 July 2004; received in revised form 3 November 2004; accepted 3 November 2004 Available online 4 February 2005

Abstract In this work, direct determination of lorazepam, an anxiolytic and sedative agent, in pharmaceutical formulations and biological fluids (urine and human plasma) was accomplished based on ultraviolet spectrophotometry (260–380 nm) using parallel factor analysis (PARAFAC) and partial least squares (PLS). The study was carried out in the pH range from 1.0 to 12.0 and with a concentration range from 0.50 to 8.75 ␮g ml−1 of lorazepam. Multivariate calibration models using PLS at different pH and PARAFAC were elaborated for ultraviolet spectra deconvolution and lorazepam quantitation. The best models for the system were obtained with PARAFAC and PLS at pH = 2.05 (PLS-PH2). The capabilities of the method for the analysis of real samples were evaluated by determination of lorazepam in pharmaceutical preparations and biological (urine and plasma) fluids with satisfactory results. The accuracy of the method, evaluated through the root mean square error of prediction (RMSEP), was 0.0429 for lorazepam with best calibration curve by PARAFAC and 0.0467 for lorazepam with PLS model at best pH. The protolytic equilibria of lorazepam at 25 ◦ C and ionic strength of 0.1 M have also been determined spectrophotometrically. Protolytic equilibria of lorazepam were evaluated by DATAN program using the corresponding absorption spectra-pH data. The obtained pKa values of lorazepam are 1.54 and 11.61 for pKa1 and pKa2 , respectively. © 2004 Elsevier B.V. All rights reserved. Keywords: Lorazepam; PARAFAC; PLS; DATAN; Pharmaceutical formulations; Biological fluids; Protolytic equilibria; Ultraviolet spectrophotometry

1. Introduction Lorazepam [1], 7-chloro-5-(2-chlorophenyl)-3-hydroxy2,3-dihydro-2H-1,4-benzodiazepin-2-one (Fig. 1), is one of the 1,4-benzodiazepine derivatives are most widely used for treatments of anxiety, relief of insomnia and sleep disturbances. They have sedative, hypnotic, muscle relaxant, anticonvulsant and amnesic properties [2]. Hence, the identification and quantitation of this drug in biological fluids can be of use in clinical toxicology and forensic medicine. Lorazepam is extensively metabolized to its inactive glucuronide conjugate; therefore only negligible amounts of free lorazepam are present in blood and excreted in urine. The mean half∗

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life of unconjugated lorazepam in human plasma is about 12 h and for its major metabolite, lorazepam glucuronide, about 18 h. At clinically relevant concentrations, lorazepam is approximately 85% bound to plasma proteins. Lorazepam is rapidly conjugated at its 3-hydroxy group into lorazepam glucuronide which is then excreted in the urine. The plasma levels of lorazepam are proportional to the dose given. There is no evidence of accumulation of lorazepam on administration up to 6 months. For this reason, a specific and sensitive analytical method is required especially in case of blood examinations, because of the low drug concentrations present in this matrix, unless a hydrolysis step is included. Several methods have been reported for the determination of benzodiazepines in various matrices using high-performance liquid chromatography (HPLC) [2,3], gas chromatography–mass spectrometry (GC–MS) [4,5],

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represented as follows:
aif bjf ckf + eijk Xijk =

Fig. 1. Chemical structure of lorazepam.

HPLC–MS [6], GC–tandem mass spectrometry [7] and voltammetry [8]. However, at moment, few methods have been developed for determination of lorazepam using ultraviolet spectrophotometry. Thus, with the increase of the production and consumption of drugs that employ lorazepam, it becomes interesting to develop new method for its determination. On the other hand, due to the sophisticated experimental designs and the increasing amount of data originating from modern instrumentation, the investigation of N-dimensional (or N-way or N-mode) data arrays has attracted much attention. Three-dimensional arrays may be generated by collecting data tables with a fixed set of objects and variables under different experimental conditions, such as sampling time, temperature, pH, etc. The tables obtained under various conditions can be stacked providing a cubic arrangement of data (a parallelepiped whose lines can be objects, whose columns, variables and whose slices, conditions). In many practical relevance situations even higher-dimensional arrays may be considered [9]. The data generated by hyphenated methods, having at least three dimensions, can be considered as one of the most suitable types of data for N-dimensional analysis. Parallel factor analysis (PARAFAC), is a multi-way method originating from psychometrics [10]. It is gaining more and more interested in chemometrics and associated areas for many reason; simply increased awareness of the method and its possibilities, the increased complexity of the data dealt with in science and industry, and increased computational power. PARAFAC, one of several decomposition methods for N-way data, is a generalization of principal component analysis (PCA) [11] to higher orders. It can be considered a constrained version of the more general method Tucker3 [9,12,13] with and identity core matrix. It is less flexible, uses fewer degrees of freedom and provides a unique solution independent of rotation. This last feature is a great advantage to the modeling of spectroscopic data. The true underlying spectra (or whatever constitute the variables) will be found if the data is indeed tri-linear, the right number of components is used and the signal-to-noise ratio is appropriated [10,14]. A PARAFAC model of a three-way array is given by three loading matrices, A, B and C, with elements aif , bjf and ckf (Eq. (1)), respectively (f = 1 − F principal components). The tri-linear model is found to minimize the sum of squares of the residues, eijk in the model [10,14], which is

(1)

where af , bf and cf are the fth columns of the loading matrices A, B and C, respectively. An important difference between the two-way PCA and multi-way PARAFAC is that the PARAFAC model is not nested. This fact means that the parameters of an F + 1 component model are not equal to the parameters of an F component model plus one additional component. The reason for this is that the components are not required to be orthogonal, hence independent. Therefore, every model has to be calculated specifically with all its components [10]. The algorithm used to solve the PARAFAC model is alternating least squares (ALS) [9,12]. ALS successively assumes the loadings in two modes and then estimates the unknown set of parameters of the last mode. The algorithm converges iteratively until the relative change in fit between two iterations is below a certain value (the default is 1 × 10−6 ). It is initialized by either random values or values calculated by a direct tri-linear decomposition based on the generalized eigenvalue problem [9]. Constraining the PARAFAC solution can sometimes be helpful in terms of the interpretability or the stability of the model. The fit of a constrained model will always be lower than the fit of an unconstrained model, but if the constrained one is more interpretable and realistic, this may justify the decrease in fit. The most often used constraints are orthogonality and non-negativity. The resolution of spectra used to require the non-negativity constraint since negative spectral parameters do not make sense [10,14]. The theory and application of PARAFAC in spectrophotometry have been discussed by several workers [10,15–20]. The basic principle of the multivariate calibration is the simultaneous utilization of many independent variables, x1 , x2 , . . ., xn , to quantify one or more dependent variables of interest, y. The partial least squares (PLS) regression analysis [21] is the most widely used method for this purpose, and it is based on the latent variable decomposition relating two blocks of variables, matrices X and Y, which may contain spectral and concentration data, respectively. These matrices can be simultaneously decomposed into a sum of f latent variables, as follows:
X = TP T + E = tf pf  + E (2)
uf qf  + F Y = UQT + F = (3) in which T and U are the score matrices for X and Y, respectively, P and Q the loadings matrices for X and Y, respectively, and E and F the residual matrices. The two matrices are correlated by the scores T and U, for each latent variable, as follows: uf = bf tf

(4)

in which bf is the regression coefficient for the f latent variable. The matrix Y can be calculated from uf , as Eq. (5), and the concentration of the new samples can be estimated from

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the new scores T* , which are substituted in Eq. (5), leading to Eq. (6) Y = TBQT + F

(5)

Ynew = T ∗ BQT

(6)

In this procedure, it is necessary to find the best number of latent variables, which normally is performed by using cross-validation, based on determination of minimum prediction error [21]. Application of PLS in spectrometry has been discussed by several workers [22–25]. In addition, several multicomponent determinations based on the application of these methods to spectrophotometric data have been reported [26–32]. In this paper, a method for determination of lorazepam in pharmaceutical formulations and biological fluids (urine and plasma) based on ultraviolet spectrophotometric measurements is proposed. The study was carried out in the pH range from 1.0 to 12.0 and with a concentration range from 0.50 to 8.75 ␮g ml−1 . Partial least squares (PLS) at different pH and PARAFAC were employed for ultraviolet spectra deconvolution and lorazepam quantitation. During the spectra deconvolution step by PARAFAC, core consistency diagnostic (CORCONDIA) procedure was used to determine the number of different species present in the data set. In PARAFAC quantitation, the sample factor loadings were used to establish a linear relationship with lorazepam concentrations and good results were obtained for samples at low ␮g ml−1 concentrations. Dissociation constants (i.e. pKa values) can be a key parameter for understanding and quantifying chemical phenomena such as reaction rates, biological activity, biological uptake, biological transport and environmental fate [33]. So, we were interested in obtaining acidity constants of lorazepam and also using their results in pH selection for PARAFAC data manipulation. The protolytic equilibria of lorazepam at 25 ◦ C and ionic strength of 0.1 M have been determined spectrophotometrically. DATa ANalysis (DATAN) program applied for determination of protolytic equilibria. Output of DATAN program is pKa values, number of principal components, concentration distribution diagrams and pure spectrum of each assumed species. The theory and application of the physical constraints method was discussed by Kubista et al., in several papers [34–40]. For the evaluation of the predictive ability of a multivariate calibration model, the root mean square error of prediction (RMSEP) and relative standard error of prediction (RSEP) can be used [41]:  n 2 i=1 (ypred − yobs ) RMSEP = (7) n  n 2 i=1 (ypred − yobs ) RSEP (%) = 100 × (8)  (yobs )2

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where ypred is the predicted concentration in the sample, yobs the observed value of the concentration in the sample and n the number of samples in the validation set.

2. Experimental 2.1. Reagents Lorazepam, acetic acid, phosphoric acid, boric acid, hydrochloric acid, potassium nitrate and sodium hydroxide were purchased from Merck. All the reagents were of analyticalreagent grade. Stock standard solution of lorazepam, 1000 ␮g ml−1 was prepared by dissolving the compound in methanol. This solution was stored in the dark at 4 ◦ C and was found to be stable for at least 4 weeks. It does not show any considerable changing in its spectral profile. All the solutions were prepared in deionized water. Universal buffer solutions in pH range from 1.0 to 12.0 were prepared by Ref. [42]. 2.2. Instrumentation and software A Hewlett-Packard 8453 diode-array spectrophotometer controlled by a computer and equipped with a 1 cm path length quartz cell was used for ultraviolet spectra acquisition. Spectra were acquired between 260 and 380 nm (1 nm resolution). A Metrohm 692 pH-meter furnished with a combined glass-saturated calomel electrode was calibrated with at least two buffer solutions at pH 3.00 and 9.00. The data were treated by an AMD 2000 XP (256 MB RAM) microcomputer using MATLAB software (version 6.5, The MathWorks). The N-way toolbox for Matlab version 2.1, available at http://www.models.kvl.dk/source, was employed for PARAFAC calculations, while PLS calculus was carried out by the PLS-Toolbox, version 2.0 (Eigenvector Technologies). 2.3. Procedure Known amounts of standard solutions were placed in a 10 ml volumetric flask and completed to the final volume with deionized water and universal buffer in pH range from 1.0 to 12.0. The final concentration of these solutions varied between 0.50 to 8.75 ␮g ml−1 for lorazepam. Commercial tablets form containing 1 or 2 mg lorazepam. 2.3.1. Sample (tablets formulation) preparation The pharmaceutical preparations assayed had the following composition per tablets: Chemidarou (Iran), 1 mg of lorazepam and Zahravi (Iran), 2 mg of lorazepam. Five tablets of each pharmaceutical formulation were weighed individually to an average weight. The tablets were finely powdered and mixed, and a mass corresponding to one tablet for each formulation was weighed and dissolved in 100 ml of methanol/water (10:90, v/v) in a volumetric flask. An aliquot of 50 ␮l of each sample was added into a cuvette contain-

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ing 2.0 ml of the respective buffer with the specified pH. The spectra were obtained in the same conditions described previously. All these determinations were performed in triplicate. 2.3.2. Analysis of urine samples Urine spiked with lorazepam was obtained by following procedure; an aliquot of pure lorazepam was added into 10 ml urine sample. A 1 ml of the resulting urine solution was mixed with 5 ml (0.2 M) sodium carbonate buffer and 10 ml butyl chloride. The mixture was rotated for 20 min and centrifuged at 2500 rpm for 10 min. The butyl chloride layer was separated and then evaporated till dryness [43]. Resultant residue was dissolved in universal buffer (at different pH) into a 10 ml volumetric flask and diluted to the mark with buffer solution. 2.3.3. Analysis of plasma samples Plasma spiked with lorazepam was obtained by diluting aliquots of the stock standard lorazepam solution with the human plasma. A 1 ml aliquot of this spiked solution was diluted to 5 ml with ethanol in 10 ml centrifuge tube. The precipitated protein was separated by centrifugation for 10 min at 2500 rpm. The clear supernatant layer was filtrated by Whatman filter to produce protein free-spiked human plasma [44], and then it was added into 10 ml volumetric flask and diluted to mark by universal buffer (at different pH).

ter are shown in Fig. 2. The principal component analysis of all absorption data matrix obtained at various pH shown at least three significant factors. This claim is, also, supported by the statistical indicators method that has been recently developed by Elbergali et al. [37], which has predicted three distinguishable components in the samples. These factors could be attributed to the two dissociation equilibria of lorazepam. The pKa values of lorazepam were investigated spectrophotometrically at 25 ◦ C and ionic strength of 0.1 M. Protolytic equilibria of lorazepam were evaluated by DATAN program using the corresponding absorption spectra-pH data. Output of DATAN program is pKa values, number of principal components, concentration distribution diagrams and pure spectrum of each assumed species. The pKa values of lorazepam were reported, pKa1 = 1.3 and pKa2 = 11.5, previously [45,46]. The first acidity constant corresponds to the protonation of the nitrogen in the azomethine group. However, both N H group and O H group were suggested to be potential deprotonation sites [45]. In this study, we obtained pKa values of lorazepam, 1.54 and 11.61 for pKa1 and pKa2 , respectively. The concentration distribution diagram and pure spectra are shown in Fig. 3.

3. Results and discussion 3.1. Determination of protolytic constants The electronic absorption spectra of lorazepam in water at various pH values at 260–380 nm intervals were recorded. Sample spectra of lorazepam at different pH values in wa-

Fig. 2. Absorption spectra of lorazepam at different pH values: (1) 0.81, (2) 1.23, (3) 1.87, (4) 2.03, (5) 2.67, (6) 3.12, (7) 3.88, (8) 4.65, (9) 5.73, (10) 6.69, (11) 7.74, (12) 8.65, (13) 9.23, (14) 10.83, (15) 11.14, (16) 11.26, (17) 11.56, (18) 11.87, (19) 12.41, (20) 12.83, (21) 13.16.

Fig. 3. (a) Distribution of major species of lorazepam as function of pH for the spectral data of Fig. 2. (b) The pure absorption spectra of different form of lorazepam, (1) cationic form, (2) neutral form and (3) anionic form.

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can reproduce the experimental data and it is given as:    I J K 2 ˆ (X − X ) ijk ijk i=1 j=1 k=1  fit (%) = 100 × 1 − I J K 2 X i=1 j=1 k=1 ijk (9) ˆ ijk the ijkth where Xijk is the ijkth experimental element and X element predicted by the model. The results are presented in Table 2. It is possible to note that this parameter is not conclusive for selection of the number of factors, since percentage of fit higher than 99% were obtained using from 3 to 5 factors. This parameter is important to identify if there are factors lacking in the model. Therefore, other more conclusive tools, such as CORCONDIA was used in this study. Fig. 4. Spectral data used in determination of lorazepam by PARAFAC, at pH = 1.01, 2.05, 6.02, 10.08 and 12.01.

3.2. Parallel factor analysis (PARAFAC) The main advantage of three-way multivariate calibration is that it allows concentration information of an individual component to be extracted in the presence of any number of uncalibrated constituents. Therefore, it is highly useful for solving analytical problems involving a complex matrix. Fig. 4 shows the experimentally obtained spectra of lorazepam at pH = 1.01, 2.05, 6.02, 10.08 and 12.01. The data was arranged in a three-way array 21 × 120 × 5, composed of 21 solutions, with different lorazepam concentrations (Table 1), in the rows, 120 wavelengths in the columns and 5 pH values in the slices. No preprocessing (centering or auto scaling) was applied to the data. When using PARAFAC, an initial definition of the number of factors to build the model is necessary. This choice is of fundamental importance because all conclusions about the deconvolution and quantitation results will be related with this number of factors. In PARAFAC, it is possible to use several constraints such as non-negativity, unimodality or orthogonality. In this work an unconstrained model was preferred as more realistic results can be obtained. Unconstrained PARAFAC models of the lorazepam data at different pH were developed using one to five components and the percentage of fit was used as the initial approach to select the number of factors. The percentage of fit value corresponds to how well the model

3.2.1. Core consistency diagnostic (CORCONDIA) All data set (21 × 120 × 5) was utilized for the core consistency evaluation, using one to five factors, with the values calculated according to Eq. (2). The core consistency diagnostic (CORCONDIA) is defined as: CORCONDIA  = 100 × 1 −

F F F

2 e=1 f =1 (gdef − tdef ) F F F 2 d=1 e=1 f =1 tdef



d=1

(10)

where gdef is the calculated element of the core using the PARAFAC model, defined by dimensions (d × e × f); tdef the element of a binary array with zeros in all elements and ones in the super-diagonal and F the number of factors in the model. In ideal PARAFAC model, gdef is equal to tdef and, in this case, CORCONDIA will be equal to 100%. The appropriate number of factors is accessed by the model with the highest number of factors and a valid value of core consistency diagnostic test. The analysis of the core consistency supports that three factors are necessary, because the utilization of more factors leads to a great decrease of the core consistency [19]. Three factors give a CORCONDIA value of 100% (a perfect trilinear model) whilst, when using four or more factors, this value diminishes to values below to 1%. The results are also shown in Table 2. 3.2.2. Deconvolution and calibration As presented in Section 3.2.1, three factors for unconstrained PARAFAC model furnished the best model for the deconvolution of the data. The decomposition of the three-

Table 1 Concentration data of the calibration and prediction set of lorazepam for PARAFAC and PLS models (␮g ml−1 ). Calibration

Concentration

Calibration

Concentration

Prediction

Concentration

C1 C2 C3 C4 C5 C6 C7

0.50 1.00 1.50 2.00 2.50 3.25 4.25

C8 C9 C10 C11 C12 C13 C14

4.75 5.50 6.00 6.75 7.25 8.00 8.75

P1 P2 P3 P4 P5 P6 P7

1.75 8.25 4.50 5.25 6.25 3.00 7.00

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Table 2 Fit values and core consistency diagnostic values in percentages vs. the number of components in the PARAFAC model Number of factors Fit (%) CORCONDIA (%)

1 92.14 100

2

3

4

5

94.86 82.11

98.78 48.56

99.82 0.69

99.89 0.47

Table 3 Statistical parameters of the linear relationship between the proportion loadings calculated by PARAFAC and the true concentration of lorazepam First loading of C-loading (first calibration) Number of data points Intercept Standard deviation of intercept Slope Standard deviation of slope Correlation coefficient* Standard deviation of regression ∗

14 0.1341 0.0214 0.5806 0.0042 0.9997 0.0406

Second loading of C-loading (second calibration) 14 0.0838 0.0147 0.2430 0.0029 0.9992 0.0279

Third loading of C-loading (third calibration) 14 −0.0308 0.0069 −0.1897 0.0013 0.9997 0.0131

P < 0.001 at 95% confidence level.

way data by PARAFAC gives rise to three loading matrices, one of which, C, corresponds to the sample mode. The Cloading are the relative concentrations of the lorazepam in the solutions. In the calibration step, these loadings are regressed against the real concentrations of lorazepam to get a linear calibration. By plotting these loadings (C-loading) versus real concentrations of lorazepam, three calibration curves obtained that are shown in Fig. 5. The average recoveries for the PARAFAC procedure were 100.7% for first calibration curve, 101.5% for second calibration curve and 114.3% third calibration curve. According to obtained results from these three

calibration curves, the first and second calibration curve is more suitable. Linear regression results and standard deviation of results, line equations and correlation coefficient are summarized in Table 3. In the prediction step, this regression line can then be used to predict the concentration of lorazepam in future test samples. The results obtained by applying PARAFAC to seven synthetic samples are listed in Table 4. Table 4 also shows the recovery for prediction series of lorazepam and root mean square error of prediction (RMSEP) and relative standard error of prediction (RSEP). The prediction results for lorazepam are very good.

Fig. 5. Calibration graphs for lorazepam: (a) first loading of C-loadings, (b) second loading of C-loading, and (c) third loading of C-loading.

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Table 4 Added and found results of the prediction set of lorazepam using PARAFAC method (␮g ml−1 ) Added lorazepam

First calibration

Second calibration

Third calibration

Found

Recovery (%)

Found

Recovery (%)

1.75 8.25 4.50 5.25 6.25 3.00 7.00

1.78 8.20 4.54 5.30 6.23 3.07 7.01

101.7 99.4 100.9 101.0 99.7 102.3 100.1

1.83 8.11 4.60 5.30 6.29 3.08 7.09

104.6 98.3 102.2 101.0 100.6 102.7 101.3

RMSEP RSEP

0.0429a 0.7728

a

Found

Recovery (%)

1.02 6.70 3.10 3.89 4.77 1.59 5.56

0.0883 1.5898

87.4 137.0 112.0 121.2 127.1 83.0 132.3

1.3626 24.5992

This value shows considerable superiority with respect to PLS method at different pH (Table 5).

3.3. PLS analysis 3.3.1. Calibration and validation The multivariate calibration is a powerful tool for determinations, because it extracts more information from the data and allows building more robust models. Therefore, it was decided to perform a multivariate calibration using PLS models built for each pH value individually and compare it with PARAFAC model. According to an experimental design (Table 1), 14 solutions were used to construct the models (calibration set) and another seven solutions to validate them (validation set). The models were validated using crossvalidation. The root mean square error of prediction (RMSEP) and relative standard error of prediction (RSEP) values were used as parameters for comparison among the models. 3.3.2. Selection of the optimum number of factors The optimum number of factors (latent variables) to be included in the calibration model was determined by computing the prediction error sum of squares (PRESS) for crossvalidated models using a high number of factors (half the number of total standard + 1), which is defined as follows: PRESS =




(yi − yˆ i )2

(11)

where yi is the reference concentration for the ith sample and yˆ i represents the estimated concentration. The cross-validation method employed was to eliminate only one sample at a time and then PLS calibrate the remaining standard spectra. By using this calibration the concentration of the sample, left out was predicted. This process was repeated until each standard had been left out once. One reasonable choice for the optimum number of factors would be that number which yielded the minimum PRESS. Since there are a finite number of samples in the training set, in many cases the minimum PRESS value causes overfitting for unknown samples that were not included in the model. A solution to this problem has been suggested by Haaland and Thomas [47] in which the PRESS values for all previous factors are compared to the PRESS value at the minimum. The F-statistical test can be used to determine the significance of PRESS values greater than the minimum. The maximum number of factors used to calculate the optimum PRESS was selected as 8 and the optimum number of factors obtained by the application of PLS models are summarized in Table 5. In all instances, the number of factors for the first PRESS values whose F-ratio probability drops below 0.75 was selected as the optimum.

Table 5 Added and found results of the prediction set of lorazepam using PLS method at different pH (␮g ml−1 ) PLS-PH1 (pH = 1.01)

PLS-PH2 (pH = 2.05)a

PLS-PH3 (pH = 6.02)

PLS-PH4 (pH = 10.08)

PLS-PH5 (pH = 12.04)

Found

Recovery

Found

Recovery

Found

Recovery

Found

Recovery

Found

Recovery

1.75 8.25 4.50 5.25 6.25 3.00 7.00

1.82 8.30 4.48 5.24 6.14 3.03 7.04

103.7 100.6 99.6 99.8 98.2 100.8 100.5

1.68 8.22 4.43 5.29 6.29 3.00 7.05

96.0 99.6 98.5 100.7 100.6 100.0 100.7

1.88 8.10 4.53 5.37 6.33 3.19 6.95

107.3 98.2 100.6 102.2 101.3 100.6 99.3

1.79 8.29 4.55 5.29 6.25 3.00 6.94

102.1 100.5 101.1 100.7 100.0 100.0 99.2

1.80 8.19 4.56 5.34 6.25 3.04 7.07

103.0 99.3 101.4 101.7 100.0 101.2 100.9

No. of factor RMSEP RSEP

2 0.0547 0.9857

Added

2 0.0467 0.8418

3 0.1364 2.4567

RMSEP = 0.0986 and RSEP = 1.7743. a Univariate calibration equation: A 2 (λ = 326) = 0.0064Clorazepam − 0.0008 (R = 0.9985).

3 0.0766 1.3806

4 0.0913 1.6448

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Table 6 Determination of lorazepam in pharmaceutical preparations using the PARAFAC and PLS-PH2 models Pharmaceutical preparations

Label claim (mg)

Amount Found (PARAFAC)

Recovery (%)

Amount found (PLS-PH2)

Recovery (%)

Chemidaroua

1 2

0.98 1.93

98.0 96.5

0.96 1.89

96.0 94.5

Zahravib a b

Tablet (from Chemidarou Ltd., Iran). Tablet (from Zahravi Ltd., Iran).

Table 7 Determination of lorazepam in urine and human plasma using PARAFAC and PLS-PH2 models (␮g ml−1 ) Type of samples

Added (ppm)

Amount found (PARAFAC)

Recovery (%)

Amount found (PLS-PH2)

Recovery (%)

Plasma sample 1 Plasma sample 2 Urine sample 1 Urine sample 2

0.90 3.50 1.50 6.00

0.77 3.31 1.42 5.71

85.6 94.6 94.7 95.2

0.72 3.21 1.31 5.17

80.0 91.7 87.3 86.2

3.3.3. Determination of lorazepam in synthetic solution The predictive ability of both two- and three-way models at each pH was determined using seven synthetic solutions (their compositions are given in Table 5). The results obtained by applying PLS at each pH to seven synthetic samples are listed in Table 5. Table 5 also shows the root mean square error of prediction (RMSEP) and relative standard error of prediction (RSEP). As can be seen, PLS model at PH2 is the best model. 3.4. Determination of lorazepam in pharmaceutical formulations and biological fluids In order to show the analytical applicability of the proposed methods, first calibration curve obtained from PARAFAC and PLS model at PH2 were applied to determination of lorazepam in real samples (pharmaceutical formulations) and complex matrices, i.e. urine and human plasma. The results showed that satisfactory recovery for lorazepam could be obtained (Tables 6 and 7) using the recommended procedures. Results of the determination are summarized in Tables 6 and 7. The data obtained by these methods reveal the capability of the methods for determination of lorazepam in real samples such as pharmaceutical formulations and complex matrices such as urine and plasma without considerable error. The average recoveries in pharmaceutical formulations (Chemidarou and Zahravi Tablets) and complex matrices (urine and human plasma) are summarized in Tables 6 and 7, respectively.

4. Conclusion In this work, we determined lorazepam in pharmaceutical formulations was accomplished based on ultraviolet spectrophotometry using PARAFAC and PLS calibration. The study was carried out in the pH range from 1.0 to 12.0 and with a concentration range from 0.50 to 8.75 ␮g ml−1 of lorazepam. Multivariate calibration models using PLS at differ-

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