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Current Analytical Chemistry, 2014, 10, 574-580
Radial Basis Functions-Partial Least Squares for Simultaneous Determination of Ethinylestradiol and Levonorgestrel Masoud Shariati-Rad1*, Mohsen Irandoust1, Tayyebeh Amini1 and Farhad Ahmadi2 1
Department of Analytical Chemistry, Faculty of Chemistry, Razi University, Kermanshah, Iran; 2Department of Medicinal Chemistry, Faculty of Pharmacy, Kermanshah University of Medical Sciences, Kermanshah, Iran Abstract: Resolution of complex binary mixtures of Ethinylestradiol (ST) and Levonorgestrel (LEV) was successfully achieved with minimum sample pre-treatment and without analyte separation. The work is based on the radial basis functions-partial least squares (RBF-PLS) analysis of UV spectral data. For calibration and external test sets, binary mixtures were rationally designed. The results for modeling and subsequent prediction in external test set samples resulted in Q2 values of 94.1 and 99.4% for ST and LEV, respectively. The RBF-PLS models were then successfully applied to determine the analytes in real samples consisting of pharmaceutical preparations. In the analysis of the real samples, we excluded the spectral regions where the unknown interferences are absorbed and matrix effect exists. The mean recoveries for the real samples were between 90.6 and 106.8%. The estimated precisions of the method in terms of RSD% were in most cases below 4%.
Keywords: Ethinylestradiol, levonorgestrel, radial basis functions-partial least squares, UV spectroscopy, design, spectral interference. 1. INTRODUCTION Ethinylestradiol (ST) is a semisynthetic estrogen female sex hormone and levonorgestrel (LEV) is a synthetic steroid with an extremely potent progestational action. Structures of these compounds are shown in Scheme 1. Some analytical methods including colorimetry [1-3], UV-spectrophotometry [4-6], and fluorimetry [7,8] and voltammetry [9] have been developed for quantitative determination of relatively small amounts of individual steroid hormones in oral contraceptives. On the other hand, several techniques including reverse phase high-performance liquid chromatography (RP-HPLC) [10-13], derivative spectrophotometry [14, 15], micellar electrokinetic chromatography (MEKC) [16] and liquid chromatography–mass spectrometry (LC–MS) [13, 17-19] have been reported for the simultaneous determination of levonorgestrel and ethinyloestradiol in oral contraceptives used. However, most of these methods belong to the timeconsuming and costly methods of chromatography. These analytical methods have very good sensitivity and the capacity to determine many similar compounds together even in highly complicated matrices, but they are expensive and thus not available for many laboratories. Notwithstanding the existence of few reports on the simultaneous determination of LEV and ST in pharmaceutical preparations using spectrophotometric methods [5, 6, 14, 15], the presence of matrix effect in the analysis of real
pharmaceutical samples has not been considered. In fact, the applied spectrophotometric methods are not able to determine the drugs in the presence of matrix effects. On the other hand, the results of application of derivative methods will accompany by bias in the presence of matrix effect. The presence of matrix effect has not been studied and handled in the reported derivative spectroscopic methods [5,14]. We successfully report here the application of radial basis functions-partial least squares (RBF-PLS) in simultaneous determination of LEV and ST using spectrophotometric data. 2. THEORY 2.1. Radial Basis Functions-Partial Least Squares (RBFPLS) In RBF-PLS [20, 21] instead of applying PLS to the X and y containing the initial data, it can be applied to the matrices A and y, where A is the so called activation matrix. The elements of A are defined as: (1) where xi is a vector containing the values of the variables taken from the ith object (ith mixture), aij is the element of A at ith row and jth column, is the norm which denotes here the Euclidean distance, cj and σj are the center and width of the jth RBF hidden unit, respectively which are presented as: (2)
*Address correspondence to this author at the Department of Analytical Chemistry, Faculty of Chemistry, Razi University, Kermanshah, Iran; Tel: +98 831 4274559; Fax: +98 831 4274559; E-mail:
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RBF-PLS in Determination of ST and LEV
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Scheme 1. Structures of levonorgestrel and ethynylestradiol.
where e is an assigned positive number. Thus the resulting symmetrical matrix A has ones on its diagonal. Then, the PLS procedure will be applied to the matrices A and y in a similar way as linear one. By combining PLS algorithm with RBF network, the nonlinear relation between X and y is transformed to problem in linear algebra. After training, the RBF-PLS network can be used to make predictions on new observations (4) where Aunk is the activation matrix of Xunk which is used for prediction, yunk is the resulting dependent matrix. 2.2. Statistical Measures of RBF-PLS Model Quantitatively, all model performances of RBF-PLS are expressed in terms of root mean square error of crossvalidation (RMSECV), root mean square error of prediction (RMSEP), and cross-validated correlation coefficient (Q2) [22]: (5) (6) (7) In all these expressions, ci, cˆi , cmean are the real and predicted concentration of the component, and mean of the real concentrations, respectively. It must be mentioned that ci and cˆi in Eq. (1) are those in calibration set and ci , cˆi , and cmean in Eqs. (2) and (3) are those in validation set. m and n are the number of the samples in the calibration and validation sets, respectively. RMSECV was calculated in a leave-one-out approach. The F statistic was used to make the significance determination of the number of LVs and to avoid over-fitting [23]. 3. EXPERIMENTAL 3.1. Reagents, Stock Solutions and Commercial Tablets All experiments were performed with analytical grade chemicals acquired as gift samples from Bakhtar Biochimi Co. (Kermanshah, Iran) and water was double distilled. Stock 100 mg L-1 solutions of LEV and ST were prepared by
exact weighing and dissolution of the drugs in methanolwater (20:80, v/v) mixture. Working solutions were prepared daily. Commercial “HD tablets (high dose)” declared to contain 0.25 mg LEV and 0.05 mg ST and “LD tablets (low dose)” to contain 0.15 mg LEV and 0.03 mg ST were acquired from Bakhtar Biochimi Co. (Kermanshah, Iran) also available in local drugstores. Standard addition calibration solutions in the studied concentration ranges were obtained by appropriate addition of the above standard solutions to the solutions of HD and LD tablets. 3.2. Apparatus, Hardware and Software All spectrophotometric measurements were carried out with an Agilent 8453 UV-Vis spectrophotometer (SantaClara, CA, 95051, United States) with diode array detector connected to a computer equipped with ChemStation software. Samples were measured in a quartz cell of 10 mm path-length. Spectra were acquired with a fixed slit width of 2 nm, over the wavelength range 200–350 nm at intervals of 1 nm. The treatment of the absorption spectral data was performed by using MATLAB 6.5 software (MATLAB 6.5, The Mathworks Inc., Natick). RBF-PLS multivariate calibrations were performed using a series of m-files written in MATLAB environment [20]. 3.3. Analysis of Tablet Formulations Separately, ten tablets of each HD and LD were accurately weighed, ground to fine powder and a sample of the powder equivalent to the average weight of a tablet was transferred into a 10 mL volumetric flask and solved and diluted to the volume with methanol-water (20:80, v/v) mixture. In order to dissolve the powders, the mixtures were sonicated for 15 min followed by shaking by mechanical means for 20 min. The mixtures were then filtered. A 4 mL aliquot of the filtrate was placed in a 10 mL volumetric flask, completed to the mark with the solvent and mixed. This sample was then submitted for the analysis. 3.4. Designing the Synthetic Binary Mixtures 27 synthetic binary mixtures were prepared by appropriate mixing and subsequent dilution of volumes of stock solutions of drugs in 25 mL flasks ensuring that the final concentrations lied in the linear ranges of the corresponding univariate calibration curves. All the samples were
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then submitted for analysis under the conditions described in the “Apparatus, hardware and software” section. The compositions of the 35 binary mixtures have been included in Table 1. The mixtures were designed based on the central composite design with star points outside the specified minimum and maximum of the analytes in the mixtures. Minimum and maximum analytes considered in designing the mixtures are 4.0 and 12.0 mg L-1 for LEV and 0.6 and 2.4 mg L-1 for ST. Moreover, in order to construct a more robust calibration model, we decided to repeat some mixtures specially those in the vicinity of the design.
Table 1.
4.1. Electronic Absorption Spectra In Fig. (1), the spectra of LEV and ST in the wavelength range of 200–350 nm are shown. It can be seen that the absorption spectra of LEV and ST are highly overlapped. The determination of ST directly could be easy at the start, but the small content of this steroid and the high content of LEV in commercial tablets (the ST: LEV ratio is normally 1:5) presume a large contribution of the spectrum of LEV to the maxima in the spectrum of ST. The broad spectrum of LEV shows only a maximum at 246 nm. The ST spectrum shows a maximum at 203 nm and another at 279 nm. This latter band is very weak.
Designed binary mixtures of ST and LEV. Concentrations are in mg L-1. No.
ST
LEV
1
2.4
6.0
2
0.6
12.0
3
2.0
4.0
4
2.0
6.0
5
2.0
10.0
6
1.2
8.0
7
2.0
12.0
8
1.6
10.0
9
0.6
4.0
10
1.6
10.0
11
1.6
4.0
12
2.0
8.0
a
2.0
6.0
14a
1.2
10.0
15a
1.2
8.0
16
a
1.2
8.0
17
a
1.2
8.0
18a
1.6
10.0
19
0.4
14.0
20
1.2
10.0
21a
2.0
10.0
22
2.4
2.0
a
2.6
6.0
24
1.2
8.0
25
1.6
6.0
26
0.6
2.0
27a
1.2
6.0
13
23
a
4. RESULTS AND DISCUSSION
Mixtures used in external test set
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Fig. (1). Spectra of LEV (19 mg L-1) and ST (12 mg L-1) in methanol-water (20:80, v/v) mixture.
4.2. One Component Univariate Calibration In order to find the linear dynamic range for each compound and the slope of the variation of absorbance with concentration, possible concentration levels of the related compounds were tested. Individual calibration curves were constructed with more than 20 points as absorbance versus drugs concentrations in the dynamic linear ranges and were evaluated by linear regression [24]. Statistical results of the univariate calibration for ST and LEV have been reported in Table 2. 4.3. Method Development The spectra of real samples after dissolution of the tablets and filtration show differences with the mixtures synthesized by probably identical concentrations. These have been shown in Fig. (2). As can be seen in Fig. (2), the differences are specially noticeable in the wavelength range of 200-240 nm. In order to perform analysis with lower influence from unwanted effects, we decided to use the spectral region of 245-350 nm for the analysis of ST and 245-285 nm for LEV. In the selection of these regions, the maximum absorbances of the analytes Fig. (1) have also been accounted. Moreover, we wanted to show the ability of nonlinear method of RBF-PLS in prediction when spectral interferences are present with some matrix effect. It is known that PLS as a first-order linear multivariate method cannot predict when matrix effect exists. 4.4.Determination of ST and LEV in Synthetic Mixtures For simultaneous determination, 18 calibration and 9 external test samples containing LEV and ST (Table 1) were analyzed by RBF-PLS. In order to evaluate the performance of the RBF-PLS models, the 9 external test samples were considered in the validation set. Division of the samples into calibration and validation sets was carried out by KennardStone algorithm [25]. In the designed mixtures, the amount of LEV was at least twice that of ST. The concentration of the analytes lies in their known linear absorbanceconcentration ranges.
The spectrum of each standard mixture was recorded in the wavelength range of 210 to 350 nm with 1 nm intervals. Therefore, after selection of wavelength regions based on the previous section, the X matrices for calibration are of 18×106 and 18×41 dimensions and for prediction are of 9×106 and 9×41 for modeling of ST and LEV, respectively. As data pre-treatment, all UV spectra were auto-scaled before RBF-PLS modeling. The calibration stage of multivariate chemometric methods is followed by a prediction step, in which the results of the calibration model are used to determine concentration of the components in the external test set from their multivariate signals. The statistical parameters found upon application of the PLS to calibration and external test sets are given in Table 3. High Q2 and low RMSECV and RMSEP values indicate the validity of the multivariate calibration and the analytical method. The high quality of the models was evident from the Q 2 value which is a parameter indicating predictive ability of the model. As shown in Table 3, the RBF-PLS models explained more than 94% of the variation in the y (Q 2 values). Predictive ability for LEV is excellent (Q 2 = 99.4%). Number of latent variables is higher for modeling of ST. 4.5. Determination of ST and LEV in Commercial Contraceptives The method developed was applied for the estimation of LEV and ST in pharmaceutical preparations. The calibration models were validated for accuracy and precision with five times determination of tablets contents. The precision is expressed as the RSD%. The percentage of recoveries and other statistics have been presented in Table 4. As the data in Table 4 show, the amounts of drugs found by PLS method were within the range of 90.6106.8% relative to the declared contents. The recoveries were better for ST in the analysis of LD tablets. This can be clear when we refer to Fig. (2). It can be seen that matrix effect is more intense in HD tablets.
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Table 2.
Shariati-Rad et al.
Statistical parameters of the univariate calibration of ST and LEV. Parameter
ST
LEV
Wavelength (nm)
210
245
Number of points
23
23
Linear range (mgL )
0.3-30
0.3-30
Intercept
5.1×10-3
5.3×10-3
Slope
4.0×10-2
5.6×10-2
Limit of detection (mgL-1)a
1.08×10-2
1.20×10-2
Limit of quantification (mgL-1)a
3.60×10-2
4.00×10-2
Coefficient of determination (R2)
0.999
0.999
-1
a
They were calculated based on the definitions in [24].
Fig. (2). Spectra of real HD and LD tablets and synthetic mixtures of LEV and ST with amounts identical to the real pharmaceutical samples in methanol-water (20:80, v/v) mixture. Table 3.
Statistical parameters obtained by application of RBF-PLS to calibration and test sets data. Analyte
σ
LV
RMSECV
RMSEP
Q2
ST
0.88
13
0.023
0.117
0.941
LEV
0.75
6
0.117
0.129
0.994
Precision of the method described by RSD% was good. Similar to the results of recovery, precision of the method in determination of ST and in the analysis of LD is better. As for prediction in external test set, LEV has been predicted with more accuracy. 4.6. Comparison with Spectrophotometric Methods In order to validate the obtained results, literatures for determination of the studied analytes and related ones based on spectrophotometric methods were explored. Two reports
were chosen. The results of the methods upon application to real pharmaceutical samples have been collected in Table 5. We decided to compare methods with a view to accuracy (Recovery %) and precision (RSD %). As data in Tables 4 and 5 show, precision of our method is comparable with those in the literatures especially for LEV in both analyzed tablets and two analytes in LD tablets. In terms of accuracy, using RBF-PLS leads to better results compared with those obtained by PLS and PCR. Though the second report in Table 5 is for different drugs
RBF-PLS in Determination of ST and LEV
Table 4.
Current Analytical Chemistry, 2014, Vol. 10, No. 4
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Results of application of RBF-PLS to real pharmaceutical samples. HD Tableta Declared Amount
Found
Recovery%
RSD%
ST
0.5
0.534
106.8
6.58
LEV
2.5
2.264
90.6
1.23
LD Tableta
a
ST
0.3
0.296
98.7
3.39
LEV
1.5
1.415
94.3
1.14
Results are for five times determination of real samples.
Table 5.
Comparison of formulations analysis by different methods. Analyte
Recovery%
RSD%
Reference
ST
97-117
1.17
[6]
LEV
98-107
0.408
ST
91-110
1.08
LEV
99-106
0.467
Estradiol valerate
96.0-104.8
2.44
Cyproterone acetate
98.4-101.9
1.49
Estradiol valerate
99.5-103.0
1.21
Cyproterone acetate
99.0-101.0
0.54
Estradiol valerate
99.5-102.2
0.71
Cyproterone acetate
98.8-101.0
0.69
PLS
PCRa
First derivative [26]
CLSb
ILSc
a
. Principal component regression. . Classical least squares. . Inverse least squares.
b c
from this group [26], comparison of the results can be valuable. The method of first derivative, classical least squares (CLS) and inverse least squares (ILS) have been used. In most cases, accuracies are good (Recoveries % are close to 100). However, in the corresponding reference [26], there is no discussion about the matrix effect and interferences. It is known that multivariate methods like CLS and ILS can’t perform well in the presence of matrix effect and unknown interferences. It can be concluded that in simultaneous determination of estradiol valerate and Ccyproterone acetate, no matrix effect is present. This can be accounted for percent recoveries close to 100 for the results [26].
5. CONCLUSION RBF-PLS was found to be useful in multicomponent determination even when some matrix effect exists. The proposed method is suitable for the simultaneous determination of ST and LEV and can be employed to analyze commercial formulations of low-dose oral contraceptives. Compared to other procedures available for this simultaneous determination like HPLC, the proposed method is characterized by minimum sample pre-treatment. It therefore provides a fast, accurate and convenient alternative for the simultaneous determination of the analytes in routine quality control of their pharmaceutical formulations. The proposed method could be regarded as a useful alternative to the
580 Current Analytical Chemistry, 2014, Vol. 10, No. 4
Shariati-Rad et al.
chromatographic techniques (HPLC) in the routine quality control of pharmaceutical formulations, allowing quantitative information to rapidly be achieved with a relatively inexpensive instrumentation.
[12]
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CONFLICT OF INTEREST The authors confirm that this article content has no conflict of interest. ACKNOWLEDGEMENTS The authors acknowledge the Razi University Research Council for support of this work.
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Revised: September 17, 2012
Accepted: December 12, 2012
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