Ratio Spectra-Continuous Wavelet Transform and Ratio Spectra-Derivative Spectrophotometry for the Quantitative Analysis of Effervescent Tablets of Vitamin C and Aspirin

ERDAL DINC1*, DUMITRU BALEANU2,3 1 Department of Analytical Chemistry, Faculty of Pharmacy, Ankara University, 06100 Tandogan, Ankara, Turkey 2 Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Çankaya University, 06530 Ankara, Turkey 3 National Institute for Laser, Plasma and Radiation, Physics, Institute of Space Sciences, Magurele-Bucharest, P.O. Box, MG-23, R 76911, Romania

As it is known the wavelets were developed independently in the several fields [1,2].Continuous wavelet transform (CWT) methods together with their applications in the field of analytical chemistry as well as the related branches have increased the resolution power of the spectrophotometric methods for analysis of complex mixture systems.Recently, the CWT method, in combination with zero crossing and ratio spectra, was used for the resolution of the overlapping spectra and the quantitative analysis of mixtures [3,4,5].
In the analytical study, various graphical and numerical methods have been used for the simultaneous quantitative analysis of the mixtures containing two or more ingredients without any separation step.These methods contain some analytical disadvantages such us selectivity and sensitivity, namely these methods don't give correct results in some cases.CWT being flexible and versatile for the analytical purposes gives a good resolution of the above mentioned inconvenient problems.
As it was pointed out recently, the wavelet method in combination with zero-crossing and ratio spectra treatment give reliable, sensitivity precision and accurate results for the complex mixture analyses [3][4][5][6].
A combination of VC and ASP compounds are used for pain and fever relief in the pharmaceutical preparations.The content of VC and ASP drugs have been analyzed simultaneously by LC [7,8].The investigated active compounds in combination with other compounds were analyzed by differential spectrophotometr y [9], spectrofluorimetry [10], HPLC [11,12], potentiometry [13], derivative spectrophotometry [14,15], voltametry [16], double divisor ratio spectra-derivative method [17] and by using the zero crossing technique with CWT and derivative spectrophotometry and partial least squares approach [18,19].
The goal of this study is to develop and apply a new approach based on the combined use of ratio spectra with CWT and derivative spectrophotometry for the resolution of the overlapping spectra and simultaneous determination of VC and ASP in mixtures and commercial effervescent tablets.In this paper, the combined use of ratio spectra with CWT and DS is based on the measurements of the ratio-CWT and ratio-DS signals at the points corresponding to the maxima and minima corresponding to the zerocrossing point other compound.RS-CWT and RS-DE were validated by analyzing the synthetic mixtures of VC and ASP and by taking into account the standard addition technique.
The proposed signal processing methods were successfully applied to the quantitative analysis of effervescent tablets consisting of VC and ASP and a good coincidence was found.

Experimental Part Apparatus and software
In this study, a Shimadzu UV-160 double beam UV-VIS spectrophotometer with a fixed slit width (2 nm) having Shimadzu UVPC software and a LEXMARK E-320 printer were used for the registration of the absorption spectra of VS and ASP, and their samples.All data treatments, regressions and statistical analysis were processed by using the EXCEL and the Wavelet toolbox in Matlab 7.0 software.

Commercial effervescent tablet
A commercial effervescent tablet formulation (ASPIRIN ® Plus C effervescent tablets produced by Bayer Drug Industry, Istanbul-Turkey) consisting of 240 mg VC and 400 mg ASP per effervescent tablet were analyzed by using RS-CWT and RS-DS methods.

Standard solutions
Stock solutions of VC and ASP were prepared by dissolving 25 mg of each compound in 50 mL volumetric flask within 0.1M HCl.Calibration solutions of VC and ASP in the linear concentration range 4-20µg/mL were obtained from the above stock solutions for both CWT and DS application.An independent validation set of 10 binary mixture containing two compounds in the above concentration range was also prepared by using the same stock solutions.For the standard addition technique, the solutions at three different concentration levels for six replicates, adding the stock solutions to tablet solutions, were prepared to control the excipient effect on the analysis.

Sample solution preparation
Ten effervescent tablets were weighted and powdered in a mortar.A half tablet amount was transferred to a 50 mL volumetric flask and its volume was completed with 0.1M HCl after stirred until effervescence tablet particles dissolved completely.The prepared solutions were filtered with 0.2 µm disposable membrane filter (Sartorious, minisart) by using an injector.The final solution was diluted to the calibration concentration range in order to apply RS-CWT and RS-DS methods.This sample preparation was repeated ten times.

Results and discussions
During the last decade the wavelet approach become a very useful tool in the field of the analytical chemistry as well as in various branches of science and engineering.Particularly, for the chemometric applications, the method has been successfully applied for denoising and compressing mainly for the spectrophotometric signals as well as for other types of signals.
Let us assume that we start with a mother wavelet ψ(λ).By making use of the dilatation and the shifting of ψ(λ), we obtain a set of functions ψ a,b (λ) , namely [1] (1 where a is entitled the scale parameter and b is the translation parameter. As a result the CWT of a given analyzed signal f (λ) is defined as (2) Here, the superscript * means the complex conjugate and is the inner product of function f (λ) onto the wavelet function ψ a,b (λ).In this study we applied BIOR1.5 continuous wavelet transform.

Ratio spectra method
In the spectrophotometric quantitative analysis, if the absorbance value of the binary mixture containing two analytes, X and Y is measured at λ i , then we obtain (3) where Am λi is the absorbance of the binary mixture at wavelength λ i , and the coefficients αX,λi and βY,λi denotes absorptivities of X and Y compounds.C X and C Y denote the concentrations of compounds.
If ( 3) is divided by the spectrum of a standard solution (C o x ) of one of compounds in binary mixture, we obtain (4)

Ratio spectra CWT-zero crossing approach
If CWT is applied to (4), the following equation is obtained as (5) Assuming that , we obtain (6) The calibration graphs can be obtained by plotting signals against the concentration of C Y .This analogous procedure is repeated for both compounds in the binary mixture.

Method development and application
Absorption spectra of VC and ASP in the linear concentration range of 4, 8, 12, 16 and 20 µg/mL and effervescent tablet sample were plotted in the wavelength region of 200-310 nm as shown in figure 1.As it can be seen,the simultaneous determination of both compounds in binary mixtures is not possible from the direct use of the zero order absorption spectra.In order to overcome this analytical problem, the combined use of ratio spectra with CWT and DS methods was proposed for the simultaneous determination of VC and ASP in their binary mixtures and commercial effervescent tablets.The application of both methods will be explained below.

Ratio spectra procedure
Ratio spectra of VC and ASP, and their samples were obtained by dividing the absorption of VC and ASP, and their binary mixture by the absorption spectra of 12 µg/ mL ASP and VC, respectively, in the spectral region 205.0-307.3nm for the VC analysis by RS-BIOR1.5CWT, in the Ratio spectra-continuous wavelet transform By using the above ratio spectra, various continuous wavelet families have been tested and Biorthogonal 1.5 CWT (BIOR1.5)at a=64 was retained to be suiatible for the smultaneous determination of the concentration of VC and ASP in binary mixture.
BIOR1.5 CWT was applied to the unsmoothed ratio spectra of VC and ASP, and their effervescent tablet shown in figure 2A and figure 3A.Their BIOR1.5 CWT spectra were obtaied as indicated in figure 2B and figure 3B.By using BIOR1.5 CWT, the calibration graphs for VC and ASP were obtained by reading the BIOR1.5-CWTamplitudes at 260.8 nm for VC and 234.6 nm respectively.
Linear regression analysis and coresponding statistical results were presented in table 1. VC and ASP in samples were determined by the above calculated calibration line.

Ratio spectra-derivative spectrophotometry
Unsmoothed ratio spectra of VC and AS, and their effervescent tablet, shown in figure 2A and figure 3A, were calculated by using D 2 and D 1 divisors, respectively.The obtained ratio spectra were smoothed with the interval of ∆λ=5 nm in the wavelength range 200-300 nm for VC and in the spectral region 200.0-260.0nm for ASP as ilustrated in figure 4A and figure 5A.
First derivative of the smoothed ratio spectra was obtaied by using ∆λ=5 nm as indicated in figure 4B and figure 5B.The calibration graphs of VC and ASP were calculated by measuring the ratio-first derivative amplitude at 256.0 nm for VC and 230.7 nm for ASP, respectively.
The linear regression analysis and the corresponding statistical results are given in table 1.The obtained calibration equations were used for the dedermination of the amounts of VC and ASP in samples.

Method validation
The correlation coefficients (r) for the calbration equations were presented in table 1 indicate a good linearity in the concentration range of 4-20 mg mL -1 for both VC and ASP.The precision of the proposed methods was obtained by analyzing 10 mixture solutions by the stock solutions.Percentage recoveries and their corresponding relative standard deviation (RSD) values for the precision were depicted in table 1.The limit of detection (LOD:signal/ noise=3:1) and the limit of quantitation (LOQ:signal/ noise=10:1) were obtaied by using the standard deviation of intercept of the calibration lines and illustrated in table 1.
The standard addition technique was used to investigate the effect of excipients for the determination of the     deviation, relative standard deviation, relative standard error and the mean percent recovery were shown in table 3. It was observed that no excipients interferences exist in the analysis.

Analysis of the commercial effervescent tablets
The quantitative determination of VC and ASP in commercial effervescent tablets was acomplished by the proposed RS-CWT and RS-DS methods.The obtained determination results for the commercial preparation were presented in table 4.
Statistical values: mean value, SD (standard deviation), RSD (relative standard deviation), SE (statistical value), CL (P=0.05)(confidential limit) are summarized in table 4. A good coincidence was observed in between the determination results in application of RS-CWT and RS-DS methods to tablets.

Conclusions
In this paper we proposed a new and fast combined use of CWT and DS with the graphical method ratio-spectra approach in order to investigate the simultaneous determination of VC and ASP in samples.By analyzing the statistical parameters we conclude that our new method is suitable for the routine quality control of the commercial effervescent tablet formulation of mixtures containing VC and ASP.The results obtained in this manuscript are comparable with ones reported in [20] by using the firstderivative spectrophotometric method.

Table 1
CALIBRATION DATA OBTAINED BY THE LINEAR REGRESSION ANALYSIS

Table 3 STATISTICAL
RESULTS OBTAINED BY USING THE STANDARD ADDITION TECHNIQUE WITH THE PROPOSED METHODSmg/effervescent tablet (*)