Applications of Mexican Hat Wavelet Function to Binary Mixture Analysis

The simultaneous determination of pyridoxine hydrochloride (B6) and isoniazide (INH) in tablets was performed by using the Mexican hat wavelet function (MEXH). The absorption spectra of B6, INH and their samples were recorded in the spectral range of 200-330 nm. Linear regression functions for B6 and INH in the linear concentration range of 5-45 µ g/mL were obtained by measuring the transformed signals at 253.5 nm corresponding to the zero-crossing point for INH and at 270.6 nm corresponding to the zero-points for B6, respectively. The validation of MEXH method was performed by using the synthetic mixtures. The percent mean recoveries and their relative standard deviations were found as 98.7% and 2.06 for B6 and 98.9 % and 1.89 for INH in the synthetic mixture analysis. The MEXH method was applied to the real samples and a good sensitivity and selectivity was reported. The MEXH method was sucessfully compared with classical derivative method.

In recent years, the advancements in computer and information science, statistics with applied mathematics have caused the major changes of the content of the analytical chemistry.All these developments together with other factors offer a new possibility to chemists and pharmacists for the researches and analytical applications.A new sophisticated technology called hyphenated instrumentation such as the liquid chromatography-diode array detector system (LC-DAD), gas chromatography-mass spectrometry (GC-MS) and liquid chromatography-mass spectrometry (LC-MS) etc., has been used for the multicomponent determination.
The above enumerated sophisticated analytical methods require chemical separation step such as derivation, extraction and other chemical processes during analysis.In some specific cases, these analysis methods may not give better results for the multicomponent determination of active compunds in samples.At the same time, the related techniques having complex components bring high cost and time consumption.
The transformation of original absorption spectra has been widely used in the analytical chemistry for the quantitative resolution of mixtures containing active compounds.This method, called derivative spectrophotometr y, is based on the derivation of absorption spectra.However, one of the main problems of the derivative method is that the signal-to-noise ratio (S/N) becomes progressively worse as increasing the higher order.This influences the accuracy and precision of the analysis results.
In the analytical chemistry, the signals obtained from analytical instruments have been processed by using the wavelet transform or classical Fourier transform for compressing, to eliminate the noise effect or to improve the signal-to-noise ratio, and other chemical purposes [1][2].
Recently, the developments of the continuous wavelet transform (CWT) methods and their applications in the analytical chemistr y have significantly amplified the potential power of various spectral techniques.One promising way to eliminate the above mentioned problems is to apply the continuous wavelet transform for the quantitative analysis of multi-component mixtures without using a chemical separation step [3][4][5].
Very recently, the CWT methods in combination with zero-crossing and ratio spectra treatment in the analytical applications give reliable, sensitive, precise and accurate results for the complex mixture analyses [6][7][8][9].
The aim of this study is to develop and apply a new approach based on the combined use of CWT approach and zero-crossing technique for the resolution of the overlapping signal analysis and the simultaneous determination of INH and B6 in mixtures and commercial pharmaceutical tablets.This new approach is based on the measurements of the CWT amplitudes at the selected wavelength corresponding to a zero crossing point of wavelength.In our study various wavelet families with different scale parameters were tested and Mexican hat wavelet function (MEXH) was found to be more suitable than other wavelet family.
To compare MEXH-CWT approach, traditional derivative spectrophotometr y, which has different experimental conditions than the previous derivative method [10] was used for the quantitative resolution of the mixture containing INH and B6.The experimental results obtained were statistically compared with those obtained by the classical derivative method and good agreements were reported.

Experimental part Instruments and softwares
A Shimadzu UV-1601 double beam UV-V is spectrophotometer equipped with a fixed slit width (2 nm) connected to a computer loaded with Shimadzu UVPC software and a LEXMARK E-320 printer were utilized to record the absorption spectra.The absorption data were transformed to Microsoft EXCEL and transferred into wavelet domain.After that the transferred data vectors were processed by the proposed CWT approach.All data treatments, regressions and statistical analysis were performed within the EXCEL and Wavelet toolbox in Matlab 7.0 software.

Commercial tablet product
A commercial product (ISOVIT Ò tablet, Deva Pharm.Ind., Turkey, Batch no.5051087), containing 25 mg B6 and 100 mg INH per tablet, was analyzed by the proposed analytical methods.

Standard solutions
Stock solutions of INH and B6, (100 mg/100 mL), were prepared in in 0.1 M HCl.A standard series for each drug in the concentration range of 5-45 µg/mL in the same solvent was obtained from the above mentioned stock solutions.The synthetic mixture solutions were prepared as a validation set in the above working concentration range.The absorbance spectra were recorded with a sampling interval of ∆λ = 0.1 nm and at 1500 nm/min of scanning speed against a reagent blank (0.1 M HCI) and stored in the computer.

Sample solution preparation
20 tablets of commercial preparations selected were accurately weighed and powdered in a mortar.A quantity of the powder equivalent to one tablet was dissolved in 0.1 M HCl in 50 ml calibrated flasks.After a period of 30 min of shaking, the solution was filtrated and the residue was washed three times with 10 mL solvent and the volume was completed to 100 mL with 0.1 M HCl.The obtained solution was diluted to the working concentration range by using 0.1 M HCl.

Basic Tools
Wavelets are mathematical functions generated from one basic function by the dilatation (scale parameter) (W(Z) → W (2Z)) and translation (shift parameter) (W(Z) → W(Z+1)).Projection of a signal onto wavelet basis functions is called wavelet transform (WT).In a continuous transform, the mother wavelet corresponding to scale (a) and shift (b) is given as (1) The CWT of a given signal, f (λ) is given by the following equation: (2) where the superscript * represent the complex conjugate.
is a notation used for inner products or the projection of function f(λ) onto the wavelet function Ψa,b.
In the spectral wavelet signal processing , several wavelet families with different scale parameters are tested to find an optimal signal processing technique.The Mexican hat wavelet function (MEXH), which was found to be suitable in the present study, is given by the following formula (3) The graph corresponding to (3) is given in figure 1.

CWT and zero-crossing technique
If a binar y mixture of two analytes, X and Y is considered and if the absorbance value of this binary mixture is measured at λ i , the following equation can be written as (4) where A mix,λi is the absorbance of the binary mixture at the wavelength λ i , and the coefficients, α M,λi and β N,λi , are absorptivities of M and N analytes.C M and C N represent the concentrations of analytes.
If the CWT treatment is applied to (4), the following equation can be obtained as , (5) If CWT {β N,λi C N } = 0 then we obtain the following result , In equation ( 6), the CWT amplitude of M compound in its binary mixture depends only on the M compounds concentration and is independent on the N compounds concentration.After that, a calibration graph for the M compound can be obtained by measuring the CWT amplitudes corresponding to VWT{β M,λi , C N } = 0 .This procedure is repeated for N compound.Calibration functions obtained are used for the quantitative determination of the compounds in their mixtures.

Results and discussion
The absorption spectra of the standard series of INH and B6 drugs were plotted in the spectral range of 200-330 nm as depicted in figure 2. The spectra of the sample solutions containing the analyzed drugs were also registered in the above wavelength region.As it can be seen in figure 2, the quantitative determination of these two drugs, INH and B6, is not possible by using the direct absorbance measurements due to their overlapping spectra in the same spectral region.
The CWT approach does not need any optimization such as smoothing function, scaling factor and sampling interval (∆λ).In addition to this, this combined CWT method does not produce any problem like diminishing peak intensity in higher order derivative calculation as well as derivative spectrophotometry.
The purpose of this study was to offer a new possibility and perspective for the application of CWT method with zero-crossing technique to the simultaneous quantitative resolution of binary mixtures of INH and B6 drugs without using any separation step.

CWT method with zero crossing technique
The absorption spectra of the standard series and samples solutions in the linear concentration range mentioned in the standard solution section were recorded in the range of 200-330 nm and transferred to the wavelet domain.The obtained wavelet signals were subjected to all wavelet families available on Wavelet Toolbox in the Matlab 7.0 software and the optimally family was retained.The criteria for obtaining the optimal family are highest sensitivity and selectivity.As a result of this optimization procedure, the MEXH method with the scale parameter, a=150, was found to be the optimal CWT family.The obtained wavelet coefficients were plotted versus wavelengths and the Mexican hat wavelet function spectra were obtained (fig.3).
By using the CWT spectra, a zero-crossing technique was used to construct the calibration graphs.The CWT amplitudes at 253.5 nm for B6 corresponding to the zerocrossing point for INH and at 270.6 nm for INH corresponding to the zero-crossing point for B6 were measured to construct the linear regression analysis based on the relation between their peak amplitudes and concentration.
The linear regression analysis and their statistical results were presented in table 1.The results show those high correlation coefficients (r) and satisfactory slope, intercept, the limit of detection and the limit of quantitation provided by application of the MEXH (a=150) with the selected optimal zero-crossing points.This method was applied to the samples in the above mentioned optimized experimental conditions.

Classical derivative method
For a comparison of the CWT approach, classical derivative transform with the intervale of ∆λ= 5 nm and   In the case of this classical derivative method, two calibration graphs for INH and B6 were obtained by measuring the dA/dλ values at 255.6 nm corresponding to a zero-crossing point for B6 and at 269.8 nm, which corresponds to a zero-crossing point, for INH in the first derivative spectra of the original absorption spectra in the wavelength range of 210-230 nm, respectively.Calibration graphs obtained in the above steps were used for the quantitative evaluation of INH and B6 in samples.
Linear regression and its statistical parameters for both drugs were presented in table 1.When the calculated statistical parameters were observed for MEXH-CWT and classical derivative approaches, the slope values of MEXH-CWT were found bigger than those of classical derivative method.The limit of detection (LOD; signal-to -noise ratio of 3:1) and the limit of quantitation (LOQ; signal-to-noise ratio of 10:1) were calculated by using the data obtained from 6 replicates for standard solutions of 40 µg/mL INH and 10 µg/mL HCT.These results can be seen in table 1.

Method validation
In the method validation, the linearity of the calibration graphs of INH and B6 at the selected wavelengths for MEXH (a=150) and classical derivative approaches for both drugs was verified by high correlation coefficients (r) as shown in table 1.Ten replicate determination at the different concentration levels containing binary mixtures were used to test the precision of the proposed methods.The relative  The accuracy of the applied methods was tested by analyzing the above mentioned binary mixtures.The mean percentage recover y results were observed between 98.3 and 98.9 % (table 2).A good coincidence of the obtained experimental results was observed for the validation of the methods.
In the presence of the inactive ingredients (colloidal silicon dioxide, crospovidone, magnesium stearate and microcrystalline cellulose) in tablets, the analysis of the related compounds was performed by the proposed MEXH-CWT.In some cases, these inactive ingredients may cause a spectral interference.However, compounds may be decomposed due to the selected experimental conditions or the properties of substances.In our case, no degradation product, interference and systematical errors were observed during the analysis procedure.

Tablet analysis
In the analysis of the commercial tablet formulation, the Mexican hat wavelet function (a=100) was successfully applied to the quantitative determination of INH and B6 in commercial tablet formulation.The obtained experimental results for the commercial preparation were presented in table 3. Statistical values: mean value, SD (standard deviation), RSD (relative standard deviation), SE (statistical value), CL (P=0.05)(confidential limit) are summarized in table 3. The results obtained by applying the classical derivative method to the same tablet samples were given in the same table.As it can be seen a good coincidence observed in-between the experimental results obtained from the application of two proposed approaches to the tablet formulation.

Conclusions
In this study it was observed that the application of CWT approach to absorption spectra of INH and B6 in samples provided higher peak amplitudes, fewer noises, sharp peaks and does not produce any diminishing of signal intensity in transformation of signals as well as the derivative spectroscopy.On the other hand chemometric calibration technique posses abstract mathematical theory and difficult applicability such us calibration concentration matrix design that takes a period of time.However the algorithm of CWT is very fast, its application becomes simpler for researchers in the analytical applications.Besides, the proposed hybrid approach based on CWT with zero-crossing does not need any optimization such us scaling factors, sampling interval and smoothing function as well as derivative spectroscopy.In some cases classical derivative method get unsolvable problems due to the interference of main absorption bands with noise signals in higher derivative calculation.
Therefore we conclude that our hybrid approaches are more reliable and efficient for the resolution of overlapping spectra than classical derivative spectrophotometric methods.
It was conclude that the new combined CWT method can be applied successfully to the routine quality control of the commercial tablet formulation containing INH and B6 in tablets.

Table 1
LINEAR REGRESSION ANALYSIS AND THEIR STATISTICAL RESULTS

Table 3
COMMERCIAL TABLETS RESULTS BY THE PROPOSED APPROACHES (n=10)

Table 2
RECOVERIES OBTAINED BY APPLYING THE PROPOSED APPROACHES TO THE SYNTHETIC MIXTURES standard deviations were found between 1.08 and 2.85%, and these values demonstrate satisfactor y reproductibility of the methods as presented in table.2.