Continuous Wavelet Transform Methods for the Simultaneous Quantification of Brimonidine Tartrate and Timolol Maleate in an Eye Drop Formulation

Instrument and Software

The UV absorption spectra data were obtained using Shimadzu UV-2520 double beam UV–Vis spectrophotometer connected to a computer loaded with UV Probe 2.32 software. The spectra of the calibration and validation samples were plotted with the intervals of Δλ= 0.1 nm in wavelength range of 220.0-340.0 nm. Microsoft EXCEL and Wavelet toolbox in Mat lab software (The Math Works, Natick, MA, USA) were used for the spectral data treatments and statistical calculations.

Pharmaceutical Ophthalmic Dosage Form

Stock solutions of both compounds separately were prepared by dissolving 10 mg BRI and 10 mg TIM in a volume of 100 mL in methanol. The calibration samples of BRI and TIM in the concentration ranges 5.0-25.0 µg/mL and 8.0-72.0 µg/mL were prepared by diluting stock solutions. For the method validation processes, 11 different synthetic mixtures containing BRI and TIM in the working concentration ranges were prepared from the above stock solutions. Inter-day and intra-day studies containing BRI and TIM at three different concentration levels (low: 6 µg/mL, medium: 15 µg/mL and high: 24 µg/mL for BRI and low: 10 µg/mL, medium: 40 µg/mL and high: 70 µg/mL for TIM) were freshly prepared. Standard addition samples containing three different levels for BRI and TIM; low: 6 µg/mL, medium: 12 µg/mL and high: 16 µg/mL and low: 8 µg/mL, medium: 30 µg/mL and high: 40 µg/mL, were prepared, respectively. All samples were prepared in methanol during this study.

Preparation of Commercial Eye Drop Samples.

A 1.0 mL of commercial eye drop sample was transferred into a 50 mL calibrated flask and then the volume was made up to 50 mL with methanol. The content of the sample was sonicated for about 10 min and then the solution was filtered through a 0.45µm Sartorius Minisart membrane filter. The similar sample preparation was repeated 10 times for the analysis of the commercial eye drop samples.

CWT Application to the UV Spectra Data

The absorption spectra of the calibration solutions of BRI and TIM in the range of 5.0-25.0 µg/mL, 8.0-72.0 µg/mL were recorded between 220.0-340.0 nm as indicated in Figure 1a. As it can be seen in this figure 1a, the absorption spectra of BRI and TIM over the range of 220.0–340.0 nm overlap with each other. To overcome this problem, we applied new signal processing methods (the CWT methods) to the raw UV data vectors obtained from the UV absorption spectra of BRI and TIM for the calibration samples, synthetic mixtures, intra-day and inter-day samples, standard addition samples and commercial eye drop samples. In practice, we tested several wavelet families for the find suitable signal processing approach to reach the highest recovery results of the simultaneous quantification of BRI and TIM in eye drop samples. After these experiments, we decided that two wavelet families, sym5 and mexhwavelet tools for the quantitative estimation of the analyzed drugs.

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Figure 1a: UV spectra of BRI and TIM of the calibration samples, b) the mexh-CWT spectra and c) the sym5-CWTspectra.

The chosen sym5-CWT and mexh-CWT methods were applied to the UV spectral vectors of the calibration samples in the 220.0-340.0 nm wavelength regions and the sym5-CWT and Mexh-CWT spectra were obtained by plotting the CWT-coefficients against the wavelength. Figure 1b and c shows the sym5-CWT and mexh-CWT spectra, respectively. In the application of the mexh-CWT method, calibration graphs were calculated by measuring the amplitudes at a wavelength of 277.1 nm for BRI and 295.2 nm for TIM. Calibration graph in the application of the sym5-CWT method; was computed by using the measurements of the amplitudes at 233.2 nm for BRI and 288.1 nm for TIM. The linear regression analysis of calibration samples and corresponding statistical results were illustrated in Table 1. Figure 2 shows the calibration lines for BRI and TIM using the proposed signal processing methods. BRI and TIM in the analyzed samples were determined by the calibration curves of the related drugs.

m = Slope of the linear regression equation n = Intercept of the linear regression equation r = Correlation coefficient of the linear regression equation SD (m) = Standard error of slope SD (n) = Standard error of intercept SD(r) = Standard error of correlation LOD = Limit of detection (µg/mL) LOQ = Limit of quantitation (µg/mL)

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Validation of the Applied CWT Methods

In the mexh-CWT and sym5-CWT applications, the a good linearity for BRI and TIM in the working range of 5.0-25.0 μg/mL an 8.0-72.0 μg/mL, respectively, was reported from the regression coefficients indicated in Table 1. The limit of quantitation (LOD, signal/noise=3) and limit of detection (LOQ, signal/noise=10) were computed using standard deviation of the linear regression equations of the analyzed drugs. For the validity of 11 different synthetic mixtures were prepared and analyzed by the mexh-CWT and Sym5-CWT methods. Their recovery results were listed in Table 2.The analysis results demonstrate that satisfactory accuracy and precision of the proposed CWT signal processing methods. In order to visualize the reproducibility of the Mexh-CWT and Sym5-CWT methods, the intra-day and inter-day experiments were done by analyzing the intra-day and inter-day samples as described in the section “2.3. Standard, calibration and validation solutions”. Percent mean recoveries; relative standard deviations and relative standard errors were presented in Table 3. These results show that the newly applied CWT methods are very useful for the analysis of BRI and TIM in samples with desirable precision and accuracy. Before analyzing commercial eye drop samples, the standard addition technique was used to determine whether the excipients in the commercial eye drop preparation were an effect on the analysis of the mexh-CWT and Sym5-CWT methods. In order to observe the presence and absence of the excipient effect on the analysis of the related drugs, standard addition samples were analyzed and then assay results were presented in Table 4. From analysis results in Table 4, noexcipient effect on the determination of BRI and TIM was reported.

X ̅= Mean SD= Standard deviation RSD= Relative standard deviation

RSD= Relative standard deviation RSE= Relative standard error (n= 3 for every concentration level)

RSD= Relative standard deviation

In this research paper, the proposed signal processing methods, Mexh-CWT and Sym5-CWT, were applied to the simultaneous quantitative quantification of BRI and TIM in eye drop samples. Assay results were presented in Table 5. As it can be seen in Table 5, a good accordance with the acceptable standard deviation and relative standard deviation mg/mL mexh-CWT sym5-CWT *UPLC method Exp. No. BRI TIM BRI TIM BRI TIM 1 2.01 4.98 1.99 5.02 1.94 5.06 2 1.99 5.02 2.02 5.01 1.94 5.01 3 1.94 5.06 1.94 5.08 1.98 4.97 4 2.01 5.04 1.96 4.98 1.94 4.93 5 1.97 5.12 2.03 4.99 2 5.15 6 2 5.03 2.01 4.97 2.03 5.08 7 2.04 5.05 2.04 4.98 2.05 5.29 8 1.95 5.03 1.98 4.96 2.06 5.17 9 1.96 4.92 1.97 4.95 1.99 5.01 10 1.98 5.01 1.98 4.91 1.96 4.96 Mean 1.98 5.03 1.99 4.99 1.99 5.06 SD 0.03 0.05 0.03 0.05 0.05 0.11 RSD 1.51 1.05 1.71 0.91 2.37 2.23 Confidence interval Mean ± 0.02 Mean ± 0.04 Mean ± 0.02 Mean ± 0.04 Mean ± 0.04 Mean ± 0.08 was reported for the analysis results obtained by applying the validated mexh-CWT and sym5- CWTmethods to the commercial eye drop formulation. Using one-way ANOVA test, the determination results of BRI and TIM in analyzed commercial sample were statistically compared with those of UPLC method in the literature [23]. It was observed that there is no difference between analysis by signal processing methods and UPLC approach.