RP-HPLC and UV Spectrophotometric Analysis of Paracetamol, Ibuprofen, and Caffeine in Solid Pharmaceutical Dosage Forms by Derivative, Fourier, and Wavelet Transforms: A Comparison Study

Different signal-transforming algorithms were applied for UV spectrophotometric analysis of paracetamol, ibuprofen, and caffeine in ternary mixtures. Phosphate buffer pH 7.2 was used as the spectrophotometric solvent. Severe overlapping spectra could be resolved into individual bands in the range of wavelengths 200–300 nm by using Savitzky–Golay smoothing and differentiation, trigonometric Fourier series, and mother wavelet functions (i.e., sym6, haar, coif3, and mexh). To optimize spectral recoveries, the concentration of various types of divisors (single, double, and successive) was tested. The developed spectrophotometric methods showed linearity over the ranges 20–40 mg/L for paracetamol, 12–32 mg/L for ibuprofen, and 1–3.5 mg/L for caffeine (R2 > 0.990). They could be successfully applied to the assay and dissolution test of paracetamol, ibuprofen, and caffeine in their combined tablets and capsules, with accuracy (99.1–101.5% recovery) and precision (RSD < 2%). For comparison, an isocratic RP-HPLC analysis was also developed and validated on an Agilent ZORBAX Eclipse XDB–C18 (150 × 4.6 mm, 5 µm) at an ambient temperature. A mixture of methanol : phosphate buffer 0.01 M pH 3 (30 : 70 v/v) was used as the mobile phase delivered at 2 mL/min, and the effluent was monitored at 225 nm. It was shown that spectrophotometric data were statistically comparable to HPLC (p > 0.05), suggesting possible interchange between UV spectrophotometric and HPLC methods for routine analysis of paracetamol, ibuprofen, and caffeine in their solid pharmaceutical dosage forms.


Introduction
Combined pharmaceutical dosage forms have been more and more manufactured and used for better treatment outcome.
ere was considerable clinical evidence that a multicomponent therapy (like combined analgesics) is more efficient than monocomponent therapies because it can expand the array of therapeutic options, facilitate the completeness of therapeutic effect, and permit the doctors (and, in self-medication with over-the-counter (OTC) medications, the patients themselves) to personalize any treatment based on the patient's specific needs [1].
Paracetamol (a.k.a. acetaminophen, Figure 1(a)) was popularly used to combat fever in the 1950s and now becomes the antipyretic and analgesic of first choice in most countries [2]. It is thought to increase human pain threshold by reducing the production of prostaglandins in the brain and spinal cord. Despite of having few adverse effects and little interaction with other pharmaceutical agents, this drug exhibits very little anti-inflammatory activity probably due to its inability to suppress COX in the presence of the elevated cellular peroxides found in inflamed cells [3]. To enhance the painkilling effect, paracetamol can be orally taken in combination with ibuprofen (a nonsteroidal antiinflammatory drug, Figure 1(b)) and caffeine (a mild neurostimulant that produces cerebral vasoconstriction by antagonizing adenosine receptors and helps reduce fatigue, Figure 1(c)) [4].
In analytical chemistry, signal transforms (derivative, Fourier, and wavelet) demonstrated to be an encouraging means to deconvolve UV overlapping spectra of ternary and quaternary mixtures [30][31][32][33]. Based on this signal-processing approach, the present study aims at developing analytical methods based on signal-transforming UV ratio spectra for the simultaneous determination of paracetamol, ibuprofen, and caffeine in coformulated ternary mixtures, using RP-HPLC as a reference method. It specifically assesses the applicability of developed UV spectrophotometric methods for both assay and dissolution test of paracetamol, ibuprofen, and caffeine in their combined solid pharmaceutical dosage forms.

Apparatus and Software.
A UNICAM UV 300 double beam spectrophotometer ( ermo Spectronic, USA) was used with a 1.5 nm fixed slit width and equipped with 1 cm quartz cuvettes. e absorption spectra were registered between 190 and 325 nm, using phosphate buffer pH 7.2 as blank. e spectrophotometer operated at the data interval fixed at Δλ � 0.1 nm, and the scan speed varied (i.e., 30-120 nm/min) to boost the spectral signal-to-noise ratio without the prolonged scan period. For derivative transform, the ratio spectra were subjected to Savitzky-Golay differentiation and smoothing ( ermo Spectronic VISION32 software). For Fourier and wavelet transforms, the data treatment was performed by using Microsoft Excel and Wavelet Toolbox, MATLAB R2015a software ( e Math-Works, Inc. USA), respectively.
Dissolution test was performed at 37 C by using the dissolution medium (phosphate buffer pH 7.2) on an Erweka DT 626 (Erweka GmbH, Germany) dissolutor (six vessels containing 900 mL of the dissolution medium) with a paddle apparatus set at 150 rpm.

Reagents and Standard
Solutions. Paracetamol (PA), caffeine (CA), and ibuprofen (IB) primary reference standards were provided from the National Institute of Drug Quality Control (Vietnam). All chemicals used were of analytical grade. e spectrophotometric solvent was made up of 250 mL of potassium dihydrophosphate, 0.2 M and 175 mL of sodium hydroxide, and 0.2 M in a final volume of 1 L with deionized double-distilled water. e preparation of a set of standard solutions was accomplished in 100-mL volumetric flasks by using stock solutions freshly prepared in the same solvent (PA 500 mg/L, CA 200 mg/L, and IB 500 mg/L).

Sample Solutions.
ree Vietnamese formulations were purchased in the local market (i.e., Glotasic (30) mg/L + IB 20 mg/ L + CA 2.5 (2) mg/L, was obtained in a 100-mL volumetric flask by ultrasonic dissolution and appropriate dilution of an accurate quantity equivalent to one tenth of a tablet or capsule. Dissolution samples were collected at predetermined time intervals within a time period of 1 hour, appropriately diluted with the spectrophotometric solvent (2-10 times), and filtered before spectral measurement.

Method Development
eoretically speaking, the three drug molecules under study (PA, IB, and CA) can absorb light of certain wavelength ≥ 200 nm, allowing electrons in the valence band to jump from the ground state to excited state because they have both chromophores (benzene ring, carbonyl group, carboxyl group, and heterocyclic nitrogen ring) and auxochromes (hydroxyl group, amide group, and alkyl group).
It is truly justified by data displayed in Figures 2(a) and 2(b) (i.e., the zero-order UV spectra being subjected to Savitzky-Golay smoothing filter (3 rd order polynomial and 125 convolution coefficients)). Suppose that the content of all drugs complies with label claim, the existence of inactive substances in their solid pharmaceutical dosage forms does not modify considerably the spectral characteristics of ternary mixtures of PA 32.5 (30) mg/L + IB 20 mg/L + CA 2.5 (2) mg/L. However, a significant spectral overlap is seen in the range 200-300 nm for PA, IB, and CA. As PA's spectral absorption dominated over the wavelength region studied, the coassay of all drugs in their combined mixtures is inhibited by traditional UV spectrophotometry, especially for IB and CA. It is worth mentioning that phosphate buffer pH 7.2 was chosen as the spectrophotometric solvent herein because it could well dissolve all drugs in the range of concentrations investigated and was also suggested for the dissolution test of IB tablets [11].
Unlike previously published data (i.e., using multivariate concentration determination: partial least-squares regression (PLS), genetic algorithm coupled with PLS (GA-PLS), and principal component-artificial neural network (PC-ANN) [21], a fully questionable determination of zerocrossing points with no divisor [34,35]), in this study, different algorithms (i.e., derivative, Fourier, and wavelet transforms) were employed to separate severe overlapping spectra of PA-IB-CA ternary mixtures into individual bands for quantification. In principle, these transforms could be done with UV ratio spectra using different types of divisor: single [33], double [36], and successive [37] as once proposed. With a single divisor, detecting crossing or zerocrossing points is prerequisite. In contrast, the appropriateness of other divisors counts on locating signal coincidence at a region or for the transformed spectra of a compound and its corresponding mixture. To obtain the highest spectral recovery, the choice of relevant divisor concentrations and signal-transforming functions for transformed ratio spectra must be taken into consideration. Considering the virtue of clarity, the transformed ratio spectra were distinctly presented for PA 32.5 (30) mg/L, IB 20 mg/L, CA 2 mg/L, and their corresponding mixture to point out the working wavelengths for double and successive divisor ratio spectrophotometric methods.
(1) Derivative Transform. e differentiation and smoothing of UV spectra were done by using the Savitzky-Golay algorithm [38], optimally fitting a data subset of 2n + 1 measurement points to a polynomial in the least-squares sense.
Using the derivative transform with single divisor, the ratio spectra were obtained by dividing PA and IB spectra by a spectrum of CA 2 mg/L. ese ratio spectra were computed for their first-order derivative (5 th order polynomial and 125 convolution coefficients) and subsequently smoothed (3 rd order polynomial and 125 convolution coefficients) by using Savitzky-Golay filters (Figure 3(a)). In the PA-IB-CA mixture, the concentration of PA was figured out by measuring the derivative amplitude at 225.2 nm (IB zerocrossing point). Similarly, the concentrations of IB and CA were achieved with the working wavelengths of 212.8 nm (CA zero-crossing point) and 270.7 nm (IB zero-crossing point), respectively, when IB and CA spectra were being divided by a spectrum of PA 30 mg/L ( Figure 3 Under other conditions, the assay of PA could be done with double divisor (i.e., the ratio spectra were obtained by dividing the UV spectra of PA-IB-CA ternary mixtures by the spectrum of an IB-CA binary mixture). In contrast to Dinç's proposal [33,36] specifying that a double divisor contains approximately equimolar concentrations of each component, the binary mixture of IB 20 mg/L + CA 2 mg/L was established as an acceptable double divisor to determine PA at 238.8 nm. It is a peak wavelength of the first-order derivative of the ratio spectra in the spectral region coexisted for PA 32.5 mg/L and its ternary mixture of PA 32. Moreover, PA and CA could be also quantified in their ternary mixtures with successive divisors. For example, the first ratio spectra were obtained when the spectra of PA containing ternary mixtures was divided by a spectrum of CA 2 mg/L (the first divisor). ese ratio spectra were firstorder differentiated and subsequently divided by the second divisor (the first-order derivative of the ratio spectrum acquired by dividing IB 20 mg/L by CA 2 mg/L). ereafter, the second ratio spectra were subjected to first-order differential computation and again smoothing to expose the working wavelength of 279.8 nm (Figure 3(f )). In the same way, CA was determined at 285.6 nm with successive divisors ((i) PA 32.5 mg/L; (ii) IB 20 mg/L/PA 32.5 mg/L) (Figure 3(g)), whereas no working wavelength was found for IB determination with successive divisors.
It is obviously seen that the amplitude of derivative signals in our study is much higher than that reported in others [29,34,35].
(2) Discrete Fourier Transform. Using the discrete Fourier transform, the UV spectra at a set of (n + 1) equally spaced wavelengths could be expanded as the sum of deterministic continuous trigonometric functions sine and cosine [39].
is approach, however, was only able to help quantify PA in PA-IB-CA ternary mixtures using double divisor with all Journal of Analytical Methods in Chemistry trigonometric functions readily available; i.e., the spectra in the range 210-300 nm were deconvolved, and a set of Fourier coefficients were calculated by using 6-or 8-point combined trigonometric functions (i.e., cosx i + cos(x i + 60 ); cos2x i + cos2 (x i + 60 ); sinx i -sin (x i + 60 ); sin2x i -sin 2(x i + 60 ); cosx i + cos(x i + 45 ); cos2x i + cos2 (x i + 45 ); sinx i -sin (x i + 45 ); and sin2x i -sin 2(x i + 45 )). Figures 4(a) and 4(b) exhibit some representative discrete Fourier-transformed signals of ratio spectra with ∆λ � 1 nm (i.e., the highest and smallest signal amplitudes obtained with discrete Fourier transform). It is noted that although the discrete Fourier transform generated lower amplitude signals as compared with corresponding derivative ones, there was no need to perform an additional smoothing step to Fouriertransformed signals as already explained [40].
(3) Wavelet Transform. In mathematics, a wavelet transform (WT) means that a signal is decomposed into a set of basic functions that are related to dilation and scaling of a transforming function ψ(t), so-called the "mother wavelet" [41]. In other words, WT is dependent upon the approval of a single prototype wavelet function for generating the other window functions. With reference to spectral analysis, WT has strongly proved to be one of the most crucial and attractive signal-processing algorithms for noise elimination, background amelioration, differentiation, data smoothing and filtering, data compression, and separation of signals with overlapping spectra, etc. [42]. In particular, WT-based UV spectroscopy has been profitably utilized for the assay of pharmaceuticals in binary and ternary mixtures [43]. is is because the original signal or function could be mathematically expressed in terms of a linear combination of wavelets (i.e., a sum of a series where each term is the product of a constant coefficient and a wavelet), making the wavelet transform of UV spectra feasible.
Using the wavelet transform, the signal decomposition of UV ratio spectra of PA-IB-CA ternary mixtures into individual bands was scrutinized with all MATLAB built-in wavelet families. Sym6, haar, coif3, and mexh were mother wavelets chosen for signal-transforming ratio spectra with single, double, and successive divisors. WTs were optimally performed at the scaling factor, a � 256. Figures 5(a)-5(f) display representatively UV ratio spectra resolved by using these mother wavelets. It is obvious that the intensity of transformed signals has been remarkably augmented by WT as compared to derivative transform, especially for IB and CA (minor components in mixtures) transformed ratio spectra.

Reversed-Phase
High-Performance Liquid Chromatography Method. As stated in the United States Pharmacopeia [11], chromatographic analysis was applied to the assay of these drugs using the C18 column and UV detection. e mobile phases are regulated to be (i) a mixture of methanol: water: glacial acetic acid (28 : 69 : 3 v/v/v) for PA-CA combined tablets, and (ii) a mixture of acetonitrile and water (containing chloroacetic acid 1% and being pH-adjusted to 3.0 with ammonium hydroxide) (6 : 4 v/v) for IB tablets.
For comparison, the chromatographic determination was investigated to concurrently analyze PA, IB, and CA in their ternary mixtures. e RP-HPLC development was done with a 150 × 4.6 mm, 5 µm ZORBAX Eclipse XDB-C18 column installed on the system.  is densely covered, deactivated column packing is exclusively beneficial for HPLC analysis of acidic, basic, and other highly polar analytes (e.g., CA).
To attain a good RP-HPLC performance, chromatographic conditions (i.e., flow rate, injection volume, organic modifier type and ratio, buffer pH, and concentration) were scrutinized. In RP-HPLC, the hydrophobicity of an analyte molecule (often expressed as log P) is usually the primary indicator of its retentivity. In literature, log P values are 0.46     [44], -0.07 [45], and 3.97 [46] for PA, CA, and IB, respectively. Provided that the higher the value of log P the more hydrophobic the molecule, it reasonably agrees with the observation that IB was the last eluting compound. In contrast, the fact that PA was eluted out before CA and could be attributable to some limitation of log P value (only describing the partition coefficient of neutral or unionized drug molecules). With regard to the chemical structure, CA is both a weak acid and a weak base with pKa values of 14.0 (tertiary amine) and 0.7 (caffeine cation) [47,48]. As the degree of ionization also dictates the analyte hydrophobicity (ionic analytes are much less hydrophobic) and possibly shows secondary interactions with the column (free silanol groups), the polarity of the mobile phase was enhanced by addition of the 10-50 mM phosphate buffer over the pH range 3-7. It makes CA predominantly protonated species, and CA is probably less polar than PA in this chemical form.
It is reported that methanol, acetonitrile, and/or combinations of these two modifiers are the most commonly   Figure 7: Dissolution profiles of Bidi-Ipalvic capsules (a) and Glotasic tablets (b) determined by using wavelet transform of UV ratio spectra (n � 6, RSD < 5%).  When methanol was used, different selectivity was produced and all drugs were fully resolved. e following condition was selected as optimal for RP-HPLC analysis. PA, IB, and CA were separated by isocratic liquid chromatography with a flow rate of 2.0 mL/min at an ambient temperature of 25 C. e eluent was composed of methanol : phosphate buffer (KH 2 PO 4 0.01 M pH 3 and phosphoric acid used for pH adjustment) (30 : 70 v/v). Sample injection volume was 20 μL, and PDA detector was set at 225.0 nm.
Under this chromatographic condition, PA, CA, and IB were eluted at 2.58, 2.85, and 9.81 min, respectively (Figure 6). e suitability of our HPLC method could be apparently assured for all drugs with respect to basic chromatographic parameters describing a resolution between two adjacent peaks (R s > 1.5), peak asymmetry factor (A s � 0.8-0.9), and column efficiency (theoretical plate number, N > 5500/15 cm).

Method Validation and Application.
e validity of all the developed methods was assessed in terms of precision, accuracy, and linearity according to ICH guidelines [49]. e repeatability (within-run precision) was evaluated by RSD for six replicate determinations of the same sample. e accuracy was evaluated by % recovery using the standard addition technique (known amounts of three analytes equal to 20% of their label claim were directly added to the aliquots of analyzed tablets and capsules). RP-HPLC analysis showed to be fairly precise (RSD values < 2.0 %) and accurate (percent recovery ranged 99.5-101.1%). e calibration curves demonstrated a good linear relationship (R 2 > 0.990) over the concentration ranges of PA (20-40 mg/L), IB (12-32 mg/L), and CA (1-3.5 mg/L). In a similar manner, these ranges of linearity were also spectrophotometrically established (Table 1). For Fourier-transformed ratio spectra, exceptionally, the content of PA was determined by using the plots of signal amplitude versus natural logarithm of concentration. Indication of good precision (evaluated by RSD values < 2%) and accuracy (evaluated by recovery percentages 99.1-101.5%) was also found for all spectrophotometric methods. e RP-HPLC method was well applied to the simultaneous determination of PA, IB, and CA in their combined tablets and capsules. Moreover, the content of PA, IB, and CA could be successfully coassayed by using derivative-, Fourier-, and wavelet-transformed spectrophotometric methods, implying negligible interfering excipients used in the solid pharmaceutical dosage forms under study (Table 2). Figure 7 displays the dissolution profiles of PA, IB, and CA, clearly showing that > 80% of the label content released after 30 min for capsules and 45 min for tablets. Table 3 presents statistical analysis for comparison of spectrophotometric and RP-HPLC assay of PA, IB, and CA in their combined tablets and capsules. At the 95% confidence level, no statistically significant difference was seen in the precision (Bartlett test checking homogeneity of variances of all groups, observed χ 2 value < critical χ 2 value) and accuracy (one-way ANOVA test comparing means of all groups, observed F value < critical F value) among all the proposed methods.

Conclusion
UV ratio spectrophotometric methods, which are relied on the first-order derivative and Fourier and wavelet transforms, were developed for the estimation of PA, IB, and CA in ternary mixtures requiring no prior purification and/or separation step. ese methods proved to be precise (RSD < 2%) and accurate (in the range of 98-102% recovery). It is clearly observed that wavelet transform outperformed derivative and Fourier transforms with regard to improving the sensitivity of the assay (i.e., signal strength greatly enhanced). e developed spectrophotometric methods showed statistically comparable precision and accuracy, but more eco-friendly, cost-effective, and time-saving than RP-HPLC.
us, they could be used for the routine assay and dissolution test of commercially available tablets and capsules simultaneously containing PA, IB, and CA.

Data Availability
No data were used to support this study.

Conflicts of Interest
e authors declare that they have no conflicts of interest.