Paracetamol (PAR), Pseudoephedrine hydrochloride (PSE) and cetirizine dihydrochloride (CET ) is a ternary mixture that composes tablets which are popular for the relief of flu in Egypt. The spectra of the drugs were overlapped and no spectrophotometric methods were reported to resolve the mixture. This research proposes four spectrophotometric methods that are efficient and require water only as a solvent. The first method was ratio subtraction ‑ ratio difference method (RSDM) where PAR was initially removed from the mixture by ratio subtraction and determined at 292.4 nm, then PSE and CET were quantified by subtracting the amplitudes of their ratio spectra between 257.0 and 230.0 nm for PSE and between 228.0 and 257.0 nm for CET. The second method was derivative ratio spectra—zero cross‑ ing (DRZC) which was based on determining both PSE and CET from the zero‑ crossing points of the first and third derivative of their ratio spectra at 252.0 and 237.0 nm, respectively while PAR was determined using its first derivative at 292.4 nm. Moreover, the ternary mixture was resolved using successive derivative ratio (SDR) method where PAR, PSE and CET were determined at 310.2, 257.0 and 242.4 nm, respectively. The fourth proposed method was pure component contribution algorithm (PCCA) which was applied to quantify the drugs at their λ . Recovery percent‑ max ages for RSDM were 100.7 ± 1.890, 99.69 ± 0.8400 and 99.38 ± 1.550; DRZC were 101.8 ± 0.8600, 99.04 ± 1.200 and 98.95 ± 1.300; SDR were 101.9 ± 1.060, 99.59 ± 1.010 and 100.2 ± 0.6300; PCCA were 101.6 ± 1.240, 99.10 ± 0.5400 and 100.4 ± 1.800 for PAR, PSE and BRM; respectively. The suggested methods were effectively applied to analyze labora‑ tory prepared mixtures and their combined dosage form. Keywords: Paracetamol, Pseudoephedrine, Cetirizine, Ratio subtraction–ratio difference, Successive derivative ratio, Derivative ratio spectra–zero crossing, Pure component contribution algorithm Introduction ((1S,2S)-2-(methylamino)-1-phenylpropan-1-ol hydro- The drugs under study in this research include par - chloride) , is a nasal decongestant which acts by reduc- acetamol (PAR), pseudoephedrine HCl (PSE) and ing inflamed membranes of mucosa, also it is used for cetirizine dihydrochloride (CET). PAR (N-(4-hy- bronchodilation . CET ((RS)-2-[2-[4-[(4-chlorophenyl) droxyphenyl) acetamide)  is an analgesic and phenylmethyl]piperazin-1-yl]ethoxy] acetic acid dihydro- an antipyretic, used to treat many conditions such chloride) , is an antihistamine known for its stabilizing as muscle ache, tooth ache and arthritis . PSE effect on mast-cells thus used in the treatment of allergies . The ternary mixture is present in the Egyptian mar - ket as Allercet Cold and it is famous for its effectiveness in relieving symptoms associated with common cold, *Correspondence: firstname.lastname@example.org Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, sinusitis and flu. The chemical structures of the three October University for Modern Sciences and Arts, 6 October City 11787, drugs are illustrated in Fig. 1. Egypt Full list of author information is available at the end of the article © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creat iveco mmons .org/ publi cdoma in/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Youssef et al. Chemistry Central Journal (2018) 12:67 Page 2 of 14 Fig. 1 Chemical structure of a paracetamol, b pseudoephedrine HCl, c cetirizine 2HCl Nowadays, effective cold treatments are on high adopted for resolution of overlapped spectra of ternary demand especially for people with busy schedules and mixtures. need to be alert and focused as fast as they can. This was successfully achieved by pharmaceutical companies Experimental by including more components in their formulations to Apparatus and software treat more symptoms in one pill or capsule. Nevertheless, Shimadzu—UV 1800 double beam UV–Visible spectro- quality control lab analysts faced many challenges regard- photometer (Japan) and quartz cells (1 cm) at a range of ing the analysis of the more complex dosage forms, hence 200.0–400.0 nm was used for measuring the absorbance. the development of novel analytical techniques was nec- Spectral manipulations were carried out by Shimadzu essary. It was important to consider methods which were UV-Probe 2.32 system software. simple, rapid and low in cost without affecting accuracy and reliability of the results. The literature revealed many Chemicals and solvents methods for the determination of each drug as a single Pure samples component or in mixtures [3–9]. However, only two PAR, PSE and CET were kindly provided by GlaxoS- HPLC–UV [10, 11] methods for the determination of this mithKline (Cairo, Egypt). The purity of the samples combination were available. That being said, chromato - was 99.40 ± 0.7780, 100.1 ± 0.4270 and 100.0 ± 0.2340, graphic methods consume time and solvents contributing respectively, according to the reported method of analy- in the high cost of method development and optimization sis . which is disadvantageous for quality control laboratories. In addition, highly trained staff are required to operate Market sample the apparatus. On the other hand, mathematical spectro-Allercet Cold capsules were bought from a local phar- photometric methods are considered faster and cheaper. macy and were labeled to consist of 400 mg of PAR, Also, spectrophotometers are available in most labs and 30 mg PSE and 10 mg CET per one capsule (Batch Num- easier to operate therefore offering substitute resolutions ber: B10518), manufactured by Global Napi pharmaceu- for the complex mixtures of analytes without the need of ticals (6th of October city, Egypt). prior separation or extraction . The absence of any analytical approaches using spectrophotometry for the Solvents quantitation of this mixture has motivated us to develop Double distilled water. spectrophotometric methods with good accuracy and precision for the analysis of the proposed combination. Standard solutions −1 The methods utilized simple manipulation steps and did Stock solutions with concentrations of 1000 µg mL −1 not require any sophisticated instruments using distilled for PAR and CET and 4000 µg mL for PSE using dis- water as a solvent which causes no environmental harm tilled water as a solvent were prepared. Next, fresh work- and safe for analysts in the field. ing solutions with concentrations of 100.0, 2000 and −1 100.0 µg mL for PAR, PSE and CET, respectively, were Theoretical background made by diluting the corresponding stock solutions with The methods applied for the analysis of the ternary distilled water. mixture were ratio subtraction —ratio difference  (RSDM), derivative ratio spectra–zero crossing Procedures  (DRZC), successive derivative ratio  (SDR) and Linearity pure component contribution algorithm  (PCCA). Accurately measured volumes of PAR (0.2500–2.500 mL), These methods are well developed and were successfully PSE (0.5000–6.000 mL) and CET (0.2000–4.500 mL) were Youssef et al. Chemistry Central Journal (2018) 12:67 Page 3 of 14 −1 …… Fig. 2 a Zero‑ order, b first derivative absorption spectra of 20.00, 600.0 and 20.0 µg mL of PAR ( ), PSE (‑ ‑ ‑ ‑) and CET (—), respectively accurately taken from their working standard solutions Derivative ratio spectra–zero crossing spectrophotometric into series of volumetric flasks (10 mL), the volumes were method (DRZC) For PAR As under “Ratio subtraction– completed with water to prepare final concentrations of ratio difference method (RSDM)”. −1 −1 0 2.500–25.00 µg mL for PAR, 100.0–1200 µg mL for For PSE The D spectra were divided by a standard −1 −1 1 PSE and 2.000–45.00 µg mL for CET. The prepared spectrum of PAR (20.00 µg mL ) and the D of the solutions were scanned from 200.0 to 400.0 nm and their ratio spectra was obtained. PSE was determined from absorption spectra were stored in the computer and were the D amplitudes at 252.0 nm which represented the used in the manipulation steps of RDSM, DRZC and zero-crossing point for CET. A calibration graph was SDR. constructed between the absorbance of D of PSE at 252.0 nm versus the corresponding concentrations and Ratio subtraction–ratio difference method (RSDM) For the regression equation was then computed. PAR The first derivative ( D) spectrum of PAR is extended For CET The spectra were divided by a standard spec - 1 −1 over the D spectra of PSE and CET, so it can be deter- trum of PAR (20.00 µg mL ) and the third derivative mined at wavelength 292.4 nm without the interference ( D) of the ratio spectra was obtained. The concentration of the other two components as demonstrated in Fig. 2b. of CET was determined from D amplitudes at 237.0 nm A calibration graph was constructed relating the absorb- which represented the zero-crossing point of PSE. A ance of D of PAR at 292.4 nm against the corresponding calibration graph was constructed between the absorb- concentrations and the regression equations were then ance of D of CET at 237.0 nm versus the correspond- computed. ing concentrations and the regression equation was then For PSE and CET The stored zero order spectra ( D) of computed. −1 PSE were divided by the spectrum of 25.00 μg mL CET, while ( D) spectra of CET were divided by the spectrum Successive derivative ratio method (SDR) For PAR The −1 −1 of 600.0 μg mL of PSE. Calibration graphs for both PSE spectra were divided by the spectrum of 25.00 µg mL and CET were constructed by plotting the amplitude dif- CET. The D was computed for the ratio spectra and then ference of the obtained ratio spectra between 257.0 and a division process was carried out using the D spectrum −1 −1 230.0 nm for PSE and 228.0 and 257.0 nm for CET versus of 600.0 µg mL PSE/25.00 µg mL CET as a divisor, their corresponding concentrations and the regression and the second ratio spectra were obtained. Afterwards, equations were then computed. the D was obtained allowing the concentration of PAR to Youssef et al. Chemistry Central Journal (2018) 12:67 Page 4 of 14 be determined at the maximum amplitude at 310.2 nm. A RSDM method PAR was determined directly from the calibration graph was created by plotting the amplitudes D at 292.4 nm (Δλ = 8.0, scaling factor 100), where PSE from the resulting curves at 310.2 nm against the cor- and CET have no contribution and concentrations of PAR responding concentrations and the regression equation were calculated from the obtained regression equation. parameters were then computed. The zero order absorption spectra of the laboratory pre - For PSE The spectra were divided by the spectrum pared mixtures were divided by a carefully chosen con- −1 1 −1 of 25.00 µg mL CET and D was computed for these centration of PAR’ (20.00 µg mL ) as a divisor. Thus, ratio spectra. The obtained derivative of ratio spec - ratio spectra were produced represented by (PSE + CET)/ 1 −1 tra were then divided by D spectrum of 20.00 µg mL PAR’ + constant, the values of these constants PAR/PAR’ −1 PAR/25.00 µg mL CET, where the second ratio spec- in the plateau region (278.0–297.0 nm) were then sub- tra were obtained, and then the D was calculated. PSE tracted, this is followed by multiplying the obtained ratio −1 was quantified at the minimum amplitude at 257.0 nm. A spectra by the divisor PAR’ (20.00 µg mL ). Finally, the calibration graph was created by plotting the amplitudes original spectra of PSE + CET were obtained for their from the resulting curves at 257.0 nm against the cor- determination by ratio difference. responding concentrations and the regression equation In order to determine PSE and CET by ratio difference parameters were obtained. method, the same steps as under linearity “Ratio subtrac- For CET The spectra were divided by the spectrum of tion–ratio difference method (RSDM)” were performed −1 1 600.0 µg mL PSE and the D was computed for these and their concentrations obtained from the computed ratio spectra. Next, the obtained derivative of ratio regression equations. 1 −1 spectra were divided by D spectrum of 20.00 µg mL −1 PAR/600.0 µg mL PSE, and the second ratio spectra DRZC method PAR was determined as under “RSDM were obtained. The D was calculated where the con- method”. As for PSE and CET, the zero order absorption centration of CET was determined at the minimum spectra of the laboratory prepared mixtures were divided −1 amplitude at 242.4 nm. A calibration graph was created by 20.00 µg mL PAR. This was then followed by calcu - by plotting the amplitudes from the resulting curves at lating the first and third derivatives for determining PSE 242.4 nm against the corresponding concentrations and and CET at 252.0 and 237.0 nm, respectively. the regression equation parameters were then computed. SDR method Procedures for determining each drug in Pure component contribution algorithm (PCCA) Accu- laboratory prepared mixture were applied as described rately measured volumes of PAR (0.2500–2.500 mL), PSE under “Successive derivative ratio method (SDR)”. (0.5000–5.000 mL) and CET (0.5000–5.000 mL) were separately taken from their working standard solutions PCC A method For PAR The spectra of the mixtures were −1 into a series of volumetric flasks (10 mL), the volumes divided using the normalized spectrum of 45.00 µg mL were completed with water producing solutions with final CET (αCET) as a divisor, then mean centering of the −1 concentration ranges of 2.500–25.00 µg mL for PAR, obtained ratio spectra was carried out and divided by −1 −1 −1 100.0–1000 µg mL for PSE and 5.000–50.00 µg mL MC (αPSE/αCET), the spectrum of 400.0 µg mL of PSE for CET. The prepared solutions were scanned from was used. The produced curves were mean centered and 200.0 to 400.0 nm and the values of absorbance at λ divided by MC [MC (αPAR/αCET)/MC (αPSE/αCET)]. max were recorded. These absorbance values were used to cre - Constants representing the concentration of PAR in the ate different plots for the three drugs against their cor - mixtures were obtained and multiplied by the stand- responding concentrations and the regression equation ard normalized spectrum of PAR and the absorbance at parameters were then computed. 245.0 nm were recorded in the obtained spectra. For PSE The spectra mixtures were divided by the −1 Analysis of laboratory‑prepared mixtures normalized spectrum of 45.00 µg mL CET (αCET), Different volumes of PAR, PSE and CET were accurately and the obtained ratio spectra were then mean cen- taken from their corresponding working standard solu- tered and divided by MC (αPAR/αCET), the spectrum −1 tions and placed in volumetric flasks of 10 mL capacity, of 10.00 µg mL of PAR was used. Then, the produced finally, the volumes were completed using water. The pre - curves were mean centered and divided by MC [MC pared mixtures consisted of varying ratios of the three (αPSE/αCET)/MC (αPAR/αCET)]. The obtained con - drugs. The laboratory prepared mixtures were scanned stants were multiplied by the standard normalized in the range from 200.0 to 400.0 nm and their absorption spectrum of PSE and the absorbance at 256.0 nm was spectra were stored in the computer. recorded in the obtained spectra. Youssef et al. Chemistry Central Journal (2018) 12:67 Page 5 of 14 For CET The spectra of the mixtures were divided by encouraged to develop sensitive spectrophotometric −1 the normalized spectrum of 10.00 µg mL PAR (αPAR), techniques for the determination of PAR, PSE and CET the obtained ratio spectra were then mean centered and simultaneously in their pure powders and dosage form the produced curves were mean centered and divided with acceptable accuracy and precision especially as by MC [MC (αCET/αPAR)/MC (αPSE/αPAR)]. The there are no reported spectrophotometric methods for obtained constants were multiplied by the standard nor- their analysis. malized spectrum of CET (αCET). The absorbance value The spectra of PAR, PSE and CET are severely over - was recorded at 230.0 nm in the obtained spectra. lapped as shown in Fig. 2a, therefore direct determina- Concentrations representing each drug was computed tion of the three drugs was not possible from measuring from their corresponding regression equation. The per - the absorption directly from zero order spectra. The pro - centage recoveries, the mean percentage recovery and posed methods were successful in determining each com- the standard deviations were calculated. ponent simultaneously without prior separation. They were also found to be simple, precise and reproducible. Application to pharmaceutical preparation Ten Allercet Cold capsules were ground, mixed well RSDM method and accurately weighed. An amount of the mixed pow- Ratio subtraction coupled with ratio difference (RSDM) der equivalent to one capsule was accurately weighed is a successive spectrophotometric technique which was and placed in a beaker; extracted with 3 × 30 mL water. successful in the determination of the ternary mixture. 1 1 The extract was sonicated for 15 min (for each extrac - The D spectrum of PAR was extended over the D tion). Filtration was carried out into a 100-mL volumetric spectra of PSE and CET Fig. 2b, so PAR could be directly flask and completed to volume with the same solvent to determined by utilizing the first derivative at 292.4 nm obtain a solution (Stock 1) with the following concentra- as the spectrum showed maximum absorbance value −1 −1 tions 4000 µg mL of PAR, 300.0 µg mL of PSE and and no interfering signals from PSE and CET (∆λ = 8 −1 100.0 µg mL of CET. Then 1.000 mL from Stock 1 was and scaling factor = 10) as shown in Fig. 3 where its con- accurately transferred into a 10-mL volumetric flask and centrations was determined from the computed regres- diluted with water to prepare a solution (stock 2) with the sion equation. Then the spectrum of PAR was eliminated −1 −1 concentration of 400.0 µg mL of PAR, 30.00 µg mL of using RS  which could be applied as the spectrum of −1 PSE and 10.00 µg mL of CET. An aliquot equivalent to PAR was extended over the spectra of PSE and CET in 2.500 mL from Stock 2 was accurately transferred into a their ternary mixture. To analyze PSE and CET in the 100-mL volumetric flask. The solution was then spiked mixtures, the zero order absorption spectra of the labora- with 5.000 mL PSE and 2.000 mL CET from their cor- tory-prepared mixtures were divided by the spectrum of −1 responding working solutions and completed to volume standard PAR (20.00 μg mL ) as a divisor. The obtained with water forming a solution composed of 10.00, 100.8 ratio spectra represented PSE + CET/PAR + constant. −1 and 2.250 µg mL of PAR, PSE and CET, respectively. The values of these constants in the plateau region The procedure under “ Analysis of laboratory-prepared (278.0–297.0 nm) were subtracted. The obtained spectra mixtures” was carried out and the concentration of PAR, PSE and CET were computed from their corresponding regression equation. The standard addition technique was performed by adding various amounts of pure standard drugs to the pharmaceutical dosage form before continuing the meth- ods described previously. Results and discussion Resolution of multicomponent mixtures which possess overlapping spectra is a challenging concern for analyti- cal chemists. Although, chromatographic methods are usually chosen for the analysis of such mixtures, nev- ertheless, in the past few years the mathematical spec- trophotometric methods have significantly substituted chromatography as they offer some advantages of being rapid, simple to apply, do not need any optimization of Fig. 3 First order derivative spectra of Paracetamol conditions, sensitive and cost-effective. Thus, we were Youssef et al. Chemistry Central Journal (2018) 12:67 Page 6 of 14 were then multiplied by spectrum of the divisor PAR wavelengths where the ratio spectrum of the interfering −1 (20.00 μg mL ). Subsequently, the original spectra of component showed the same value (constant) whereas PSE + CET were obtained which were used for their the component of interest shows a significant difference direct determination by utilizing RD. in these two ratio values at these two selected wave- To determine PSE and CET by the RD method  the lengths . zero order spectra of different laboratory prepared mix - tures were divided by the absorption spectra of standard DRZC method −1 −1 600.0 μg mL PSE and standard 25.00 μg mL CET to Nevado et al. , invented this method to resolve ter- obtain different ratio spectra as demonstrated in Figs. 4 nary mixtures. The method depends on the measurement and 5. Calibration curves were created by plotting the of the amplitudes of the components of the mixture at amplitude difference at 257.0 and 230.0 nm for PSE the zero-crossing points in the derivative spectrum of the and the amplitude difference at 228.0 and 257.0 nm for ratio spectra. CET versus their corresponding concentrations and the PAR was determined as under “RSDM method”. Then, regression equations were calculated. The only require - the spectra of the laboratory prepared mixtures were −1 ment for the selection of these two wavelengths is the divided by the spectrum of standard PAR 20.00 µg mL contribution of the two components at these two selected as a divisor to obtain the corresponding ratio spectra. Both the first derivative and third derivative of these ratio spectra were calculated. The concentration of PSE was proportional to the first order amplitudes at 252.0 nm (zero-crossing point for CET) as demonstrated in Fig. 6, while, the concentration of CET was proportional to the third order amplitudes at 237.0 nm (zero-crossing point of PSE) as shown in Fig. 7. The different concentrations of PSE and CET were determined from the computed regression equations. SDR method Afkhami and Bahram  have proposed the SDR tech- nique for the quantitation of ternary mixtures without prior separation. This method depends on successive steps; first the derivative of ratio spectra is calculated, and then these derivative ratio spectra are divided by the derivative ratio spectra of a divisor of the other two components. Finally, the derivative is computed for those obtained ratio spectra. −1 Fig. 4 Ratio spectra of PSE using 25.00 µg mL CET as divisor Fig. 6 First derivative ratio spectra of PSE and CET using PAR −1 −1 Fig. 5 Ratio spectra of CET using 600.0 µg mL PSE as divisor (20.00 µg mL ) as divisor Youssef et al. Chemistry Central Journal (2018) 12:67 Page 7 of 14 Fig. 7 Third derivative ratio spectra of CET and PSE using PAR −1 (20.00 µg mL ) as divisor Fig. 9 The vectors of the first derivative of the second ratio spectra for PSE in water Fig. 8 The vectors of the first derivative of the second ratio spectra for PAR in water For the determination of PAR and PSE; the absorption Fig. 10 The vectors of the first derivative of the second ratio spectra spectra of the laboratory prepared mixtures were divided −1 for CET in water by the spectrum of 25.00 μg mL of CET and the first derivative was calculated for the ratio spectra (V1). For PAR, the vectors (V1) were divided by the D spectrum 1 −1 −1 −1 were then divided by D spectrum of 20.00 µg mL of 600.00 µg mL PSE/25.00 µg mL CET, thus the sec- −1 PAR/600.0 µg mL PSE, thus, the second ratio spectra ond ratio spectra were obtained (V2). Finally, the first were obtained. Finally, the concentration of CET was derivative was calculated for these vectors (V2) where determined by measuring the maximum amplitude at the concentration of PAR was determined at the maxi- 242.4 nm as shown in Fig. 10. According to Afkhami and mum amplitude at 310.2 nm as illustrated in Fig. 8. For 1 Bahram , there are no limitations regarding the selec- PSE, the vectors (V1) were divided by the D spectrum of −1 −1 tion of wavelengths for the construction of the calibra- 20.00 µg mL PAR/25.00 µg mL CET, where the sec- tion graphs therefore the wavelengths used were selected ond ratio spectra were obtained (V3). First derivative was after trying several others and the selected ones demon- calculated for these vectors (V3) and the concentration of strated the best regression parameters. PSE was determined by measuring the maximum ampli- For all the proposed methods; the chosen divisor to set- tude at 257.0 nm as demonstrated in Fig. 9. To determine tle between the lowest noise level and highest sensitivity CET, the absorption spectra of the laboratory prepared −1 and obtain optimal findings regarding average recovery mixtures were divided by the spectrum of 600.0 μg mL percent for the analysis of laboratory prepared mixtures PSE followed by calculating the first derivative for these were analyzed. To refine D method, many smoothing ratio spectra. The obtained derivative of ratio spectra Youssef et al. Chemistry Central Journal (2018) 12:67 Page 8 of 14 and scaling factors were tried, where a smoothing Δλ = 8 and a scaling factor = 10 demonstrated acceptable signal to noise ratio and good resolution of spectra. PCCA method The UV absorption spectra of PAR, PSE and CET, Fig. 2a showed sever overlapping as a result the determination of the proposed drugs using conventional spectropho- tometric methods was not possible. An algorithm able to resolve and extract the pure component contribution from their mixture signal without any special require- ments was applied. The PCCA method is characterized Fig. 12 The pure contribution of paracetamol in the prepared by its varying applications, as it has no limitations, as mixtures opposed to other methods which require the extention of one spectrum over the others or the presence of zero- crossing or isoabsorptive points. The method is based on Following the procedure previously stated, PSE was obtaining the pure component from its mixture and its determined in synthetic mixtures and dosage forms; the determination at its λ providing maximum sensitiv- max spectra of the mixtures were divided by the normalized ity, accuracy and precision results. For quantifying PAR in lab prepared ternary mixtures and dosage forms; the spectra of the mixtures, Fig. 11 were divided by the nor- malized spectrum of CET (αCET), the obtained ratio spectra were then mean centered and divided by MC (αPSE/αCET). Mean centering was applied on the pro- duced curves then divided by MC [MC (αPAR/αCET)/ MC (αPSE/αCET)]. Constants which represent the con- centration of PAR in the mixtures were obtained. At the final step, the constants were multiplied by the standard normalized spectrum of PAR (αPAR) and the pure con- tribution of PAR in each mixture was obtained, Fig. 12. The estimated absorbance value of each of the obtained spectra at 245.0 nm was used for determining the con- centration of PAR from the regression equation of PAR Fig. 13 The pure contribution of pseudoephedrine hydrochloride in standard solutions. the prepared mixtures Fig. 11 The spectra of laboratory prepared mixtures of paracetamol, Fig. 14 The pure contribution of cetirizine dihydrochloride in the pseudoephedrine hydrochloride and cetirizine dihydrochloride prepared mixtures Youssef et al. Chemistry Central Journal (2018) 12:67 Page 9 of 14 Table 1 Regression and validation parameters of the proposed spectrophotometric methods for the determination of PAR, PSE and CET Parameters RSDM method SDR method DRZC method PCCA method PAR PSE CET PAR PSE CET PAR PSE CET PAR PSE CET Linearity 2.500–25.00 100.0–1100 2.000–50.00 2.500–25.00 100.0–1200 2.000–45.00 2.500–25.00 100.0–1200 2.000–45.00 2.500 –25.00 100.0 –900.0 5.000–50.00 range −1 (µg mL ) −3 −2 −1 −1 −2 −1 −3 −3 −2 −2 −4 −2 Slope 5.500 × 10 1.740 × 10 5.620 × 10 2.930 × 10 2.860 × 10 4.600 × 10 5.500 × 10 1.100 × 10 2.610 × 10 6.160 × 10 9.000 × 10 3.140 × 10 −3 −1 −1 −1 −2 −1 −4 −3 −4 −3 −3 −3 Intercept 1.100 × 10 2.130 × 10 2.560 × 10 2.930 × 10 1.630 × 10 1.560 × 10 7.000 × 10 2.200 × 10 9.000 × 10 6.000 × 10 6.100 × 10 7.900 × 10 −5 −5 −3 −1 −4 −3 −5 −6 −5 −4 −6 −5 SE of slope 1.210 × 10 8.140 × 10 3.060 × 10 1.100 × 10 1.680 × 10 1.650 × 10 3.030 × 10 7.150 × 10 8.660 × 10 6.850 × 10 4.270 × 10 5.310 × 10 −4 −2 −2 −1 −2 −4 −3 −3 −2 −3 −3 SE of intercept 2.040 × 10 5.620 × 10 9.270 × 10 1.740 1.300 × 10 4.770 × 10 4.980 × 10 5.430 × 10 2.730 × 10 1.040 × 10 2.69 × 10 1.70 × 10 Correlation 1.000 1.000 1.000 1.0000 1.000 1.0000 1.000 1.000 1.000 1.000 1.000 1.000 coefficient (r) Accuracy 100.4 ± 0.8000 99.40 ± 0.3900 100.1 ± 0.8700 99.57 ± 1.090 99.88 ± 1.280 100.2 ± 0.7100 100.9 ± 0.7100 99.68 ± 1.090 100.1 ± 0.6300 100.7 ± 1.529 98.82 ± 0.5310 100.4 ± 0.3980 (n = 6) mean ± SD Precision 0.07800 0.05280 0.07700 0.5280 0.09100 0.1550 0.07800 0.2250 0.2200 0.1560 0.2260 0.1140 (n = 3 × 3) 1.220 1.010 1.230 0.9050 0.8370 1.300 1.220 0.4290 0.5200 0.8810 0.9970 0.8000 (RSD %) Repeatability intermedi ate preci sion LOD 0.1520 12.91 0.6570 0.2850 17.42 0.4470 0.3760 23.13 0.3690 0.6430 9.900 0.2210 LOQ 0.4610 39.11 1.990 0.8640 52.78 1.350 1.140 70.08 1.120 1.948 30.00 0.6690 a −1 −1 −1 Relative standard deviations (RSD) of three concentrations, the concentrations were as follows: PAR (5.000, 10.00, 25.00 µg mL ), PSE (100.0, 600.0, 1000 µg mL ) and CET (5.000, 15.00, 35.00 µg mL ) LOD = 3.3 × Standard deviation of residuals/slope; LOQ = 10 × Standard deviation of residuals/slope Youssef et al. Chemistry Central Journal (2018) 12:67 Page 10 of 14 Table 2 Analysis of laboratory prepared mixtures by the proposed spectrophotometric methods RSDM method DRZC method SDR method PCCA method PAR (Mean ± SD) 100.7 ± 1.890 101.9 ± 1.060 101.8 ± 0.8600 100.4 ± 1.390 PSE (Mean ± SD) 99.69 ± 0.8400 99.59 ± 1.010 99.04 ± 1.200 98.76 ± 0.6800 CET (Mean ± SD) 99.38 ± 1.550 100.2 ± 0.6300 98.95 ± 1.300 100.4 ± 1.980 Average of 6 experiments spectrum of CET (αCET), and the obtained ratio spec- Limits of detection (LOD) and quantification (LOQ) tra were then mean centered and divided by MC (αPAR/ The LOD and LOQ were calculated (Table 1) for the αCET). Then, the produced curves were mean centered studied drugs using the proposed techniques according and divided by MC [MC (αPSE/αCET)/MC (αPAR/ to the following equations: αCET)]. Constants which represent the concentration LOD = 3.3 ∗ SD of residuals/Slope of PSE in the mixtures were obtained. Lastly, the result- ing constants were multiplied by the standard spectrum LOQ = 10 ∗ SD of residuals/Slope of PSE (αPSE) and the pure contribution of PSE in each mixture was obtained, Fig. 13. The estimated absorbance Accuracy value of each of the obtained spectra at 256.0 nm was The proposed methods were utilized for the analysis used for calculating the concentration of PSE from the of different solutions of PAR, PSE and CET in order to previously calculated regression equation of PSE. validate the accuracy. The concentrations were deduced Finally, for the determination of the concentration of from the corresponding regression equations, then the CET in synthetic mixtures and dosage form samples; the percentage recoveries and standard deviation were calcu- spectra of the mixtures were divided by the normalized lated. The results demonstrated in Table 1 have assured spectrum of PAR (αPAR), the obtained ratio spectra were the accuracy of all methods. then mean centered and divided by MC (αPSE/αPAR). Then, the produced curves were mean centered and Repeatability and intermediate precision divided by MC [MC (αCET/αPAR)/MC (αPSE/αPAR)]. Three concentrations of PAR (5.000, 10.00, −1 −1 Constants which represent the concentration of CET in 25.00 µg mL ), PSE (100.0, 600.0, 1000 µg mL ) and −1 the mixtures were obtained. The obtained constants were CET (5.000, 15.00, 35.00 µg mL ) were analyzed three multiplied by the standard spectrum of CET (αCET) times intra-daily and inter-daily (on three different days) and the pure contribution of CET in each mixture was using the proposed spectrophotometric methods. The obtained, Fig. 14. The estimated absorbance value of each relative standard deviations were calculated proving the of the obtained spectra at 230.0 nm was used for calculat- precision of the methods (Table 1). ing the concentration of CET from the previously calcu- lated regression equation of CET standard solutions. Selectivity The contribution of each of PAR, PSE and CET were The methods’ selectivity was accomplished by analyzing resolved and their contribution in each mixture was different laboratory prepared mixtures with varying con - extracted, from which the absorbance values of the com- centrations of the three drugs within the linearity range. ponents were determined at their λ which are asso- Acceptable results were illustrated in Table 2. max ciated with maximum sensitivity, highest accuracy and precision and lowest error. Application of the proposed methods in Allercet capsules The suggested procedures were used for the determina - Method validation tion of PAR, PSE and CET in Allercet c old capsules. The Validation according to ICH guidelines were applied for obtained recovery and standard deviation have estab- the suggested methods  where good results were lished the absence of interference from the excipients. obtained. Standard addition technique was also applied to further assure the validity of the proposed methods as demon- Range and linearity strated in Table 3. The calibration curves of the different proposed methods were handled on three different days in order to evaluate the linearity. The analytical data of the calibration graph were demonstrated in Table 1. Youssef et al. Chemistry Central Journal (2018) 12:67 Page 11 of 14 Table 3 Application of standard addition technique to the analysis of PAR, PSE and CET in Allercet Cold capsules using the proposed spectrophotometric methods Drug RSDM method SDR method DRZC method PCCA method a, b a, b a, b a, b Claimed amount Added Recovery % Claimed amount Added Recovery % Claimed amount Added Recovery % Claimed amount Added Recovery % taken taken taken taken −1 −1 −1 −1 PAR 10.00 (µg mL ) 5.000 104.6 10.00 (µg mL ) 5.000 105.9 10.00 (µg mL ) 5.000 101.1 10.00 (µg mL ) 5.000 103.1 10.00 104.0 10.00 104.9 10.00 100.8 10.00 103.8 15.00 105.1 15.00 105.3 15.00 101.2 15.00 102.3 Mean ± SD 104.6 ± 0.5210 Mean ± SD 105.4 ± 0.5490 Mean ± SD 101.0 ± 0.2330 Mean ± SD 103.1 ± 0.7360 −1 −1 −1 −1 PSE 100.75 (µg mL )* 50.00 104.0 100.8 (µg mL ) 50.00 105.6 100.8 (µg mL ) 50.00 104.1 100.8 (µg mL ) 50.00 102.9 100.0 103.2 100.0 104.3 100.0 105.0 100.0 102.8 200.0 103.2 200.0 105.0 200.0 104.9 200.0 102.4 Mean ± SD 103.5 ± 0.4780 Mean ± SD 105.0 ± 0.6500 Mean ± SD 104.6 ± 0.5030 Mean ± SD 102.7 ± 0.2310 −1 −1 −1 −1 CET 2.250 (µg mL )* 2.000 105.7 2.250 (µg mL ) 2.000 105.9 2.250 (µg mL ) 2.000 103.8 2.250 (µg mL ) 2.000 101.9 2.500 104.5 2.500 104.5 2.500 102.9 2.500 101.0 10.00 105.6 10.00 104.0 10.00 102.8 10.00 101.1 Mean ± SD 105.3 ± 0.6970 Mean ± SD 104.8 ± 1.018 Mean ± SD 103.2 ± 0.5460 Mean ± SD 101.3 ± 0.4800 −1 −1 * Amount spiked was 100.00 µg mL for PSE and 2.00 µg mL for CET Average of three experiments Recovery of the claimed amount taken Youssef et al. Chemistry Central Journal (2018) 12:67 Page 12 of 14 Table 4 Statistical comparison of the results obtained by the proposed spectrophotometric methods and reference method for the determination of PAR, PSE and CET Param- PAR PSE CET eter RSDM SDR DRZC PCCA Reference RSDM SDR DRZC PCCA Reference RSDM SDR DRZC PCCA Reference method method method Mean 99.72 100.1 99.80 100.7 99.40 100.3 100.2 99.39 99.92 100.1 100.1 99.82 99.97 100.1 100.0 SD 0.5870 0.6200 0.9230 1.384 0.7780 0.8050 0.7310 1.130 1.110 0.4270 0.5720 0.5290 0.4290 0.5390 0.2340 N 6 6 6 6 4 6 6 7 6 4 6 6 6 6 4 Variance 0.3450 0.3840 0.8520 1.915 0.6050 0.6480 0.5340 1.277 1.232 0.1820 0.3270 0.2800 0.1840 0.2910 0.05500 Student’s t 0.7570 1.540 0.7130 1.660 0.3310 0.9290 1.200 2.070 0.2380 0.6830 0.2100 0.1290 (2.310) (2.310) (2.310) (2.310) (2.310) (2.310) (2.260) (2.310) (2.310) (2.310) (2.310) (2.310) F 1.760 1.580 1.410 3.170 3.560 2.930 7.020 6.770 5.950 5.090 3.350 5.280 (5.410) (5.410) (9.010) (9.010) (9.010) (9.010) (8.940) (9.010) (9.010) (9.010) (9.010) (9.010) Figures between parentheses represent the corresponding tabulated values of t and F at P = 0.05 The reported method is an HPLC method using C18 column, a mobile phase composed of 25 mM phosphate buffer (pH = 5): methanol: acetonitrile (30:60:10, v/v/v) Youssef et al. Chemistry Central Journal (2018) 12:67 Page 13 of 14 Competing interests Statistical analysis The authors declare that they have no competing interests. The results of the analysis of the pure drugs obtained from the proposed methods were compared to those Availability of data and materials All data is included in the manuscript. obtained by applying the reference method  where no significant difference was observed from the calculated t- Ethics approval and consent to participate and F values, Table 4. Not applicable. Funding Conclusion The research was personally funded by the authors. The introduced study has demonstrated the application of simple and accurate mathematical based spectropho- Publisher’s Note tometric methods for the analysis of the ternary mixture; Springer Nature remains neutral with regard to jurisdictional claims in pub‑ lished maps and institutional affiliations. paracetamol, pseudoephedrine and cetirizine in bulk and in Allercet Cold capsules the available dosage form Received: 22 February 2018 Accepted: 25 May 2018 in the Egyptian market. These methods have neither required any chemical pretreatment for the analyte nor demanded the availability of a complicated or advanced instrument. Moreover, these methods have employed the References use of water as a solvent, thus, they could be considered 1. Moffat AC, Osselton MD, Widdop B, Watts J (2011) Clarke’s analysis of as eco-friendly methods of analysis. The privileges of drugs and poisons. Pharmaceutical press London, London 2. 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Aly FA, Nahed E‑E, Elmansi H, Nabil A (2017) Simultaneous determination of cetirizine, phenyl propanolamine and nimesulide using third derivative spectrophotometry and high performance liquid chromatography in Abbreviations pharmaceutical preparations. Chem Cent J 11(1):99 CET: cetirizine dihydrochloride; DRZC: derivative ratio–zero crossing method; 8. Abdelwahab NS, Abdelaleem EA (2017) Stability indicating RP‑HPLC HPLC–UV: high performance liquid chromatography–ultra violet detection; method for simultaneous determination of guaifenesin and pseu‑ PAR: paracetamol; PCCA : pure component contribution algorithm; PSE: pseu‑ doephedrine hydrochloride in the presence of syrup excepients. Arabian doephedrine hydrochloride; RSDM: ratio subtraction–ratio difference method; J Chem 10:S2896–S2901 SDR: successive derivative ratio. 9. 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Chemistry Central Journal – Springer Journals
Published: Jun 1, 2018
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