Accepted Manuscript Simultaneous determination of Cinnarizine and Domperidone by area under curve and dual wavelength spectrophotometric methods Maha M. Abdelrahman PII: DOI: Reference:
S1386-1425(13)00470-8 http://dx.doi.org/10.1016/j.saa.2013.04.120 SAA 10511
To appear in:
Spectrochimica Acta Part A: Molecular and Biomo‐ lecular Spectroscopy
Received Date: Revised Date: Accepted Date:
14 November 2012 25 April 2013 29 April 2013
Please cite this article as: M.M. Abdelrahman, Simultaneous determination of Cinnarizine and Domperidone by area under curve and dual wavelength spectrophotometric methods, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy (2013), doi: http://dx.doi.org/10.1016/j.saa.2013.04.120
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Simultaneous determination of Cinnarizine and Domperidone by area under curve and dual wavelength spectrophotometric methods Maha M. Abdelrahman* Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Bani-Suef University, Alshaheed Shehata Ahmad Hegazy St., 62111, Beni-Suef, Egypt
Abstract Accurate, selective and sensitive spectrophotometric methods have been developed and validated for simultaneous determination of Cinnarizine and Domperidone, a binary mixture with overlapping spectra, without preliminary separation. These methods include area under the curve (AUC) and dual wavelength spectrophotometry. For the AUC method, the area under curve of mixture solutions in the wavelength ranges 241-258 nm and 280-292 nm were selected for determination of Cinnarizine and Domperidone and by applying Cramer's rule, concentration of each drug was obtained. In dual wavelength method, two wavelengths were selected for each drug in a way so that the difference in absorbance is zero for another drug. Domperidone shows equal absorbance at 240.2 nm and 273.2 nm, where the differences in absorbance were measured for the determination of Cinnarizine. Similarly, differences in absorbance at 230.8 nm and 259.2 nm were measured for determination of domperidone. The proposed methods were applied for determination of Cinnarizine and Domperidone over the concentration ranges of 2-20 and 2-22 µg mL-1, respectively. The suggested methods were validated as per USP guidelines and the results revealed that they are reliable, reproducible and precise for routine use with short analysis time. The results obtained by the proposed methods were statistically compared to the reported method, and there was no significant difference between them regarding both accuracy and precision.
Keywords: Spectrophotometry; Cinnarizine; Domperidone; Area under curve; Dual wavelength; Pharmaceutical Formulation. * Corresponding author: E-mail address:
[email protected] Tel.: 01141418206; fax: 082-2317950
1. Introduction Cinnarizine (CIN), chemically, known as 1-(Diphenylmethyl)-4-(3-phenyl-2-propenyl) piperazine [1]. It is a piperazine derivative with antihistamine, sedative, and calcium-channel blocking activity. It is used for the symptomatic treatment of nausea and vertigo caused by Ménière's disease and other vestibular disorders and for the prevention and treatment of motion sickness [2]. Domperidone (DOM), chemically, known as 5-Chloro-1-[1-[3-(2,3-dihydro-2-oxo-1 H- benzimidazol1-yl)propyl]-4-piperidinyl]-1,3-dihy dro-2 H- benzimidazol-2-one [1]. DOM is a dopamine antagonist used as an antiemetic for the short term treatment of nausea and vomiting of various etiologies [2]. Both drugs are formulated in a binary mixture for the treatment of motion sickness. The chemical structure of both CIN and DOM are given below:
Few methods for determination of CIN and DOM in their binary mixture have been reported in literature, including derivative [3,4] and derivative ratio [5] spectrophotometry, HPLC [6,7] and TLCdensitometry [8], capillary electrophoresis [9] methods. The aim of the present work is to develop simple, rapid and selective area under curve and dual wavelength spectrophotometric methods for simultaneous determination of components having overlapping spectra in their binary mixtures, having the advantages of minimal data processing and a wider range of applications over the previously mentioned methods, also, they did not need any computer programs (like derivative and derivative ratio) and can be applied with simple mathematical calculations. Area under curve method is a newly established spectrophotometric method provides a simple way to determine concentration of the component of interest depending on area of its absorption spectrum. This method has the advantage of being simple, sensitive and selective for determination of components in presence of other interfering substances; it is widely applied for determination of different drugs in their binary mixtures [10, 11].
To prove the ability of the newly described methods in resolving the overlapping spectral data and simultaneous determination of each component, it was applied for the analysis of a mixture of
Cinnarizine (CIN) and Domperidone (DOM) formulated together in the form of tablets widely used for the treatment of motion sickness.
2. Experimental 2.1. Apparatus Spectrophotometer: SHIMADZU UV-1601 PC, dual beam UV–visible spectrophotometer with two matched 1-cm quartz cells, connected to an IBM compatible personal computer (PC) and an HP- 600 inkjet printer. Bundled UV-PC personal spectroscopy software version (3.7) was used to process the absorption. The spectral band width was 0.2 nm with wavelength scanning speed of 2800 nm min−1.
2.2. Materials Pure standards Cinnarizine and Domperidone were kindly supplied by Sigma Pharmaceutical Industries (Egypt, S.A.E.). Their purity was found to be 99.80% and 100.48%, respectively, according to the reported spectrophotometric method [5].
Pharmaceutical dosage form Vertigun® tablets (Batch No. 82324) labeled to contain 20 mg of CIN and 15 mg of DOM, manufactured by Sigma Pharmaceutical Industries (Egypt, S.A.E.).
2.3. Chemicals and reagents Methanol of HPLC grade (CHROMASOLV®, Sigma-Aldrich Chemie GmbH, Germany).
2.4. Standard Solutions Stock standard solutions of CIN and DOM (1 mg mL−1): 0.1 gm of each of CIN and DOM were accurately weighed into two separate 100-mL volumetric flasks; 50 mL of methanol was added to each flask, shaken to dissolve and then the volume was completed to the mark with methanol. Working standard solutions of CIN and DOM (100 μg mL−1): 10 mL of each of CIN and DOM stock standard solutions (1 mg mL−1) was transferred accurately into two separate 100-mL volumetric flasks; then the volume was completed to the mark with methanol.
2.5. Laboratory prepared mixtures Accurate aliquots equivalent to (40–180 μg) of CIN were transferred from its working solution (100 μg mL−1) into a series of 10-mL volumetric flasks and portions equivalent to (60–120 μg) of DOM from its working solution (100 μg mL−1) were added to the same flasks and volumes were completed to mark with methanol and mixed well.
3. Methods The absorption spectra of 10 µg mL–1 of each of CIN and DOM in methanol were recorded over the range 200–400 nm using methanol as a blank.
3.1. Method A: Area under curve method Aliquots from CIN and DOM working solutions (100 μg mL−1) equivalent to 20–200 μg and 20–220 μg, respectively, were accurately transferred into two separate sets of 10-mL volumetric flasks and completed to the mark with methanol. The zero order absorbance of each set was scanned in the range of 200-400 nm. Area under the curve for the wavelength ranges selected for determination of CIN and DOM are 241-258 nm (λ -λ ) and 280-292 nm (λ -λ ), the absorptivity 'Y' 1
2
3
4
values of each of the two drugs were determined at the selected wavelength ranges. The absorptivity 'Y' values were determined as, Y= area under curve of component (from 241 to 258 nm or 280 to 292 nm)/concentration of the component (in g L−1). Mixed standard were prepared and their area under the curve were measured at the selected wavelength ranges. Concentration of two drugs in mixed standard and the sample solution were calculated using the corresponding equations.
3.2. Method B: Dual wavelength method Standard solutions of both CIN and DOM in the range of 2-20 µg mL-1 and 2-22 µg mL-1, respectively, were separately prepared by appropriate dilutions of their respective working solutions in methanol. The spectra of the prepared standard solutions were scanned in the range of 200-400 nm. Absorbance values at both 240.2 and 273.2 nm (for CIN) and at both 230.8 and 259.2 nm (for DOM) were measured. CIN was determined by plotting the difference in absorbance at 240.2 and 273.2 nm (difference is zero for DOM) against its corresponding concentration. Similarly, for determination of DOM, the difference in absorbance at 230.8 and 259.2 nm (difference is zero for CIN) was plotted against its corresponding concentration. The concentrations of the two drugs were calculated each from the corresponding calibration curve equation.
3.3. Analysis of laboratory prepared mixtures Different laboratory prepared mixtures containing different ratios of CIN and DOM were prepared. Zero order absorption spectra of these mixtures were recorded using methanol as a blank. For method A, area under curves of the prepared mixtures in the wavelength ranges 241258 nm (λ1-λ2) and 280-292 nm (λ3-λ4) were measured. For method B, the differences in absorbance at 240.2 and 273.2 nm (for CIN) and at 230.8 and 259.2 nm (for DOM) were recorded. From the corresponding equations, the concentrations of CIN and DOM in the prepared mixtures were calculated using the proposed methods.
3.4. Assay of pharmaceutical formulation (Vertigun® tablets) The contents of 20 Vertigun® tablets were powdered and mixed well. An accurately weighed portion of the powdered tablet equivalent to 100 mg of CIN and 75 mg of DOM was transferred into 100-mL volumetric flask; 75 mL methanol was added and sonicated for 30 min, filtered, and then completed to volume with methanol. The solution was diluted to obtain 100 μg mL−1 working solution using methanol as a solvent. The procedure of each method was followed and the concentration of CIN and DOM was calculated from the corresponding equations. The validity of the methods was assessed by applying the standard addition technique.
4. Results and discussion British Pharmacopoeia [12] states non-aqueous titration method for determination of both CIN
and
DOM,
separately.
The
proposed
area
under
curve
and
dual
wavelength
spectrophotometric methods have the advantage of being simple and selective for simultaneous determination of CIN and DOM with minimal sample and data manipulation compared to the reported derivative and derivative ratio methods [3-5] which are less sensitive and require derivatization technique whereas the reported HPLC and capillary electrophoresis [6, 7, 9] methods require sophisticated and expensive techniques. Accordingly, there was a need to develop new analytical procedures that will serve as reliable, accurate and sensitive methods for simultaneous determination of CIN and DOM. Analytical methods for the determination of binary mixture without previous separation were of interest. The absorption spectra of CIN and DOM showed severe overlap, which makes the determination of concentration of each of them in the mixture more difficult (Fig. 1). By applying the proposed techniques to the spectral data of the mixture, both CIN and DOM concentrations could be determined without any interference.
4.1. Method development and optimization Selection of the wavelength region to construct AUC method has a great effect on the analytical parameters such as slope, intercept and correlation coefficient. Different wavelength regions were tested where the wavelength ranges 241-258 nm and 280-292 nm were selected which showed good selectivity and percentage recovery, Fig. 2. For dual wavelength method, different sets of wavelengths were tried; each set was selected to have equal absorbance for the interfering component and great difference in absorbance for the component of interest. For determination of CIN, the wavelength set selected was 240.2 and 273.2 nm at which the difference in absorbance of DOM is zero. Also, for determination of DOM, the wavelength set selected was 230.8 and 259.2 nm at which the difference in absorbance of CIN is zero.
4.2. Area under curve method Area under curve of the absorption spectra in the wavelength ranges 241-258 nm (λ1-λ2) and 280-292 nm (λ3-λ4) of CIN in the concentration range of 2-20 µg mL-1 was calculated. For DOM, area under curve of the absorption spectra in the wavelength ranges 241-258 nm (λ1-λ2) and 280292 nm (λ3-λ4) in the concentration range of 2-22 µg mL-1 was also calculated. The absorptivity 'Y' values of CIN and DOM were calculated at each wavelength range (Fig. 2). The concentrations of CIN and DOM can be obtained by applying Cramer's rule and matrices in equations (1) and (2). Concentration of two the drugs in mixed standard and the sample solution were calculated according to the following equations: A1 = 1015.51 CCIN + 131.626 CDOM
(1)
at 241-258 nm (λ1-λ2)
A2 = 44.195 CCIN + 348.754 CDOM
(2)
at 280-292 nm (λ3-λ4)
Where, CCIN and CDOM are the concentrations of CIN and DOM in g L-1, respectively. 1015.51 and 44.195 are the absorptivity (Y value) of CIN at (λ -λ ) and (λ -λ ), respectively. 1
2
3
4
131.626 and 348.754 are absorptivity (Y value) of DOM at (λ -λ ) and (λ -λ ), respectively. 1
2
3
4
A and A are the area under curve of sample solutions at the wavelength range (λ -λ ) and (λ -λ ), respectively. 1
3
2
1
2
4
The proposed area under curve method was successfully applied for determination of CIN and DOM in their laboratory prepared mixtures containing different ratios of them with mean percentage recoveries 100.37 ± 0.81 and 99.75 ± 1.23, respectively, Table 1, confirming that each of the cited drugs could be successfully determined without interference from the other indicated that the method is selective for determination of the studied drugs.
4.3. Dual wavelength method The principle of dual wavelength method is that the absorbance difference at two points on the spectra is directly proportional to the component of interest, independent of the interfering component. It can be utilized to a great extent without much complication to calculate the unknown concentration of the component of interest in a mixture. The requirement for dual wavelength method is the selection of two wavelengths where the interfering component shows the same absorbance while the component of interest shows significant difference in absorbance with concentration. Fig. 2 shows that absorbance values of DOM are the same at 240.2 and 273.2 nm therefore these two wavelengths were selected for determination of CIN. The same for the two wavelengths 230.8 and 259.2 nm, the absorbance values of CIN are the same, hence those two wavelengths were selected for determination of DOM.
Difference in absorbances of CIN at 240.2 and 273.2 nm were plotted against its concentration in the range of 2-20 µg mL-1, also for DOM, difference in absorbances at 230.8 and 259.2 nm were plotted against its concentration in the range of 2-22 µg mL-1. The concentration of CIN and DOM can be calculated from the following regression equations: A1 = 0.0440 CCIN – 0.0048
, r = 0.9999
A2 = 0.0252 CDOM – 0.0082
, r = 0.9999
Where, A1 is the absorbance difference at 240.2 and 273.2 nm. A2 is the absorbance difference at 230.8 and 259.2 nm. CCIN and CDOM are the concentration of CIN and DOM in µg mL-1, respectively. r is the correlation coefficient. To check the ability of the proposed dual wavelength method for determination of CIN and DOM in their binary mixture, it was applied for determination of them in their laboratory prepared mixtures with mean percentage recovery 100.32 ± 1.07 and 100.25 ± 1.09 for CIN and DOM, respectively, as given in Table 1. The suggested methods were found to be valid and applicable for the analysis of CIN and DOM in their pharmaceutical formulation (Vertigun® tablets) with mean percentage recoveries 99.67 ± 1.05 and 100.61 ± 0.82, respectively, for area under curve method and 100.45 ± 1.22 and 100.63 ± 1.14, respectively, for dual wavelength method. Furthermore, the standard addition technique was performed to assess the accuracy of the suggested methods. The obtained results reveal that there is no interference from tablet excipients as shown in Table 2.
4.4. Method validation Methods validation has been performed according to USP guidelines [13]. a.
Linearity: The linearity of the developed methods was evaluated by analyzing different concentrations of
standard solutions of CIN and DOM in triplicates. For both methods, Beer-Lambert concentration range was found to be 2–20 μg mL−1 for CIN and 2–22 μg mL−1 for DOM. The values of correlation coefficients were close to unity indicating good linearity, the characteristic parameters for the constructed equations are summarized in Table 3. b. Selectivity: The selectivity of the proposed methods was assessed by their application to the analysis of laboratory prepared mixtures containing different ratios of CIN and DOM. Satisfactory results were obtained and presented in Table 1, confirming that each of the cited drugs could be successfully determined without interference from the other.
c. Accuracy: The accuracy of the results was checked by applying the proposed methods for determination of different concentrations of CIN and DOM within their linearity range. The concentrations were obtained from the corresponding regression equations then the percentage recoveries were calculated, Table 3. To ascertain the accuracy of the suggested methods, recovery studies were carried out by standard addition technique at three different levels, Table 2&3. d. Precision: For evaluation of precision, repeatability of three concentrations of pure CIN (4, 8 and 12 μg −1
mL ) and DOM (5, 10 and 15 μg mL−1) were performed by three replicate determinations to estimate the intraday variation and seven replicate determinations on different four days to estimate the interday variation. Then the coefficient of variation at these concentration levels was calculated in Table 3. e. Detection and quantitation limits: They were calculated from the standard deviation (σ) of the response and the slope of the calibration curve (S) in accordance to the following equations: LOD= 3.3 (σ/S) and LOQ= 10 (σ/S). Results presented in Table 3, indicated that the method is sensitive for determination of the studied drugs. f.
Robustness: In order to verify the method’s resilience to slight and deliberate variations in the analytical
parameters, CIN and DOM (10 µg mL-1 of each) were analyzed by the proposed spectrophotometric methods. The robustness was assessed by comparison of the results obtained under standard conditions against those obtained using different cuvettes, different wavelengths (± 2 nm) at different room temperatures (25 C0 ± 5), Table 3.
4.5. Statistical analysis Results obtained by the suggested methods for determination of CIN and DOM in Vertigun® tablets
were
statistically
compared
with
those
obtained
by
applying
the
reported
spectrophotometric method [5]. The calculated t- and F-values were found to be less than the theoretical ones, confirming accuracy and precision at 95% confidence level, as shown in Table 4. Moreover, the developed methods have the advantage of being more simple, rapid and economic over the reported ones and can be used for simultaneous determination of the two studied drugs without derivatization or sample pre-treatment.
5. Conclusion The work presents simple and accurate methods for the simultaneous determination of Cinnarizine and Domperidone. Area under curve and dual wavelength spectrophotometric methods could be applied to the simultaneous determination of both drugs either in their pure powder form or in their combined formulation. The results demonstrate the usefulness of the methods, which are
sensitive, precise, accurate and inexpensive. So, the proposed methods could be used in routine and quality control analysis of the cited drugs in pharmaceutical formulation containing them.
References [1] S. Budavaried, The Merck Index: An Encyclopedia of Chemicals, Drugs and Biologicals, 14th Ed., Merck & Co., Inc., Whitehouse Station, NJ, USA (2006). [2] Martindale, The Extra Pharmacopoeia: The Complete Drug Reference, 35th Ed., K. Profitt (Ed.), Royal Pharmaceutical Society, London, UK (2006). [3] M.Y. Salem, E.S. El-Zanfaly, M.F. El-Tarras and M.G. El-Bardicy; Anal. Bioanal. Chem., 375 (2003) 211-216. [4] C. Vinodhini, V. Vaidhyalingam, A. Ajithadas, A. Niramathi and A. Shantha; Indian Drugs, 39 (2002) 491-493. [5] M.Y. Salem, M.G. El-Bardicy, M.F. El-Tarras and E.S. El-Zanfally; J. Pharm. Biomed. Anal., 30 (2002) 21-33. [6] S.S. Zarapkar, N.P. Bhandari and U.P. Halker; Indian Drugs, 37 (2000) 295-298. [7] A.P. Argekar and S.J. Shah; J. Pharm. Biomed. Anal., 19 (1999) 813-817. [8] A.P. Argekar and S.G. Powar; J. Planar Chromatogr. Mod. TLC, 12 (1999) 272-274. [9] A.A. Abdelal, S. Kitagawa, H. Ohtani, N. El-Enany, F. Belal and M.I. Walash; J. Pharm. Biomed. Anal., 46 (2008) 491-497. [10] S.A. Ghorpade, M.S. Sali, A.H. Kategaonkar, D.M. Patel, V.P Choudhari and B.S. Kuchekar; J. Chil. Chem. Soc., 55 (2010) 115-117. [11] S. Paramane, L. Kothapalli, A. Thomas and A.D. Deshpande; Indian J. Pharm. Sci., 68 (2006) 819-821. [12] BP; The British Pharmacopoeia, Her Majesty's, The Stationary Office, London (2007). [13] The United States Pharmacopeia, 30th Ed., National Formulary 25, United States Pharmacopeia convention Inc. (2007).
Graphical abstract
Fig. 1: Zero order absorption spectra of 10 µg mL-1 of Cinnarizine (―) and 10 µg mL-1 of Domperidone (-----) showing wavelength ranges for area under curve method using methanol as a blank.
Fig. 2: Zero order absorption spectra of 10 µg mL-1 of Cinnarizine (―) and 10 µg mL-1 of Domperidone (-----) showing the selected wavelengths for dual wavelength method using methanol as a blank.
Table 1: Determination of Cinnarizine and Domperidone in laboratory prepared mixtures by the proposed methods. Claimed taken µg mL-1
Dual wavelength method
CIN
DOM
CIN Recoverya %
DOM Recoverya %
CIN Recoverya %
DOM Recoverya %
1
12
9
99.70
100.22
101.67
98.67
2
10
10
100.08
98.10
99.70
100.10
3
12
6
101.33
99.00
99.25
101.17
4
6
12
100.83
99.33
99.17
99.33
5
18
6
99.28
100.17
101.11
100.83
6
4
12
101.00
101.67
101.00
101.42
100.37 ± 0.81
99.75 ± 1.23
100.32 ± 1.07
100.25 ± 1.09
Mean ± SD a
Area under curve method
Mixture No.
Average of 3 determinations.
Table 2: Determination of Cinnarizine and Domperidone in their pharmaceutical formulation by the proposed methods and application of standard addition technique. Area under curve method
Cinnarizine
Found a % ± SD
99.67 ± 1.05
a
Average of 6 determinations.
b
Average of 3 determinations.
Dual wavelength method
Added (µg mL-1)
Found b (µg mL-1)
Recovery %
5
5.04
100.80
7
7.10
101.43
9
8.92
99.11
11
11.12
Mean ± SD
Domperidone
(Batch No. 82324)
CIN and 15 mg DOM/tablet
Vertigun® tablets claimed to contain 20 mg
Pharmaceutical Component formulation
Found a % ± SD
Added (µg mL-1)
Found b (µg mL-1)
Recovery %
5
5.06
101.20
7
6.88
98.29
9
8.89
98.78
101.09
11
11.07
100.64
100.61 ± 1.03
Mean ± SD 6
5.91
98.50
100.45 ± 1.22
99.73 ± 1.41
6
6.05
100.83
100.61 ±
8
7.89
98.63
100.63 ±
8
8.09
101.13
0.82
10
10.05
100.50
1.14
10
9.92
99.20
12
12.11
100.92
12
11.92
99.33
100.22 ± 1.08
Mean ± SD
Mean ± SD
99.54 ± 1.12
Table 3: Assay parameters and method validation for the determination of pure sample of Cinnarizine and Domperidone by the proposed methods. Area under curve method
Parameters
Cinnarizine λ (nm)
Domperidone
area between 241-258 and 280-292
Concentration range ( µg mL-1)
Dual wavelength method Cinnarizine
Domperidone
difference at 240.2 and 273.2
difference at 230.8 and 259.2
2–20
2–22
2–20
2–22
Linearity Slope Intercept Correlation coefficient (r)
0.0440 -0.0048 0.9999
0.0252 0.0082 0.9999
Accuracy (Mean ± SD)
99.96 ± 0.81
100.05 ± 0.74
99.81 ± 0.76
99.48 ± 0.86
Selectivity
100.37 ± 0.81
99.75 ± 1.23
100.32 ± 1.07
100.25 ± 1.09
Repeatability a
0.85
0.83
0.75
0.68
Intermediate precision b
1.02
0.92
0.77
0.84
LOD c ( µg mL-1)
0.55
0.71
0.62
0.73
1.43
1.55
1.63
1.53
Precision (%RSD)
c
-1
LOQ ( µg mL )
a
The intraday (n = 3), average of three different concentrations repeated three times within day.
b
The interday (n = 3), average of three different concentrations repeated three times in three successive days.
c
Limit of detection and limit of quantitation.
Table 4: Statistical comparison of the results obtained by applying the proposed methods and the reported method for the analysis of Cinnarizine and Domperidone in their pharmaceutical formulation.
Area under curve method
Dual wavelength method
Reported method b [5]
Item CIN
DOM
CIN
DOM
CIN
DOM
Mean
99.67
100.61
100.45
100.63
99.71
99.35
SD
1.05
0.82
1.22
1.14
1.10
0.82
n
6
6
6
6
6
6
t- test (2.18) a
0.95
0.02
0.30
0.05
F-value (4.88) a
0.92
0.99
0.83
0.48
a
The values in parenthesis are corresponding to the theoretical values of t and F (P = 0.05).
b
First derivative of ratio spectra for determination of Cinnarizine using 2.5 µg mL-1 of Domperidone as a divisor, and for determination of Domperidone using 2.5 µg mL-1 of Cinnarizine as a divisor and methanol as a solvent.
18
Highlights New spectrophotometric determination of cinnarizine and domperidone. Area under curve method is simple with minimal sample and data manipulation. Dual wavelength method can resolve binary mixture with overlapping spectra. The proposed methods are more sensitive and selective than the published methods.
19