Amlodipine (AML), chemically, is 3-O-Ethyl5-O-methyl 2-(2-aminoethoxymethyl)-4-(2-chloro-phenyl)-6-methyl-1,4-dihydropyridine-3,5 dicarboxylate (Fig. 1a). It has been used in the management of hypertension as it blocks calcium ions transmembrane influx into vascular smooth muscles and cardiac smooth muscles [1].
Atorvastatin (AVS), chemically, is [R-(R*,R*)]-2-(4-Fluorophenyl)-b,d-dihydroxy-5-(1-methyl-ethyl)-3-phenyl-4-[(phenylamino)carbonyl]-1H-pyrrole-1 heptanoic acid (Fig. 1b). It has been used as a lipid-lowering agent as it inhibits the conversion of HMG-CoA to mevalonic acid a rate limiting step in hepatic cholesterol production [2].
The combination of AML and AVS as antihypertensive and lipid-lowering medications clinically used to reduce the risk of coronary artery disease, stroke and death in patients with cardiovascular risk factors [3].
The simultaneous determination of amlodipine besylate and atorvastatin calcium combination as tablets dosage form is not yet official in any compendia; however, literature survey revealed that there are several reported methods, using analytical techniques such as chromatography, spectrophotometry, spectrofluorimetry, electrochemistry and chemometry for the simultaneous determination of AML and AVS in binary mixtures [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29].
Amlodipine and atorvastatin absorbance spectra (Fig. 2) showed extensive overlapping in the region of 220–300 nm, and resolution of these overlapping spectra and subsequent determination of the analytes concentrations in combined dosage forms is only possible if more sophisticated and expensive techniques are used. The objective of this work was to use multiwavelength regression analysis [30] and absorbance factor method [31] as simple, inexpensive, and reliable UV-spectrophotometric methods in place of expensive techniques based on separation or sophisticated methods using specialized computer programs.
Theoretical background
Multiwavelength regression analysis
Assuming additivity of absorbance and validity of Lambert–Beer’s law, the absorbance of a mixture is the sum of the absorbance values of its individual components.
If we have a mixture consisting of two components, 1 and 2, with an unknown concentration of C1 and C2, then absorbance of the unknown mixture,
$$A_{{{\text{mixture}}}} = \, A_{1} + \, A_{2}$$
applying Beer’s law: A1 = ε1bC1 and A2 = ε2bC2.
Substituting:
$$A_{{{\text{mixture}}}} = \varepsilon_{{1}} bC_{{1}} + \varepsilon_{{2}} bC_{{2}} .$$
However, the absorbencies of standard solutions of the same substances will follow the same Beer’s law relationship and have the same molar absorbance, ε, and one centimeter path length, b, as the unknown solutions under the same conditions.
Therefore, we can write:
$$A_{{\text{standard 1}}} = \varepsilon_{1} bC_{{\text{standard 1}}} \quad {\text{and}}\quad \, A_{{\text{standard 2}}} = \varepsilon_{1} bC_{{\text{standard 2}}}$$
Rearranging these relationships:
$$\varepsilon_{1} b = A_{{\text{standard 1}}} /C_{{\text{standard 1}}} \quad {\text{and}}\quad \varepsilon_{2} b = A_{{\text{standard 2}}} /C_{{\text{standard 2}}}$$
Substituting,
$$A_{{{\text{mixture}}}} = \, A_{{\text{standard 1}}} / \, C_{{\text{standard 1}}} C_{1} + \, A_{{\text{standard 2}}} + \, A_{{\text{standard 2}}} / \, C_{{{\text{standard}}}} . \, C_{2}$$
or
$$A_{{{\text{mixture}}}} = C_{1} /C_{{\text{standard 1}}} . \, A_{{\text{standard 1}}} + C_{2} /C_{{\text{standard 2}}} . \, A_{{\text{standard 2}}}$$
Dividing by Astandard 1 and simplifying we obtain:
$$A_{{{\text{mixture}}}} / \, C_{{\text{standard 1}}} = \, C_{1} / \, C_{{\text{standard 1}}} + \, C_{2} / C_{{\text{standard 2}}} . A_{{\text{standard 2}}} / \, A_{{\text{standard 1}}}$$
(1)
Therefore, a plot of
$$A_{{{\text{mixture}}}} /C_{{\text{standard 1}}} \quad {\text{versus}}\quad \, A_{{\text{standard 2}}} / \, A_{{\text{standard 1 }}}$$
(2)
will give
$${\text{slope }} = \, C_{2} / \, C_{{\text{standard 2}}} \quad {\text{and}}\quad {\text{ intercept}}\, \, C_{1} / \, C_{{\text{standard 1}}}$$
That is, the concentration of the unknown component 2 (C2) in the mixture equals the slope times the concentration of the standard solution for component 2. Likewise, the concentration of the unknown component 1 (C1) in the mixture equals the product of the intercept times the concentration of the standard solution for component1 or simply
$$C_{1} = {\text{intercept }} \times \, C_{{\text{standard 1}}}$$
(3)
and
$$C_{2} = {\text{slope }} \times \, C_{{\text{standard 2 }}}$$
(4)
Absorption factor method
The method depends on the fact that in the overlapping spectra of a mixture of two drugs, e.g., X and Y, X has some interference at λmax of Y (λ1) and has no absorption at another wavelength (λ2) that Y show absorbance at λ1; the absorbance of the mixture at (λ2) equals the absorbance of Y.
$${\text{Absorbance of }}\;Y\;{\text{at}}\; \, \lambda_{1} = \left( {{\text{abs}}\;Y_{\lambda 1} /{\text{abs}}\;Y_{\lambda 2} } \right).{\text{ abs}}_{\lambda 2} \left( {X + Y} \right)$$
(5)
$${\text{Absorbance of}}\;X\;{\text{at}}\; \, \lambda_{1} = {\text{abs}}_{\lambda 2} \left( {X + Y} \right) - \left( {{\text{abs}}\; \, Y_{\lambda 1} /{\text{abs}}\; \, Y_{\lambda 2} } \right).{\text{ abs}}_{\lambda 2} \left( {X + Y} \right)$$
(6)
The proposed methods allow accurate and precise determination of binary mixtures of compounds with highly overlapped spectra using simple and easy mathematics instead of more complex mathematical procedures.