Mathematical algorithms applied to the multi-linear regression functions for the multicomponent determination of pharmaceutical dosage form containing three-component mixtures

Abstract

In the presence of closely overlapping spectra, the quantitative multiresolution of ternary mixtures of three active compounds paracetamol (PAR), caffeine (CAF) and acetylsalycilic acid (ASP) in tablets, without using pretreatment such as separation step and graphical procedure of spectra was accomplished by the multivariate spectral calibration models, tri-linear regression calibration (TLRC), multi-linear regression calibration (MLRC) and Cramer's rule solution (CRS) of three linear equation functions in the matrix form. In the first two models, TLRC and MLRC are based on the use of the linear regression functions at selected wavelength sets in the spectral region of 210-300 nm. In the case of CRS model, A(1)(1) (1%, 1 cm) were used to obtain three linear equation functions and this linear equation system was resolved by the Cramer's rule for the prediction of PAR, CAF and ASP in samples. In the TLRC and CRS models, the selection of the appropriate wavelength set was performed by the Kaiser's technique. The algorithms of these mathematical calibration models were briefly described. The validation of TLRC, MLRC and CRS models was carried out by analyzing various synthetic ternary mixtures and by using the standard addition technique. These three calibration approaches were applied to the analysis of the real pharmaceutical tablets containing PAR, CAF and ASP The obtained results were statistically compared with each other by using experimental and statistical tests. In the comparison of TLRC and MLRC models to the classical approach, CRS technique, the successful assay results were observed for the quantitative multiresolution of ternary mixture of the subject active compounds.