Curve resolution based methods

In previous methods no pre-knowledge of the factors was used to estimate the pure factors. However, in many situations such pre-knowledge is available. For instance, all factors are non-negative and all rows of the data matrix are nonnegative linear combinations of the pure factors. These properties can be exploited to estimate the pure factors. One of the earliest approaches is curve resolution, developed by Lawton and Sylvestre [7], which was applied on two-component systems. Later on, several adaptations have been proposed to solve more complex systems [8-10]. 

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Bijlsma, S. and Smilde, A.K., Application of curve resolution based methods to kinetic data, Anal. Chim. Acta, 396, 231-240, 1999. 

Earlier, it was mentioned that due to the orthogonality constraints of scores and loadings, as well as the variance-based criteria for their determination, it is rare that PCs and LVs obtained from a PC A or PLS model correspond to pure chemical or physical phenomena. However, if one can impose specihc constraints on the properties of the scores and or loadings, they can be rotated to a more physically meaningful form. The multivariate curve resolution (MCR) method attempts to do this for spectral data. 

In addition to the dissolution testing, analytical methods need to be established and validated in order to detect low amounts of crystalline material in the amorphous solid dispersion and/or the final drug product. Xie et al. described the development of such a method, and established a reliable multivariate curve resolution (MCR) method based on the second derivative Raman measurements for quantitative determination of the solid state forms of the drug substance and tablets (Xie et al. 2008). 

A method of resolution that makes a very few a priori assumptions is based on principal components analysis. The various forms of this approach are based on the self-modeling curve resolution developed in 1971 (55). The method requites a data matrix comprised of spectroscopic scans obtained from a two-component system in which the concentrations of the components are varying over the sample set. Such a data matrix could be obtained, for example, from a chromatographic analysis where spectroscopic scans are obtained at several points in time as an overlapped peak elutes from the column. 

Rf. Two approaches have been successfully applied Rq and R, are calculated by imposing constraints on the solutions S and C. This method is called curve resolution factor analysis The second approach is based on the fact that candidate pure spectra... 

The evaluation of the peak purity as a selectivity criterion is a fundamental issue deserving thorough attention. If peaks are found to be heterogeneous, chemometric methods based on curve resolution can be used to isolate the pure analyte contributions from a mixture system, thus making possible an accurate quantification of components (16). 

Ivanisevic et al. (2009) applied pure curve resolution method (PCRM) and alternative least square (ALS) method to pXRD data of ASD for miscibility studies. The PCRM-based approach follows the analysis of the variance among the measured intensity points of pXRD patterns of ASD with varying drug loadings thus... 

Two procedures have been adopted to resolve the preceding problem. Vitha et al. have used a modified curve resolution method [14,15]. This method is based on singular value decomposition (SVD) of a matrix of spectra recorded at several concentrations of surfactant. The method assumes that only two components, namely, the indicator in the aqueous and micellar phase, contribute to the observed spectra. A knowledge of the molar volume of the surfactant and the aggregation number is also required. The curve resolution method gives three parameters the distribution coefficient and the spectra of the indicator solute in the two phases. The value of the spectroscopic parameter of interest (e.g., the position of band maximum) was then determined from the spectrum in the micellar phase. 

Carefully constructed Probe Mixtures based on small molecules and polystyrene standards are used as standardized reference points to better define the functional capabilities of individual columns and column combinations. The result using the method of Probe Mixtures to evaluate columns is better than can be attained from calibration curves alone and is especially useful in this high resolution capability situation. 

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