Quantification and handling of nonlinearity in Raman micro-spectrometry of pharmaceuticals

This work demonstrates how nonlinearity in Raman spectrometry of pharmaceuticals can be handled and accurate quantification can be achieved by applying certain chemometric methods including variable selection. Such approach proved to be successful even if the component spectra are very similar or spectral intensities of the constituents are strongly different. The relevant examples are: blends of two crystalline forms of carvedilol ("CRYST-PM" blend) and a three-component pharmaceutical model system ("PHARM-TM" blend). The widely used classical least squares regression (CLS) and partial least squares regression (PLS) quantification methods provided relatively poor root mean squared error of prediction (RMSEP) values: approximately 2-4% and 4-10% for CRYST-PM and PHARM-TM respectively. The residual plots of these models indicated the nonlinearity of the preprocessed data sets. More accurate quantitative results could be achieved with properly applied variable selection methods. It was observed that variable selection methods discarded the most intensive bands while less intensive ones were retained as the most informative spectral ranges. As a result not only the accuracy of concentration determination was enhanced, but the linearity of models was improved as well. This indicated that nonlinearity occurred especially at the intensive spectral bands. Other methods developed for handling nonlinearity were also capable of adapting to the spectral nature of both data sets. The RMSEP could be decreased this way to 1% in CRYST-PM and 3-6% in PHARM-TM. Raman maps with accurate real concentrations could be prepared this way. All quantitative models were compared by the non-parametric sum of ranking differences (SRD) method, which also proved that models based on variable selection or nonlinear methods provide better quantification.