A new multivariate approach for the optimisation of the simultaneous distillation–extraction technique for free fatty acids using a face centred cube experimental design: application to Parmigiano–Reggiano cheese Original Research Article

A face centred cube (FCC) experimental design was used to investigate effects of extraction time, solvent temperature and sample temperature on the simultaneous distillation–extraction (SDE) extraction yields of 13 fatty acids from Parmigiano–Reggiano cheese, and to find the best extraction conditions for these compounds. Each factor was tested at three levels; 20 experiments were carried out, each producing 13 responses. In order to create a mathematical model representing the relationships between factors and responses and to determine the best conditions for the SDE procedure, GC peak areas were processed by using the multiple regression analysis. The backward stepwise selection of the regression coefficients led to the identification of seven groups of compounds having similar behaviour with respect to the three variables investigated. The same set of models was found by performing principal component analysis (PCA) on the t-values of the regression coefficients of the unrefined polynomials and cluster analysis on the scores of the 13 acids obtained by PCA. The best experimental conditions were evaluated for each compound. The use of the FCC experimental design allowed to evaluate not only the main effects of the variables analysed, but also curvature effects and interaction effects among them.