A novel strategy for solving matrix effect in three-way data using parallel profiles with linear dependencies

This work presents a novel strategy for solving matrix effects using the second-order advantage and a new method called PARAllel profiles with LINear Dependencies (PARALIND). PARALIND is a generalization of parallel factor analysis (PARAFAC) and was developed to extend its use to problems with linearly dependent factors where normal PARAFAC analysis will fail to provide meaningful results. Such linearly dependent factors occur in standard addition with second-order data such as fluorescence excitation emission matrices (EEM). By successive standard addition of an analyte, the concentrations of the remaining components (interferences) remain constant and introduce linear dependency between interference concentrations in the samples. This theoretically leads to rank deficiency in the score matrix holding the relative concentrations when using PARAFAC for modeling. In practice, PARAFAC models of such data will mostly provide solutions where the score matrix is not rank deficient but a function of the noise in the data. This problem is shown to be solved by using PARALIND. In order to evaluate the applicability of the method a simulated as well as an experimental data set is tested. The results from experimental data relate to the direct determination of salicylic acid (SA), the main product of aspirin degradation, in undiluted human plasma by spectrofluorimetry.