Analytica Chimica Acta 584 (2007) 397–402 A novel strategy for solving matrix effect in three-way data using parallel profiles with linear dependencies Morteza Bahram a,∗ , Rasmus Bro b a Department of Chemistry, Faculty of Sciences, Urmia University, Urmia, Iran b Chemometrics Group, Department of Food Science Royal Veterinary & Agricultural University Rolighedsvej 30, DK-1958 Frederiksberg C, Denmark Received 9 May 2006; received in revised form 12 October 2006; accepted 28 November 2006 Available online 3 December 2006 Abstract 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. © 2006 Elsevier B.V. All rights reserved. Keywords: Parallel profiles with linear dependencies; Standard addition; Three-way data; Fluorescence excitation emission matrices 1. Introduction When a multivariate calibration model is used it is usually required that there are no new constituent(s) in the samples being analyzed. If there are new constituents, a recalibration includ- ing this new constituent will be necessary in order to be able to predict accurately, but this will be possible only if the interfer- ence(s) can be identified. In case of multi-way data, it is possible to handle unknown interferences as part of the calibration. Sev- eral methods for doing so have been developed; most notably generalized rank annihilation methods [1] and parallel factor analysis (PARAFAC). Chemical analysis can be further complicated by matrix effects [2]. When the sensitivity of the response depends on the matrix composition, quantitative predictions based on pure standards may be affected by differences in the sensitivity of the ∗ Corresponding author. Tel.: +98 441 2780952; fax: +98 441 2776707. E-mail address: m.bahram@urmia.ac.ir (M. Bahram). response of the analyte in the presence and in the absence of chemical matrix of the sample. The standard addition method can be used to compensate for such matrix effects. Standard addition can compensate for non-spectral interferences and cer- tain types of spectral interferences (e.g. non-analyte absorption) which enhance or depress the analytical signal of the analyte concentration [2]. As stated above, certain second-order calibration methods are able to resolve and recover the pure analyte response even in the presence of new interferences. In these cases pure analyte standards are commonly used for quantifying unknown sam- ples even though matrix effects may degrade the quality of the resulting predictions. Recently several methods were presented based on combin- ing the second-order advantage and standard addition. Saurina and Tauler [3] proposed a new strategy using multivariate curve- resolution based on alternating least squares (MCR-ALS). The potential of the proposed strategy for solving matrix effects has been studied using an example of determination of triphenyltin in sea water samples for excitation emission matrices (EEM) 0003-2670/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2006.11.070