Chromatographic alignment by warping and dynamic programming as a pre-processing tool for PARAFAC modelling of liquid chromatography–mass spectrometry data

Solutes analysed with LC–MS are characterised by their retention times and mass spectra, and quantified by the intensities measured. This highly selective information can be extracted by multiway modelling. However, for full use and interpretability it is necessary that the assumptions made for the model are valid. For PARAFAC modelling, the assumption is a trilinear data structure. With LC–MS, several factors, e.g. non-linear detector response and ionisation suppression may introduce deviations from trilinearity. The single largest problem, however, is the retention time shifts not related to the true sample variations. In this paper, a time warping algorithm for alignment of LC–MS data in the chromatographic direction has been examined. Several refinements have been implemented and the features are demonstrated for both simulated and real data. With moderate time shifts present in the data, pre-processing with this algorithm yields approximately trilinear data for which reasonable models can be made.