Impact of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry experimental design on data trilinearity and parallel factor analysis deconvolution

Abstract Comprehensive two-dimensional gas chromatography coupled with time-of-flight mass spectrometry (GC × GC-TOFMS) is a powerful instrument for the analysis of complex samples. Deconvolution of overlapped analytes using a suitable chemometric data analysis method such as Parallel Factor Analysis (PARAFAC) is often required. However, PARAFAC is designed to require a strict data trilinearity requirement. In this study we examine how strict this requirement is in the context of GC × GC experimental conditions, and demonstrate that under suitable conditions the data is sufficiently trilinear to achieve accurate deconvolution. The term trilinear deviation ratio ( TDR ) was previously introduced as a quantitative metric to predict the accuracy of PARAFAC deconvolution. Trilinear deviation ratio is defined as the run-to-run retention time shift, Δ 2 t R , for a given analyte on the second dimension ( 2 D) separation, divided by the 2 D analyte peak width-at-base, 2 W b . We demonstrate that experimental conditions impact the TDR range produced and PARAFAC performance. Column selection and modulation period, P M , are shown to significantly influence the TDR range. Two column sets were evaluated, giving rise to different k’ ranges for the 2 D separations. Each column set was used with an optimum P M as well as a longer P M to demonstrate the effect of P M selection on the TDR range and PARAFAC quantification. A P M of 6 s produced a Δ 2 t R range from -19.5 ms to -98 ms and TDR s from 0.157 to 0.439, translating into a PARAFAC bias from +1.6% to -13.5%. However, a P M of 1.5 s produced a Δ 2 t R range of -1.1 ms to -8.8 ms, and significantly lower TDR s from 0.013 to 0.057, translating into PARAFAC errors from +2.1% to -3.9%, with an average of -1.1% ± 1.4. These results validate the idea that a suitable GC × GC experimental design will provide accurate quantification with PARAFAC.