Mathematical model of ion chronogram from in-tube solid-phase microextraction device coupled with mass spectrometry and optimization framework.

A mathematical description and experimental outputs exhibited that an ion chronogram from an in-tube solid-phase microextraction (SPME) device linked with mass spectrometry (in-tube-SPME-MS) generally appears as a right-skew unimodal signal with a heavy right tail. Analogous to liquid chromatography coupled with mass spectrometry (LC-MS), in-tube-SPME-MS can utilize the area under its produced ion chronogram for regression analysis and has been shown to be a potential approach for fast quantification of analyte. Different level of unimodity of signal in the ion chronogram could positively or negatively affect the choice of the area used for quantification and finally impact on analysis sensitivity and time efficiency of in-tube-SPME-MS. In the paper, we showed that different in-tube SPME design choices and elution experimental setups produce ion chronograms with controllable varying unimodal peak shape patterns. An improved mathematical model was built based on the plate theory of chromatography and the Van Deemter equation to quantitatively describe the elution process from in-tube-SPME device. A computer simulation was implemented to predict ion chronograms and the results were compared with experimental ion chronograms to show the effectiveness of the model. An optimization framework was further presented based on the model to identify optimal device designs (length and diameter of device) and experimental parameters (flow rate) to track targeted ion chronograms with "desired" peak shape patterns. Empirical elution experiments with the in-tube SPME devices adopting optimized geometric parameters and optimal experimental setups confirmed the consistency between the experimental ion chronograms and the numerical simulations to a certain level.