Solving signal instability to maintain the second-order advantage in the resolution and determination of multi-analytes in complex systems by modeling liquid chromatography-mass spectrometry data using alternating trilinear decomposition method assisted with piecewise direct standardization

Multilinear Mathematical Separation in Chromatography

Chromatography is a powerful and generally applicable method for the analytical separation and quantification of the chemical constituents in complex mixtures because chromatographic separation can provide high selectivity by isolating all analytes from interferences. Multiway analysis based on the multilinear model is an increasingly widely used method for interference-free and fast determination of the chemical constituents also in complex mixtures because multilinear mathematical separation can provide high selectivity by extracting the pure signal of the analyte from the mixed signal of a real sample. By combining chromatographic separation with mathematical separation, multiway calibration method, multiway standard additions method, and multiway internal standard method can be established. Chromatography assisted by multiway analysis can reduce the requirements for complete chromatographic separation, save elution time, and decrease the consumption of the mobile phase, particularly when the peak coelution problem is difficult to solve. This review presents the fundamentals and analytical applications of multilinear mathematical separation in chromatography.

Enhancing the selectivity of liquid chromatography-mass spectrometry by using trilinear decomposition on LC-MS data: An application to three-way calibration of coeluting analytes in human plasma

The high selectivities of liquid chromatography and mass spectrometry make liquid chromatography-mass spectrometry one of the most popular tools for quantitative analysis in complex chemical, biological, and environmental systems, while the potential mathematical selectivity of liquid chromatography-mass spectrometry is rarely investigated. This work discussed the mathematical selectivity of liquid chromatography-mass spectrometry by three-way calibration based on the trilinear model, with an application to quantitative analysis of coeluting aromatic amino acids in human plasma. By the trilinear decomposition of the constructed liquid chromatography-mass spectrometry-sample trilinear model and individual regression of the decomposed relative intensity versus concentration, the proposed three-way calibration method successfully achieved quantitative analysis of coeluting aromatic amino acids in human plasma, even in the presence of uncalibrated interferent(s) and a varying background. This analytical method can ease the requirements for sample preparation and complete chromatographic separation of components, reduce the use of organic solvents, decrease the time of chromatographic separation, and increase the peak capacity of liquid chromatography-mass spectrometry. As a "green analytical method", the liquid chromatography-mass spectrometry three-way calibration method can provide a promising tool for direct and fast quantitative analysis in complex systems containing uncalibrated spectral interferents, especially for the situation where the coelution problem is difficult to overcome.

A novel systematic absence of cross peaks-based 2D-COS approach for bilinear data

A novel approach to use two-dimensional correlation spectroscopy (2D-COS) to analyze bilinear data is proposed. A phenomenon called Systematic Absence of Cross Peaks (SACPs) is observed in a 2D asynchronous spectrum. Two theorems relevant to SACPs have been derived. The SACP-based 2D-COS method has been successfully applied on analyzing bilinear data from mixed samples (including one model system and two real systems). Implicit isolated peaks can be identified and assigned to different components based on characteristic pattern of SACPs even if the time-related profiles of different components are severely overlapped. Based on the results of SACPs, spectra of pure components can be retrieved. Identification of SACPs can still be achieved in the presence of artifacts. Thus, neither noise nor baseline drift can produce significant influence on the results obtained from the approach described in this paper. We have used several well-established chemometric methods, including N-Findr, VCA, and MCR with various initial settings, on two systems that can be successfully solved using the 2D-COS method. The chemometric methods mentioned above cannot provide correct spectra of pure components because of severe problem of rotational ambiguity derived from severe overlapping of the time-related profiles. Only when the information from SACPs in 2D-COS is used as additional constraints in MCR calculation, correct spectra can be obtained. That is to say, the SACP-based 2D-COS method provides intrinsic information which is crucial in the analysis of chromatographic-spectroscopic and analogous data even if the time-related profiles of different components overlap severely.