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Analysis of GC×GC-TOFMS data for large numbers of poorly-resolved peaks, and for large numbers of samples remains an enduring problem that hinders the widespread application of the technique. For multiple samples, GC×GC-TOFMS data for specific chromatographic regions manifests as a 4 th order tensor of I mass spectral acquisitions, J mass channels, K modulations, and L samples. Chromatographic drift is common along both the first-dimension (modulations), and along the second-dimension (mass spectral acquisitions), while drift along the mass channel is for all practical purposes nonexistent. A number of solutions to handling GC×GC-TOFMS data have been proposed: these involve reshaping the data to make it amenable to either 2 nd order decomposition techniques based on Multivariate Curve Resolution (MCR), or 3 rd order decomposition techniques such as Parallel Factor Analysis 2 (PARAFAC2). PARAFAC2 has been utilised to model chromatographic drift along one mode, which has enabled its use for robust decomposition of multiple GC-MS experiments. Although extensible, it is not straightforward to implement a PARAFAC2 model that accounts for drift along multiple modes. In this submission, we demonstrate a new approach and a general theory for modelling data with drift along multiple modes, for applications in multidimensional chromatography with multivariate detection. The proposed model captures over 99.9% of variance for a synthetic data set, presenting an extreme example of peak drift and co-elution across two modes of separation., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier B.V. All rights reserved.)

There are many challenges associated with analysing gas chromatography - mass spectrometry (GC-MS) data. Many of these challenges stem from the fact that electron ionization (EI) can make it difficult to recover molecular information due to the high degree of fragmentation with concomitant loss of molecular ion signal. With GC-MS data there are often many common fragment ions shared among closely-eluting peaks, necessitating sophisticated methods for analysis. Some of these methods are fully automated, but make some assumptions about the data which can introduce artifacts during the analysis. Chemometric methods such as Multivariate Curve Resolution (MCR), or Parallel Factor Analysis (PARAFAC/PARAFAC2) are particularly attractive, since they are flexible and make relatively few assumptions about the data - ideally resulting in fewer artifacts. These methods do require expert user intervention to determine the most relevant regions of interest and an appropriate number of components, k, for each region. Automated region of interest selection is needed to permit automated batch processing of chromatographic data with advanced signal deconvolution. Here, we propose a new method for automated, untargeted region of interest selection that accounts for the multivariate information present in GC-MS data to select regions of interest based on the ratio of the squared first, and second singular values from the Singular Value Decomposition (SVD) of a window that moves across the chromatogram. Assuming that the first singular value accounts largely for signal, and that the second singular value accounts largely for noise, it is possible to interpret the relationship between these two values as a probabilistic distribution of Fisher Ratios. The sensitivity of the algorithm was tested by investigating the concentration at which the algorithm can no longer pick out chromatographic regions known to contain signal. The algorithm achieved detection of features in a GC-MS chromatogram at concentrations below 10 pg on-column. The resultant probabilities can be interpreted as regions that contain features of interest., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier B.V. All rights reserved.)

Dunaliella tertiolecta is a marine microalgae that has been studied extensively as a potential carbon-neutral biofuel source (Tang et al., 2011). Microalgae oil contains high quantities of energy-rich fatty acids and lipids, but is not yet commercially viable as an alternative fuel. Carefully optimised growth conditions, and more recently, algal-bacterial co-cultures have been explored as a way of improving the yield of D. tertiolecta microalgae oils. The relationship between the host microalgae and bacterial co-cultures is currently poorly understood. Here, a complete workflow is proposed to analyse the global metabolomic profile of co-cultured D. tertiolectra and Phaeobacter italicus R11, which will enable researchers to explore the chemical nature of this relationship in more detail. To the best of the authors' knowledge this study is one of the first of its kind, in which a pipeline for an entirely untargeted analysis of the algal metabolome is proposed using a practical sample preparation, introduction, and data analysis routine., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

Comprehensive two-dimensional gas chromatography (GC × GC) provides enhanced separation power over its one-dimensional counterpart - gas chromatography (GC). This enhancement is achieved by the inclusion of a secondary column, the choice of which is a major determinant on the quality of the ultimate separation. When developing and optimizing a new GC × GC method, the choices of stationary phase chemistries, geometries and configurations (which phase serves in which dimension) are of fundamental importance, and must often be addressed even before the manipulation of instrumental conditions. These choices are often made using educated guesses, literature searches, or trial and error. Thermodynamic models of GC separations; however, provide a fast and easy means of acquiring information for guiding these choices. By using characteristic thermodynamic parameters (characteristic temperatures, T char , and characteristic thermal constants, θ char ), we demonstrate the generation of maps that can inform the choices of column chemistries, phase ratios and configurations for GC × GC separations., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Thermodynamic parameters of ΔH(T0), ΔS(T0), and ΔCP for 156 compounds comprising alkanes, alkyl halides and alcohols were determined for a 5% phenyl 95% methyl stationary phase. The determination of thermodynamic parameters relies on a Nelder-Mead simplex optimization to rapidly obtain the parameters. Two methodologies of external and leave one out cross validations were applied to assess the robustness of the estimations of thermodynamic parameters. The largest absolute errors in predicted retention time across all temperature ramps and all compounds were 1.5 and 0.3s for external and internal sets, respectively. The possibility of an in silico extension of the thermodynamic library was tested using a quantitative structure-retention relationship (QSRR) methodology. The estimated thermodynamic parameters were utilized to develop QSRR models. Individual partial least squares (PLS) models were developed for each of the three classes of the molecules. R(2) values for the test sets of all models across all temperature ramps were larger than 0.99 and the average of relative errors in retention time predictions of the test sets for alkanes, alcohols, and alkyl halides were 1.8%, 2.4%, and 2.5%, respectively., (Copyright © 2014 Elsevier B.V. All rights reserved.)

A new method for calibrating thermodynamic data to be used in the prediction of analyte retention times is presented. The method allows thermodynamic data collected on one column to be used in making predictions across columns of the same stationary phase but with varying geometries. This calibration is essential as slight variances in the column inner diameter and stationary phase film thickness between columns or as a column ages will adversely affect the accuracy of predictions. The calibration technique uses a Grob standard mixture along with a Nelder-Mead simplex algorithm and a previously developed model of GC retention times based on a three-parameter thermodynamic model to estimate both inner diameter and stationary phase film thickness. The calibration method is highly successful with the predicted retention times for a set of alkanes, ketones and alcohols having an average error of 1.6s across three columns., (Copyright © 2014 Elsevier B.V. All rights reserved.)

A new method for estimating the thermodynamic parameters of ΔH(T0), ΔS(T0), and ΔCP for use in thermodynamic modeling of GC×GC separations has been developed. The method is an alternative to the traditional isothermal separations required to fit a three-parameter thermodynamic model to retention data. Herein, a non-linear optimization technique is used to estimate the parameters from a series of temperature-programmed separations using the Nelder-Mead simplex algorithm. With this method, the time required to obtain estimates of thermodynamic parameters a series of analytes is significantly reduced. This new method allows for precise predictions of retention time with the average error being only 0.2s for 1D separations. Predictions for GC×GC separations were also in agreement with experimental measurements; having an average relative error of 0.37% for (1)tr and 2.1% for (2)tr., (Copyright © 2013 Elsevier B.V. All rights reserved.)

A three-dimensional extension of a previously developed metric termed cluster resolution is presented. The cluster resolution metric considers confidence ellipses (here three-dimensional confidence ellipsoids) around clusters of points in principal component or latent variable space. Cluster resolution is defined as the maximum confidence limit at which confidence ellipses do not overlap and can serve to guide automated variable selection processes. Previously, this metric has been used to guide variable selection in a two-dimensional projection of data. In this study, the metric is refined to simultaneously consider the shapes of clusters of points in a three-dimensional space. We couple it with selectivity ratio-based variable ranking and a combined backward elimination/forward selection strategy to demonstrate its use for the automated optimization of a six-class PCA model of gasoline by vendor and octane rating. Within-class variability was artificially increased through evaporative weathering and intentional contamination of samples, making the optimization more challenging. Our approach was successful in identifying a small subset of variables (644) from the raw GC-MS chromatographic data which comprised ≈ 2 × 10(6) variables per sample. In the final model there was clear separation between all classes. Computational time for this completely automated variable selection was 36 h; slower than solving the same problem using three two-dimensional projections, but yielding an overall better model. By simultaneously considering three dimensions instead of only two at a time, the resulting overall cluster resolution was improved., (Copyright © 2012 Elsevier B.V. All rights reserved.)

Retention behaviors of alkyl phosophates were studied on a series of ionic liquid gas chromatography columns. The selectivity of the IL columns for alkyl phosphates were compared with a 5% phenyl column as a route to evaluating the potential use of IL columns in the analysis of alkyl phosphates in petroleum samples in both one- and multi-dimensional GC. Most interestingly, we demonstrate for the first time the dependence of elution order on separation temperature for members of a homologous series of compounds. At low temperatures it was found that trihexyl phosphate eluted before trioctyl phosphate, while at higher temperatures this pattern was reversed., (Copyright © 2012 Elsevier B.V. All rights reserved.)

A method was developed to accurately predict both the primary and secondary retention times for a series of alkanes, ketones and alcohols in a flow-modulated GC×GC system. This was accomplished through the use of a three-parameter thermodynamic model where ΔH, ΔS, and ΔC(p) for an analyte's interaction with the stationary phases in both dimensions are known. Coupling this thermodynamic model with a time summation calculation it was possible to accurately predict both (1)t(r) and (2)t(r) for all analytes. The model was able to predict retention times regardless of the temperature ramp used, with an average error of only 0.64% for (1)t(r) and an average error of only 2.22% for (2)t(r). The model shows promise for the accurate prediction of retention times in GC×GC for a wide range of compounds and is able to utilize data collected from 1D experiments., (Copyright © 2012 Elsevier B.V. All rights reserved.)

Quantification of comprehensive two-dimensional gas chromatographic (GC×GC) data in a commercial software package is examined. ChromaTOF(®) (Leco Instruments) includes a smoothing step prior to data integration. Improper choice of integration parameters can introduce errors in excess of ±10% and as high as 60% in the total peak area. Herein we demonstrate the critical nature of the smoothing parameters in this software, particularly the expected peak width in the second dimension ((2)w) which should be verified as part of a QA/QC protocol., (Copyright © 2012 Elsevier B.V. All rights reserved.)

Petroleum analysis presents many unique challenges as a result of the overwhelming number of compounds present in petroleum samples. Consequently the use of multidimensional separation techniques will almost invariably be required in order to overcome these challenges. Within this paper we review recent developments in the application of comprehensive multidimensional techniques for petroleum analysis focusing on more recent applications. Basic instrumentation for various comprehensive multidimensional techniques is outlined along with an overview of a broad range of applications in both group-type and target molecule analyses for petroleum and biofuel analysis. In addition, strategies for data interpretation and chemometric analysis of multidimensional data are also reviewed., (Copyright © 2012 Elsevier B.V. All rights reserved.)

Alkyl phosphate based gellants used as viscosity builders for fracturing fluids used in the process of hydraulic fracturing have been implicated in numerous refinery-fouling incidents in North America. In response, industry developed an inductively coupled plasma optical emission spectroscopy (ICP-OES) based method for the analysis of total volatile phosphorus in distillate fractions of crude oil; however, this method is plagued by poor precision and a high limit of detection (0.5±1μg phosphorus mL(-1)). Furthermore this method cannot provide speciation information, which is critical for developing an understanding of the challenge of alkyl phosphates at a molecular level. An approach using comprehensive two-dimensional gas chromatography with nitrogen phosphorus detection (GC×GC-NPD) and post-column Deans switching is presented. This method provides qualitative and quantitative profiles of alkyl phosphates in industrial petroleum samples with increased precision and at levels comparable to or below those achievable by ICP-OES. A recovery study in a fracturing fluid sample and a profiling study of alkyl phosphates in four recovered fracturing fluid/crude oil mixtures (flowback) are also presented., (Copyright © 2012 Elsevier B.V. All rights reserved.)

Direct chemometric interpretation of raw chromatographic data (as opposed to integrated peak tables) has been shown to be advantageous in many circumstances. However, this approach presents two significant challenges: data alignment and feature selection. In order to interpret the data, the time axes must be precisely aligned so that the signal from each analyte is recorded at the same coordinates in the data matrix for each and every analyzed sample. Several alignment approaches exist in the literature and they work well when the samples being aligned are reasonably similar. In cases where the background matrix for a series of samples to be modeled is highly variable, the performance of these approaches suffers. Considering the challenge of feature selection, when the raw data are used each signal at each time is viewed as an individual, independent variable; with the data rates of modern chromatographic systems, this generates hundreds of thousands of candidate variables, or tens of millions of candidate variables if multivariate detectors such as mass spectrometers are utilized. Consequently, an automated approach to identify and select appropriate variables for inclusion in a model is desirable. In this research we present an alignment approach that relies on a series of deuterated alkanes which act as retention anchors for an alignment signal, and couple this with an automated feature selection routine based on our novel cluster resolution metric for the construction of a chemometric model. The model system that we use to demonstrate these approaches is a series of simulated arson debris samples analyzed by passive headspace extraction, GC-MS, and interpreted using partial least squares discriminant analysis (PLS-DA)., (Copyright © 2011 Elsevier B.V. All rights reserved.)

We present an investigation into the influence of carrier gas on the thermodynamics governing a capillary gas chromatographic separation. Thermodynamic parameters are estimated for a series of alkanes and alcohols on three common stationary phases using helium, hydrogen, and nitrogen carrier gases. It is shown that the substitution of carrier gases for one another results in a change in the thermodynamic parameters governing the separation. The effect of the carrier gas on the thermodynamic parameters is large enough to compromise the accuracy of the retention time calculations based on thermodynamic parameters collected in a carrier gas other than the one actually in use in a specific gas chromatographic system. A possible kinetic explanation for these observations is also investigated., (Copyright © 2010 Elsevier B.V. All rights reserved.)

The ability to predict the amount of time that a light petroleum mixture has been weathered could have many applications, such as aiding forensic investigators in determining the cause and intent of a fire. In our study, an evaporation chamber that permits control of airflow and temperature was constructed and used to weather a model nine-component hydrocarbon mixture. The composition of the mixture was monitored over time by gas chromatography and a variety of chemometric models were explored, including partial least squares (PLS), nonlinear PLS (PolyPLS) and locally weighted regression (LWR or loess). A hierarchical application of multivariate techniques was able to predict the time for which a sample had been exposed to evaporative weathering. A classification model based on partial least squares discriminant analysis (PLS-DA) could predict whether a sample was relatively fresh (< 12 h exposure time) or highly weathered (>20 h exposure time). Subsequent regression models for these individual classes were evaluated for accuracy using the root mean square error of prediction (RMSEP). Prior to regression model calculation, y-gradient generalized least squares weighting (GLSW) was used to preprocess the data by removing variance from the X-block, which was orthogonal to the Y-block. LWR was found to be the most successful regression method, whereby fresh samples could be predicted to within 40 min of exposure and highly weathered samples predicted to within 5.6h. These results suggest that our hierarchical chemometric approach may also allow us to estimate the age of more complicated light petroleum mixtures, such as gasoline., (Copyright © 2011 Elsevier B.V. All rights reserved.)

A novel metric termed cluster resolution is presented. This metric compares the separation of clusters of data points while simultaneously considering the shapes of the clusters and their relative orientations. Using cluster resolution in conjunction with an objective variable ranking metric allows for fully automated feature selection for the construction of chemometric models. The metric is based upon considering the maximum size of confidence ellipses around clusters of points representing different classes of objects that can be constructed without any overlap of the ellipses. For demonstration purposes we utilized PCA to classify samples of gasoline based upon their octane rating. The entire GC-MS chromatogram of each sample comprising over 2 × 10(6) variables was considered. As an example, automated ranking by ANOVA was applied followed by a forward selection approach to choose variables for inclusion. This approach can be generally applied to feature selection for a variety of applications and represents a significant step towards the development of fully automated, objective construction of chemometric models., (Copyright © 2010 Elsevier B.V. All rights reserved.)

Metabolomics has been defined as the quantitative measurement of all low molecular weight metabolites (sugars, amino acids, organic acids, fatty acids and others) in an organism's cells at a specified time under specific environmental/biological conditions. Currently, there is considerable interest in developing a single method of derivatization and separation that satisfies the needs for metabolite analysis while recognizing the many chemical classes that constitute the metabolome. Chemical derivatization considerably increases the sensitivity and specificity of gas chromatography-mass spectrometry for compounds that are polar and have derivatizable groups. Microwave-assisted derivatization (MAD) of a set of standards spanning a wide range of metabolites of interest demonstrates the potential of MAD for metabolic profiling. A final protocol of 150 W power for 90 s was selected as the derivatization condition, based upon the study of each chemical class. A study of the generation of partially derivatized components established the conditions where this could potentially be a problem; the use of greater volumes of reagent ensured this would not arise. All compounds analyzed by comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry in a standard mixture showed good area ratio reproducibility against a naphthalene internal standard (RSD<10% in all but one case). Concentrations tested ranged from 1 microg/mL to 1000 microg/mL, and the calibration curves for the standard mixtures were satisfactory with regression coefficients generally better than 0.998. The application to gas chromatography-quadrupole mass spectrometry and comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry for a typical reference standard of relevance to metabolomics is demonstrated., (Copyright 2010 Elsevier B.V. All rights reserved.)