Quantification of naphthalenes in jet fuel with GC x GC/Tri-PLS and windowed rank minimization retention time alignment

Comprehensive, two-dimensional gas chromatography (GC x GC) is used in conjunction with trilinear partial least squares (Tri-PLS) to quantify the percent weight of naphthalenes (two-ring aromatic compounds) in jet fuel samples. The increased peak capacity and selectivity of GC x GC makes the technique attractive for the rapid, and possibly less tedious analysis of jet fuel. The analysis of complex mixtures by GC x GC is further enhanced through the use of chemometric techniques, including those designed for use on 2-D data such as Tri-PLS. Unfortunately, retention time variation, unless corrected, can be an impediment to chemometric analysis. Previous work has demonstrated that the effects of retention time variation can be mitigated in sub-regions of GC x GC chromatograms through the application of an objective retention time alignment algorithm based on rank minimization. Building upon this previous work, it is demonstrated here that the effects of retention time variation can be mitigated throughout an entire GC x GC chromatogram with an objective retention time alignment algorithm based on windowed rank minimization alignment. A significant decrease in calibration error is observed when the algorithm is applied to chromatograms prior to construction of Tri-PLS models. Fourteen jet fuel samples with known weight percentages of naphthalenes (ASTM D1840) were obtained. Each sample was subjected to five replicate five-minute GC x GC separations over a period of two days. A subset of nine samples spanning the range of weight percentages of naphthalenes was chosen as a calibration set and Tri-PLS calibration models were subsequently developed in order to predict the naphthalene content of the samples from the GC x GC chromatograms of the remaining five samples. Calibration models constructed from GC x GC chromatograms that were retention time corrected are shown to exhibit a root mean square error of prediction of roughly half that of calibration models constructed from uncorrected chromatograms. The error of prediction is lowered further to a value that nearly matches the uncertainty in the standard percent weight values (ca. 1% of the median percent volume value) when the aligned chromatograms are truncated to include only regions of the chromatogram populated by naphthalenes and compounds of similar polarity and boiling point.     

Decoding of complex isothermal chromatograms recovered from space missions. Identification of molecular structure

A chemometric approach, based on the study of the autocovariance function, is described to study isothermal GC chromatograms of multicomponent mixtures: isothermal GC analysis is the method of choice in space missions since it is, to date, the only method compatible with flight constraints. Isothermal GC chromatograms look inhomogeneous and disordered with peak density decreasing at higher retention times: a time axis transformation is proposed to make retention an homogeneous process so that CH2 addition in terms of an homologous series yields a constant retention increment. The time axis is transformed into a new scale based on the retention times of n-alkanes, as they are the basis of the universal Kovats indices procedure. The order introduced into the chromatogram by retention time linearization can be simply singled out by the experimental autocorrelation function (EACF) plot: if constant inter-distances are repeated in different regions of the chromatogram, well-shaped peaks are evident in the EACF plot. By comparison, with a standard mixture it is possible to identify peaks diagnostic of specific molecular structures: study of the EACF plot provides information on sample chemical composition. The procedure was applied to standard mixtures containing compounds representative of the planetary atmospheres that will be investigated in the near future: in particular, those related to Titan's atmosphere (Cassini-Huygens mission) and cometary's nucleus (Rosetta mission). The employed experimental conditions simulated those applied to GC instruments installed on space probes and landers in space missions. The method was applied to two specific investigations related to space research, i.e., a comparison of retention selectivity of different GC columns and identification of the chemical composition of an unknown mixture.     

Study of the interdependency of the data sampling ratio with retention time alignment and principal component analysis for gas chromatography

An in-depth study is presented to better understand how data reduction via averaging impacts retention alignment and the subsequent chemometric analysis of data obtained using gas chromatography (GC). We specifically study the use of signal averaging to reduce GC data, retention time alignment to correct run-to-run retention shifting, and principal component analysis (PCA) to classify chromatographic separations of diesel samples by sample class. Diesel samples were selected because they provide sufficient complexity to study the impact of data reduction on the data analysis strategies. The data reduction process reduces the data sampling ratio, S(R), which is defined as the number of data points across a given chromatographic peak width (i.e., the four standard deviation peak width). Ultimately, sufficient data reduction causes the chromatographic resolution to decrease, however with minimal loss of chemical information via the PCA. Using PCA, the degree of class separation (DCS) is used as a quantitative metric. Three "Paths" of analysis (denoted A-C) are compared to each other in the context of a "benchmark" method to study the impact of the data sampling ratio on preserving chemical information, which is defined by the DCS quantitative metric. The benchmark method is simply aligning data and applying PCA, without data reduction. Path A applies data alignment to collected data, then data reduction, and finally PCA. Path B applies data reduction to collected data, and then data alignment, and finally PCA. The optimized path, namely Path C, is created from Paths A and B, whereby collected data are initially reduced to fewer data points (smaller S(R)), then aligned, and then further reduced to even fewer points and finally analyzed with PCA to provide the DCS metric. Overall, following Path C, one can successfully and efficiently classify chromatographic data by reducing to a S(R) of ～15 before alignment, and then reducing down to S(R) of ～2 before performing PCA. Indeed, following Path C, results from an average of 15 different column length-with-temperature ramp rate combinations spanning a broad range of separation conditions resulted in only a ～15% loss in classification capability (via PCA) when the loss in chromatographic resolution was ～36%.     

Association and discrimination of diesel fuels using chemometric procedures

Five neat diesel samples were analyzed by gas chromatography-mass spectrometry and total ion chromatograms as well as extracted ion profiles of the alkane and aromatic compound classes were generated. A retention time alignment algorithm was employed to align chromatograms prior to peak area normalization. Pearson product moment correlation coefficients and principal components analysis were then employed to investigate association and discrimination among the diesel samples. The same procedures were also used to investigate the association of a diesel residue to its neat counterpart. Current limitations in the retention time alignment algorithm and the subsequent effect on the association and discrimination of the diesel samples are discussed. An understanding of these issues is crucial to ensure the accuracy of data interpretation based on such chemometric procedures. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Inner chromatogram projection (ICP) for resolution of GC-MS data with embedded chromatographic peaks

The chromatographic peak located inside another peak in the time direction is called an embedded or inner peak in contradistinction with the embedding peak, which is called an outer peak. The chemical components corresponding to inner and outer peaks are called inner and outer components, respectively. This special case of co-eluting chromatograms was investigated using chemometric approaches taking GC-MS as an example. A novel method, named inner chromatogram projection (ICP), for resolution of GC-MS data with embedded chromatographic peaks is derived. Orthogonal projection resolution is first utilized to obtain the chromatographic profile of the inner component. Projection of the two-way data matrix columnwise-normalized along the time direction to the normalized profile of the inner component found is subsequently performed to find the selective m/z points, if they exist, which represent the chromatogram of the outer component by itself. With the profiles obtained, the mass spectra can easily be found by means of a least-squares procedure. The results for both simulated data and real samples demonstrate that the proposed method is capable of achieving satisfactory resolution performance not affected by the shapes of chromatograms and the relative positions of the components involved.     

Utilizing a constant peak width transform for isothermal gas chromatography

A computational approach to partially address the general elution problem (GEP), and better visualize, isothermal gas chromatograms is reported. The theoretical computational approach is developed and applied experimentally. We report a high speed temporally increasing boxcar summation (TIBS) transform that, when applied to the raw isothermal GC data, converts the chromatographic data from the initial time domain (in which the peak widths in isothermal GC increase as a function of their retention factors, k), to a data point based domain in which all peaks have the same peak width in terms of number of points in the final data vector, which aides in preprocessing and data analysis, while minimizing data storage size. By applying the TIBS transform, the resulting GC chromatogram (initially collected isothermally), appears with an x-axis point scale as if it were instrumentally collected using a suitable temperature program. A high speed GC isothermal separation with a test mixture containing 10 compounds had a run time of ～25 s. The peak at a retention factor k ～0.7 had a peak width of ～55 ms, while the last eluting peak at k ～89 (i.e., retention time of ～22 s) had a peak width of ～2000 ms. Application of the TIBS transform increased the peak height of the last eluting peak 45-fold, and S/N ～20-fold. All peaks in the transformed test mixture chromatogram had the width of an unretained peak, in terms of number of data points. A simulated chromatogram at unit resolution, studied using the TIBS transform, provided additional insight into the benefits of the algorithm.     

GC-MS in space research: decoding complex isothermal chromatograms recovered from space missions

An analytical procedure is described to study GC-MS isothermal chromatograms simulating those recovered from space missions: in fact GC plays a predominant role in space missions devoted to characterizing the chemical composition of extra-terrestrial atmospheres. SIM (selected ion monitoring) detection was used for monitoring selected chemical classes: a simplified chromatogram can be obtained giving information on the chemical composition of the complex mixture. Since only isothermal GC chromatograms are allowed by flight constraints, a time axis transformation is required to make them homogeneous: i.e., constant retention increments for CH2 additions in terms of a homologous series. The order in the linearized chromatogram can be simply singled out with a chemometric approach based on the study of the Autocovariance Function (ACVF) computed on the digitized chromatogram: the plot of the experimental autocorrelation function (EACF) shows well-shaped peaks if constant interdistances are repeated in different regions of the chromatogram. The method was applied to standard mixtures representative of planetary atmospheres--hydrocarbons, nitriles and oxygenated compounds with between 3 and 12 carbon atoms--analyzed in flight simulating conditions. The coupling of the selectivity of SIM detection with the interpretation power of the EACF procedure proves to be a powerful tool for interpreting data recovered from space missions: the chemical composition of the mixture can be identified by handling the raw SIM chromatograms.     

Correction of retention time shifts for chromatographic fingerprints of herbal medicines

In this study, the combination of chemometric resolution and cubic spline data interpolation was investigated as a method to correct the retention time shifts for chromatographic fingerprints of herbal medicines obtained by high-performance liquid chromatography-diode array detection (HPLC-DAD). With the help of the resolution approaches in chemometrics, it was easy to identify the purity of chromatographic peak clusters and then resolve the two-dimensional response matrix into chromatograms and spectra of pure chemical components so as to select multiple mark compounds involved in chromatographic fingerprints. With these mark components determined, the retention time shifts of chromatographic fingerprints might be then corrected effectively. After this correction, the cubic spline interpolation technique was then used to reconstruct new chromatographic fingerprints. The results in this work showed that, the purity identification of the chromatographic peak clusters together with the resolution of overlapping peaks into pure chromatograms and spectra by means of chemometric approaches could provide the sufficient chromatographic and spectral information for selecting multiple mark compounds to correct the retention time shifts. The cubic spline data interpolation technique was user-friendly to the reconstruction of new chromatographic fingerprints with correction. The successful application to the simulated and real chromatographic fingerprints of two Cortex cinnamomi, fifty Rhizoma chuanxiong, ten Radix angelicae and seventeen Herba menthae samples from different sources demonstrated the reliability and applicability of the approach investigated in this work. Pattern recognition based on principal component analysis for identifying inhomogenity in chromatographic fingerprints from real herbal medicines could further interpret it.     

Retention time alignment of LC/MS data by a divide-and-conquer algorithm

Liquid chromatography-mass spectrometry (LC/MS) has become the method of choice for characterizing complex mixtures. These analyses often involve quantitative comparison of components in multiple samples. To achieve automated sample comparison, the components of interest must be detected and identified, and their retention times aligned and peak areas calculated. This article describes a simple pairwise iterative retention time alignment algorithm, based on the divide-and-conquer approach, for alignment of ion features detected in LC/MS experiments. In this iterative algorithm, ion features in the sample run are first aligned with features in the reference run by applying a single constant shift of retention time. The sample chromatogram is then divided into two shorter chromatograms, which are aligned to the reference chromatogram the same way. Each shorter chromatogram is further divided into even shorter chromatograms. This process continues until each chromatogram is sufficiently narrow so that ion features within it have a similar retention time shift. In six pairwise LC/MS alignment examples containing a total of 6507 confirmed true corresponding feature pairs with retention time shifts up to five peak widths, the algorithm successfully aligned these features with an error rate of 0.2%. The alignment algorithm is demonstrated to be fast, robust, fully automatic, and superior to other algorithms. After alignment and gap-filling of detected ion features, their abundances can be tabulated for direct comparison between samples.     

Peak alignment using wavelet pattern matching and differential evolution

Retention time shifts badly impair qualitative or quantitative results of chemometric analyses when entire chromatographic data are used. Hence, chromatograms should be aligned to perform further analysis. Being inspired and motivated by this purpose, a practical and handy peak alignment method (alignDE) is proposed, implemented in this research for one-way chromatograms, which basically consists of five steps: (1) chromatogram lengths equalization using linear interpolation; (2) accurate peak pattern matching by continuous wavelet transform (CWT) with the Mexican Hat and Haar wavelets as its mother wavelets; (3) flexible baseline fitting utilizing penalized least squares; (4) peak clustering when gap of two peaks is smaller than a certain threshold; (5) peak alignment using differential evolution (DE) to maximize linear correlation coefficient between reference signal and signal to be aligned. This method is demonstrated with both simulated chromatograms and real chromatograms, for example, chromatograms of fungal extracts and Red Peony Root obtained by HPLC-DAD. It is implemented in R language and available as open source software to a broad range of chromatograph users (http://code.google.com/p/alignde).     

Signal processing of GC-MS data of complex environmental samples: characterization of homologous series

Identification and characterization of homologous series by GC-MS analysis provide very relevant information on organic compounds in complex mixtures. A chemometric approach, based on the study of the autocovariance function, EACVF_tot, is described as a suitable tool for extracting molecular-structural information from the GC signal, in particular for identifying the presence of homologous series and quantifying the number of their terms. A data pre-processing procedure is introduced to transform the time axis in order to display a strictly homogenous retention pattern: n-alkanes are used as external standard to stretch or shrink the original chromatogram in order to build up a linear GC retention scale. This addition can be regarded as a further step in the direction of a signal processing procedure for achieving a systematic characterization of complex mixture from experimental chromatograms. The EACVF_tot was computed on the linearized chromatogram: if the sample presents terms of homologous series, the EACVF_tot plot shows well-defined deterministic peaks at repeated constant interdistances. By comparison with standard references, the presence of such peaks is diagnostic for the presence of the ordered series, their position can be related to the chemical structure of the compounds, their height is the basis for estimating the number of terms in the series. The power of the procedure can be magnified by studying SIM chromatograms acquired at specific m/z values characteristic of the compounds of interest: the EACVF_tot on these selective signals makes it possible to confirm the results obtained from an unknown mixture and check their reliability.The procedure was validated on standard mixtures of known composition and applied to an unknown gas oil sample. In particular, the paper focuses on the study of two specific classes of compounds: n-alkanes and oxygen-containing compounds, since their identification provides information useful for characterizing the chemical composition of many samples of different origin. The robustness of the method was tested in experimental chromatograms obtained under unfavorable conditions: chromatograms acquired in non-optimal temperature program conditions and chromatographic data affected by signal noise.     

基于遗传算法的色谱指纹峰配对识别方法

指纹峰配对识别是色谱指纹图谱分析中的关键环节之一，本文提出一种基于遗传算法的色谱指纹峰配对识别方法。该法根据对照色谱指纹图谱的峰分布特性初选出若干标定蜂，将其存入一个候选标定蜂库；同时根据这些候选标定峰从待测指纹图谱中选出相应的候选标定峰，也存入候选标定峰库；再用遗传算法从库中选取一组标定峰用于校正待测指纹图谱中各峰的峰位，并自动识别出与对照色谱指纹图谱相对应的各指纹峰。仿真实验及实际分析实验结果均表明，该法识别指纹峰准确可靠，可用于色谱指纹图谱相似度的快速自动计算。     

Mathematical algorithm for qualitative and semiquantitative analysis of petroleum hydrocarbons in solid wastes using on-line gas chromatography

Non-degradated mineral-oils like gasoline, solvent naphtha, diesel fuel, fuel and lubricating oils provide a characteristic fingerprint gas chromatogram. This visual classification, e.g. in solid wastes, is complicated due to the simultaneous presence of several mineral-oils. Therefore, a mathematical algorithm for the separation of gas chromatographic fingerprint of “single mixtures” of aliphatic hydrocarbons is developed. The technique ¶is essential for analysis of time-overlapping “single mixtures” of petroleum hydrocarbons (so-called “complex mixtures”) and it relies on the concentration-varying hydrocarbons during evaporation. It is possible to separate the data from the gas chromatogram of a “complex mixture” of hydrocarbons into the chromatograms of the pure “single mixtures” and to give their respective concentrations. A synthetic ?complex mixture” of kerosene, diesel fuel and lubricating oil is used to illustrate the method.     

Mathematical algorithm for qualitative and semiquantitative analysis of petroleum hydrocarbons in solid wastes using on-line gas chromatography

Non-degradated mineral-oils like gasoline, solvent naphtha, diesel fuel, fuel and lubricating oils provide a characteristic fingerprint gas chromatogram. This visual classification, e.g. in solid wastes, is complicated due to the simultaneous presence of several mineral-oils. Therefore, a mathematical algorithm for the separation of gas chromatographic fingerprint of "single mixtures" of aliphatic hydrocarbons is developed. The technique is essential for analysis of time-overlapping "single mixtures" of petroleum hydrocarbons (so-called "complex mixtures") and it relies on the concentration-varying hydrocarbons during evaporation. It is possible to separate the data from the gas chromatogram of a "complex mixture" of hydrocarbons into the chromatograms of the pure "single mixtures" and to give their respective concentrations. A synthetic "complex mixture" of kerosene, diesel fuel and lubricating oil is used to illustrate the method.     

Unsupervised parameter optimization for automated retention time alignment of severely shifted gas chromatographic data using the piecewise alignment algorithm

Simulated chromatographic separations were used to study the performance of piecewise retention time alignment and to demonstrate automated unsupervised (without a training set) parameter optimization. The average correlation coefficient between the target chromatogram and all remaining chromatograms in the data set was used to optimize the alignment parameters. This approach frees the user from providing class information and makes the alignment algorithm applicable to classifying completely unknown data sets. The average peak in the raw simulated data set was shifted up to two peak-widths-at-base (average relative shift=2.0) and after alignment the average relative shift was improved to 0.3. Piecewise alignment was applied to severely shifted GC separations of gasolines and reformate distillation fraction samples. The average relative shifts in the raw gasolines and reformates data were 4.7 and 1.5, respectively, but after alignment improved to 0.5 and 0.4, respectively. The effect of piecewise alignment on peak heights and peak areas is also reported. The average relative difference in peak height was -0.20%. The average absolute relative difference in area was 0.15%.     

Comprehensive Two-Dimensional Gas Chromatography with Mass Spectrometric Detection (GC × GC/MS) Applied to the Analysis of Petroleum

Comprehensive two-dimensional gas chromatography coupled with mass spectrometric detection (GC × GC/MS) is a three-dimensional analytical method. In its application to petroleum analysis, the high peak capacity of GC × GC produced chromatographic resolution of over 750 peaks from a marine diesel fuel. The MS detector provided a full-scan mass spectrum for each resolved peak. The integration of an MS detector with GC × GC provides increased capability to identify minor components, determine members of homologous series, and characterize ordered peak patterns of related components that are visible in the GC × GC chromatogram.     

Real-time target selection optimization to enhance alignment of gas chromatograms

An improved method for real-time selection of the target for the alignment of gas chromatographic data is described. Further outlined is a simple method to determine the accuracy of the alignment procedure. The target selection method proposed uses a moving window of aligned chromatograms to generate a target, herein referred to as the window target method (WTM). The WTM was initially tested using a series of 100 simulated chromatograms, and additionally evaluated using a series of 55 diesel fuel gas chromatograms obtained with four fuel samples. The WTM was evaluated via a comparison to a related method (the nearest neighbor method (NNM)). The results using the WTM with simulated chromatograms showed a significant improvement in the correlation coefficient and the accuracy of alignment when compared to the alignments performed using the NNM. A significant improvement in real-time alignment accuracy, as assessed by a correlation coefficient metric, was achieved with the WTM (starting at ∼1.0 and declining to only ∼0.985 for the 100th sample), relative to the NNM (starting at ∼1.0 and declining to ∼0.4 for the 100th sample) for the simulated chromatogram study. The results determined when using the WTM with the diesel fuels also showed an improvement in correlation coefficient and accuracy of the within-class alignments as compared to the results obtained from the NNM. In practice, the WTM could be applied to the real-time analysis of process and feedstock industrial streams to enable real-time decision making from the more precisely aligned chromatographic data.     

Spurenbestimmung von Vergaser- und Dieselkraftstoffen im Wasser mittels Capillar-Gas-Chromatographie/automatischer Mustererkennung

Summary A method for trace analysis determination of carburetor and diesel fuels in water is described. The isolation and concentration of fuel traces is carried out by microextraction with n-hexane using a suitable micro-separator. After their separation by capillary gas chromatography fuels provide typically structured chromatographic patterns and, therefore, a chromatogram (sample pattern) of the extract is generated. The sample pattern is searched for fuel patterns by comparing the chromatogram with reference chromatograms of these fuels in a library. An automatic pattern recognition algorithm is applied, using elements of the fuzzy set theory. As preliminary interpretation the computer delivers a list of identification proposals which have to be assessed and submitted to a final interpretation by the analyst.     

Chemometric detection of thermally degraded samples in the analysis of drugs of abuse with gas chromatography-Fourier-transform infrared spectroscopy

We present a chemometric procedure for the identification of the reference standard chromatographic peak in cases where the GC-FTIR analysis of commercial standards results in the appearance of more than one peak in the GC chromatogram. The procedure has been designed for phenethylamines, which represent the class with the largest number of individual molecules on the illicit drug market, and which are abused for their stimulant and/or hallucinogenic effects. The similarity between their vapor-phase FTIR spectra was modeled using principal component analysis (PCA), and class identity was assigned on the basis of soft independent modeling of class analogy (SIMCA). Additional peaks could be assigned to impurities in the standards, but most often they were artifacts formed during the GC-FTIR analysis of thermolabile or chemically unstable compounds. The latter case is illustrated by the identification of the reference standard chromatographic peak and FTIR spectrum of the potent psychotropic amphetamine derivative N-methyl-1-(3,4-methylenedioxyphenyl)-2-butanamine (MBDB), and by the elucidation of the chemical changes that occur in the molecule of MBDB due to thermal degradation.     

Quality assessment of cortex cinnamomi by HPLC chemical fingerprint, principle component analysis and cluster analysis

HPLC fingerprint analysis, principle component analysis (PCA), and cluster analysis were introduced for quality assessment of Cortex cinnamomi (CC). The fingerprint of CC was developed and validated by analyzing 30 samples of CC from different species and geographic locations. Seventeen chromatographic peaks were selected as characteristic peaks and their relative peak areas (RPA) were calculated for quantitative expression of the HPLC fingerprints. The correlation coefficients of similarity in chromatograms were higher than 0.95 for the same species while much lower than 0.6 for different species. Besides, two principal components (PCs) have been extracted by PCA. PC1 separated Cinnamomum cassia from other species, capturing 56.75% of variance while PC2 contributed for their further separation, capturing 19.08% variance. The scores of the samples showed that the samples could be clustered reasonably into different groups corresponding to different species and different regions. The scores and loading plots together revealed different chemical properties of each group clearly. The cluster analysis confirmed the results of PCA analysis. Therefore, HPLC fingerprint in combination with chemometric techniques provide a very flexible and reliable method for quality assessment of traditional Chinese medicines.