Handling within run retention time shifts in two-dimensional chromatography data using shift correction and modeling

The use of PARAFAC for modeling GC × GC-TOFMS peaks is well documented. This success is due to the trilinear structure of these data under ideal, or sufficiently close to ideal, chromatographic conditions. However, using temperature programming to cope with the general elution problem, deviations from trilinearity within a run are more likely to be seen for the following three cases: (1) compounds (i.e., analytes) severely broadened on the first column hence defined by many modulation periods, (2) analytes with a very high retention factor on the second column and likely wrapped around in that dimension, or (3) with fast temperature program rates. This deviation from trilinearity is seen as retention time-shifted peak profiles in subsequent modulation periods (first column fractions). In this report, a relaxed yet powerful version of PARAFAC, known as PARAFAC2 has been applied to handle this shift within the model step by allowing generation of individual peak profiles in subsequent first column fractions. An alternative approach was also studied, utilizing a standard retention time shift correction to restore the data trilinearity structure followed by PARAFAC. These two approaches are compared when identifying and quantifying a known analyte over a large concentration series where a certain shift is simulated in the successive first column fractions. Finally, the methods are applied to real chromatographic data showing severely shifted peak profiles. The pros and cons of the presented approaches are discussed in relation to the model parameters, the signal-to-noise ratio and the degree of shift.     

Toward automated chromatographic fingerprinting: A non-alignment approach to gas chromatography mass spectrometry data

In contrast to targeted analysis of volatile compounds, non-targeted approaches take information of known and unknown compounds into account, are inherently more comprehensive and give a more holistic representation of the sample composition. Although several non-targeted approaches have been developed, there's still a demand for automated data processing tools, especially for complex multi-way data such as chromatographic data obtained from multichannel detectors. This work was therefore aimed at developing a data processing procedure for gas chromatography mass spectrometry (GC–MS) data obtained from non-targeted analysis of volatile compounds. The developed approach uses basic matrix manipulation of segmented GC–MS chromatograms and PARAFAC multi-way modelling. The approach takes retention time shifts and peak shape deformations between samples into account and can be done with the freely available N-way toolbox for MATLAB. A demonstration of the new fingerprinting approach is presented using an artificial GC–MS data set and an experimental full-scan GC–MS data set obtained for a set of experimental wines.     

Quantification of Kerosene in Gasoline by Comprehensive Two-Dimensional Gas Chromatography and N-Way Multivariate Analysis

Abstract

In brazil, gasoline is usually adulterated by diesel oil, ethanol (in addition to the amount legally specified), petrochemical raffinates, and kerosene. This is an illegal action performed mainly in an attempt to raise profits. Therefore, methods for reliable identification of adulterated gasoline are very attractive. The aim of this work was to propose a method to quantify kerosene in gasoline through N-way multivariate analysis and a homemade Comprehensive Two-Dimensional Gas Chromatography with Flame Ionization Detection (GC × GC-FID). Models generated by Parallel Factor Analysis (PARAFAC), PARAFAC2, and Multi-way Partial Least Squares (N-PLS) allowed the quantification of kerosene in gasoline with Root Mean Square Error of Cross-Validation (RMSECV) values of 2.98%, 2.65%, and 2.08%, respectively.     

Vibrational overtone combination spectroscopy (VOCSY)—a new way of using IR and NIR data

This work explores a novel method for rearranging 1st order (one-way) infra-red (IR) and/or near infra-red (NIR) ordinary spectra into a representation suitable for multi-way modelling and analysis. The method is based on the fact that the fundamental IR absorption and the first, second, and consecutive overtones of NIR absorptions represent identical chemical information. It is therefore possible to rearrange these overtone regions of the vectors comprising an IR and NIR spectrum into a matrix where the fundamental, 1st, 2nd, and consecutive overtones of the spectrum are arranged as either rows or columns in a matrix, resulting in a true three-way tensor of data for several samples. This tensorization facilitates explorative analysis and modelling with multi-way methods, for example parallel factor analysis (PARAFAC), N-way partial least squares (N-PLS), and Tucker models. The vibrational overtone combination spectroscopy (VOCSY) arrangement is shown to benefit from the “order advantage”, producing more robust, stable, and interpretable models than, for example, the traditional PLS modelling method. The proposed method also opens the field of NIR for true peak decomposition—a feature unique to the method because the latent factors acquired using PARAFAC can represent pure spectral components whereas latent factors in principal component analysis (PCA) and PLS usually do not.     

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.     

Determination of pesticides and metabolites in wine by high performance liquid chromatography and second-order calibration methods

The models parallel factor analysis (PARAFAC) and the recently introduced bilinear least squares (BLLS) were applied to develop second-order calibration methods to high performance liquid chromatography with diode array detection (HPLC-DAD) data, where overlap of interferences with the compounds of interest was observed, making the determination and resolution of the analytes possible. In this work, the simultaneous determination of five pesticides and two metabolites in wine samples by HPLC-DAD was performed, using the second-order advantage. The results of two chromatographic methods were compared, involving either isocratic or gradient elution. An appropriate preprocessing method was necessary to correct the effects of time shifts, baseline variations and background. BLLS presented results that were of the same quality as PARAFAC in five cases, but in two other situations only PARAFAC enabled analyte quantitation. Relative errors of prediction lower than 10% for all compounds were obtained, indicating that the methodology employing HLPC-DAD and second-order calibration can handle complex analytical systems.     

Mitigating model deficiency in three-way data analysis by the combination of background constraining and iterative correcting techniques

PARAFAC is a popular model for trilinear data analysis in analytical chemistry. The prerequisite for the successful application of PARAFAC in analytical chemistry is that the three-way data array should follow a trilinear model, which is always violated by the presence of deviations such as Rayleigh scattering in fluorescence spectroscopy. In order to mitigate the influence of model deviations, background constraining and iterative correcting techniques are advocated in this contribution. The method established on these two techniques can nearly eliminate the effect of model deviation on the chemical loading parameters estimated. Compared with other methods for mitigating model deviations, the proposed method requires no prior knowledge about the chemical loading parameters. It is also unnecessary to assign weights to data entities as the weighted PARAFAC of Anderson does. Its implementation is comparable to PARAFAC-ALS and can be programmed to be completely automatic. Its performance has been demonstrated by fluorescent and chromatographic experiments.     

Multivariate curve resolution based chromatographic peak alignment combined with parallel factor analysis to exploit second-order advantage in complex chromatographic measurements

In the present contribution, a new combination of multivariate curve resolution-correlation optimized warping (MCR-COW) with trilinear parallel factor analysis (PARAFAC) is developed to exploit second-order advantage in complex chromatographic measurements. In MCR-COW, the complexity of the chromatographic data is reduced by arranging the data in a column-wise augmented matrix, analyzing using MCR bilinear model and aligning the resolved elution profiles using COW in a component-wise manner. The aligned chromatographic data is then decomposed using trilinear model of PARAFAC in order to exploit pure chromatographic and spectroscopic information. The performance of this strategy is evaluated using simulated and real high-performance liquid chromatography-diode array detection (HPLC-DAD) datasets. The obtained results showed that the MCR-COW can efficiently correct elution time shifts of target compounds that are completely overlapped by coeluted interferences in complex chromatographic data. In addition, the PARAFAC analysis of aligned chromatographic data has the advantage of unique decomposition of overlapped chromatographic peaks to identify and quantify the target compounds in the presence of interferences. Finally, to confirm the reliability of the proposed strategy, the performance of the MCR-COW-PARAFAC is compared with the frequently used methods of PARAFAC, COW-PARAFAC, multivariate curve resolution-alternating least squares (MCR-ALS), and MCR-COW-MCR. In general, in most of the cases the MCR-COW-PARAFAC showed an improvement in terms of lack of fit (LOF), relative error (RE) and spectral correlation coefficients in comparison to the PARAFAC, COW-PARAFAC, MCR-ALS and MCR-COW-MCR results.     

Three‐way analysis of a designed compost experiment using near‐infrared spectroscopy and laboratory measurements

Composts are complex organic systems that undergo batch fermentation processes. Traditional monitoring of such processes is usually based on measuring important chemical (physical) laboratory parameters but the common trend includes using more rapid and non‐destructive methods like near‐infrared (NIR) spectroscopy. A lab‐scale designed (simplex mixture) experiment with nine compost batches, including three repeated centre point batches, was monitored over 5 weeks by NIR spectroscopy (900–1700 nm) and by wet chemical and physical measurements: pH, energy content, moisture content, NH₃/NH and temperature. The data were organized in three‐way data arrays and different three‐way methods were used for analysis: (1) PARAFAC, (2) Tucker3 and (3) PARAFAC2. The present paper stresses the advantages and the possibilities of three‐way methods compared to traditional two‐way analysis methods such as principal component analysis (PCA). Two‐way methods have a tendency to mix variables and produce, from a parsimony point of view, more complex models which are hard to interpret. The results from the three‐way methods reproduced the mixture triangle, gave common time profiles (PARAFAC and Tucker3) for all compost batches and rate constants (half‐lives) could be calculated: 6.9 days for the PARAFAC loadings from the chemical/physical parameters and between 6 and 10 days for the PARAFAC loadings from the NIR data. PARAFAC2 includes the possibility of getting individual time profiles for each compost batch. The results show that chemical/physical data and the NIR data give similar interpretations. The conclusion is that three‐way methods can be used to monitor composts batches over time. Copyright © 2011 John Wiley & Sons, Ltd.     

Quantification from highly drifted and overlapped chromatographic peaks using second-order calibration methods

For determining low levels of pesticides and phenolic compounds in river and wastewater samples by high performance liquid chromatography (HPLC), solid phase extraction (SPE) is commonly used before the chromatographic separation. This preconcentration step is not necessarily selective for the analytes of interest and it may retain other compounds of similar characteristics as well. In this case, we present, humic and fulvic acids caused a large baseline drift and overlapped the analytes to be quantified. The inaccurate determinations of the area of the peaks of these analytes made it difficult to quantify them with univariate calibration. Here we compare three second-order calibration algorithms (generalized rank annihilation method (GRAM), parallel factor analysis (PARAFAC) and multivariate curve resolution-alternating least squares (MCR-ALS)) which efficiently solve this problem. These methods use second-order data, i.e., a matrix of responses for each peak, which is easily obtained with a high performance liquid chromatography-diode array detector (HPLC-DAD). With these methods, the area does not need to be directly measured and predictions are more accurate. They also save time and resources because they can quantify analytes even if the peaks are not resolved. GRAM and PARAFAC require trilinear data. Biased and imprecise concentrations (relative standard deviation, %R.S.D. = 34) were obtained without correcting the time-shift. Hence, a time-shift correction algorithm to align the peaks was needed to obtain accurate predictions. MCR-ALS was the most robust to the time-shift. All three algorithms provided similar mean predictions, which were comparable to those obtained when sulfite was added to the samples. However, the predictions for the different replicates were more similar for the second-order algorithms (%R.S.D. = 3) than the ones obtained by univariate calibration after the sulfite addition (%R.S.D. = 13).     

Automated resolution of overlapping peaks in chromatographic data

Parallel factor analysis 2 (PARAFAC2) has been shown to be a powerful tool for resolution of complex overlapping peaks in chromatographic analyses. It is particularly useful because of its ability to handle shifts in the elution time mode and peak shape changes. Like all curve resolution techniques, PARAFAC2 will only find chemically meaningful parameters (elution time profiles and mass spectra) if the correct number of factors are determined. So far, the primary way to determine an appropriate number of factors, when using PARAFAC2, is to calculate models with different number of factors and then inspect the models manually. This approach is time consuming, and the result may be biased because of the manual assessment of the model quality, making PARAFAC2 inaccessible for analytical chemists in general. Here, we develop a method that can determine an appropriate number of factors in an automated way. The automation is based on a number of model diagnostics (quality criteria) collected from models with different numbers of factors. Combining these diagnostics, it is possible to assess what the appropriate number of components is. In this work, only gas chromatography–mass spectrometry data are considered. However, it will most likely be fairly straightforward to expand the work to also cover liquid chromatography data (with a multivariate detector). Automating the model quality evaluation of the PARAFAC2 model enables both the inexperienced and trained user to perform comprehensive and advanced analysis of chromatographic data with a minimum of manual work. © 2013 The Authors. Journal of Chemometrics Published by John Wiley & Sons Ltd.     

Parallel factor analysis of HPLC-DAD data for binary mixtures of lidocaine and prilocaine with different levels of chromatographic separation

A set of 17 samples containing a constant amount of lidocaine (667 μM) and a decreasing amount of prilocaine (667-0.3 μM) was analysed by LC-DAD at three different levels of separation, followed by parallel factor analysis (PARAFAC) of the data obtained. In Case 1 no column was connected, the chromatographic resolution (R_s) therefore being zero, while Cases 2 and 3 had partly separated peaks (R_s=0.7 and 1.0). The results showed that in Case 1, analysed without any separation, the PARAFAC decomposition with a model consisting of two components gave a good estimate of the spectral and concentration profiles of the two compounds. In Cases 2 and 3, the use of PARAFAC models with two components resolved the underlying chromatographic, spectral and concentration profiles. The loadings related to the concentration profile of prilocaine were used for regression and prediction of the prilocaine content. The results showed that prediction of prilocaine content was possible with satisfactory prediction (RMSEP<0.01). This study shows that PARAFAC is a powerful technique for resolving partly separated peaks into their pure chromatographic, spectral and concentration profiles, even with completely overlapping spectra and the absence or very low levels of separation.     

PARAFAC and PARAFAC2 calibration models for antihypertensor Nifedipine quantification

Two-way data structures were obtained by acquiring UV-vis spectra as function of the time of the alkaline hydrolysis reaction of the antihypertensor Nifedipine in dimethylsulfoxide (DMSO). Sets of three-way data structures were obtained from the analysis of solutions with different concentrations of Nifedipine generated by standard additions to DMSO, Nifedipine standard and a pharmaceutical formulation. PARAFAC and PARAFAC2 methods were used in the analysis of these multi-way data structures and calibration models were developed for Nifedipine quantification in pharmaceutical formulations. For all the three-way data structures a better model fit was found with the PARAFAC2 suggesting that the experimental data sets have deviations from trilinearity. The best concentrations estimations were found with the PARAFAC2 model in the analysis of a [concentration × time (s) × wavelength (nm)] three-way data structure which allows the quantification of Nifedipine in pharmaceutical formulations.     

Mixture Design PARAFAC HPLC-DAD Metabolomic Fingerprints of Fractionated Organic and Basic Extracts from <Emphasis Type="Italic">Erythrina speciosa</Emphasis> Andrews Leaves

HPLC-DAD analysis of statistical mixture design extracts of Erythrina speciosa Andrews leaves provided chromatographic and UV–visible profiles of their basic and organic fractions that were treated with the PARAFAC multivariate method. The design extracts provided greater varieties and amounts of metabolites than could be obtained by classical extraction methods. Fractionation provided more diverse fingerprint information than obtained previously from only the crude extract. The two largest chromatographic peaks, one with a 4.8 min elution time having an intense spectral band at 235 nm and the other a 5.8 min peak with an intense 238 nm band for the basic fraction were obtained with the ternary 1:1:1 ethanol–dichloromethane–hexane mixture. These can be assigned to diene-type and lactonic alkaloids. Peaks with the same retention times are also found in the organic fraction but are extracted with different mixtures and have distinct spectral behavior in the 235 nm region, probably being aromatic alkaloids. The above strategy permits a more unambiguous assignment of metabolic groups to specific chromatographic peaks. This can be expected to provide higher quality chromatographic fingerprints for natural products’ chemistry.     

不同产地白芷药材高效液相色谱指纹图谱研究

本文采用高效液相色谱-二极管阵列检测器(HPLC-DAD)法建立中药白芷的指纹图谱.应用化学计量学中两种不同的模式识别方法(主成分分析法和系统聚类分析法)对实验数据进行处理,以找出来自三个不同产地30个中药白芷样品间的相似性及差异性.两种模式识别方法均能成功地按样品的来源将不同产地的样品正确分类.建立了不同产地中药白芷的识别方法,该方法能有效地控制中药白芷的质量,并能为其它中药产品的化学模式识别提供参考.     

Comprehensive analysis of chromatographic data by using PARAFAC2 and principal components analysis

The most straightforward method to analyze an obtained GC–MS dataset is to integrate those peaks that can be identified by their MS profile and to perform a Principal Component Analysis (PCA). This procedure has some important drawbacks, like baseline drifts being scarcely considered or the fact that integration boundaries are not always well defined (long tails, co-eluted peaks, etc.). To improve the methodology, and therefore, the chromatographic data analysis, this work proposes the modeling of the raw dataset by using PARAFAC2 algorithm in selected areas of the GC profile and using the obtained well-resolved chromatographic profiles to develop a further PCA model. With this working method, not only the problems arising from instrumental artifacts are overcome, but also the detection of new analytes is achieved as well as better understanding of the studied dataset is obtained. As a positive consequence of using the proposed working method human time and work are saved. To exemplify this methodology the aroma profile of 36 apples being ripened were studied. The benefits of the proposed methodology (PARAFAC2 + PCA) are shown in a practitioner perspective, being able to extrapolate the conclusions obtained here to other hyphenated chromatographic datasets.     

Photoinduced spectrofluorimetric determination of fluoroquinolones in human urine by using three- and two-way spectroscopic data and multivariate calibration

Multivariate methods comprise of a group of chemometric tools allowing the analysis of different analytical data, i.e., spectroscopic, chromatographic obtained from multichannel detector systems. Second-way data are widely used in analytical applications in combination with multivariate calibration methods, but three- and higher-way data are yet not as widely applied. In complex biological samples, the employment of the three-way data is of special interest, as they may be combined with methods that exploit the second-order advantage allowing calculating individual concentrations of the analytes of interest in the presence of unknown interferences in untreated samples. A very sensitive and selective method is proposed, by coupling photoinduced fluorescence and multivariate analysis of the three-way data excitation-emission fluorescence matrices (EEMs), of the photoproducts obtained from UV irradiation of three fluoroquinolones: enoxacin (ENO), norfloxacin (NOR) and ofloxacin (OFLO). The application of a previous photoirrradiation process allows the determination of mixtures of ENO, NOR and OFLO, in urine samples at biological levels without sample pretreatments. The resolution ability of N-way partial least squares (N-PLS), parallel factor analysis (PARAFAC) and self weighted alternating trilinear decomposition (SWATLD), is compared with partial least squares (PLS) and unfolded-PLS (U-PLS), in the analysis of ENO, NOR and OFLO in human urine samples.     

Principal component and Tucker3 analyses of high performance liquid chromatography with diode-array detection fingerprints of crude extracts of Erythrina speciosa Andrews leaves

Mixtures of ethanol, dichloromethane, hexane and acetone obtained according to a statistical design have been used to extract substances from Erythrina speciosa Andrew leaves for chromatographic fingerprinting. The plant extracts from each mixture were analyzed by HPLC-DAD providing UV–vis spectra for each chromatographic peak. These chromatograms and spectra for the design mixtures were then treated with principal component (PCA), Tucker3 and PARAFAC analyses. PCA indicated the existence of five different chromatographic fingerprints for the leave extracts depending on the solvent mixture composition. Different chromatographic peak areas were strongly correlated with the mixture proportions of acetone, dichloromethane and ethanol. Tucker3 and PARAFAC analyses were very useful for identifying simultaneous correlations between chromatographic peak areas, spectral band absorbances and solvent proportions. The acetone proportion was highly correlated with the area of the 3.69 min retention time peak and the spectral absorbances between 250 and 260 nm, consistent with the presence of natural polyphenols. The dichloromethane mixture proportion was strongly correlated with the 12.19 min chromatographic peak area and a single spectral absorbance at 201 nm. This spectral absorption is characteristic of the electronic structures of terpenes and alkaloids.     

Detection of verapamil drug by fluorescence and trilinear decomposition techniques

A three-way analytical methodology experimentally based on fluorescence excitation emission matrix (EEM) and in PARAFAC and TLD chemometric analysis was assessed for the quantification of verapamil drug in a tablet formulation. A standard addition procedure generates experimental information compatible with the chemometric data analysis model allowing the estimation of verapamil with a detection limit of about 0.04 mg/l using methanol as solvent. The structure of the verapamil EEM follows a trilinear model, but background signals (first- and second-order scatter bands) did not—a trilinear three-factor model is necessary to describe experimental datasets. The comparison of a three-factor PARAFAC model with a United States Pharmacopoeia (USP) standard chromatographic method showed similar results.     

Classification of Rhizoma et Radix Notoperygii by HPLC Fingerprints with the Aid of Chemometrics

Chromatographic profiles of Rhizoma et Radix Notoperygii (RRN, “Qianghuo” in Chinese), a complex traditional Chinese medicine (TCM), were collected by high-performance liquid chromatography with diode array detection (HPLC-DAD) at 330 nm. These data profiles were used as fingerprints to investigate quality control classification modeling of the RRN samples. In contrast to the classical methods for discrimination of TCMs, that is, just using common HPLC peaks, all chromatographic profile data were pre-processed by the correlation optimized warping method and polynomial functions; then, these data were submitted as fingerprints (variables) for classification on the basis of sample origin. Chemometrics methods used for calibration modeling and subsequent sample classification-least square support vector machine (LS-SVM), artificial neural network (ANN), and partial least square discriminant analysis (PLS-DA); all produced satisfactory calibrations as well as classification results.