Second-order standard addition for deconvolution and quantification of fatty acids of fish oil using GC-MS

In the present work two second-order calibration methods, generalized rank annihilation method (GRAM) and multivariate curve resolution-alternating least square (MCR-ALS) have been applied on standard addition data matrices obtained by gas chromatography-mass spectrometry (GC-MS) to characterize and quantify four unsaturated fatty acids cis-9-hexadecenoic acid (C16:1ω7c), cis-9-octadecenoic acid (C18:1ω9c), cis-11-eicosenoic acid (C20:1ω9) and cis-13-docosenoic acid (C22:1ω9) in fish oil considering matrix interferences. With these methods, the area does not need to be directly measured and predictions are more accurate. Because of non-trilinear conditions of GC-MS data matrices, at first MCR-ALS and GRAM have been used on uncorrected data matrices. In comparison to MCR-ALS, biased and imprecise concentrations (%R.S.D. = 27.3) were obtained using GRAM without correcting the retention time-shift. As trilinearity is the essential requirement for implementing GRAM, the data need to be corrected. Multivariate rank alignment objectively corrects the run-to-run retention time variations between sample GC-MS data matrix and a standard addition GC-MS data matrix. Then, two second-order algorithms have been compared with each other. The above algorithms provided similar mean predictions, pure concentrations and spectral profiles. The results validated using standard mass spectra of target compounds. In addition, some of the quantification results were compared with the concentration values obtained using the selected mass chromatograms. As in the case of strong peak-overlap and the matrix effect, the classical univariate method of determination of the area of the peaks of the analytes will fail, the “second-order advantage” has solved this problem successfully.     

Using second-order calibration to identify and quantify aromatic sulfonates in water by high-performance liquid chromatography in the presence of coeluting interferences

We used the Generalized Rank Annihilation Method (GRAM), a second-order calibration method, to quantify aromatic sulfonates in water with high-performance liquid chromatography (HPLC) when interferences coeluted with the analytes of interest. With GRAM, we can quantify in only two chromatographic analyses, one for a calibration sample and one for the unknown sample. The calculated concentrations were not statistically different to those obtained when the chromatographic separation of the unknown sample was modified in order to completely separate the analyte from the interferences before univariate calibration. With GRAM, the concentrations are determined much more quickly because a complete resolution is not required.     

Second-order multivariate calibration procedures applied to high-performance liquid chromatography coupled to fast-scanning fluorescence detection for the determination of fluoroquinolones

Different second-order multivariate calibration algorithms, namely parallel factor analysis (PARAFAC), N-dimensional partial least-squares (N-PLS) and multivariate curve resolution-alternating least-squares (MCR-ALS) have been compared for the analysis of four fluoroquinolones in aqueous solutions, including some human urine samples (additional four fluoroquinolones were simultaneously determined by univariate calibration). Data were measured in a short time with a chromatographic system operating in the isocratic mode. The detection system consisted of a fast-scanning spectrofluorimeter, which allows one to obtain second-order data matrices containing the fluorescence intensity as a function of retention time and emission wavelength. The developed approach enabled us to determine eight analytes, some of them with overlapped profiles, without the necessity of applying an elution gradient, and thus significantly reducing both the experimental time and complexity. The study was employed for the discussion of the scopes of the applied second-order chemometric tools. The quality of the proposed technique coupled to each of the evaluated algorithms was assessed on the basis of the figures of merit for the determination of fluoroquinolones in the analyzed water and urine samples. Univariate calibration of four analytes led to limits of detection in the range 20–40 ng mL⁻¹ and root mean square errors for the validation samples in the range 30–60 ng mL⁻¹ (corresponding to relative prediction errors of 3–8%). The ranges for second-order multivariate calibration (using PARAFAC and N-PLS) of the remaining four analytes were: limit of detection, 2–8 ng mL⁻¹, root mean square errors, 3–50 ng mL⁻¹ and relative prediction errors, 1–5%.     

Spectrofluorimetric determination of chlorophylls and pheopigments using parallel factor analysis

In this study, parallel factor analysis (PARAFAC) was applied to fluorescence excitation emission matrices (EEM) of chlorophylls and pheopigments dissolved in acetone:water (9:1). The excitation wavelength range was from 350 to 500 nm and the emission was recorded from 600 to 730 nm. Nine standards, comprising mixtures of six analytes, were decomposed into a six-component PARAFAC model. Each component resembled the corresponding EEM of the pure analyte, demonstrating the uniqueness properties of PARAFAC. The score matrix obtained from the model was used for calibration and prediction of an independent set of standards and for eleven samples collected in the Baltic proper. The results obtained by the proposed method were compared to classical least squares (CLS) and to predictions by reference methods (HPLC and visible spectroscopy). For the independent set of standards the proposed method and CLS performed equal well in terms of predictive ability. But for the samples the proposed method yielded results that were in good agreement to the reference methods, whereas CLS failed. Also the so-called "second-order advantage" was examined, showing that not all constituents must be included in the calibration set. The concentration range was for chlorophyll a varied between 10 and 75 mug l(-1), and similar for the other analytes.     

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.     

Outlier detection for the Generalized Rank Annihilation Method in HPLC-DAD analysis

The Generalized Rank Annihilation Method (GRAM) is a second-order calibration method that is used in chromatography to quantify analytes that coelute with interferences. For a correct quantification, the peak of the analyte in the standard and in the test sample must be aligned and have the same shape (i.e., have a trilinear structure). Variations in retention time and shape between the two peaks may cause the test sample to behave as an outlier and produce an incorrect prediction. This situation cannot be detected by checking the coincidence of the recovered spectrum with the known spectrum of the analyte because the spectral domain is not affected. It cannot be detected either by checking if the recovered profile is correct (i.e., unimodal and positive). Several plots are presented to detect such outliers. The first plot compares the particular elution profiles in the standard and in the test sample that are recovered by least-squares regression from the spectra estimated by GRAM. The calculated elution profiles from both peaks should coincide. A second plot uses the elution profiles and spectra calculated by GRAM to define the vector space spanned by the interferences. The measured peaks in the standard and in the test sample are projected onto the space that is orthogonal to the space spanned by the interferences. These projections are proportional (up to the noise) if data are trilinear. The proportionality is checked graphically from the first singular vector of the projected peaks, or from the plot of the orthogonal signal versus the net sensitivity. The use of these graphs is shown for simulated data and for the determination of 4-nitrophenol in river water samples with liquid chromatography/UV-Vis detection.     

Modeling four and three-way fast high-performance liquid chromatography with fluorescence detection data for quantitation of fluoroquinolones in water samples

This paper presents a study regarding the acquisition and analytical utilization of four and three-way data, acquired by following the excitation–emission fluorescence matrices at different elution times, in a fast liquid chromatographic HPLC procedure. This kind of data were implemented for first time for quantitative purposes, and applied to the determination of two fluoroquinolones in tap water samples, as a model to show the potentiality of the proposed strategy of four-way data generation. The data were modeled with three well-known algorithms: PARAFAC, U-PLS/RTL and MCR-ALS, the latter conveniently adapted to model third-order data. The second-order advantage was exploited when analyzing samples containing uncalibrated interferences. PARAFAC and MCR-ALS were the algorithms that better exploited the second-order advantage when no peak time shifts occurred among samples. On the other hand, when the quadrilinearity was lost due to the occurrence of temporal shifts, MCR-ALS furnished the better results. Relative error of prediction (REP%) obtained were 9.9% for ofloxacin and 14.0% for ciprofloxacin. In addition, a significant enhancement in the analytical figures of merit was observed when going from second- to third-order data (reduction of ca. 70% in LODs).     

Interference-free determination of Sudan dyes in chilli foods using second-order calibration algorithms coupled with HPLC-DAD

This paper presents a new method for the determination of Sudan dyes contained in hot chilli samples. The method employs second-order calibration algorithms to handle the recorded data. The second-order calibration algorithms are based on the popular parallel factor analysis (PARAFAC), alternating trilinear decomposition (ATLD) and self-weighted alternating trilinear decomposition (SWATLD), respectively. These chemometric methodologies have the second-order advantage, which is the ability to get accurate concentration estimates of interested analytes even in the presence of uncalibrated interfering components. The results on a set of spiked chilli test shows that low contents of Sudan I and Sudan II in complex chilli mixtures can be accurately determined using the new method. The sample preparation was based on solvent extraction, and internal standard was not required. Quantification was carried out with simple mobile phase.     

Simultaneous determination of tyrosine and dopamine in urine samples using excitation-emission matrix fluorescence coupled with second-order calibration

A "green" and quick analytical method for complex compounds was developed for simultaneous determination of tyrosine (Tyr) and dopamine (DA) in urine samples in this paper. The three-way responsive data recorded by excitation-emission matrix fluorescence (EEM) spectrometer was analyzed using second-order calibration methods based on both parallel factor analysis (PARAFAC) and selfweighted alternating trilinear decomposition (SWATLD) algorithms. The EEM spectra of the analytes were overlapped with the background in urine samples. However the second-order advantage of both PARAFAC and SWATLD methods was exploited, even in the presence of unknown interferences and the satisfactory results can be obtained. Furthermore, the linear ranges of Tyr and DA were determined to be 0.042-6.42 μg/mL and 0.18-4.43 μmg/mL, respectively, and the accuracies of both methods were validated by the analytical figures of merit (FOM).     

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.     

Using second-order calibration method based on trilinear decomposition algorithms coupled with high performance liquid chromatography with diode array detector for determination of quinolones in honey samples

A novel strategy that combines the second-order calibration method based on the trilinear decomposition algorithms with high performance liquid chromatography with diode array detector (HPLC-DAD) was developed to mathematically separate the overlapped peaks and to quantify quinolones in honey samples. The HPLC-DAD data were obtained within a short time in isocratic mode. The developed method could be applied to determine 12 quinolones at the same time even in the presence of uncalibrated interfering components in complex background. To access the performance of the proposed strategy for the determination of quinolones in honey samples, the figures of merit were employed. The limits of quantitation for all analytes were within the range 1.2-56.7 μg kg⁻¹. The work presented in this paper illustrated the suitability and interesting potential of combining second-order calibration method with second-order analytical instrument for multi-residue analysis in honey samples.     

Second-order advantage from kinetic-spectroscopic data matrices in the presence of extreme spectral overlapping A multivariate curve resolution--alternating least-squares approach

Multivariate curve resolution coupled to alternating least-squares (MCR-ALS) has been employed to model kinetic-spectroscopic second-order data, with focus on the achievement of the important second-order advantage, under conditions of extreme spectral overlapping among sample components. A series of simulated examples shows that MCR-ALS can conveniently handle the studied analytical problem unlike other second-order multivariate calibration algorithms, provided matrix augmentation is implemented in the spectral mode instead of in the usual kinetic mode. The approach has also been applied to three experimental examples, which involve the determination of: (1) the antiparkinsonian carbidopa (analyte) in the presence of levodopa as a potential interferent, both reacting with cerium (IV) to produce the fluorescent species cerium (III) with different kinetics; (2) Fe(II) (analyte) in the presence of the interferent Zn(II), both catalyzing the oxidation of methyl orange with potassium bromate; and (3) tartrazine (analyte) in the presence of the interferent brilliant blue, both oxidized with potassium bromate, with the interferent leading to a product with an absorption spectrum very similar to tartrazine. The results indicate good analytical performance towards the analytes, despite the intense spectral overlapping and the presence of unexpected constituents in the test samples.     

Matrix-free analysis of aflatoxins in pistachio nuts using parallel factor modeling of liquid chromatography diode-array detection data

In the present study a second-order calibration strategy for high performance liquid chromatography with diode-array detection (HPLC-DAD) has been developed using parallel factor analysis (PARAFAC) and has been applied for simultaneous determination of aflatoxins B₁, B₂, G₁ and G₂ in pistachio nuts in the presence of matrix interferences. Sample preparation was based on solvent extraction (SE) followed by solid phase extraction (SPE) on Bond Elut C18 cartridges. Since the sample preparation procedure was not selective to the analytes of interest, exploiting second-order advantage to obtain concentrations of individual analytes in the presence of uncalibrated interfering compounds seemed necessary. Appropriate pre-processing steps have been applied to correct background signals and the effect of retention time shifts. Transferred calibration data set obtained from standardization of solvent based calibration data has been used in prediction step. The results of PARAFAC on a set of spiked and naturally contaminated pistachio nuts indicated that the four aflatoxins could be successfully determined. The method was validated and multivariate analytical figures of merit were calculated. The advantages of the proposed method are using a low-cost SPE step relative to standard method of aflatoxin analysis (immune affinity column assay), a unique and simple isocratic elution program for all samples and a calibration transfer for saving both chemicals and time of analysis. This study show that coupling of SPE-HPLC-DAD with PARAFAC as a powerful second-order calibration method can be considered as an alternative method for resolution and quantification of aflatoxins in the presence of unknown interferences obtained through analysis of highly complex matrix of pistachio samples and cost per analysis can be reduced significantly.     

A review on advanced oxidation processes: From classical to new perspectives coupled to two- and multi-way calibration strategies to monitor degradation of contaminants in environmental samples

This paper offers a critical review from classical to new perspectives of advanced oxidation processes (AOPs) coupled to two- and multi-way calibration strategies based on multivariate curve resolution – alternating least-squares (MCR-ALS) and parallel factory analysis (PARAFAC) with various analytical techniques to monitor the degradation of contaminants in environmental samples. It focuses on the generation of highly reactive hydroxyl (HO•) radicals (classical AOPs with emphasis on Fenton, photo-Fenton and ozonation processes) and emerging reactive sulphate (SO₄^•−) radicals (new perspectives of AOPs) for effective degradation of recalcitrant compounds. Other new perspectives of AOPs were also addressed, namely semiconductor photocatalysis (TiO₂/UV), combination of processes involving at least one AOP (hybrid or single-step processes and sequential or two-step processes), novel advanced electrochemical oxidation technologies (electro-Fenton and electro-photo-Fenton) and nanocatalytic heterogeneous Fenton technology with high specific surface area. Literature reports since 2008 for real applications in the environmental remediation based on AOPs (from classical to new perspectives) coupled to PARAFAC and MCR-ALS with first-, second- and third-order data were reviewed and the improvements obtained were briefly discussed. The two- and multi-way calibration strategies allow one the successful decomposition of first-, second- and third-order data collected from different analytical techniques. Therefore, the respective profiles obtained allowed qualitative (spectral profiles) and quantitative (concentration profiles) analysis of complex samples during the degradation of contaminants through the second-order advantage. Finally, trends of future research directions for AOPs coupled to various analytical techniques and advanced chemometric models were provided.     

Chemometric processing of second-order liquid chromatographic data with UV–vis and fluorescence detection. A comparison of multivariate curve resolution and parallel factor analysis 2

Second-order liquid chromatographic data with multivariate spectral (UV–vis or fluorescence) detection usually show changes in elution time profiles from sample to sample, causing a loss of trilinearity in the data. In order to analyze them with an appropriate model, the latter should permit a given component to have different time profiles in different samples. Two popular models in this regard are multivariate curve resolution-alternating least-squares (MCR-ALS) and parallel factor analysis 2 (PARAFAC2). The conditions to be fulfilled for successful application of the latter model are discussed on the basis of simple chromatographic concepts. An exhaustive analysis of the multivariate calibration models is carried out, employing both simulated and experimental chromatographic data sets. The latter involve the quantitation of benzimidazolic and carbamate pesticides in fruit and juice samples using liquid chromatography with diode array detection, and of polycyclic aromatic hydrocarbons in water samples, in both cases in the presence of potential interferents using liquid chromatography with fluorescence spectral detection, thereby achieving the second-order advantage. The overall results seem to favor MCR-ALS over PARAFAC2, especially in the presence of potential interferents.     

Time shift correction in second-order liquid chromatographic data with iterative target transformation factor analysis

When the generalized rank annihilation method (GRAM) is applied to liquid chromatographic data with diode-array detection, an important problem is the time shift of the peak of the analyte in the test sample. This problem leads to erroneous predictions. This time shift can be corrected if a time window is selected so that the chromatographic profile of the analyte in the test sample is trilinear with the peak of the analyte in the calibration sample. In this paper we present a new method to determine when this condition is met. This method is based on the curve resolution with iterative target transformation factor analysis (ITTFA). The calibration and test matrices are independently decomposed into profiles and spectra, and aligned before GRAM is applied. Here we study two situations: first, when the calibration matrix has one analyte and second, when it has two analytes. When the calibration matrix has two analytes, we selectively determine the time window for the analyte to be quantified. There were considerably fewer prediction errors after correction.     

Second-order data by flow injection analysis with spectrophotometric diode-array detection and incorporated gel-filtration chromatographic column

A flow injection analysis (FIA) system furnished with a gel-filtration chromatographic column and with photodiode-array detection was used for the generation of second-order data. The system presented is a model system in which the analytes are blue dextran, potassium hexacyanoferrate(III) and heparin. It is shown that the rank of the involved sample data matrices corresponds to the number of chemical components present in the sample. The PARAFAC (parallel factor analysis) algorithm combined with multiple linear regression and tri-PLS (tri-linear partial least-squares regression), which allows unknown substances to be present in the sample, are implemented for FIA systems and it is illustrated how these three-way algorithms can handle spectral interferents. The prediction ability of the two methods for pure two-component samples and also the predictions ability in the presence of unknown interferents are satisfactory. However, the predictions obtained by tri-PLS are slightly better than those obtained using PARAFAC regression algorithm.     

Second-order advantage in determining Co (II) in real samples using kinetic-spectrophotometric data matrices and multivariate curve resolution-alternating least square approach

In the present study, multivariate curve resolution coupled to alternating least-squares (MCR-ALS) was used to analyze kinetic-spectroscopic second-order data. The purpose of the study was to achieve important second-order advantage under the conditions of extreme spectral overlapping among sample components. The obtained experimental data indicated that MCR-ALS, unlike other second-order multivariate calibration algorithms, can conveniently handle the investigated analytical problem provided that matrix augmentation is implemented in the spectral mode instead of the usual kinetic mode. In this work, row-wise augmentation was used to break rank deficiency under conditions of extreme spectral overlapping among sample components. The approach was applied to determine Cobalt (II) based on its oxidation reaction with Fe (III) and 1, 10-phenantroline in micellar media. The results indicated good analytical performance toward the analyte despite the intense spectral overlapping and the presence of unexpected constituents in the test samples. The maximum and minimum band boundaries of feasible solutions corresponding to the species profiles were estimated by multivariate curve resolution. The results of the study indicated that unique solution can be practically obtained using MCR-ALS under the selection of suitable constraints such as trilinearity.     

Quantitative analysis of hydrolysis of carbaryl in tap water and river by excitation-emission matrix fluorescence coupled with second-order calibration

A novel method was proposed to determine simultaneously carbaryl and its degradation product 1-naphthol in river and tap water in this paper. The parallel factor analysis (PARAFAC) algorithm was adopted to analyze the excitation–emission matrix (EEM) fluorescence data. The second-order advantage of the PARAFAC-based second-order calibration algorithm was exploited, which make it possible that calibration can be performed even in the presence of unknown interferences. Good recoveries were obtained although the excitation and emission spectral profiles of the analytes were overlapped with background in the river water. It was also applied to investigate the hydrolysis kinetics of carbaryl in river water and tap water. The rate equation, the rate constant and the half life were calculated.     

Simultaneous determination of 6-methylcoumarin and 7-methoxycoumarin in cosmetics using three-dimensional excitation-emission matrix fluorescence coupled with second-order calibration methods

This paper reports a simple, rapid, and effective method for quantitative analysis of 6-methylcoumarin (6-MC) and 7-methoxycoumarin (7-MOC) in cosmetics using excitation–emission matrix (EEM) fluorescence coupled with second-order calibration. After simple pretreatments, the adopted calibration algorithms exploiting the second-order advantage, i.e., parallel factor analysis (PARAFAC) and self-weighted alternating tri-linear decomposition (SWATLD), could allow the individual concentrations of the analytes of interest to be predicted even in the presence of uncalibrated interferences. In the analysis of facial spray, with the external calibration method, the average recoveries attained from PARAFAC and SWATLD with the factor number of 3 (N = 3) were 101.4 ± 5.5 and 97.5 ± 4.1% for 6-MC, and 103.3 ± 1.7 and 101.7 ± 1.8% for 7-MOC, respectively. Moreover, in the analysis of oil control nourishing toner, the standard addition method (SAM) was suggested to overcome the partial fluorescence quenching of 6-MC induced by the analyte–background interaction, which also yielded satisfactory prediction results. In addition, the accuracy of the two algorithms was also evaluated through elliptical joint confidence region (EJCR) tests as well as figures of merit (FOM), including sensitivity (SEN), selectivity (SEL) and limit of detection (LOD). It was found that both algorithms could give accurate results, only the performance of SWATLD was slightly better than that of PARAFAC in the cases suffering from matrix effects. The method proposed lights a new avenue to determine quantitatively 6-MC and 7-MOC in cosmetics, and may hold great potential to be extended as a promising alternative for more practical applications in cosmetic quality control, due to its advantages of easy sample pretreatment, non-toxic and non-destructive analysis, and accurate spectral resolution and concentration prediction.