Second- and third-order multivariate calibration: data, algorithms and applications

Multivariate curve resolution-alternating least-squares and second-order advantage in first-order calibration. A systematic characterisation for three-component analytical systems

BACKGROUND

Recent interest has been focused on the application of multivariate curve resolution-alternating least-squares (MCR-ALS) to systems involving the measurement of first-order and non-bilinear second-order data. The latter pose important challenges to bilinear decomposition models, due to the phenomenon of rotational ambiguity in the solutions, even under the application of the full set of chemical constraints that is usually employed in MCR-ALS calibration.

RESULTS

After the analysis of several simulated and experimental datasets, important conclusions regarding the role of the selectivity patterns in the constituent spectra have been drawn concerning the achievement of the second-order advantage. Theoretical considerations based on the calculation of the areas of feasible solutions helped to support the observations regarding the predictive ability of MCR- ALS in the various datasets.

SIGNIFICANCE

The understanding of the impact of rotational ambiguity in obtaining the second-order advantage with both first-order and non-bilinear second-order data is of paramount importance in the future development of analytical protocols of complex samples.

The advantages behind the efforts of performing higher-order calibration methods - A case study

BACKGROUND

Across numerous investigations delved into second- and higher-order data, an undoubted finding emerges: models based on such data can effectively exploit the second-order advantage. However, whether further benefits can be achieved by modeling data of higher dimensions remains a subject of inquiry. In this regard, a prevailing question emerges in third-order data-based applications regarding the fundamental need to increase the data dimension and, hence, the data analysis complexity. This study aims to provide meaningful evidence to support the advantages inherent in employing third-order calibration methods despite the associated efforts, such as instrumentation and data analysis complexity.

RESULTS

This study compares the analytical performance achieved using a third-order calibration method with those obtained from most of the possible second-order calibration approaches derived from the same dataset. This work delves into the structural properties of the data, modeling limitations, and analytical characteristics associated with each model. Additionally, it includes a comprehensive statistical comparison of the models based on their recovery performance. First, the outcomes demonstrate the importance of capitalizing on all available chemical information and harnessing the full potential of data to maximize its benefits. Moreover, the results provide evidence that asserts the fact that third-order calibration methods bring the opportunity to increase the number of analytes that can be simultaneously determined, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.

SIGNIFICANCE

this research marks the first extensive comparison of third-order data calibration models with possible second-order calibration methods. Moreover, this work pioneers the incorporation of highly challenging non-multilinear data. The advancements detailed in this study emphasize the advantages of third-order data acquisition, notwithstanding the need for more tedious experimental protocols, specialized instrumentation (sometimes), and quite complex data analysis.

Green Approach for Simultaneous Quantitative Analysis of Fluoroquinolones in the Environment using Three-Dimensional Fluorescence Coupled with Second-Order Calibration Method

In this study, a straightforward and quick analytical technique based on the self-weighted alternating trilinear decomposition (SWATLD) algorithm in conjunction with excitation-emission matrix (EEM) fluorescence for the simultaneous determination of the antibiotics levofloxacin (LVFX) and ciprofloxacin (CIP) in environmental waters and sediments was developed. This approach completely utilizes the "second-order advantage" and inherits the great sensitivity of classic fluorescence. It replaces or improves the conventional "physical/chemical separation" with "mathematical separation", enabling direct and quick quantification of the target analytes even in the presence of unknown interferences, greatly streamlining sample preparation procedures, consuming less solvent, and speeding up analysis time, and allows successful and environmentally friendly solution of overlapping fluorescence spectra of multiple components in complicated environmental matrices without cumbersome pretreatment steps and complex and expensive instrumentation. The limits of detection varied between 0.34 and 0.67 ng mL- 1, and the average spiking recoveries of LVFX and CIP in water and sediment ranged from 97.6 to 107.7% with relative standard deviations lower than 6.6%. The developed method shows the reliability of the technology and the ability to quickly detect trace antibiotics in lake water even in the presence of unidentified interferents.

An optimized methodology for the determination of multiclass organic ultraviolet sunscreens and metabolites in human milk through chromatographic and chemometric resolution

Organic UV filters (UVFS) are used to mitigate the dermal effects associated with health risks from UV radiation, making them essential in personal care products. UVFS are frequently identified in environmental samples due to their high lipophilicity and persistence, underscoring the urgency of comprehensive assessments and regulatory measures aimed at safeguarding ecosystems and human health. The present study reports a multiclass analytical method for determining 16 UV sunscreens and metabolites in breast milk based on an ultrasound-assisted-dispersive liquid-liquid micro-extraction (UA-DLLME) with further chromatographic and chemometric resolution. The experimental conditions of the UA-DLLME were optimized through the implementation of the Design of Experiment tools. To model the responses, least-squares and artificial neural network methodologies were implemented. The optimal conditions were found by employing the desirability function. The samples were analyzed through reverse-phase liquid chromatographic separation, UV diode array, and fast-scanning fluorescence detection. The chromatographic analysis enabled the resolution of 16 analytes in a total time of 13.0 min. Multivariate curve resolution-alternating least-square (MCR-ALS) modelling was implemented to resolve analytes that were not fully resolved and to determine analytes that coeluted with endogenous components of the breast milk samples. An enrichment factor of 5-fold concentration was obtained with this methodology, reaching recoveries between 65 % and 105 % for 13 multiclass UV sunscreens and metabolites in breast milk samples with RSD % and REP % lower than 12 %.

Third-order calibration applied to process surfactant-modulated excitation-emission matrix four-way fluorescence data for the direct determination of four polycyclic aromatic hydrocarbons in oilfield produced water

Fluorescence spectroscopy is a powerful tool to determine polycyclic aromatic hydrocarbons (PAHs) owing to the strong endogenous fluorescence of these compounds. However, the presence of unknown interferences and overlapped spectra hinders the accurate determination of PAHs in oilfield produced water. Moreover, surfactants frequently coexist in oilfield produced water and will seriously affect the fluorescence signals of PAHs. Herein, a new methodology applying third-order calibration to process four-way (4D) fluorescence data was proposed to solve these problems and achieve accurate determination of pyrene, fluorene, phenanthrene, and fluoranthene as an example in oilfield produced water. The methodology is based on excitation-emission matrix fluorescence modulated by different concentrations of sodium dodecyl benzene sulfonate (SDBS) in the analyzed samples. The 4D fluorescence data were processed by third-order calibration methods including four-way parallel factor analysis (4-PARAFAC) and alternating weighted residue constraint quadrilinear decomposition (AWRCQLD), and the results were compared with those of second-order calibration methods. It was proved that third-order calibration was capable of accurately identifying and quantifying PAHs together with SDBS in oilfield produced water, which has better quantitative results and figures of merit compared to second-order calibration. This study provided a new approach to generating 4D fluorescence data and opened up an avenue for the accurate determination of PAHs in complex oilfield produced water with surfactants.

Simultaneous Determination of Adulterants in Dietary Food Supplements Using Multivariate Data Analysis after Preconcentration with Novel Nanosorbents and Chromatographic Measurement

Background

The increasing popularity of dietary supplements and, consequently, related adulteration emphasizes the rising need to examine the association of food supplements with fraud. Intentional or unintentional fraud in food supplements by hazardous chemicals compounds is a problem that many countries are struggling with. Much effort have been made to effectively and reliably control the quality of food supplements.

Objective

Due to the importance of the subject, an analytical method for the simultaneous and reliable detection and quantitative determination of three key adulterants in dietary food supplements was developed. The proposed method benefits from analytical methods and multivariate calibration methods to progress the determination of adulterants in a complex matrix.

Methods

HPLC assisted by multivariate curve resolution-alternating least square (MCR-ALS) analysis was used to detect adulterants in real samples after separation and preconcentration using novel mesoporous carbon nanoparticles. Solid-phase extraction (SPE) optimization was accomplished by central composite design (CCD). In order to obtain the best results, the MCR-ALS model was compared with the parallel factor analysis 2 (PARAFAC2) model and validated by estimation of linearity, detection limits, and recovery.

Results

The detection limits and linear dynamics were calculated as 1.5, 4.27, and 4.77 µg/mL, and 1–50, 5–20, and 5–20 µg/mL for caffeine, ephedrine, and fluoxetine, respectively. Mean recovery for determination of caffeine, ephedrine, and fluoxetine using the developed method was reported as 101.75, 91.7, and 92.36, respectively.

Conclusion

The results showed that to avoid negative health outcomes associated with the excessive consumption of adulterated food supplements releasing such products should be carefully regulated. The developed method was validated using statistical factors and showed acceptable and reliable results.

Highlights

(1) The application of MCR-ALS coupled with HPLC-Diode-Array Detection data sets allowed the simultaneous identification and quantification of three key adulterants (caffeine, ephedrine, and fluoxetine) in dietary food supplements. (2) A small amount of the novel adsorbent was successfully used to preconcentrate the trace amounts of adulterants in samples. (3) This method benefits from the chemometrics tools and experimental design to significantly reduce the use of toxic solvents and complicated instruments to propose a less time-consuming method for quantification of multicomponents in the presence of uncalibrated interferents.

On four-way CP model estimation efficiency

The latent structure of four-dimensional tensors can be investigated by means of the four-way CANDECOMP/PARAFAC model. This technique is seldom used because its estimating design is challenging from an algorithmic and interpretational standpoint. Parameter estimation with a least-squares approach can be computationally costly, especially under difficult conditions such as factor collinearity and model over-specification. In this work, we implement a 4th-order extension of the efficient trilinear procedure INT-2 to tackle estimating setbacks and test it in a simulation study.

Advanced tuning of the ion management parameters in GC × GC-HRMS using a Fourier transform Orbitrap mass analyzer for pixel-based data handling and multivariate analysis

GC × GC investigations are well known to generate a substantial amount of information-rich and structurally complex data, requiring advanced data processing strategies like chemometrics. Many workflows are available for data handling and processing, such as the peak-table and pixel-based approaches. The goal of this work is to present a solution based on method development to solve the missing pixel problem that may be encountered in experiments performed with GC and GC × GC coupled to the Fourier transform orbital ion trap (FT-Orbitrap) mass analyzer. Data input is vital for pixel-based chemometric analyses, as some post-processing solutions may lead to significant loss of chemical information in the data set. Hence, a key requisite is that the chemical information is consistently indexed in the data arrays for proper pixel-based data handling and analysis. In this study, we carefully evaluated the ion management parameters to preserve the intrinsic structure and information of the data arrays of the GC × GC-FT-Orbitrap for future pixel-oriented chemometric analysis. The most acceptable conditions yielded acquisition rates up to 42.6 spectra per s, while a routine setting of 24.7 Hz was successfully employed in analyses of different petroleum fractions, producing both consistent tensor sizes and acceptable peak reconstructions. A data acquisition rate of 24.7 spectra per s and a mass resolving power of 15 000 allowed the resolution of a mass split of only 0.004 Da - which is an interesting configuration for challenging applications in petroleomics. Using such advanced settings, the missing pixel problem was reduced from up to 30% to much less than 0.04% of the data array dimension. Thus, the proposed configuration can be employed in studies that require pixel-oriented multivariate data analysis.

An overview on multi-elemental profile integrated with chemometrics for food quality assessment: toward new challenges

Food products, especially those with high value-added, are commonly subjected to strict quality controls, which are of paramount importance, especially for attesting to some peculiar features related, for instance, to their geographical origin and/or the know-how of their producers. However, the sophistication of fraudulent practices requires a continuous update of analytical platforms. Different analytical techniques have become extremely appealing since the instrumental analysis tools evolution has substantially improved the capability to reveal and understand the complexity of food. In light of this, multi-elemental composition has been successful implemented solving a plethora of food authentication and traceability issues. In the last decades, it has existed an ever-increasing trend in analysis based on spectrometry analytical platforms in order to obtain a multi-elemental profile that combined with chemometrics have been noteworthy analytical methodologies able to solve these problems. This review provides an overview of published reports in the last decade (from 2011 to 2021) on food authentication and quality control from their multi-element composition in order to evaluate the state-of-the-art of this field and to identify the main characteristics of applied analytical techniques and chemometric data treatments that have permit achieve accurate discrimination/classification models, highlighting the strengths and the weaknesses of these methodologies.

Rapid determination of sulfamethoxazole and trimethoprim illegally added to health products using excitation-emission matrix fluorescence coupled with the second-order calibration method

In this work, a simple and fast analytical method based on a self-weighted alternating trilinear decomposition (SWATLD) algorithm coupled with excitation-emission matrix (EEM) fluorescence was developed for the simultaneous determination of sulfamethoxazole (SMZ) and trimethoprim (TMP) illegally added to health products. With the second-order advantage, the proposed method obtained satisfactory results in the presence of peak overlap and unknown interferences. The analysis time for a single sample is only 0.8 minutes. The average spiked recoveries of SMZ and TMP in three health product spiked samples were in the range of 91.0-106.2% and 86.8-107.8%, respectively. The relative standard deviations (RSDs) were lower than 8.6%. In addition, verification parameters including sensitivity (SEN), selectivity (SEL), the limit of detection (LOD), the limit of quantification (LOQ), intra-day precision, and inter-day precision were calculated, and the results show that the proposed method is feasible. The quantitative results of the proposed method were further confirmed by the LC-MS/MS method, which proved that the proposed method was efficient and green for drug-abuse monitoring of SMZ and TMP in health products.

Chromatographic Applications in the Multi-Way Calibration Field

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

Achieving the analytical second-order advantage with non-bilinear second-order data

Multi-way calibration based on second-order data constitutes a revolutionary milestone for analytical applications. However, most classical chemometric models assume that these data fulfil the property of low rank bilinearity, which cannot be accomplished by all instrumental methods. Indeed, various techniques are able to generate non-bilinear data, which are all potentially useful for the development of novel second-order calibration methodologies. However, the achievement of the second-order advantage in these cases may be severely limited, since methods for comprehensive modelling of non-bilinear second-order data remain only partially explored. In this research, the analytical performance of three well-known second-order models, namely non-bilinear rank annihilation (NBRA), unfolded partial least-squares with residual bilinearization (U-PLS-RBL) and multivariate curve resolution - alternating least-squares (MCR-ALS) is systematically assessed through sets of simulated and experimental non-bilinear second-order data, involving one analyte and one interferent. Although it is not possible to establish a single strategy to model any type of non-bilinear second-order data with the studied methods, each approach may lead to successful predictions under certain circumstances. It is shown that the prediction capacity is severely affected by data properties such as the level of instrumental noise, the rank of the response matrices and the signal selectivity pattern of the analyte.

Multi-Way Analysis Coupled with Near-Infrared Spectroscopy in Food Industry: Models and Applications

Near-infrared spectroscopy (NIRS) is a fast and powerful analytical tool in the food industry. As an advanced chemometrics tool, multi-way analysis shows great potential for solving a wide range of food problems and analyzing complex spectroscopic data. This paper describes the representative multi-way models which were used for analyzing NIRS data, as well as the advances, advantages and limitations of different multi-way models. The applications of multi-way analysis in NIRS for the food industry in terms of food process control, quality evaluation and fraud, identification and classification, prediction and quantification, and image analysis are also reviewed. It is evident from this report that multi-way analysis is presently an attractive tool for modeling complex NIRS data in the food industry while its full potential is far from reached. The combination of multi-way analysis with NIRS will be a promising practice for turning food data information into operational knowledge, conducting reliable food analyses and improving our understanding about food systems and food processes. To the best of our knowledge, this is the first paper that systematically reports the advances on models and applications of multi-way analysis in NIRS for the food industry.

Multilinear Mathematical Separation in Chromatography

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

Determination of ochratoxin A in coffee and tea samples by coupling second-order multivariate calibration and fluorescence spectroscopy

A new method to quantify the mycotoxin ochratoxin A (OTA) in coffee and tea samples is proposed based on second-order multivariate calibration and excitation-emission fluorescence matrix (EEFM) data. Experimental conditions were optimized by studying the effect of pH and various organized media on the fluorescence signal of OTA. For each analysed matrix (coffee grains and tea leaves), several sample pretreatments and calibration methods (external or standard addition) and data processing by chemometric models (e.g., parallel factor analysis/PARAFAC and multivariate curve resolution-alternating least squares/MCR-ALS) were evaluated and discussed. The MCR-ALS algorithm provided an adequate fit to the data for both samples, while PARAFAC was satisfactory only for the tea samples. Regarding the figures of merit, the limits of detection were in the range of 0.2-0.3 ng mL^-1; furthermore, low relative prediction errors, between 2% and 4%, were achieved in both the fortified and real samples. Accordingly, the proposed methodology was applied to analyse fortified roasted and green coffee and real tea leaf samples. Satisfactory recoveries were achieved (ranging from 92 to 110%), and the obtained concentrations were in agreement with the values obtained by the reference method (based on high-performance liquid chromatography with fluorescence detection/HPLC-FLD). In addition, all samples contained OTA levels lower than the maximum permissible levels. Finally, the proposed strategy allows the use of green analytical chemistry principles; for instance, the use of organic solvents and the generation of waste products were significantly lower than for similar analytical methods reported in the literature.

Three-way analysis of pH-UV absorbance dataset for the determination of paracetamol and its pKa value in presence of excipients

A three-way analysis method, parallel factor analysis (PARAFAC) model was applied to the pH-absorbance dataset for the simultaneous determination of paracetamol and its acid-base dissociation constant in presence of excipient interference in a syrup formulation without using chemical pretreatment or chromatographic separation step. The UV spectroscopic data matrices of calibration set, validation and unknown samples were obtained from the absorbance measurements at the five different pH media, considering conjugate acid/base properties of the related drug. Their pH-absorbance data matrices were arranged as a cubic data array (wavelength x sample x pH) (425x52x5). Three-way array of pH-absorbance dataset was decomposed into a trilinear set of spectral, pH and relative concentration profiles of paracetamol and excipients in the commercial syrup using PARAFAC model. In the PARAFAC implementation, paracetamol in the commercial syrup formulation and its pKa value were simultaneously predicted from the relative concentration and pH profiles, respectively. In the method validation step of this study, the performance of PARAFAC model was checked by analyzing the validation samples in terms of selectivity, sensitivity, accuracy and precision of the method. The determination results of paracetamol and its pKa value provided from PARAFAC application were compared to those obtained by a newly developed ultra-performance liquid chromatography (UPLC) method, in terms of simplicity, applicability, interpretability with low cost and short analysis time.

Green approach for simultaneous determination of multi-pesticide residue in environmental water samples using excitation-emission matrix fluorescence and multivariate calibration

Pesticides are among the most widespread organic contaminants in aquatic environments. In this work, a new green fluorescence application was proposed for the simultaneous determination of four widely employed pesticides in environmental water samples. To overcome the highly overlapped spectra within the analytes, and with the tissue matrix interferences in complex solutions, we have used the multivariate calibration methods such as parallel factor analysis (PARAFAC) and unfolded partial least squares coupled to residual bilinearization (U-PLS/RBL). These four pesticides can be identified simultaneously, and the correlation coefficients between resolved and actual spectra are all above 0.95. The second-order advantage allowed the determination of four pesticides at the ng mL^-1 level, even in the presence of humic acid (HA). The best results were obtained with the limits of detection of 1.72-18.69 for Carbendazim (CBZ), 0.30-5.19 for carbaryl (CAR), 0.35-6.32 for chlorothalonil (CHL), and 4.92-29.96 for tsumacide (TSU) (ng mL^-1), which can fully meet the quantitative detection and analysis requirements of trace pesticides in water samples. The real water sample of Bohai Seawater was used to check the performance of this approach in practical applications, which have achieved good prediction results of U-PLS/RBL. This study demonstrated the proposed method is rapid, accurate, sensitive, low detection limit, and environmentally friendly to determinate multi-pesticide residues in environmental water samples.

Rapid and simultaneous determination of three fluoroquinolones in animal-derived foods using excitation-emission matrix fluorescence coupled with second-order calibration method

The matter of fluoroquinolone residues in various foods still arouses wide public concern nowadays. In the present work, the strategy of excitation-emission matrix (EEM) fluorescence data coupled with second-order calibration method based on alternating normalization-weighted error (ANWE) algorithm was used to determine ofloxacin, lomefloxacin and ciprofloxacin in milk powder, milk and beef. Owning the unique "second-order advantage", the ANWE-assisted analytical method was proved to successfully and eco-friendly resolve the overlapped fluorescence spectra of multi-component in complex food matrixes without tedious pretreatment steps and sophisticated high-cost instrumentations. The feasibility of the proposed method was validated by experiments. The average spiked recoveries of three fluoroquinolones range from 82.6% to 110.5% with relative standard deviations lower than 7.4%, and the limits of detection range from 0.18 and 2.41 ng mL^-1. For further evaluation, analytical figures of merit such as sensitivity and selectivity, as well as the RSDs of intra-day (≦10.6%) and inter-day (≦9.4%) were calculated. The satisfactory analytical results demonstrated that the proposed strategy could be a competitive alternative for simple, rapid and simultaneous determination of multiple fluoroquinolones in animal-derived food samples.

Why should the pharmaceutical industry claim for the implementation of second-order chemometric models-A critical review

Today, pharmaceutical products are submitted to a large number of analytical tests, planned to either ensure or construct their quality. The official methods of analysis used to perform these determinations are very different in nature, but almost all demand the intensive use of reagents and manpower as major drawbacks. Thus, analytical development is continuously evolving to find fast and smart approaches. First-order chemometric models are well-known in the pharmaceutical industry, and are extensively used in many fields. Such is the impact of chemometric models that regulatory agencies include them in guidelines and compendia. However, the mention or practical application of higher-order models in the pharmaceutical industry is rather scarce. Herein, we try to bring a brief introduction to chemometric models and useful literature references, focusing on higher-order chemometric models (HOCM) applied to reduce manpower, reagent consumption, and time of analysis, without sacrificing accuracy or precision, while gaining selectivity and sensitivity. The advantages and drawbacks of HOCM are also discussed, and the comparison to first-order chemometric models is also analyzed. Along the work, HOCM are evidenced as a powerful tool for the pharmaceutical industry; moreover, its implementation is shown during several steps of production, such as identification, purity test and assay, and other applications as homogeneity of API distribution, Process Analytical Technology (PAT), Quality by Design (QbD) or natural product fingerprinting. Among these topics, qualitative and quantitative applications were covered. Experimental approaches of chemometrics coupled to several analytical techniques such as UV-vis, fluorescence and vibrational spectroscopies (NIR, MIR and Raman), and other techniques as hyphenated-chromatography and electrochemical techniques applied to production and analysis are discussed throughout this work.

A Bottom-Up Approach for Data Mining in Bioaromatization of Beers Using Flow-Modulated Comprehensive Two-Dimensional Gas Chromatography/Mass Spectrometry

In this study, we report the combination of comprehensive two-dimensional gas chromatography (GC×GC) with multivariate pattern recognition through template matching for the assignment of the contribution of Brazilian Ale 02 yeast strain to the aroma profile of beer compared with the traditional Nottingham yeast. Volatile organic compounds (VOC) from two beer samples, which were fermented with these yeast strains were sampled using headspace solid-phase microextraction (HS-SPME). The aroma profiles from both beer samples were obtained using GC×GC coupled to a fast scanning quadrupole mass spectrometer. Data processing performed through multiway principal components analysis succeeded in separating both beer samples based on yeast strain. The execution of a simple and reliable procedure succeeded and identified 46 compounds as relevant for sample classification. Furthermore, the bottom-up approach spotted compounds found exclusively in the beer sample fermented with the Brazilian yeast, highlighting the bioaromatization properties introduced to the aroma profile by this yeast strain.

Four- and five-way excitation-emission luminescence-based data acquisition and modeling for analytical applications. A review

The latest advances in both theory and experimental procedures on third-order/four-way and fourth-order/five-way calibration methods are discussed. This report is focused on excitation-emission (fluorescence and phosphorescence) matrices generation, employing different variables as the third data mode (time retention in chromatography, pH gradient, fluorescence/phosphorescence lifetime, kinetics, or other chemical treatments). Fully capitalizing on the second-order advantage, it has been possible to develop appealing analytical applications in spite of the complexity of the data. Extraction of the significant chemical information about the system under study as well as the individual abundance of the contributing constituents after proper higher-order data decomposition has allowed to analytical researchers performing quantitative analysis of complex samples. The experimental works reported up to the present are introduced and discussed in order to illustrate concepts. Throughout this work, the analytical benefits achieved by modeling third- and fourth-order data are exposed, attempting to contribute to the ongoing debate in the chemometric community regarding the existence and the true nature of the third-order advantage.

Comparison of several third-order correction algorithms applied to fluorescence excitation-emission-sample data array: Interference-free determination of polycyclic aromatic hydrocarbons in water pollution

Interference-free determination of polycyclic aromatic hydrocarbons (PAHs) in water pollution is proposed based on third-order correction algorithms with quadrilinear component modeling applied to the constructed four way fluorescence excitation-emission-sample data array with higher accuracy and better predictive ability than second-order (three-dimension) correction. Alternating weighted residue constraint quadrilinear decomposition (AWRCQLD), quadrilinear parallel factor analysis (4-PARAFAC), alternate penalty quadrilinear decomposition (APQLD) and alternate penalty trilinear decomposition (APTLD) are applied to acenaphthene (ANA), naphthalene (NAP) and fluorene (FLU) respectively. Fulvic acid affects PAHs determination seriously in real-world situation, so it is simulated as an interfering agent. Excitation-emission fluorescence matrixes (EEMs) of PAHs are measured at different volumes of fulvic acid simulated different interference conditions, to construct a four-way data array. After the four-way spectra data is analyzed by AWRCQLD, 4-PARAFAC, and APQLD, three-way EEMs analyzed by APTLD, results show that, on the one hand, PAHs can be measured more accurately with four-way data combined with third-order calibration than lower-order. On the other hand, AWRCQLD algorithm can reflect the superiority of third-order advantage better with higher recovery rate and smaller root mean square error, than other third-order or second-order correction algorithms.

Rapid, simultaneous and interference-free determination of three rhodamine dyes illegally added into chilli samples using excitation-emission matrix fluorescence coupled with second-order calibration method

In this study, a smart and green analytical method based on the second-order calibration algorithm coupled with excitation-emission matrix (EEM) fluorescence was developed for the determination of rhodamine dyes illegally added into chilli samples. The proposed method not only has the advantage of high sensitivity over the traditional fluorescence method but also fully displays the "second-order advantage". Pure signals of analytes were successfully extracted from severely interferential EEMs profiles via using alternating trilinear decomposition (ATLD) algorithm even in the presence of common fluorescence problems such as scattering, peak overlaps and unknown interferences. It is worth noting that the unknown interferents can denote different kinds of backgrounds, not only refer to a constant background. In addition, the method using interpolation method could avoid the information loss of analytes of interest. The use of "mathematical separation" instead of complicated "chemical or physical separation" strategy can be more effective and environmentally friendly. A series of statistical parameters including figures of merit and RSDs of intra- (≤1.9%) and inter-day (≤6.6%) were calculated to validate the accuracy of the proposed method. Furthermore, the authoritative method of HPLC-FLD was adopted to verify the qualitative and quantitative results of the proposed method. Compared with the two methods, it also showed that the ATLD-EEMs method has the advantages of accuracy, rapidness, simplicity and green, which is expected to be developed as an attractive alternative method for simultaneous and interference-free determination of rhodamine dyes illegally added into complex matrices.

Qualitative and quantitative analysis of Teucrium polium essential oil components by GC-MS coupled with MCR and PARAFAC methods

INTRODUCTION

Teucrium polium is a herbal plant which has curative potential and pharmacological characteristics. Therefore, establishment of accurate analytical methods for characterising its active components is of prime importance.

OBJECTIVE

Because of the complex nature of essential oil samples, some results of direct gas chromatography-mass spectrometry (GC-MS) analysis maybe unreliable. Therefore, GC-MS is coupled with chemometric methods to resolve experimental information taken from chromatographic peaks, and assign compounds to them more correctly.

METHODS

Essential oil of T. Polium of Koohbanan suburb (Kerman, Iran) was extracted by hydro-distillation. Then the T. polium essential oil was qualitatively analysed using GC-MS coupled with multivariate curve resolution (MCR), to resolve experimental information taken from chromatographic peaks, and assign compounds to them more correctly. After that, the method of parallel factor analysis (PARAFAC) was implemented to quantify the concentrations of five major components of the T. polium essential oil.

RESULTS

The number of identified components increases from 74 using the direct method of analysis to 106 using the MCR method. It is shown that α-pinene (8.93 μg/L), cis-verbenol (3.98 μg/L) and myrtenal (1.02 μg/L) are the most abundant components in the T. polium essential oil.

CONCLUSION

By coupling GC-MS and chemometric resolution methods such as MCR-alternating least squares (ALS) and PARAFAC more information with higher precision and accuracy can be obtained from raw experimental data. Also, it is shown that by implementing the PARAFAC method on the GC-MS data, it is possible to measure the concentration of the constituents of co-eluted, overlapped or embedded chromatographic peaks.