New Developments for the Sensitivity Estimation in Four-Way Calibration with the Quadrilinear Parallel Factor Model

Quantification of resveratrol and pyrimethanil in agricultural wastewater by using excitation-emission matrix fluorescence and a novel second-order calibration algorithm

Botrytis cinerea is a common disease in crops such as cucumbers and grapes, and pyrimethanil (PYR) is often used to prevent and control it. Studies have found that resveratrol (RES) and PYR have a synergistic interaction that can prevent botrytis cinerea, but their residues pose a potential threat to the environment. To accurately detect these substances in agricultural wastewater, a new trilinear decomposition algorithm, alternating residual mean trilinear decomposition (ARMTLD), was proposed for second-order calibration of three-way data arrays. The performance of the ARMTLD algorithm was evaluated on a simulated data set and compared with four other iterative trilinear decomposition algorithms. The results show that ARMTLD has a fast convergence speed, strong noise robustness, and low component dependence, and can accurately determine RES and PYR in farmland wastewater under complex conditions. Their average recovery rate exceeded 95 %, and the LOD were 3.0 ng mL-1 and 9.2 ng mL-1 (RES) and LOQ were 0.4 ng mL-1 and 1.3 ng mL-1 (PYR), respectively. The ARMTLD-assisted excitation-emission matrix (EEM) method provides high-precision decomposition, strong anti-interference capability, and excellent sensitivity, making it particularly well-suited for analytical scenarios with low target concentrations, high noise levels, and complex interferences.

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.

Quantitative analysis of carbaryl and thiabendazole in complex matrices using excitation-emission fluorescence matrices with second-order calibration methods

In this paper, a fast and efficient analytical strategy was proposed that chemometrics assisted with excitation-emission fluorescence matrices was used to quantify carbaryl (CAR) and thiabendazole (TBZ) in peach, soil and sewage. Even if there are serious overlapped peaks and unknown interferences in fluorescence analysis, the second-order calibration method based on alternating trilinear decomposition (ATLD) algorithm can be used to analyze CAR and TBZ in peach, soil and sewage. The recoveries of CAR and TBZ in peach are 110.4% and 99.7% and their standard deviations are lower than 2.1% and 0.3%, respectively. In addition, the accuracy of the method was assessed with figures of merit as well as intra-day and inter-day precision. The limit of detection, the limit of quantitation of CAR and TBZ in peach are 1.2 ng mL^-1 and 0.3 ng mL^-1, 3.5 ng mL^-1 and 0.8 ng mL^-1, respectively. And their root-mean-square error of prediction are 17.0 ng mL^-1 and 5.0 ng mL^-1 and there are high sensitivity and selectivity in this method. Meanwhile, the results obtained by ATLD algorithm were compared with those obtained by the self-weighted alternate trilinear decomposition algorithm (SWATLD) and the parallel factor analysis (PARAFAC) algorithm, and statistical methods such as the t-test, F-test and the elliptic joint confidence region were used to evaluate for analysis. There were no significant differences among these methods. At last, high performance liquid chromatography-fluorescence detector (HPLC-FLD) was used to evaluate the accuracy and reliability of the proposed method. These results are satisfactory and indicate that the proposed method can be used for accurate and rapid determination of pesticides in complex systems.

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.

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.

Analytical Figures of Merit for Multisensor Arrays

Multisensor arrays employing various sensing principles are a rapidly developing field of research as they allow simple and inexpensive quantification of various parameters in complex samples. Quantitative analysis with such systems is based on multivariate regression techniques, and deriving of traditional analytical figures of merit (e.g., sensitivity, selectivity, limit of detection, and limit of quantitation) for such systems is not obvious and straightforward. Nevertheless, it is absolutely needed for further development of the multisensor research field and for introducing these instruments into the general context of analytical chemistry. Here, we report on the protocol for calculation of sensitivity, selectivity, and detection limits for multisensor arrays. The results are provided and discussed in detail for several real-world data sets.

Simultaneously quantifying intracellular FAD and FMN using a novel strategy of intrinsic fluorescence four-way calibration

The simultaneous quantitative analysis of intracellular metabolic coenzymes flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN) is of interest because they participate in many electron-transfer reactions of metabolism. But, the simultaneous quantitative analysis of FAD and FMN is hard to be achieved by traditional analytical methods. This paper proposes a novel strategy of intrinsic fluorescence coupled with four-way calibration method for simultaneous quantitative analysis of intracellular metabolic coenzymes FAD and FMN. Through mathematical separation, this proposed analytical method efficiently achieved the simultaneous quantitative analysis of metabolic coenzymes FAD and FMN in the cell, despite the fact that uncalibrated spectral interferents coexist in the system. The predicted concentrations of FAD and FMN in the cell are 217.0 ± 6.9 and 155.0 ± 1.7 pmol/10⁶ cells respectively, which were validated by the approved liquid chromatography-tandem mass spectrometry (LC-MS/MS) method. This analytical method with second-order advantage simply requires the cell solution to be diluted by a buffer, it could introduce an interesting analytical strategy for multianalyte direct quantitative analysis in complex biological systems. In addition, we explore the third-order advantage of four-way calibration by a comparative study based on this real fluorescence data. The comparisons indicate that a four-way calibration method can provide higher sensitivity and more resolving power than a three-way calibration method.

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.

Simultaneous determination of umbelliferone and scopoletin in Tibetan medicine Saussurea laniceps and traditional Chinese medicine Radix angelicae pubescentis using excitation-emission matrix fluorescence coupled with second-order calibration method

A chemometrics-assisted excitation-emission matrix (EEM) fluorescence method is presented for simultaneous determination of umbelliferone and scopoletin in Tibetan medicine Saussurea laniceps (SL) and traditional Chinese medicine Radix angelicae pubescentis (RAP). Using the strategy of combining EEM fluorescence data with second-order calibration method based on the alternating trilinear decomposition (ATLD) algorithm, the simultaneous quantification of umbelliferone and scopoletin in the two different complex systems was achieved successfully, even in the presence of potential interferents. The pretreatment is simple due to the "second-order advantage" and the use of "mathematical separation" instead of awkward "physical or chemical separation". Satisfactory results have been achieved with the limits of detection (LODs) of umbelliferone and scopoletin being 0.06ngmL(-1) and 0.16ngmL(-1), respectively. The average spike recoveries of umbelliferone and scopoletin are 98.8±4.3% and 102.5±3.3%, respectively. Besides, HPLC-DAD method was used to further validate the presented strategy, and t-test indicates that prediction results of the two methods have no significant differences. Satisfactory experimental results imply that our method is fast, low-cost and sensitive when compared with HPLC-DAD method.

A systematic study on the effect of noise and shift on multivariate figures of merit of second-order calibration algorithms

In the present study, multivariate analytical figures of merit (AFOM) for three well-known second-order calibration algorithms, parallel factor analysis (PARAFAC), PARAFAC2 and multivariate curve resolution-alternating least squares (MCR-ALS), were investigated in simulated hyphenated chromatographic systems including different artifacts (e.g., noise and peak shifts). Different two- and three-component systems with interferences were simulated. Resolved profiles from the target components were used to build calibration curves and to calculate the multivariate AFOMs, sensitivity (SEN), analytical sensitivity (γ), selectivity (SEL) and limit of detection (LOD). The obtained AFOMs for different simulated data sets using different algorithms were used to compare the performance of the algorithms and their calibration ability. Furthermore, phenanthrene and anthracene were analyzed by GC-MS in a mixture of polycyclic aromatic hydrocarbons (PAHs) to confirm the applicability of multivariate AFOMs in real samples. It is concluded that the MCR-ALS method provided the best resolution performance among the tested methods and that more reliable AFOMs were obtained with this method for the studied chromatographic systems with various levels of noise, elution time shifts and presence of unknown interferences.

Quantitative fluorescence kinetic analysis of NADH and FAD in human plasma using three- and four-way calibration methods capable of providing the second-order advantage

The metabolic coenzymes reduced nicotinamide adenine dinucleotide (NADH) and flavin adenine dinucleotide (FAD) are the primary electron donor and acceptor respectively, participate in almost all biological metabolic pathways. This study develops a novel method for the quantitative kinetic analysis of the degradation reaction of NADH and the formation reaction of FAD in human plasma containing an uncalibrated interferent, by using three-way calibration based on multi-way fluorescence technique. In the three-way analysis, by using the calibration set in a static manner, we directly predicted the concentrations of both analytes in the mixture at any time after the start of their reactions, even in the presence of an uncalibrated spectral interferent and a varying background interferent. The satisfactory quantitative results indicate that the proposed method allows one to directly monitor the concentration of each analyte in the mixture as the function of time in real-time and nondestructively, instead of determining the concentration after the analytical separation. Thereafter, we fitted the first-order rate law to their concentration data throughout their reactions. Additionally, a four-way calibration procedure is developed as an alternative for highly collinear systems. The results of the four-way analysis confirmed the results of the three-way analysis and revealed that both the degradation reaction of NADH and the formation reaction of FAD in human plasma fit the first-order rate law. The proposed methods could be expected to provide promising tools for simultaneous kinetic analysis of multiple reactions in complex systems in real-time and nondestructively.

Solving signal instability to maintain the second-order advantage in the resolution and determination of multi-analytes in complex systems by modeling liquid chromatography-mass spectrometry data using alternating trilinear decomposition method assisted with piecewise direct standardization

The application of calibration transfer methods has been successful in combination with near-infrared spectroscopy or other tools for prediction of chemical composition. One of the developed methods that can provide accurate performances is the piecewise direct standardization (PDS) method, which in this paper is firstly applied to transfer from one day to another the second-order calibration model based on alternating trilinear decomposition (ATLD) method built for the interference-free resolution and determination of multi-analytes in complex systems by liquid chromatography-mass spectrometry (LC-MS) in full scan mode. This is an example of LC-MS analysis in which interferences have been found, making necessary the use of second-order calibration because of its capacity for modeling this phenomenon, which implies analytes of interest can be resolved and quantified even in the presence of overlapped peaks and unknown interferences. Once the second-order calibration model based on ATLD method was built, the calibration transfer was conducted to compensate for the signal instability of LC-MS instrument over time. This allows one to reduce the volume of the heavy works for complete recalibration which is necessary for later accurate determinations. The root-mean-square error of prediction (RMSEP) and average recovery were used to evaluate the performances of the proposed strategy. Results showed that the number of calibration samples used on the real LC-MS data was reduced by using the PDS method from 11 to 3 while producing comparable RMSEP values and recovery values that were statistically the same (F-test, 95% confidence level) to those obtained with 11 calibration samples. This methodology is in accordance with the highly recommended green analytical chemistry principles, since it can reduce the experimental efforts and cost with regard to the use of a new calibration model built in modified conditions.

Total synchronous fluorescence spectroscopic data modeled with first- and second-order algorithms for the determination of doxorubicin in human plasma

In this work, we present the development of a method for the determination of doxorubicin in plasma samples in the presence of an unexpected component (riboflavin) by using total synchronous fluorescence spectroscopic data matrices. To the best of our knowledge, this is the first time that the second-order advantage is obtained with this kind of data. Two strategies including unfolding the data and: (a) processing with multivariate curve resolution coupled to alternating least-squares as first-order data or (b) processing with unfolded partial least-squares and exploiting the second-order advantage by the residual bilinearization procedure were considered. The calibration set was built with human plasma samples spiked with doxorubicin, while the validation set was prepared with human plasma samples spiked with both doxorubicin and riboflavin, a drug whose spectrum highly overlaps with the one corresponding to doxorubicin. Both methodologies reached good indicators of accuracy: recoveries of ca. 100 ± 8% and REP of ca. 5%; and precision: coefficient of variations between 7 and 9%.

Simultaneous determination of metoprolol and α-hydroxymetoprolol in human plasma using excitation–emission matrix fluorescence coupled with second-order calibration methods

Background: Metoprolol (MET) is a β1-adrenoceptor antagonist, which is widely used in the treatment of cardiovascular diseases, and α-hydroxymetoprolol (α-OHM) is its hydroxylated metabolite. Owing to their similar structures, optimization of the condition for the chromatography approach, which is in common use for determination, is both time consuming and laborious. Results: A new and effective strategy that combines the excitation–emission matrix fluorescence with second-order calibration methods was developed for simultaneous determination of MET and α-OHM in human plasma. Conclusion: Although the fluorescence spectra of MET and α-OHM overlapped and a large number of unknown and uncalibrated fluorescent components coexisted, the developed method enables accurate concentrations together with reasonable resolution of excitation and emission profiles for the analytes of interest. An additional advantage of the proposed method is that there is no need for separation and sample pretreatment, in addition to lower cost than traditional methods.