Rapid Determination of Costunolide and Dehydrocostuslactone in Human Plasma Sample and Chinese Patent Medicine Xiang Sha Yang Wei Capsule Using HPLC‐DAD Coupled with Second‐order Calibration

A novel methodology that combines high performance liquid chromatography with photodiode‐array detector (HPLC‐DAD) coupled with second‐order calibration method based on alternating trilinear decomposition (ATLD) algorithm was used in determination of the effective constituents such as costunolide and dehydrocostuslactone, in plasma sample and Chinese patent medicine Xiang Sha Yang Wei (XSYW) capsule. Complicated systems such as plasma and Chinese patent medicine which have intricate components are tedious to isolate and purify. The problem that chromatographic peaks are heavily overlapped among the analytes and interferents from the background matrices can be resolved, and the satisfactory quantification results have been gained with the help of the ATLD algorithm which utilized "mathematical separation" instead of partial "physical or chemical separation". Meanwhile, HPLC‐MS/MS method was used to validate the accuracy of the proposed determination method.     

A study on the differential strategy of some iterative trilinear decomposition algorithms: PARAFAC‐ALS,ATLD, SWATLD,and APTLD

This study presents an in‐depth discussion of the differential properties of various iterative trilinear decomposition algorithms, including Parallel Factor Analysis‐Alternating Least Squares (PARAFAC‐ALS), Alternating Trilinear Decomposition (ATLD), Self‐Weighted Alternating Trilinear Decomposition (SWATLD), and Alternating Penalty Trilinear Decomposition (APTLD). The shape of each algorithm's objective function (“convex” or “strictly convex”) is related to the algorithm's sensitivity to the estimated component number of the trilinear system. Different situations near the objective solution are analyzed both theoretically and numerically. The wall of perturbation generated by deviations in the iterative steps prevents the PARAFAC algorithm from achieving the objective solution when the component number is overestimated. This may explain, from a calculational perspective, why the PARAFAC algorithm could not obtain the objective solution or any equivalent thereto (although equivalents might still be chemically meaningful optimal solutions). The different effects of deviation and residual on the algorithms are demonstrated by numerical analysis in this paper. The convergence rate can be improved by the use of high‐performance computing strategy of the specific algorithm. The concept of solution set discussed in this paper complements the theory of the uniqueness of trilinear decomposition. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Towards a rehabilitation of the generalized rank annihilation method (GRAM)

The trilinear PARAFAC model occupies a central place in multiway analysis, because the components of a data array can often be uniquely resolved. This paper compares the resolution for a large variety of methods, namely the generalized rank annihilation method (GRAM), alternating least squares (ALS), alternating trilinear decomposition (ATLD), alternating coupled vectors resolution (ACOVER), alternating slice-wise diagonalization (ASD), alternating coupled matrices resolution (ACOMAR), self-weighted alternating trilinear decomposition (SWATLD), and pseudo alternating least squares (PALS). The comparison was conducted using Monte Carlo simulations. It was shown that GRAM performs well for moderately and highly overlapped data. These results argue strongly against the previously claimed superiority of the alternatives listed above.     

三维荧光校正法直接测定尿液中的利血平

利用化学计量学三维数据校正方法中的交替三线性分解算法(ATLD)和自加权交替三线性分解算法(SWATLD), 不经化学分离, 对采用激发-发射矩阵荧光法所得到的三维响应数据阵进行三线性成分分解, 再基于标样已知浓度, 利用简单回归法直接测定尿液中利血平(Reserpine)的含量. 结果表明, 当体系的主要组分数取3时, 两种方法均可迅速、 快捷地得到待测物的浓度, 有效地解决了荧光法定量测定时未知背景及干扰物光谱严重重叠而引起的问题.     

An alternative quadrilinear decomposition algorithm for four-way calibration with application to analysis of four-way fluorescence excitation–emission–pH data array

A novel quadrilinear decomposition algorithm for four-way calibration (third-order tensor calibration), which was called as regularized self-weighted alternating quadrilinear decomposition (RSWAQLD), has been developed in this work. It originates from the alternating trilinear decomposition (ATLD) algorithm, inherits the philosophy behind self-weighting operation from the self-weighted alternating trilinear decomposition (SWATLD) algorithm. The RSWAQLD algorithm is based on a nearby least-squares scheme, in which two extra terms are added to each loss function, making it more stable and flexible. Experiment shows that RSWAQLD has the features of fast convergence and being insensitive to the excess estimated factors in the model. Owing to its unique optimizing approach, RSWAQLD is much more efficient than four-way PARAFAC. Moreover, the performance of RSWAQLD is quit stable as the number of factors used in calculation varies (as long as it is no less than the true number of factors). Such a feature will simplify the analysis of four-way data arrays, since it is unnecessary to spend a lot of time and effort on accurately determining the appropriate number of factors in the matrix. In addition, the result of four-way fluorescence excitation–emission–pH data, as well as that of simulated data, illustrated that RSWAQLD can not only remain the “higher-order advantage” but also provide a satisfying result even in high collinear systems.     

A new third‐order calibration method with application for analysis of four‐way data arrays

A novel third‐order calibration algorithm, alternating weighted residue constraint quadrilinear decomposition (AWRCQLD) based on pseudo‐fully stretched matrix forms of quadrilinear model, was developed for the quantitative analysis of four‐way data arrays. The AWRCQLD algorithm is based on the new scheme that introduces four unique constraint parts to improve the quality of four‐way PARAFAC algorithm. The tested results demonstrated that the AWRCQLD algorithm has the advantage of faster convergence rate and being insensitive to the excess component number adopted in the model compared with four‐way PARAFAC. Moreover, simulated data and real experimental data were analyzed to explore the third‐order advantage over the second‐order counterpart. The results showed that third‐order calibration methods possess third‐order advantages which allow more inherent information to be obtained from four‐way data, so it can improve the resolving and quantitative capability in contrast with second‐order calibration especially in high collinear systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Second‐order calibration serves as a remedial measure for the simultaneous determination of andrographolide and dehydroandrographolide in Andrographis paniculata and its preparations by HPLC without complete baseline separation

In this work, high‐performance liquid chromatography with diode array detection was applied for the simultaneous determination of andrographolide and dehydroandrographolide in Andrographis paniculata and its preparations. As a result of the incomplete baseline separation caused by complex backgrounds, the classical univariate calibration method failed to determine accurate contents of the analytes. On this occasion, chemometric second‐order calibration based on the well‐known alternating trilinear decomposition algorithm was then explored to serve as a post‐experimental remedial tool to solve this problem. By using the intelligent “mathematical separation” of alternating trilinear decomposition, the peak areas of the analytes do not need to be directly measured and the predictive results become accurate. The contents of andrographolide and dehydroandrographolide were determined to be (7.95 ± 0.15) and (1.85 ± 0.02) μg/mL for Andrographis paniculata, (1.34 ± 0.01) and (5.53 ± 0.04) μg/mL for its preparations, which was in agreement with those obtained by a reference liquid chromatography with mass spectrometry method. This study showed the superiority of second‐order calibration method over classical univariate calibration method for simultaneous determination of multi‐analytes in complex samples. It also proved that second‐order calibration may be a good choice for remedying incomplete baseline separation problem, with the accompanied reduction of experimental burden and toxic organic solvents as well as analysis time and cost.     

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).     

Fast and simultaneous determination of 12 polyphenols in apple peel and pulp by using chemometrics‐assisted high‐performance liquid chromatography with diode array detection

In this work, a smart chemometrics‐enhanced strategy, high‐performance liquid chromatography, and diode array detection coupled with second‐order calibration method based on alternating trilinear decomposition algorithm was proposed to simultaneously quantify 12 polyphenols in different kinds of apple peel and pulp samples. The proposed strategy proved to be a powerful tool to solve the problems of coelution, unknown interferences, and chromatographic shifts in the process of high‐performance liquid chromatography analysis, making it possible for the determination of 12 polyphenols in complex apple matrices within 10 min under simple conditions of elution. The average recoveries with standard deviations, and figures of merit including sensitivity, selectivity, limit of detection, and limit of quantitation were calculated to validate the accuracy of the proposed method. Compared to the quantitative analysis results from the classic high‐performance liquid chromatography method, the statistical and graphical analysis showed that our proposed strategy obtained more reliable results. All results indicated that our proposed method used in the quantitative analysis of apple polyphenols was an accurate, fast, universal, simple, and green one, and it was expected to be developed as an attractive alternative method for simultaneous determination of multitargeted analytes in complex matrices.     

Simultaneous Determination of Dextromethorphan and Quinidine Contents in Biological Fluid Samples Using Excitation-Emission Matrix Fluorescence Coupled with Second-Order Calibration Methods

This paper presents a novel method for simultaneous determination of dextromethorphan and quinidine contents in biological fluid samples using excitation–emission matrix fluorescence (EEM) coupled with second-order calibration methods. The adopted calibration methods, i.e., parallel factor analysis (PARAFAC), self-weighted alternating tri-linear decomposition (SWATLD), and alternating penalty trilinear decomposition (APTLD), could adequately exploit the second-order advantage. The accuracy of the three methods was evaluated through figures of merit and elliptical joint confidence region (EJCR) tests. It has been found that all the methods could give good results. But, with correct number of factors, the PARAFAC model performed slightly better than the others.     

交替拟合残差算法与高效液相色谱-二极管阵列检测方法结合同时测定两种抗结核药物

本文利用化学计量学交替拟合残差(AFR)算法与高效液相色谱-二极管阵列检测(HPLC-DAD)方法相结合,同时测定两种抗结核药物异烟肼和吡嗪酰胺的含量。该法与交替三线性分解算法(ATLD)、自加权交替三线性分解(SWATLD)算法相比较,从预测均方差、预测相对误差以及平均回收率等结果来看,其预测结果更接近实际值。研究表明,基于交替拟合残差等算法的二阶校正法,可以迅速准确地给出色谱重叠情况下两个组分的预测结果,是复杂体系成分直接定量分析的一个有力的化学计量学工具。     

Chemometrics‐assisted liquid chromatography with full scan mass spectrometry for the interference‐free determination of glucocorticoids illegally added to face masks

A smart chemometrics‐assisted strategy that combines the full scan mode of liquid chromatography with mass spectrometry with second‐order calibration method based on alternating trilinear decomposition algorithm was developed for the rapid determination of 15 glucocorticoids including the epimers betamethasone and dexamethasone illegally added into face masks. Fifteen glucocorticoids were rapidly eluted (11 min) under a simple elution program. By means of the second‐order calibration method, 15 target analytes were successfully quantified in the presence of peak overlaps, unknown interferences and baseline drifts. Notably, the epimers, namely, betamethasone and dexamethasone, were simultaneously quantified by the proposed method under a simple elution program. The average spiked recoveries for all target analytes ranged from 87.3 ± 2.2 to 119.4 ± 5.8%. The validation parameters including sensitivity, selectivity, limit of detection, limit of quantitation, and precision were calculated to validate the accuracy of the proposed method, and the quantitative analysis results were further confirmed by liquid chromatography with tandem mass spectrometry. All results proved that the proposed chemometrics‐assisted liquid chromatography with mass spectrometry strategy was an accurate and fast method to determine epimers and multiple glucocorticoids in complex face mask samples.     

Direct determination of reserpine in urine using excitation-emission fluorescence combined with three-way chemometric calibration methodologies

The concentration of reserpine in urine was directly and quantitatively measured by using the excitation-emission fluorescence (EEM) combined with three-way calibration methodologies. Two calibration methods are based on the alternating trilinear decomposition (ATLD) and the self-weighted alternating trilinear decomposition (SWATLD) algorithms, respectively. These chemometric methodologies have the second-order advantage, which is the ability to get accurate concentration estimates of interested analyte(s) even in the presence of uncalibrated interferences. The satisfactory results on spiked urine samples are obtained, when the component number was chosen to 3 (N = 3) for both the methods. This experiment is easily carried out without time-consuming and complicated pretreatment. It has proved that the three-way calibration methodologies based on ATLD and SWATLD can be feasible to directly quantify the medical content of reserpine in urine. __________ Translated from Chemical Journal of Chinese Universities, 2007, 28 (5): 827–830 [译自: 高等学校化学学报]     

三维荧光二阶校正法用于尿液样和血浆样中左旋多巴的定量测定

本文采用激发发射荧光光谱分别与化学计量学中平行因子分析(PARAFAC)和交替三线性分解(ATLD)二阶校正法相结合,对尿液样和血浆样中左旋多巴含量进行定量测定。实验不需对尿液和血浆预测样进行萃取等分离预处理。在尿液样中,当组分数取2时,用PARAFAC算法和ATLD算法获得的平均回收率分别为(98.9±2.3)%和(99.6±2.8)%。在血浆样中,当组分数取3时,PARAFAC算法和ATLD算法获得的平均回收率分别为(103.1±3.7)%和(99.2±4.2)%。研究结果表明,该法能够解决尿液样和血浆样中左旋多巴因尿液和血浆内源物质与待分析物光谱重叠所引起的难分辨的问题,可用于未知干扰共存下左旋多巴含量的直接快速定量测定。     

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

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

Trilinear decomposition method applied to removal of three-dimensional background drift in comprehensive two-dimensional separation data

A novel technique for removal of three-dimensional background drift in comprehensive two-dimensional (2D) liquid chromatography coupled with diode array detection (LCxLC-DAD) data is proposed. The basic idea is to perform trilinear decomposition on the instrumental response data, which is based on the alternating trilinear decomposition (ATLD) algorithm. In model construction, the background drift is modeled as one component or factor as well as the analytes of interest, hence, the drift is explicitly included into the calibration. The method involves performing trilinear decomposition on the raw data, then extracting the background component and subtracting this background data from the raw data, leaving the analytes' signal on a flat baseline. Simultaneous evaluation of three-dimensional background drift and true signals may improve the quality of the data. This method is applied to the determination and removal of three-dimensional background drifts in simulated multidimensional data as well as experimental comprehensive two-dimensional liquid chromatographic data. It is shown that this technique yield a good removal of background drift, without the need to perform a blank chromatographic run, and required no prior knowledge about the sample composition.     

A flexible trilinear decomposition algorithm for three-way calibration based on the trilinear component model and a theoretical extension of the algorithm to the multilinear component model

There is a great deal of interest in decompositions of multilinear component models in the field of multi-way calibration, especially the three-way case. A flexible novel trilinear decomposition algorithm of the trilinear component model as a modification of an alternating least squares algorithm for three-way calibration is proposed. The proposed algorithm (constrained alternating trilinear decomposition, CATLD) is based on an alternating approximate least-squares scheme, in which two extra terms are added to each loss function, making it more efficient and flexible. The analysis of simulated three-way data arrays shows that it converges fast, is insensitive to initialization, and is insensitive to the overestimated number of components used in the decomposition. The analysis of real excitation–emission matrix (EEM) fluorescence and real high performance liquid chromatography–photodiode array detection (HPLC–DAD) data arrays confirms the results of the simulation studies, and shows that the proposed algorithm is favorable not only for EEMs but also for HPLC–DAD data. The three-way calibration method based on the CATLD algorithm is very efficient and flexible for direct quantitative analysis of multiple analytes of interest in complex systems, even in the presence of uncalibrated interferents and varying background interferents. Additionally, a theoretical extension of the proposed algorithm to the multilinear component model (constrained alternating multilinear decomposition, CAMLD) is developed.     

First- and second-order multivariate calibration applied to biological samples: determination of anti-inflammatories in serum and urine

First- and second-order multivariate calibration of fluorescence data have been compared as regards the determination of anti-inflammatories and metabolites in the biological fluids serum and urine. The simultaneous resolution of naproxen-salicylic acid mixtures in serum and naproxen-salicylic acid-salicyluric acid mixtures in urine was accomplished and employed for a discussion of the relative advantages of the applied chemometric tools. The analysis of second-order fluorescence excitation-emission matrices was performed using iteratively reweighted generalized rank annihilation method (IRGRAM), parallel factor analysis (PARAFAC), and self-weighted alternating trilinear decomposition (SWATLD). The results were compared with first-order fluorescence emission data analyzed with partial least-squares regression (PLS). In all cases, the performance of the methods was improved through the formation of inclusion complexes of the analytes with beta-cyclodextrin. The concentration ranges in which the analytes could be determined were as follows: naproxen, 0-250 ng mL(-1) in serum and 0-200 ng mL(-1) in urine; salicylic acid, 0-500 ng mL(-1) in serum and 0-300 ng mL(-1) in urine, and salicyluric acid, 0-300 ng mL(-1) in urine.     

Photoinduced fluorimetric determination of folic acid and 5-methyltetrahydrofolic acid in serum using the kinetic evolution of the emission spectra accomplished with multivariate second-order calibration methods

Second-order multivariate calibration methods in combination with a continuous flow system, which allows for the continuous on-line irradiation of the analytes, have been employed for the determination of folic acid and its main metabolite 5-methyltetrahydrofolic acid in serum samples. An experimental central composite design, together with response surface methodology, has been used to find the optimum instrumental variables to perform the photochemical reaction. The time evolution of the emission spectra of the generated photoproducts, in the range 330-540 nm, after irradiation at 275 nm for 20 min, provided the three-way data set employed. On the basis of the differences on the kinetic rates of the photoreaction of both analytes, direct determination of the compounds in human plasma has been accomplished. The second-order methods assayed were parallel factor analysis (PARAFAC), self-weighted alternating trilinear decomposition (SWATLD), and unfolded partial least-squares (U-PLS), multidimensional partial least-squares (N-PLS), and bilinear least-squares (BLLS), all three in combination with the residual bilinearization procedure (RBL).