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

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

Analytical applications of second-order calibration methods

Second-order calibration methods are gaining widespread acceptance among the analytical community mainly because: (1) a wide range of analytical instrumentation is available that enables high dimensionality data to be obtained; (2) the chemometric techniques for treating these data are highly developed; and (3) they have the so-called “second-order advantage”, i.e. they can predict the concentration of the analyte of interest even in the presence of unknown interferents. This also enables several analytes to be determined simultaneously.In this paper we describe the most common instrumental and chemometric techniques used in second-order calibration and discuss their applications since 2000. First, we introduce briefly the techniques and then we comment the applications. Given the practical nature of this paper, we have classified the techniques according to five fields of application: pharmaceuticals, biological matrices, foods, environmental matrices and synthetic matrices.     

毒鼠强薄层色谱分析的检出限

建立薄层色谱法快速对毒鼠强进行简易分析的方法,利用薄层色谱进行层析分离,采用特殊显色方法,对毒鼠强进行显色,以能正常观察到斑点的色泽状态,辅助GC-MS方法确定检出极限。薄层色谱法分析毒鼠强检出限可达5~10μg。能用此方法对大多数中毒案件提取的检材进行定性分析。     

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%.     

The maintenance of the second-order advantage: second-order calibration of excitation-emission matrix fluorescence for quantitative analysis of herbicide napropamide in various environmental samples

A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence was proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples. With 0.10 mol L⁻¹ sodium citrate-hydrochloric acid (HCl) buffer solution of pH 2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method was employed. Satisfactory results have been achieved for NAP in complex environmental samples. The limit of detection obtained for NAP in soil, river sediment, wastewater and river water samples were 0.80, 0.24, 0.12, 0.071 ng mL⁻¹, respectively. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determinations of the analyte of interests in the environmental samples of various matrices.     

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.     

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).     

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.     

Limits of detection and decision. Part 1

Extensive Monte Carlo studies of instrumental limits of detection were performed on a simple univariate chemical measurement system having homoscedastic, Gaussian measurement noise and using ordinary least squares (OLS) processing of tens of millions of independent calibration curve data sets. It was found that prediction interval-based experimental detection limits were significantly negatively biased, in both the net response domain and the chemical content domain, resulting in substantially higher rates of false negatives than specified via customary critical t values. The diagnostic fix for the bias problem provided clear proof that hypothesis-based detection limits need not be unique, even as distributions of random variates, if the alternate hypothesis is non-unique. It was also demonstrated that hypothesis-based decision and detection limits have finite support that does not include the region near zero analyte content, so that both have finite moments and finite confidence intervals.     

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.     

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.     

Quantitative analysis of triazine herbicides in environmental samples by using high performance liquid chromatography and diode array detection combined with second-order calibration based on an alternating penalty trilinear decomposition algorithm

A novel application of second-order calibration method based on an alternating penalty trilinear decomposition (APTLD) algorithm is presented to treat the data from high performance liquid chromatography-diode array detection (HPLC-DAD). The method makes it possible to accurately and reliably analyze atrazine (ATR), ametryn (AME) and prometryne (PRO) contents in soil, river sediment and wastewater samples. Satisfactory results are obtained although the elution and spectral profiles of the analytes are heavily overlapped with the background in environmental samples. The obtained average recoveries for ATR, AME and PRO are 99.7 ± 1.5, 98.4 ± 4.7 and 97.0 ± 4.4% in soil samples, 100.1 ± 3.2, 100.7 ± 3.4 and 96.4 ± 3.8% in river sediment samples, and 100.1 ± 3.5, 101.8 ± 4.2 and 101.4 ± 3.6% in wastewater samples, respectively. Furthermore, the accuracy and precision of the proposed method are evaluated with the elliptical joint confidence region (EJCR) test. It lights a new avenue to determine quantitatively herbicides in environmental samples with a simple pretreatment procedure and provides the scientific basis for an improved environment management through a better understanding of the wastewater-soil-river sediment system as a whole.     

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.     

Limits of determination and calibration in HPLC

Summary In HPLC calibration the expressions lowest calibration limit and determination limit are defined in statistical terms. The lowest calibration limit is the minimum mass in the measured series of calibration points. It is calculated from the confidence interval of the inverse of the calibration function as the lowest mass limit that may be differentiated from zero mass with a preset probability of error. If the calculated lowest calibration limit is lower than the actual data, points at lower concentration may be measured. The determination limit is the smallest concentration of an analysis that is differentiated from the concentration zero or an apparent blind value in the calibration curve with a given probability of error.Using two different UV-detectors (variable wavelength and photodiode-array) the lowest calibration limit is experimentally evaluated and compared with specific data for the detectors.Dedicated to Prof. Dr. E. Bayer, Tübingen on ocassion of his 60th birthday.     

Prediction of precision from signal and noise measurement in liquid chromatography: Limit of detection

Summary A method to determine the limit of detection (LOD) in high performance liquid chromatography (HPLC) is described. The power spectral density of instrumental baseline variation is fitted by the simplex least squares methods with a mixed random process of white noise and Markov process as a model. The white noise is characterized by standard deviation (SD), w; the Markov process by the SD, m, and auto-correlation degree, . All required parameters for calculating the LOD signal are obtained by experiment without repeat measurements. No arbitrary constants are needed. The LOD signal is uniquely determined and is characterized by 33.3% relative standard deviation (RSD) of analyte measurements and 0.13% of the error of the first type. This signal also specifies that the signal-to-noise ratio=3, using the definition of noise originating from the white noise and Markov process. The theoretical conclusion is verified by the Monte Carlo simulation using real baseline and peaks. The LOD concentrations for naphthalene, acenaphthene, pyrene and perylene are given.First part of series cited as Ref. [1].     

Prediction of precision from signal and noise measurement in liquid chromatography: Limit of detection

Summary A method to determine the limit of detection (LOD) in high performance liquid chromatography (HPLC) is described. The power spectral density of instrumental baseline variation is fitted by the simplex least squares methods with a mixed random process of white noise and Markov process as a model. The white noise is characterized by standard deviation (SD),; the Markov process by the SD, , and auto-correlation degree, ρ. All required parameters for calculating the LOD signal are obtained by experiment without repeat measurements. No arbitrary constants are needed. The LOD signal is uniquely determined and is characterized by 33.3 % relative standard deviation (RSD) of analyte measurements and 0.13 % of the error of the first type. This signal also specifies that the signal-to-noise ratio =3, using the definition of noise originating from the white noise and Markov process. The theoretical conclusion is verified by the Monte Carlo simulation using real baseline and peaks. The LOD concentrations for naphthalene, acenaphthene, pyrene and perylene are given. First part of series cited as Ref. [1].     

Interference-free determination of fluoroquinolone antibiotics in plasma by using excitation-emission matrix fluorescence coupled with second-order calibration algorithms

Fluoroquinolones or so-called second-generation quinolones, in particular, ofloxacin (OFL), norfloxacin (NOR), and enoxacin (ENO), with therapeutic advantages possess strongly overlapped fluorescence spectra. In this paper, two strategies were proposed for simultaneous direct determination of OFL, NOR and ENO in plasma by combining fluorescence excitation-emission matrix (EEM) with second-order calibration based on the alternating trilinear decomposition algorithm (ATLD) and parallel factor analysis (PARAFAC). The results showed that both algorithms could solve the problem of serious fluorescence spectral overlapping of the sought-for analytes even in the presence of uncalibrated interferents. However, ATLD has advantages of being insensitive to overestimated component number and fast convergence. The results by using ATLD with an estimated component number of five were reasonably acceptable for clinical analysis. The average recoveries of OFL, NOR and ENO in synthetic samples were 99.7 ± 2.4, 101.5 ± 2.4 and 97.3 ± 3.8%, respectively; the average recoveries of OFL, NOR and ENO in complex plasma were 94.3 ± 2.6, 85.6 ± 3.3 and 103.3 ± 3.0%, respectively.     

Simultaneous determination of metronidazole and tinidazole in plasma by using HPLC–DAD coupled with second-order calibration

<正>A method using HPLC-DAD coupled with second-order calibration was developed to simultaneously determine metronidazole and tinidazole in plasma samples in this paper.The second-order calibration method based on APTLD(alternating penalty trilinear decomposition) algorithm was proposed to analyze the three-way HPLC-DAD data from both standard and prediction samples, which makes it possible that calibration can be performed even in the presence of unknown interferences with a simple and green chromatographic condition and short analysis time.The results showed that good recoveries were obtained although the chromatographic and spectral profiles of the analytes of interest as well as background were partially overlapped with each other in plasma samples.     

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.     

Determination of testosterone propionate in cosmetics using excitation-emission matrix fluorescence based on oxidation derivatization with the aid of second-order calibration methods

A sensitive excitation-emission fluorescence method was proposed to determine testosterone propionate (TP) in several cosmetics with the aid of second-order calibration methods based on the self-weighted alternating trilinear decomposition (SWATLD) and parallel factor analysis (PARAFAC) algorithms. TP can be transformed into a highly fluorescent derivative through oxidation reaction with concentrated sulfuric acid (H₂SO₄). Both algorithms have been recommended to enhance the selectivity and attain TP concentration in cosmetics free from interference from potential interfering matrix contaminants introduced during simple cosmetic pretreatment procedure, even in the presence of other homogeneous drugs. Satisfactory results have been achieved for TP in complicated cosmetics, fully exploiting “second-order advantage”. The correlation coefficients of TP obtained by using both SWATLD and PARAFAC with N = 3 are 0.9968 and 0.9974, and the average recoveries, 99.3 ± 4.7% and 101.3 ± 5.9%, respectively. Furthermore, in order to investigate the performance of the proposed methods, some statistical parameters and figures of merit of SWATLD and PARAFAC, i.e., sensitivity (SEN), selectivity (SEL) and limit of detection (LOD) were evaluated, and the accuracy of both algorithms was also validated by the elliptical joint confidence region (EJCR) test.