A hybrid of exponential and gaussian functions as a simple model of asymmetric chromatographic peaks

A hybrid of exponential and Gaussian functions is developed as a model of asymmetric peak profiles. This exponential-Gaussian hybrid function (EGH) is mathematically simple, numerically stable, and its parameters are readily determined by making graphical measurements and applying simple equations. Furthermore, the statistical moments of the EGH function can be accurately approximated (within+/-0.15% error) at any level of asymmetry using formulae that are easily programmed into a computer. These features of the EGH make it very easy to implement by most chromatographers. The EGH serves as a useful alternative to the exponentially modified Gaussian (EMG) for modeling slightly asymmetric peaks since the two models produce nearly the same profile at relatively low asymmetries. The EGH also serves as an addition to the extensive list of alternative models that are sometimes better than the EMG at describing highly asymmetric peaks. A comparison between EMG and EGH curves at various asymmetries is made by analysis of toluene, phenylalanine, and pyridine on a reversed-phase liquid chromatographic system.     

Classification of weathered petroleum oils by multi-way analysis of gas chromatography-mass spectrometry data using PARAFAC2 parallel factor analysis

The application of multi-way parallel factor analysis (PARAFAC2) is described for the classification of different kinds of petroleum oils using GC-MS. Oils were subjected to controlled weathering for 2, 7 and 15 days and PARAFAC2 was applied to the three-way GC-MS data set (MSxGCxsample). The classification patterns visualized in scores plots and it was shown that fitting multi-way PARAFAC2 model to the natural three-way structure of GC-MS data can lead to the successful classification of weathered oils. The shift of chromatographic peaks was tackled using the specific structure of the PARAFAC2 model. A new preprocessing of spectra followed by a novel use of analysis of variance (ANOVA)-least significant difference (LSD) variable selection method were proposed as a supervised pattern recognition tool to improve classification among the highly similar diesel oils. This lead to the identification of diagnostic compounds in the studied diesel oil samples.     

基于非接触式电导信号的土壤速效钾含量检测方法

该文针对土壤中速效钾含量采用传统测定法操作复杂、检测时效滞后的问题,建立了基于非接触式电导检测信号快速检测土壤速效钾含量的分析方法。采用高效毛细管电泳/非接触式电导检测仪获取河南潮土的非接触式电导检测信号,并使用导数法与高斯曲线拟合法相结合进行初步峰谱识别,按条件进行峰值过滤后,引入基于Levenberg-Marquardt(L-M)的高斯分峰拟合算法,实现了单峰和重叠峰的拟合计算,得到高斯峰和相应的特征参数,包括峰位、峰高、半峰宽和峰面积;最后将拟合得到的高斯峰及相应的特征参数表征原始非接触式电导检测信号离子峰谱信息结合偏最小二乘法(PLS),确定特征参数与土壤速效钾含量的关系,建立模型,实现了对土壤中速效钾含量的预测。结果表明,将基于L-M的高斯分峰拟合算法结合偏最小二乘法应用于非接触式电导检测信号测定土壤速效钾含量时具有较高精度,回归模型决定系数(R~2)为0.856 4,相对分析误差(RPD)为2.639,适用于土壤速效钾的快速检测分析。     

水体透射光谱结合主成分分析(PCA )改进化学需氧量(COD)含量估算研究

化学需氧量（Chemical Oxygen Demand,COD）是水体有机污染的一项重要指标,化学需氧量越高,表示水污染程度越严重。 为了解决传统的COD测量方法耗时较长,不利于快速、实时地获取水体中COD的信息等问题。本文提出了基于透射光谱测量结合主成分分析(Principal Component Analysis, PCA)改进水体COD含量估算模型。具体的,采集100组COD水体光谱信息,分别使用3种不同的高光谱数据预处理方法对光谱数据进行预处理,分析不同预处理方法对模型精度的影响,并基于不同的预处理方法分别建立高斯过程回归模型(Gaussian Process Regression, GPR)和BP神经网络模型,分析不同预处理方法对模型精度的影响;并对各模型结合PCA数据降维方法进行模型的改进,通过比较模型的精度选择最优模型进行水体COD含量的检测。结果显示,相比于原始光谱数据建立的GPR模型和BP神经网络模型,数据预处理后的模型精度明显提升;且结合PCA对预处理后的数据进一步降维处理后,模型精度得到了进一步的提升。其中,基于标准正态变量变换特征结合PCA改进BP神经网络模型基于PCA改进的BP神经网络模型R^2高达0.9940,均方根误差RMSE为0.022540。证明了基于PCA改进的BP神经网络数据降维方法对预处理后的光谱数据进行降维处理,有利于去除光谱中的冗余信息,提取特征信息,可以实现高光谱检测方法可以实现COD含量估算模型的优化,从而为传统COD测量方法存在的问题提出了一种新的解决思路。     

High-throughput automated post-processing of separation data

The development of an efficient method for high-throughput analysis of multiple electropherograms or chromatograms collected in series is presented. The method, encoded in a computer program designated "Cutter", utilizes batch processing for determining chromatographic figures of merit (CFOM) including peak centroid times, heights, areas, signal-to-noise ratios (S/N), variance (sigma2), skew, excess, and plate number (N) across a set of separations collected serially. The software was validated using simulated data with varying S/N, skew, and excess. The accuracy of the analysis was comparable to or improved over commercial software with area calculation relative errors (RE) below 5% for simulated data with S/N = 5. File sets containing 1300 electropherograms were analyzed in 5 min, representing a nearly 200-fold reduction in analysis time from other methods. Incorporated within the program is a novel method for automated peak deconvolution using an Empirically Transformed Gaussian function. Area measurements of deconvoluted peaks were within 3% of the true value of a simulated data set with S/N = 5 and resolution (R(S)) = 1 for equivalent peaks, and within 10% when the ratio of the overlapped peak heights was 10:1.     

A software package for the evaluation of peak parameters in an analytical signal based on a non-linear regression method

Computer-based data handling of analytical signals to extract commonly used analytical parameters often produces poor results if the signals are affected by noise and a drifting baseline. Only a minor part of the information present in the signal is used for correction. A computer package is presented, in which the total information of the signal is used to give accurate evaluation of analytical parameters. The program uses a non-linear regression method to deconvolute analytical signals into a number of peaks and a baseline. To describe the peak shape any mathematical model can be used. In the computer package, a Gaussian curve-related model is used, with variable asymmetry. The baseline is described with a polynomial of variable order. The method is simultaneously a filter procedure Deconvolution of poorly separated peaks is possible. The software is developed on a minicomputer; however, test results of this study indicate the feasibility of implementation on a microcomputer without extremely time-consuming runs of the program.     

Comprehensive two-dimensional gas chromatography/time-of-flight mass spectrometry peak sorting algorithm

We report a novel peak sorting method for the two-dimensional gas chromatography/time-of-flight mass spectrometry (GC x GC/TOF-MS) system. The objective of peak sorting is to recognize peaks from the same metabolite occurring in different samples from thousands of peaks detected in the analytical procedure. The developed algorithm is based on the fact that the chromatographic peaks for a given analyte have similar retention times in all of the chromatograms. Raw instrument data are first processed by ChromaTOF (Leco) software to provide the peak tables. Our algorithm achieves peak sorting by utilizing the first- and second-dimension retention times in the peak tables and the mass spectra generated during the process of electron impact ionization. The algorithm searches the peak tables for the peaks generated by the same type of metabolite using several search criteria. Our software also includes options to eliminate non-target peaks from the sorting results, e.g., peaks of contaminants. The developed software package has been tested using a mixture of standard metabolites and another mixture of standard metabolites spiked into human serum. Manual validation demonstrates high accuracy of peak sorting with this algorithm.     

三元重叠色谱峰面积的定量方法

本从色谱峰的ＥＭＧ模型出发，通过对重叠色谱峰的模拟和回归分析，提出了一种三元重叠色谱峰的面积的定量方法，三元重叠色谱峰的每一个峰面积可以由峰面积比和总面积求得，此法所需的数据都由实验色谱图上测得，峰面积计算结果的相对误差小于±５％，适用于相对峰谷为５０％－９５％的三元重叠色谱峰面积的定量。     

应用超临界流体萃取分离-气相色谱-质谱分析法建立中药温郁金的指纹图谱及其系统聚类分析

收集生长于浙江省瑞安市8个产地的温郁金样品14批次,分别经清洗、冷冻干燥及碾磨粉碎,得到通过0.425mm筛孔药筛的粉末状样品14个。称取此样品各30g,分别按试验选定的最佳条件[萃取温度35℃,萃取压力15MPa,萃取时间(静态30min,动态90min)]进行超临界流体萃取分离,所得萃取物收集于甲醇5mL中,并进行气相色谱-质谱法(GC-MS)分析。色谱分离采用HP-5ms石英毛细管色谱柱和在50~220℃之间程序升温模式;质谱测定采用电子轰击离子源(EI),在质荷比(m/z)50~650内进行扫描。所得总离子流色谱图中共有50多个色谱峰,选择保留时间在40min以内的共有峰26个作为考察对象,选择保留时间为17.12min的莪术二酮为参考峰,计算共有峰的相对保留时间α和峰面积百分比S以及各样品与S3的S值的最大差值ΔS(Max)%,并建立了14个样品的指纹图谱。根据GC-MS分析所得结果并与NIST 14谱库比对,对共有峰作出鉴定。通过SPSS 16.0软件,采用系统聚类分析法对所分析的14批次温郁金样品的指纹图谱进行分类比较。应用指纹图谱对2个市售温郁金产品作了组分鉴定和产地认定。     

Deconvolution of overlapped peaks based on the exponentially modified Gaussian model in comprehensive two-dimensional gas chromatography

Comprehensive two-dimensional gas chromatography (GC x GC) has attracted much attention for the analysis of complex samples. Even with a large peak capacity in GC x GC, peak overlapping is often met. In this paper, a new method was developed to resolve overlapped peaks based on the mass conservation and the exponentially modified Gaussian (EMG) model. Linear relationships between the calculated sigma, tau of primary peaks with the corresponding retention time (tR) were obtained, and the correlation coefficients were over 0.99. Based on such relationships, the elution profile of each compound in overlapped peaks could be simulated, even for the peak never separated on the second-dimension. The proposed method has proven to offer more accurate peak area than the general data processing method.     

Automated screening procedure using gas chromatography-mass spectrometry for identification of drugs after their extraction from biological samples

A novel analytical screening procedure has been developed, using computer-controlled gas chromatography-mass spectrometry (GC-MS), to detect 120 drugs of interest to road safety. This paper describes GC-MS methodology suitable for use on extracts of biological origin, while extraction procedures will be the subject of a future communication. The method was devised to identify drugs in extracts of blood samples, as part of an investigation into the involvement of drugs, other than alcohol, in road accidents. The method could be adapted to screen for other substances. The method depends on a "macro" program which was written to automate the search of GC-MS data for target drugs. The strategy used was to initially search for each drug in the database by monitoring for a single characteristic ion at the expected retention time. If a peak is found in this first mass chromatogram, a peak for a second characteristic ion is sought within 0.02 min of the first and, if found, the ratio of peak areas calculated. Probable drug identification is based on the simultaneous appearance of peaks for both characteristic ions at the expected retention time and in the correct ratio. If the ratio is outside acceptable limits, a suspected drug (requiring further investigation) is reported. The search macro can use either full mass spectra or, for enhanced sensitivity, data from selected ion monitoring (which requires switching between groups of ions during data acquisition). Quantitative data can be obtained in the usual way by the addition of internal standards.     

Differential pulse voltammetric oxidation of polyriboxanthylic acid at the pyrolytic graphite electrode and a method for detection and determination of traces of xanthine and xanthosine-5'- monophosphate in polyxanthylic acid

Poly(X) (polyriboxanthylic acid) gives up to two differential pulse voltammetric oxidation peaks (peaks I and II) at the PGE. Xanthine, which appears to be a trace contaminant of commercial poly(X) samples, exhibits a differential pulse voltammetric oxidation peak at more negative potentials than the peaks of poly(X). Xanthosine-5'-monophosphate also gives up to two differential pulse voltammetric oxidation peaks at the PGE. An analytical method has been developed to determine trace amounts of xanthine and xanthosine-5'-monophosphate in poly(X) samples based on differential pulse voltammetry.     

Resolving batch chromatographic overlapping peaks of flavoring essence using stepwise key spectrum selection

Stepwise key spectrum selection (SKSS) was introduced to resolve batch overlapping peaks from gas chromatography-mass spectrometry (GC-MS) analysis of ten batch tobacco flavoring samples in different storage times. Resolution was implemented on a software platform that embedded the SKSS method. The data from GC-MS analysis of the samples were saved and prepared in ASCII files and then were inputted into the software platform for visual inspections. The data segment with overlapping peaks was precut for subsequent analysis. Spectral background in the data was removed using a linear fitting of the baseline. Four components in the overlapping peaks were automatically detected by the SKSS method. The resolution of the concentration profiles and spectra of the four components was conducted by setting only one parameter, the negative area ratio, as 0.01. The fixed size moving window evolving factor analysis and evolving factor analysis were applied to validate the resolved concentration profiles. The resolved mass spectra were validated by the searched standard through library search at the pure component regions revealed by the resolved concentration profiles. The results showed that the SKSS method could be a simple but powerful tool in resolving batch chromatographic overlapping peaks.     

A study of the precision and accuracy of peak quantification in comprehensive two-dimensional liquid chromatography in time

Simulated chromatographic data were used to determine the precision and accuracy in the estimation of peak volumes (i.e., peak sizes) in comprehensive two-dimensional liquid chromatography in time (LC × LC). Peak volumes were determined both by summing the areas in the second dimension chromatograms and by fitting the second dimension areas to a Gaussian peak. The Gaussian method is better at predicting the peak volume than the moments method provided there are at least three second dimension injections above the limit of detection (LOD). However, when only two of the second dimension signals are substantially above baseline, the accuracy and precision of the Gaussian fit method become quite poor because the results from the fitting algorithm become indeterminate. Based on simulations in which the modulation ratio (M_R = 4¹σ/t_s) and sampling phase (?) were varied, we conclude for well-resolved peaks that the optimum precision in peak volumes in 2D separations will be obtained when the M_R is between two and five, such that there are typically four to ten second dimension peaks recorded over the eight σ width of the first dimension peak. This sampling rate is similar to that suggested by the Murphy–Schure–Foley criterion. This provides an RSD of approximately 2% for the signal-to-noise ratio used in the present simulations. The precision of the peak volume of experimental data was also assessed, and RSD values were in the range of 4–5%. We conclude that the poorer precision found in the LC × LC experimental data as compared to LC may be due to experimental imprecision in sampling the effluent from the first dimension column.     

Mathematical functions for the representation of chromatographic peaks.

About ninety empirical functions for the representation of chromatographic peaks have been collected and tabulated. The table, based on almost 200 references, reports for every function: (1) the most used name; (2) the most convenient equation, with the existence intervals for the adjustable parameters and for the independent variable; (3) the applications; (4) the mathematical properties, in relation to the possible applications. The list includes also equations originally proposed to represent peaks obtained in other analytical techniques (e.g. in spectroscopy), which in many instances have proved useful in representing chromatographic peaks as well; the built-in functions employed in some commercial peak-fitting software packages were included, too. Some of the most important chromatographic functions, i.e. the Exponentially Modified Gaussian, the Poisson, the Log-normal, the Edgeworth/Cramér series and the Gram/Charlier series, have been reviewed and commented in more detail.     

Correction method for quantitative area determination of overlapping chromatographic peaks based on the exponentially modified Gaussian (EMG) model

A simple method is presented for peak area correction of overlapping peaks. This correction is necessary for the normal approach of dealing with overlapping peaks by a vertical line at the valley point. The relative area errors caused by this vertical line are calculated as the correction factors in three dimensions of peak separation, peak ratio, and peak tailing skew. The calculation is based on the exponentially modified Gaussian asymmetric peak model.     

Rapid characterization of anthocyanins in red raspberry fruit by high-performance liquid chromatography coupled to single quadrupole mass spectrometry

This paper describes the results of a comparison of four peak functions in describing real chromatographic peaks. They are the empirically transformed Gaussian, polynomial modified Gaussian, generalized exponentially modified Gaussian and hybrid function of Gaussian and truncated exponential functions. Real chromatographic peaks of different shapes (fronting. symmetric, and tailing) are obtained by various separation conditions of reversed-phase liquid chromatography. They are then fitted to the peak functions via the Marquardt-Levenberg algorithm, a nonlinear least-squares curve-fitting procedure, by Microsoft Solver. The qualities of the fits are evaluated by the sum of the squares of the residuals. It is concluded in the study that the empirically transformed Gaussian function offers the highest flexibility (best fits) to all shapes of chromatographic peaks, including extremely asymmetric tailing peaks with a peak asymmetry of up to 8. The flexibility of this function should improve our ability to process chromatographic peaks such as deconvolution of overlapped peaks and smoothing noisy peaks for the determination of statistical moments.     

Evaluation of different warping methods for the analysis of CE profiles of urinary nucleosides

Nowadays, numerous metabolite concentrations can readily be determined in a given biological sample by high-throughput analytical methods. However, such raw analytical data comprise noninformative components due to many disturbances normally occurring in the analyses of biological material. To eliminate those unwanted original analytical data components, advanced chemometric data preprocessing methods might be of help. Here, such methods are applied to electrophoretic nucleoside profiles in urine samples of cancer patients and healthy volunteers. In this study, three warping methods: dynamic time warping (DTW), correlation optimized warping (COW), and parametric time warping (PTW) were examined on two sets of electrophoretic data by means of quality of peaks alignment, time of preprocessing, and way of customization. The application of warping methods helped to limit shifting of peaks and enabled differentiation between whole electropherograms of healthy and cancer patients objectively by a principal component analysis (PCA). The evaluation of preprocessed data and raw data by PC analysis confirms differences between the applied warping tools and proves their suitability in metabonomic data interpretation.