The utility of statistical moments in chromatography using trapezoidal and Simpson's rules of peak integration

Modern chromatographic data acquisition softwares often behave as black boxes where the researchers have little control over the raw data processing. One of the significant interests of separation scientists is to extract physico‐chemical information from chromatographic experiments and peak parameters. In addition, column developers need the total peak shape analysis to characterize the flow profile in chromatographic beds. Statistical moments offer a robust approach for providing detailed information for peaks in terms of area, its center of gravity, variance, resolution, and its skew without assuming any peak model or shape. Despite their utility and theoretical significance, statistical moments are rarely incorporated as they often provide underestimated or overestimated results because of inappropriate choice of the integration method and selection of integration limits. The Gaussian model is universally used in most chromatography softwares to assess efficiency, resolution, and peak position. Herein we present a user‐friendly, and accessible approach for calculating the zeroth, first, second, and third moments through more accurate numerical integration techniques (Trapezoidal and Simpson's rule) which provide an accurate estimate of peak parameters as compared to rectangular integration. An Excel template is also provided which can calculate the four moments in three steps with or without baseline correction.     

峰形分析辅助色谱定性的研究

尝试建立了一种通过峰形分析进行色谱定性的方法。首先选择一组既易于测量,又能较好地表征色谱峰形特性的参数（峰宽、不对称因子）作为峰形分析的基础;其次,通过理论和实验证明：对于保留时间与标准物质非常接近的未知组分,可将样品与标准物质混合进样,得到重叠谱图（表观为单峰）,然后通过对重叠谱峰与标准物质谱峰的峰形分析与比较,达到对未知物定性的目的。     

Approaches to characterise chromatographic column performance based on global parameters accounting for peak broadening and skewness

Peak broadening and skewness are fundamental parameters in chromatography, since they affect the resolution capability of a chromatographic column. A common practice to characterise chromatographic columns is to estimate the efficiency and asymmetry factor for the peaks of one or more solutes eluted at selected experimental conditions. This has the drawback that the extra-column contributions to the peak variance and skewness make the peak shape parameters depend on the retention time. We propose and discuss here the use of several approaches that allow the estimation of global parameters (non-dependent on the retention time) to describe the column performance. The global parameters arise from different linear relationships that can be established between the peak variance, standard deviation, or half-widths with the retention time. Some of them describe exclusively the column contribution to the peak broadening, whereas others consider the extra-column effects also. The estimation of peak skewness was also possible for the approaches based on the half-widths. The proposed approaches were applied to the characterisation of different columns (Spherisorb, Zorbax SB, Zorbax Eclipse, Kromasil, Chromolith, X-Terra and Inertsil), using the chromatographic data obtained for several diuretics and basic drugs (β-blockers).     

葛根提取物高效液相色谱分析方法的优化

针对葛根提取物的复杂体系,分别从色谱模式、流动相、添加剂以及梯度洗脱条件几个方面对其高效液相色谱分析 方法进行了优化。其中梯度洗脱条件的优化是根据各组分在5次线性梯度下的保留时间并借助于CSASS软件快速准确地计 算出各组分的液相色谱保留参数a,c值以及峰形参数σ和τ,在此基础上使用CSASS软件对葛根提取物的色谱分离情况进行 高精度仿真预测,从而优化了梯度洗脱条件。考察了优化条件下的分析方法的精密度和重现性,结果表明该方法稳定、可 靠、重现性好。     

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.     

Analysis of peak asymmetry in chromatography

The knowledge of the symmetry of chromatographic peaks is extremely important regarding the digital signal processing. The significant deviation of the peak shape from the symmetrical peak makes hardly possible the acquisition of chromatographic signal information, such as the retention time, the peak area, the peak width at half peak height, the peak overlapping, etc. In the literature one can find many methods for the determination of the asymmetry factor. For example it is suitable to calculate the skewness from the third central moment. However in case of noisy baseline the value of the skewness oscillates highly depending on the number of points used for the mathematical calculation. In this work a new method is presented for the determination peak shape asymmetry. We order mathematical function to the chromatographic peaks by fitting, and then symmetrical curve is generated with the same peak maximum position and height, the peak width is fitted. The difference of the two functions is constituted and areas of the data differences are calculated, which are really characteristics of the peak asymmetry. Correlation between the area of the difference signal and the asymmetry factor is established. The method was applied for different types of chromatographic peak shapes and the results were interpreted.     

Precision study on capillary electrophoresis methods for metacycline

A CE method for metacycline (MTC) determination was investigated in an inter-laboratory experiment. Many problems were encountered in this study, most of which were related to the transfer of the method to different CE equipment. The reported problems could be classified into different categories: problems related to the precision, to the parameters in the protocol, and to the MTC peak shape. As the peak shape problem was partially responsible for the poor precision, a new CE method was developed in order to obtain a good MTC peak shape on all equipment. The precision of this new method for MTC determination was examined in an intermediate precision study, where the influence of the factors "time" and "equipment" was investigated. Although the new method could be transferred to different instruments, the precision remained poor mainly due to the contributions of the between-replicate and the between-injection variances.     

Simulation of the shape of a chromatographic peak by the method of theoretical plates

The shape of a chromatographic peak and its distortions are investigated in relation to the efficiency of the chromatography column, the nonlinearity of the sorption isotherm of a substance, and “extracolumn” peak spreading. Using simulation by the method of theoretical plates, the efficiency calculated from chromatograms by various equations is related to parameters known in advance (specified beforehand). An empirical equation giving results consistent with the specified parameters is suggested.     

应用电子计算机求解色谱过程动力学方程

提出采用计算机求取色谱过程动力学方程解的方法。在此基础上考察了在Ｌａｎｇｍｕｉｒ吸附等温线情况下色谱柱效率、色谱峰的偏态、峰态与分酸系数、流动相线速、进样量之间的关系,从而明确指出,动力学过程是使色谱峰峰形拖尾的一个原因,但不是主要原因。实践中观察到的峰非对称性现象主要是分配系数非线性所致。     

Study of elution behaviour with gradient voltage in CEC using methacrylate monolithic columns

A theoretical study on the retention behaviour and chromatographic performance of neutral solutes using a lauryl methacrylate‐based monolithic column under voltage gradient mode in CEC was carried out. Through a flexible mathematical function based on a modified Gaussian model, the peak shape of compounds was firstly fitted under constant and gradient voltage. Using the peak shape parameters and retention time, the estimation of global chromatographic performance, efficiency and peak capacity under several voltage conditions was performed. The influence of voltage gradient on the separation efficiency is discussed and simple equations are presented to calculate retention and peak widths under voltage gradient conditions. A comparison in terms of chromatographic performance of a test mixture of neutral solutes under constant and gradient voltage modes was also carried out. The experiments carried out under gradient voltage showed better efficiencies (172 000 plates/m) and lower peak widths than those obtained under constant voltage (52 000 plates/m).     

Multiclass determination of 66 organic micropollutants in environmental water samples by fast gas chromatography–mass spectrometry

A multiresidue method has been developed for quantification and identification of 66 multiclass priority organic pollutants in water by fast gas chromatography (GC) coupled to mass spectrometry (MS). Capabilities and limitations of single quadrupole mass spectrometer as detector in fast GC were studied evaluating the chromatographic responses in terms of sensitivity and chromatographic peak shapes, as they were influenced by scan time. The number of monitored ions in a selected ion monitoring (SIM) group strongly conditioned the scan time and subsequently the number of data points per peak. A compromise between peak shape and scan time was adopted in order to reach the proper conditions for quantitative analysis. An average of 10–15 points per peak was attained for most compounds, involving scan times between 0.1 and 0.22 s. The method was validated for mineral, surface, and groundwater. A solid-phase extraction pre-concentration step using C₁₈ cartridges was applied. Four isotopically labeled standards were added to the samples before extraction and used as surrogates to ensure a reliable quantification. Analyses were performed by GC–MS in electron ionization mode, monitoring the three most abundant and/or specific ions for each compound and using the intensity ratios as a confirmatory parameter. With a chromatographic run of less than 10 min, SIM mode provided excellent sensitivity and identification capability due to the monitoring of three ions and the evaluation of their intensity ratio. Limits of detection below 10 ng/L were reached for most of the 66 compounds in the three matrices studied. Accuracy and precision of the method were evaluated by means of recovery experiments at two fortification levels (10 and 100 ng/L), obtaining recoveries between 70% and 120% in most cases and relative standard deviations below 20%. The possibilities of a simultaneous SIM scan method have also been explored for non-target qualitative analysis. The developed method has been applied to the analysis of surface water samples collected from the Mediterranean region of Spain.     

Assessing the detectability of antioxidants in two‐dimensional high‐performance liquid chromatography

This paper explores the analytical figures of merit of two‐dimensional high‐performance liquid chromatography for the separation of antioxidant standards. The cumulative two‐dimensional high‐performance liquid chromatography peak area was calculated for 11 antioxidants by two different methods—the areas reported by the control software and by fitting the data with a Gaussian model; these methods were evaluated for precision and sensitivity. Both methods demonstrated excellent precision in regards to retention time in the second dimension (%RSD below 1.16%) and cumulative second dimension peak area (%RSD below 3.73% from the instrument software and 5.87% for the Gaussian method). Combining areas reported by the high‐performance liquid chromatographic control software displayed superior limits of detection, in the order of 1 × 10^?6 M, almost an order of magnitude lower than the Gaussian method for some analytes. The introduction of the countergradient eliminated the strong solvent mismatch between dimensions, leading to a much improved peak shape and better detection limits for quantification.     

Liquid chromatographic determination of diminazene diaceturate (Berenil) in raw bovine milk

A simple liquid chromatographic (LC) method is presented for the determination of diminazene (DZ) in raw bovine milk. DZ is extracted from raw milk by chilled aqueous centrifugation and is isolated from milk components on a cyano solid-phase extraction column. DZ is eluted by using a methanol-ion pairing reagent. A Phenomenex LUNA CN column and an acetonitrile-buffered mobile phase with a counter ion are used for gradient LC. The LC effluent is monitored at a detection wavelength of 372 nm by using a deuterium lamp. Under the parameters described, the retention time of DZ is 8-10 min with a peak area response of 6.5 mAU/ng. The method demonstrated excellent precision over all levels tested (25-400 ppb) with an overall average recovery of 90.4 +/- 14.5%. The method is applicable to the monitoring of milk for DZ residues at the 25 ppb level with a limit of quantitation of 10 ppb.     

Evaluation and prediction of the shape of gas chromatographic peaks

The evaluation and prediction of the shape of asymmetric gas chromatographic peaks is important as the knowledge of the amount of tailing permits to foresee the resolution between closely eluting peaks and to select the best analytical conditions for an efficient and rapid separation. A model function was tested in order to approximate the true peak shape obtained on non-polar column by injecting different compounds. The trend of the parameters involved in the used equation has been investigated as a function of column temperature and inlet pressure. The reproduction of the symmetrical or asymmetrical shape of gas chromatographic peaks is satisfactory and the method also permits to predict the shape of peaks obtained in different conditions of temperature and pressure.     

Characterization of high performance glass capillary gas chromatography

Summary High resolution gas chromatography requires the highest performance characteristics of gas chromatographic systems in terms of sampling and sample handling in strumentation, columns, and data handling. This paoper describes high precision computer measurements for characterizing capillary column efficiencies which are within 75% of the theoretical limit of capillary GC. Particular emphasis is given to detailed peak shape analysis, measurement accuracy and reproducibility, and system stability. Using known instrument performance parameters, it is then possible to characterize column performance with high accuracy in a meaningful manner. It is proposed that wall-coated tubular columns be characterized in terms of their chromatographic performance by the following parameters: Trennzahl (separation number), number of theoretical plates/meter, program temperature beseline stability, acid-base ratio, and the coefficient of skewness for 1-octanol. Statistical moments (m2) and hybrid moments are used to describe capillary column chromatographic performance because they may be related to basic physico-chemical column processes. These measurements are very sensitive parameters for characterizing GC columns. Using an online computer-based data system, the limits of capillary GC are shown to be limited by the sampling and injection steps.     

A new approach to data reduction and evaluation in high-resolution time-of-flight mass spectrometry using a time-to-digital convertor data-recording system

A new effective and robust approach to the detection of incompletely resolved peaks, and evaluation of their parameters in high-resolution time-of-flight mass spectra for time-to-digital convertor (TDC) data acquisition mode, is described. The method is based on fast construction of a smoothed continuous curve that approximates the initial data (transformed to a constant relative width of time intervals for ion counting) with respect to precision of measurements. The first derivative of this curve is used for correction of skewness of the peak shape as far as possible. A contribution of the second derivative is subtracted from the smoothed curve for better resolution of partially resolved peaks. The comparison of local maxima of this resulting final curve with those for the initial smoothed curve allows reliable detection of the peaks and to test whether or not they are spoiled by overlapping. Ion counting performed by TDC gives an opportunity to estimate standard deviations of peak locations and their intensities. These values proved to be close to theoretically minimal standard deviations for these parameters for single fully resolved peaks. Thus, estimates of the main parameters of mass peaks by the described method are close to statistically efficient estimators for these parameters.     

离子色谱线性梯度淋洗分离阴离子的计算机模拟

建立了使用氢氧化钠淋洗液时用计算机模拟离子色谱梯度淋洗分离阴离子的新方法,研究了在线性梯度淋洗过程中不同时间阴离子在色谱柱中的位置及所在位置的淋洗液浓度,得出阴离子在不同时间的容量因子、迁移速度,通过积分得到保留时间。再根据离子色谱峰峰形变化的规律,得到色谱峰峰形的参数。模拟色谱图保留值与实验值的相对误差小于5%,模拟色谱图的色谱峰峰形与实验所得到的色谱图的色谱峰峰形也非常接近。     

Resolution of Overlapping Chromatographic Peaks Using a Genetic Algorithm

ABSTRACT

A genetic algorithm for resolution of overlapping chromatographic peaks (GAROCP) using real-number coding, non-uniform mutation and arithmetical crossover methods is described in this paper. It was applied to resolution of highly overlapped multicomponent high-performance liquid chromatographic peaks by fitting experimental chromatogram to the exponentially modified Gaussian (EMG) model. The genetic algorithm was used to find the minimum of fitting error to optimize the parameters in the EMG functions which determine the shape and area of each peak. The applicability of the method was investigated with both simulated signals calculated by EMG functions and experimental multicomponent overlapping chromatograms.     

一种变压器油色谱峰识别算法的设计

在变压器油色谱峰识别领域,传统的一阶导数法需要斜率阈值来实现色谱峰识别,因此自动化程度低及容易失真。针对这些缺点,本文在一阶导数法的基础上进行了改进,将迭代移动平均及归一化分析技术应用到色谱峰识别中,通过对信号曲线及方波曲线多次迭代移动平均确定最优的归一化识峰参数,结合色谱峰的绝对保留时间及识峰窗口实现对色谱峰的准确识别。实验结果表明：该算法可以准确识别色谱峰,对噪声、色谱峰的峰宽及峰形变化不敏感,具有很强的自适应性,满足变压器油中气体在线监测装置的现场使用要求。