On the contour of overlapping vibrational bands in condensed phases

An approximation of the vibrational band profile in condensed phases has been developed. The entire contour is considered as a sum of overlapping components of identical shape, given by a Cauchy-Lorentz or Gauss function. The resulting functions are asymmetrical as a rule. Examples of numerical fitting of experimental vibrational bands are presented.     

Correction of Gel Chromatograms for Instrumental Broadening

The Tikhonov regularization method was proposed for correction of gel chromatograms for instrumental broadening. The results obtained in solving the Tung equation by approximation and regularization methods and also in using the Gauss and Pearson distributions as a function of instrumental broadening were compared.     

小波变换用于重叠色谱峰组分信息的提取

提出了一个小波变换用于提取重叠色谱中组分信息的理论公式，并将它应用于三组分和五组分重叠色谱实验数据的解析。结果表明：在定定分离度范围内，当相邻色谱峰峰宽相近时，根据此公式的计算结果，可以将各组分的信息从重叠色谱峰信号中提取出来。洒工作对小波变换用于重叠峰的解析具有重要意义。     

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.     

Alternative approaches for the estimation of the band broadening parameters in single-detection size exclusion chromatography

New approaches for the determination of the extent of symmetric and asymmetric band broadening (BB) in size exclusion chromatography (SEC) are presented. For this purpose raw data was simulated by starting with either a theoretical Poisson number chain length distribution (NCLD), or a log-normal weight chain length distribution (WCLD). Each distribution was first converted to a BB-free mass chromatogram, as typically obtained from a standard differential refractive index detector. Then, the broadened (or "measured") chromatograms were simulated by convoluting the BB-free chromatograms with a BB function, which was assumed to follow symmetrical (Gauss) as well as unsymmetrical (exponentially modified Gauss) function. A broad range of BB parameters (standard deviation, sigma(BB), and exponential decay, tau(BB)) was used for the simulations. The approaches are based on the determination of the points of inflection belonging to the peak of the broadened chromatogram, and closed as well as empirically derived equations connecting the peak width, its variance, and the parameters sigma(BB) and tau(BB). The developed methods are applicable for Poisson distributions well above a peak chain length of 100.     

Evaluation of Seven Chromatographic Response Functions on Simulated and Experimentally Obtained Chromatograms in Hydrophilic Interaction Liquid Chromatography System

This paper investigates the ability of seven chromatographic response functions to measure the quality of chromatograms obtained in hydrophilic interaction liquid chromatography (HILIC). First, the functions were tested on a set of simulated chromatograms and differences in their mathematical design were discussed. Second, the functions were evaluated on the experimentally obtained chromatograms in HILIC analysis of model mixture consisted of beta agonists and antagonists. The ranking of chromatograms obtained by different functions was significantly different, implying that the accuracy of the optimization procedure is strongly dependent on the function that was selected as an output. Investigation of potential drawbacks of each function was conducted and general recommendations concerning the use of chromatographic response functions in optimization strategies are proposed.     

An immune algorithm for resolution of multicomponent overlapping chromatograms

A novel immune algorithm for resolution and quantitative determination of the components in overlapping chromatograms was proposed by imitating biological immune systems. The algorithm takes an overlapping chromatogram as its input and subtracts the chromatograms of standard samples from the input by iteration of a network. When the residual does not change, the network will converge and chromatographic information of the components in overlapping chromatogram will be obtained. Both simulated and experimental data sets were investigated by the method. Results showed that both resolved results and recoveries of quantitative determination are satisfactory. Comparing with conventional least-square method, the immune algorithm is fast in calculation.     

An immune algorithm for resolution of multicomponent overlapping chromatograms

A novel immune algorithm for resolution and quantitative determination of the components in overlapping chromatograms was proposed by imitating biological immune systems. The algorithm takes an overlapping chromatogram as its input and subtracts the chromatograms of standard samples from the input by iteration of a network. When the residual does not change, the network will converge and chromatographic information of the components in overlapping chromatogram will be obtained. Both simulated and experimental data sets were investigated by the method. Results showed that both resolved results and recoveries of quantitative determination are satisfactory. Comparing with conventional least-square method, the immune algorithm is fast in calculation.     

一种新型的信号拟合方法--免疫算法

通过对免疫系统免疫机制的模拟,提出了一种新型的信号拟合算法。该算法根据所提供的标样信息对重叠分析化学信号进行拟合,从重叠信号中提取单一组分的信息,从而实现了多组分混合信号的解析。对模拟信号的实验信号的处理结果表明,该方法可方便地用于多组分重叠色谱信号的解析。     

一种新型的信号拟合方法─—免疫算法

通过对免疫系统免疫机制的模拟,提出了一种新型的信号拟合算法。该算法根据所提供的标样信息对重叠分析化学信号进行拟合,从重叠信号中提取单一组分的信息,从而实现了多组分混合信号的解析。对模拟信号和实验信号的处理结果表明,该方法可方便地用于多组分重叠色谱信号的解析。     

Chromatogram simulation by area reproduction

A modified Poisson function has been developed for the simulation of chromatographic peaks. The proposed model is shown to have the property of exactly recreating the experimentally determined peak area. Model parameters are obtained directly from the experimental peak, and overlapping peaks are deconvoluted such that the area sum of overlapping peaks is kept unchanged. The method was applied to real, complex chromatograms.     

Deconvolution method for accurate determination of overlapping peak areas in chromatograms.

A method is described for deconvoluting chromatograms which contain overlapping peaks. Parameters can be selected to ensure that attenuation of peak areas is uniform over any desired range of peak widths. A simple extension of the method greatly reduces the negative overshoot frequently encountered with deconvolutions. The deconvoluted chromatograms are suitable for integration by conventional methods.     

An improved transmutation method for quantitative determination of the components in multicomponent overlapping chromatograms

An improved method is proposed for the quantitative determination of multicomponent overlapping chromatograms based on a known transmutation method. To overcome the main limitation of the transmutation method caused by the oscillation generated in the transmutation process, two techniques—wavelet transform smoothing and the cubic spline interpolation for reducing data points—were adopted, and a new criterion was also developed. By using the proposed algorithm, the oscillation can be suppressed effectively, and quantitative determination of the components in both the simulated and experimental overlapping chromatograms is successfully obtained.     

A New Method for Identifying and Estimating the Parameters of the Instrumental Spreading Function in Size Exclusion Chromatography-Application to Particle Size Analysis

Abstract

Herein is reported a new method for identifying and estimating the instrumental spreading function in size exclusion chromatography. The method is based on the solution of the integral equation when the size distribution of the injected standards are known. A numerical method after Ishige et al. (1) to solve the integral equation for the corrected distribution is suitably modified to estimate instead the spreading function when the true and measured chromatograms are both known. The method is evaluated for synthesized chromatograms using the particle size distribution of Dow polystyrene latices. It is then applied to experimental chromatograms of the latices obtained by size exclusion chromatography. The resulting spreading functions were then analysed for variance, skewness and kurtosis.     

免疫算法用于多组分二维色谱数据的解析

通过对免疫系统抗体对抗原消除作用及其记忆功能的模拟,提出了解析二维数据矩阵的新方法。采用模拟的EMG公式作为抗体输入,对二维信号逐行进行迭代消除,从重叠峰中提取单一组分的色谱信息和光谱信息。通过对二维色谱数据的解析,结果表明,该方法可方便地用于多组分重叠二维色谱的解析。     

Multiple peak analysis in gel permeation chromatography

Summary This paper describes the resolution of multimodal GPC chromatograms into their individual components through the use of two optimization techniques, applied sequentially. The principle of the method can be applied to any form of curve but only the mathematics for Gaussian curves is given. The method has been successfully tested against both model and real chromatograms. The model chromatograms consisted of overlapping, perfectly Gaussian, curves whilst the real chromatograms were obtained from oligomeric polyesters submitted for routine GPC analysis and contained from three to five components. These chromatograms, which would have been too complex to resolve by “pencil and ruler” techniques, were resolved by this method to a precision within experimental error.     

Single- and multi-channel detection for generalized quantitative analysis in cases of unresolved chromatographic peaks

Computerized quantification of components under overlapping chromatographic peaks is done by calibration of chromatograms against component mixtures. For conventional (single-channel) detectors, the limitations of earlier methods based on ordinary multiple regression, can be circumvented by data reduction with the aid of principal component analysis with the partial least-squares approach. Simulation studies show that the method can be applied even when there is severe peak overlap, unstable baseline, noisy chromatograms or non-linear detector response. Advantages in the quantification of fused peaks by means of multichannel detectors are outlined. Present limitations on the quantitative evaluation of several overlapping component peaks from a single spectro-chromatogram by means of the partial least-squares method combined with multiple regression on the pure component spectra, are discussed with respect to practical high-performance liquid chromatography.     

完全重叠色谱峰的二维微分色谱解析算法

利用完全重叠的色谱峰中同时消失的两组分的浓度变化速率差异，通过二维数据微分色谱法获取被掩盖组份的近似光谱，以解析完全重叠的色谱体系，将该法应用于维生素Ｃ和菸酸两组份完全重叠的二维色谱之分辨，结果令人满意，分辨光谱与标准光谱重合甚好。     

A new mathematical procedure to evaluate peaks in complex chromatograms

Automatic peak evaluation in chromatograms and subsequent quantification of compound concentrations is still a challenge in the analysis of complex samples containing hundreds or thousands of compounds. Although a number of software packages for peak evaluation exist, baseline definition and overlapping peaks of different shapes are the main reasons which prevent reliable automatic analysis of complex chromatograms. A new mathematical procedure is presented which uses peak shapes extracted from the chromatogram itself and modified by nonlinear (in fact, hyperbolic) stretching of the peak head and tail. With this approach, the peak parameters are position, height, scale of front, scale of tail, and smoothness of transition from front to tail scaling. This approach is found to give a substantially better fit than traditional analytically defined peak shapes. Together with a good peak finding heuristic and nonlinear optimization of parameters this allows a reliable automatic analysis of chromatograms with a large number of peaks, even with large groups of overlapping peaks. The analysis matches the quality of standard interactive methods, but still permits interactive refinement. This approach has been implemented and tested on a large set of data from chromatography of hydrocarbons in ambient air samples.