A software package for the orthogonal polynomial approximation of analytical signals,including a simulation program for chromatograms and spectra

The computer package calculates the coefficients of the terms of orthogonal polynomial series used to approximate the analytical signal. Two different polynomial series (Hermite and Chebyshev) are used, depending on the number of peaks and spreading of the error of the approximation over the interval. The package is applied for data reduction and filtering of the analytical signal. Part of the package facilitates optimization in chromatography, by calculating the effect of varying chromatogram parameters on polynomial terms. Some scaling methods for the analytical signal are discussed. For testing purposes, a program that generates chromatograms is added to the computer package. The program simulates chromatographic peaks with user-defined peak parameters; noise can be added. The theoretical background is described and some results are presented.     

Improving signal-to-noise ratios of liquid chromatography-tandem mass spectrometry peaks using noise frequency spectrum modification between two consecutive matched-filtering procedures

This paper reports a simple chemometric technique to alter the noise spectrum of liquid chromatography-tandem mass spectrometry (LC-MS-MS) chromatogram between two consecutive matched filter procedures to improve the peak signal-to-noise (S/N) ratio enhancement. This technique is to multiply one match-filtered LC-MS-MS chromatogram with another artificial chromatogram added with thermal noises prior to the second matched filter. Because matched filter cannot eliminate low-frequency components inherent in the flicker noises of spike-like sharp peaks randomly riding on LC-MS-MS chromatograms, efficient peak S/N ratio improvement cannot be accomplished using one-step or consecutive matched filter procedures to process LC-MS-MS chromatograms. In contrast, when the match-filtered LC-MS-MS chromatogram is conditioned with the multiplication alteration prior to the second matched filter, much better efficient ratio improvement is achieved. The noise frequency spectrum of match-filtered chromatogram, which originally contains only low-frequency components, is altered to span a boarder range with multiplication operation. When the frequency range of this modified noise spectrum shifts toward higher frequency regime, the second matched filter, working as a low-pass filter, is able to provide better filtering efficiency to obtain higher peak S/N ratios. Real LC-MS-MS chromatograms containing random spike-like peaks, of which peak S/N ratio improvement is less than four times with two consecutive matched filters typically, are remedied to accomplish much better ratio enhancement approximately 16-folds when the noise frequency spectrum is modified between two matched filters.     

Parametric studies of matched filters to enhance the signal-to-noise ratios of LC-MS-MS peaks

Chromatographic parameters of reference signals employed in matched filter methods have been studied using numerical experiments to improve the signal-to-noise (S/N) ratios of small liquid chromatography (LC) peaks obtained with electrospray tandem mass spectrometers (MS-MS). These parameters include the width, shape, and S/N ratios of chromatographic peaks used as the reference signal profiles. Our results show the effect of reference peak widths on improving the S/N ratio of chromatographic peaks; the influence of reference peak shapes is negligible. To verify simulation results, various reference signals, including analyte peaks of high concentration standards, internal standard peaks, and artificial Gaussian peaks of different widths, have been employed to enhance signal peaks on real liquid chromatography-tandem mass spectrometry (LC-MS-MS) chromatograms via matched filter methods. Our experimental results demonstrate that the S/N ratio enhancement of chromatographic peaks agree with the simulation predictions. These findings, therefore, suggest that regardless of peak shape, a well-smooth peak with a width close to that of the analyte peak is an adequate reference signal, when matched filter methods are used to improve LC-MS-MS chromatograms. Nevertheless, all methods processed LC-MS-MS peaks in this study do not achieve the ideal improvement ratios estimated with simulation results. We attribute this deficiency to spike-like noise, which have considerable low frequency components riding on LC-MS-MS chromatograms. Matched filtering, which works as a low-pass filter in the frequency domain, cannot effectively eliminate low frequency flicker noise contributed by these spikes. In addition, simple median filtering does not provide adequate improvement despite being able to smooth out most spikes in the chromatograms.     

Monolithic silica columns for high-efficiency chromatographic separations

A deconvolution methodology for overlapped chromatographic signals is proposed. Several single-wavelength chromatograms of binary mixtures, obtained in different runs at diverse concentration ratios of the individual components, were simultaneously processed (multi-batch approach), after being arranged as two-way data. The chromatograms were modelled as linear combinations of forced peak profiles according to a polynomially modified Gaussian equation. The fitting was performed with a previously reported hybrid genetic algorithm with local search, leaving all model parameters free. The approach yielded more accurate solutions than those found when each experimental chromatogram was fitted independently to the peak model (single-batch approach). The improvement was especially significant for those chromatograms where the peaks were severely affected by the tails of the preceding compounds. Peak shifts among chromatograms, which are a usual source of non-bilinearity, were modelled in a continuous domain instead of in a discrete way, which avoided some drawbacks associated with latent variable methods. An experimental design involving simulated chromatograms was applied to check the method performance. Five main factors affecting the deconvolution were examined: concentration pattern, chromatographic resolution, number of batches and replicates, and noise level, which were evaluated using first- and second-order figures of merit. The method was also tested on three real samples containing compounds showing different overlap. Four multi-batch deconvolution methods were considered differing in the nature of the processed information and kind of peak matching among chromatograms. In all cases, the multi-batch deconvolution yielded better performance than the single-batch approach.     

Inner chromatogram projection (ICP) for resolution of GC-MS data with embedded chromatographic peaks

The chromatographic peak located inside another peak in the time direction is called an embedded or inner peak in contradistinction with the embedding peak, which is called an outer peak. The chemical components corresponding to inner and outer peaks are called inner and outer components, respectively. This special case of co-eluting chromatograms was investigated using chemometric approaches taking GC-MS as an example. A novel method, named inner chromatogram projection (ICP), for resolution of GC-MS data with embedded chromatographic peaks is derived. Orthogonal projection resolution is first utilized to obtain the chromatographic profile of the inner component. Projection of the two-way data matrix columnwise-normalized along the time direction to the normalized profile of the inner component found is subsequently performed to find the selective m/z points, if they exist, which represent the chromatogram of the outer component by itself. With the profiles obtained, the mass spectra can easily be found by means of a least-squares procedure. The results for both simulated data and real samples demonstrate that the proposed method is capable of achieving satisfactory resolution performance not affected by the shapes of chromatograms and the relative positions of the components involved.     

穿心莲药材高效液相色谱指纹图谱研究及其应用

应用反相高效液相色谱(RP-HPLC)法建立穿心莲药材指纹图谱。首先以穿心莲对照药材为对象建立其乙醇提取物特征色谱图,再用5种不同来源穿心莲药材的乙醇提取物验证色谱图的指纹特性。在穿心莲药材乙醇提取物特征色谱图中有共有峰10个,各共有峰的相对保留时间与相对峰面积的相对标准偏差(RSD)均小于4%。对照药材中共有峰峰面积占总峰面积的98.5%以上。该指纹图谱用于清火栀麦胶囊中穿心莲的鉴别专属性良好。     

One-dimensional Kalman filter in a robot system for total analysis of solid dosage formulations

A one-dimensional Kalman filter for peak resolution is applied to a totally automated robot system for liquid chromatographic analysis of solid dosage formulations. Sample solutions were prepared from four tablets of clemastine fumarate (1 mg/tablet) and injected automatically at regular, short intervals onto the column by the robot system. The overlapped peaks in the resulting complicated chromatogram were resolved and evaluated quantitatively by the one-dimensional filter. The peak-resolving powers are shown to be reliable by comparison with a multidimensional Kalman filter. The applicability of the whole analytical system with the linear Kalman filter is discussed.     

气体色谱分析的多图谱归一定量法和气体组分的相对校正因子

本文报道一种扩展的气相色谱归一化定量分析方法，使两台或两台以上色谱仪对同一样品的诸多组分所完成的多张色谱力痛应用归一定量法进行计算，从而在进行多组分测定（尤其是气体样品的分析）时大大减少工作量，本方法的关键是样品中某一组分在多张图谱中均有分离很好的峰。     

Peak alignment using wavelet pattern matching and differential evolution

Retention time shifts badly impair qualitative or quantitative results of chemometric analyses when entire chromatographic data are used. Hence, chromatograms should be aligned to perform further analysis. Being inspired and motivated by this purpose, a practical and handy peak alignment method (alignDE) is proposed, implemented in this research for one-way chromatograms, which basically consists of five steps: (1) chromatogram lengths equalization using linear interpolation; (2) accurate peak pattern matching by continuous wavelet transform (CWT) with the Mexican Hat and Haar wavelets as its mother wavelets; (3) flexible baseline fitting utilizing penalized least squares; (4) peak clustering when gap of two peaks is smaller than a certain threshold; (5) peak alignment using differential evolution (DE) to maximize linear correlation coefficient between reference signal and signal to be aligned. This method is demonstrated with both simulated chromatograms and real chromatograms, for example, chromatograms of fungal extracts and Red Peony Root obtained by HPLC-DAD. It is implemented in R language and available as open source software to a broad range of chromatograph users (http://code.google.com/p/alignde).     

Improving liquid chromatography–tandem mass spectrometry determinations by modifying noise frequency spectrum between two consecutive wavelet-based low-pass filtering procedures

This paper employs one chemometric technique to modify the noise spectrum of liquid chromatography–tandem mass spectrometry (LC–MS/MS) chromatogram between two consecutive wavelet-based low-pass filter procedures to improve the peak signal-to-noise (S/N) ratio enhancement. Although similar techniques of using other sets of low-pass procedures such as matched filters have been published, the procedures developed in this work are able to avoid peak broadening disadvantages inherent in matched filters. In addition, unlike Fourier transform-based low-pass filters, wavelet-based filters efficiently reject noises in the chromatograms directly in the time domain without distorting the original signals. In this work, the low-pass filtering procedures sequentially convolve the original chromatograms against each set of low pass filters to result in approximation coefficients, representing the low-frequency wavelets, of the first five resolution levels. The tedious trials of setting threshold values to properly shrink each wavelet are therefore no longer required. This noise modification technique is to multiply one wavelet-based low-pass filtered LC–MS/MS chromatogram with another artificial chromatogram added with thermal noises prior to the other wavelet-based low-pass filter. Because low-pass filter cannot eliminate frequency components below its cut-off frequency, more efficient peak S/N ratio improvement cannot be accomplished using consecutive low-pass filter procedures to process LC–MS/MS chromatograms. In contrast, when the low-pass filtered LC–MS/MS chromatogram is conditioned with the multiplication alteration prior to the other low-pass filter, much better ratio improvement is achieved. The noise frequency spectrum of low-pass filtered chromatogram, which originally contains frequency components below the filter cut-off frequency, is altered to span a broader range with multiplication operation. When the frequency range of this modified noise spectrum shifts toward the high frequency regimes, the other low-pass filter is able to provide better filtering efficiency to obtain higher peak S/N ratios. Real LC–MS/MS chromatograms, of which typically less than 6-fold peak S/N ratio improvement achieved with two consecutive wavelet-based low-pass filters remains the same S/N ratio improvement using one-step wavelet-based low-pass filter, are improved to accomplish much better ratio enhancement 25-folds to 40-folds typically when the noise frequency spectrum is modified between two low-pass filters. The linear standard curves using the filtered LC–MS/MS signals are validated. The filtered LC–MS/MS signals are also reproducible. The more accurate determinations of very low concentration samples (S/N ratio about 7–9) are obtained using the filtered signals than the determinations using the original signals.     

Independent component analysis and its applications in signal processing for analytical chemistry

Independent component analysis (ICA) is a statistical method the goal of which is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible. In an ICA procedure, the estimated independent components (ICs) are identical to or highly correlated to the spectral profiles of the chemical components in mixtures under certain circumstances, so the latent variables obtained are chemically interpretable and useful for qualitative analysis of mixtures without prior information about the sources or reference materials, and the calculated demixing matrix is useful for simultaneous determination of polycomponents in mixtures. We review commonly used ICA algorithms and recent ICA applications in signal processing for qualitative and quantitative analysis. Furthermore, we also review the preprocessing method for ICA applications and the robustness of different ICA algorithms, and we give the empirical criterion for selection of ICA algorithms in signal processing for analytical chemistry.     

正交投影用于多波长色谱重叠峰分析

 将正交投影分辨 (OPR)技术用于多波长色谱重叠峰分辨 ,当色谱峰中最大重叠度小于或等于波长数时 ,用这一方法能从多波长色谱重叠峰中获得完全真解。基于双波长色谱分析 ,提出了一种新的色谱重叠峰中背景校正、组分数和纯组分信号区确定以及各组分重叠情况的分析方法 ,即双波长特征信息分析 (DWCI)。该法被成功的用于三组分双峰和双组分单峰重叠色谱的分析。     

小波变换用于色谱重叠峰的解析

利用小波变换的时频局部化性质，通过对色谱重叠峰信号小波变换后的某些频率段进行放大，使重叠谱峰得到了分离，并将此方法用于苯和甲苯二组分色谱体系的定量分析，重叠峰中各组分均得到了良好的线性关系及令人满意的定量分析。本文还讨论了不同小波基、分解的次数及放大系数在解析结果的影响。     

Retention time alignment of LC/MS data by a divide-and-conquer algorithm

Liquid chromatography-mass spectrometry (LC/MS) has become the method of choice for characterizing complex mixtures. These analyses often involve quantitative comparison of components in multiple samples. To achieve automated sample comparison, the components of interest must be detected and identified, and their retention times aligned and peak areas calculated. This article describes a simple pairwise iterative retention time alignment algorithm, based on the divide-and-conquer approach, for alignment of ion features detected in LC/MS experiments. In this iterative algorithm, ion features in the sample run are first aligned with features in the reference run by applying a single constant shift of retention time. The sample chromatogram is then divided into two shorter chromatograms, which are aligned to the reference chromatogram the same way. Each shorter chromatogram is further divided into even shorter chromatograms. This process continues until each chromatogram is sufficiently narrow so that ion features within it have a similar retention time shift. In six pairwise LC/MS alignment examples containing a total of 6507 confirmed true corresponding feature pairs with retention time shifts up to five peak widths, the algorithm successfully aligned these features with an error rate of 0.2%. The alignment algorithm is demonstrated to be fast, robust, fully automatic, and superior to other algorithms. After alignment and gap-filling of detected ion features, their abundances can be tabulated for direct comparison between samples.     

基于分形维数的分析信号自适应中值滤波

提出一种面向分析仪器谱图信号处理的分形维自适应中值波方法（AMeFFD）。该法延拓运用分形理论，定义了相对点盒维数概念，由此建立建立判定脉冲型噪声的特异性指标，从而可自动调节中值滤波窗口宽度，有效地滤除脉冲型噪声及其它类噪声。对仿真色谱信号及实测色谱图的处理结果表明：AMeFFD法克服了经典中值滤波算法的缺陷，无论在信号的均方根偏差还是谱峰差等指标上，均明显优于后者，能在确保谱峰不畸变的同时更有效地滤除脉冲型常见噪声，是处理化学谱图信号的有力工具。     

A Uricase Method for the Peak Identification of Uric Acid Appeared in a Liquid Chromatogram Amperometrically Monitored

Abstract

A uricase method for the peak identification of uric acid appeared in a liquid chromatogram monitored by aid of an electrochemical detector has been developed. Uricase (EC 1.7.3.3, from Candida utilis) catalyzes the conversion of uric acid to allantoin. We have found that uric acid can be oxidized under the chromatographic conditions employed in this study, whereas allantoin cannot be oxidized. The complete disappearance of a uric acid peak in a chromatogram of a biological sample after the uricase treatment indicates that the uric acid peak does not contain any other electroactive components. We observed the complete disappearance of the uric acid peaks in the chromatograms of human serum and gastric body.     

Recognizing chromatographic peaks with pattern recognition methods : Part 1. Development of a k-nearest-neighbour technique

Problems in automated peak recognition in chromatography are discussed. An algorithm based on the k-nearest neighbour technique is proposed. Recognition of a peak is done by comparing it with a predefined profile function (normally a Gaussian peak profile). The profile and a part of the chromatogram are both interpreted as points in a multi-dimensional pattern space. The distance between the two points gives the value of the peak recognition function. The effects of different properties of chromatographic peaks (i.e., peak width, peak height and noise) and of the profile parameter (i.e., dimension of the pattern space, shape and width of the function, and characteristics of the distance measure) are evaluated. The method has excellent properties for recognizing peaks with low signal/noise (S/N) ratios; an example with S/N = 1 is shown. Changing peak widths and drifting baselines have little effect on the recognition ability. Difficulties with changing peak heights can be compensated by range scaling. Problems occur when two peaks are not sufficiently separated.     

Fast, comprehensive online two-dimensional high performance liquid chromatography through the use of high temperature ultra-fast gradient elution reversed-phase liquid chromatography

A new approach to high speed, comprehensive online dual gradient elution 2DLC (LCxLC) based on the use of ultra-fast, high temperature gradient elution reversed phase chromatography is described. Entirely conventional gradient elution instrumentation and columns are assembled in a system which develops a total peak capacity of about 900 in 25 min; this is equivalent to roughly one peak/2 s. Each second dimension gradient is done in a cycle time of 21 s and the peak retention times measured for a set of twenty six indole-3-acetic acid (IAA) derivatives are reproducible to 0.2 s. Each peak eluting from the first dimension column is sampled at least twice across its width, as the corresponding peaks on the second dimension column appear in two or three consecutive second dimension chromatograms, clearly indicating that there is little loss in the resolution gained in the first dimension separation. Application to the separation of the low molecular weight components of wild-type and mutant maize seedlings indicates the presence of about 100 peaks on a timescale of 25 min. Compelling illustrations of the analytical potential of fast, high temperature 2DLC are evident in the clear presence of nine distinct peaks in a single second dimension chromatogram from a single quite narrow first dimension peak, and the great power of 2DLC to solve the "analytic dynamic range" problem inherent in the measurement of small peaks that are neighbors to a gigantic peak.     

Software for Microprocessor Controlled HPLC: Peak Area Integration

Abstract

Programs are described for determination of peak areas and peak retention times from the chromatographic data obtained by a dual-microprocessor data handling microcomputer (DHC). The programs provide the necessary equipment testing and calibration routines for an accurate reproduction of a recorded chromatogram, and they are written to be merged with the data acquisition programs to provide a true “real-time” integrator. The integration is performed with baseline stabilization and automatic peak splitting. These features make the integrator applicable to gradient elution chromatography, as well as for the integration of complex chromatograms with overlapping peaks. The integrated chromatogram can be displayed with the limits of integration for each peak. Results of peak area integration of simple and complex chromatograms demonstrate satisfactorily accurate and consistant results that are independent of chromatographic conditions and shape of the peaks.     

Influence of the peak height distribution on separation performances: Discrimination factor and effective peak capacity

Summary A new index of performance of the chromatographic separation between two adjacent peaks, the discrimination factor, d₀, is defined. It is normalized between 0 and 1 and is directly and easily determined from the chromatogram. It does not depend on any assumption regarding peak shape, except that the peak profiles of individual sample components have a single mode. Its value depends on the relative heights of the two peaks as well as on their separation. The separation power of a chromatographic system is classically measured by its peak capacity, defined on the basis of constant resolution between adjacent peaks. A previously developed statistical theory of the composition of mixtures makes it possible to extend the concept of peak capacity by taking into account the peak height distribution in typical average chromatograms. A new parameter, the effective peak capacity, is defined for this purpose on the basis of a constant discrimination factor between adjacent peaks. It allows to take into account the distribution of peak heights in statistical theories of the evaluation of complex chromatograms and in the measurement of the limit of determination in quantitative analysis. The characteristics of the two new parameters, the discrimination factor and effective peak capacity, are discussed and compared with those of their classical homologs, resolution and peak capacity, in the case of gaussian component peaks of equal widths.