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。     

Computation of distribution of minimum resolution for log-normal distribution of chromatographic peak heights

General equations are derived for the distribution of minimum resolution between two chromatographic peaks, when peak heights in a multi-component chromatogram follow a continuous statistical distribution. The derivation draws on published theory by relating the area under the distribution of minimum resolution to the area under the distribution of the ratio of peak heights, which in turn is derived from the peak-height distribution. Two procedures are proposed for the equations' numerical solution. The procedures are applied to the log-normal distribution, which recently was reported to describe the distribution of component concentrations in three complex natural mixtures. For published statistical parameters of these mixtures, the distribution of minimum resolution is similar to that for the commonly assumed exponential distribution of peak heights used in statistical-overlap theory. However, these two distributions of minimum resolution can differ markedly, depending on the scale parameter of the log-normal distribution. Theory for the computation of the distribution of minimum resolution is extended to other cases of interest. With the log-normal distribution of peak heights as an example, the distribution of minimum resolution is computed when small peaks are lost due to noise or detection limits, and when the height of at least one peak is less than an upper limit. The distribution of minimum resolution shifts slightly to lower resolution values in the first case and to markedly larger resolution values in the second one. The theory and numerical procedure are confirmed by Monte Carlo simulation.     

An automatic peak finding method for LC‐MS data using Gaussian second derivative filtering

A highly automated procedure for localising and characterising peaks in the chromatographic time domain of LC‐MS data has been developed. The work was initiated by an identified need to facilitate the detection and tracking of chromatographic peaks during method development for the analysis of impurities in pharmaceutical products. The algorithm is mainly based on a digital filter for which the settings are automatically adapted to the data set under study. The procedure was evaluated for synthetic data sets with various S/N levels, peak widths and baseline properties. It was found that even for the worst case tested with S/N=10 and a high variability in the baseline, 94% of the simulated analytical peaks could be detected without producing any false‐positive identifications. Furthermore, the number of correctly estimated peak heights and peak widths falling within a 10% error of the true values were 94 and 91%, respectively. For experimental data sets, peak height, and width estimations were more difficult, but the processed reconstructions showed an excellent agreement with the analytical signals of the raw data, and also a clearly improved visualisation in total ion‐ and base‐peak chromatograms.     

Utilizing a constant peak width transform for isothermal gas chromatography

A computational approach to partially address the general elution problem (GEP), and better visualize, isothermal gas chromatograms is reported. The theoretical computational approach is developed and applied experimentally. We report a high speed temporally increasing boxcar summation (TIBS) transform that, when applied to the raw isothermal GC data, converts the chromatographic data from the initial time domain (in which the peak widths in isothermal GC increase as a function of their retention factors, k), to a data point based domain in which all peaks have the same peak width in terms of number of points in the final data vector, which aides in preprocessing and data analysis, while minimizing data storage size. By applying the TIBS transform, the resulting GC chromatogram (initially collected isothermally), appears with an x-axis point scale as if it were instrumentally collected using a suitable temperature program. A high speed GC isothermal separation with a test mixture containing 10 compounds had a run time of ～25 s. The peak at a retention factor k ～0.7 had a peak width of ～55 ms, while the last eluting peak at k ～89 (i.e., retention time of ～22 s) had a peak width of ～2000 ms. Application of the TIBS transform increased the peak height of the last eluting peak 45-fold, and S/N ～20-fold. All peaks in the transformed test mixture chromatogram had the width of an unretained peak, in terms of number of data points. A simulated chromatogram at unit resolution, studied using the TIBS transform, provided additional insight into the benefits of the algorithm.     

Simple and Efficient Solution for Robustness Testing in Gradient Elution Liquid Chromatographic Methods

In this paper, an efficient way for robustness testing of gradient elution liquid chromatographic methods is proposed and tested on model mixtures comprising cilazapril, hydrochlorothiazide, and their degradation products, solutes that differ not only in polarities, but also in solubility and absorption characteristics. In general, the robustness could be tested with respect to various responses: resolution, retention factor, selectivity factor, change of detector response, etc. In chromatographic methods, the separation of the adjacent peaks is mandatory, and, consequently, the resolution is usually used as response. In isocratic elution methods, the resolution threshold depends on many factors, such as sizes of adjacent peaks, peak shapes, and asymmetry factor. At the same time, the situation is even more complex in gradient elution methods, because separation depends on a larger number of parameters, such as gradient profile, column geometry, mobile phase flow rate, column equilibration between gradient runs, etc. To ensure baseline separation, the authors propose application of separation criterion (s) as response and indirect modeling in the robustness evaluation. Examined response in this approach is represented by the difference between the retention time of the beginning of the peak and the retention time of the end of the previously eluting peak of the critical pair. Moreover, the proposed methodology included reusing experiments from the optimization phase to define a robust chromatographic region without increasing the number of experiments. It was shown that method robustness can be easily and efficiently evaluated by this methodology.     

Combined Kalman filtering and steepest descent minimization for quantitative analysis of unresolved misaligned chromatographic peaks. The resolution of alternariol and altenuisol mycotoxins in mixtures by HPLC

Summary The potential of a computational approach for the quantitative resolution of seriously overlapping chromatographic peaks when there is loss of collinearity between the pure component peaks and the mixture peak has been explored. The program makes iterative use of the Kalman filter algorithm for resolving the mixture peak with the component peaks aligned according to some values of the position parameters, and of a steepest descent minimization procedure to find the optimal alignment. This combined procedure has been applied to the quantitive resolution of the HPLC chromatograms of alternariol and altenuisol mycotoxins in synthetic mixtures and in real samples.     

A new chromatographic response function for use in size-exclusion chromatography optimization strategies: Application to complex organic mixtures

A new chromatographic response function (CRF) is presented aiming at designing an optimal chromatographic separation protocol for assessing the molecular size distribution of complex organic mixtures, such as those of natural organic matter from different sources (atmospheric, aqueous, and terrestrial). This CRF can be applied to mixtures of unknown solutes, being well suited for describing separation processes of pair of peaks of highly unequal area, and also for overlapping and asymmetric peaks. The performance of the developed CRF was compared to that of an existing response function, using simulated chromatograms. The capability of the new function to qualify the resolution degree that it is attained under different chromatographic conditions was further assessed through a size-exclusion chromatography study of a variety of different organic compounds, via a two-level full factorial design. It was proved that this function is a reliable alternative to optimize simultaneously the composition of the mobile phase (pH, ionic strength, and organic modifier concentration) and the instrumental variables (flow rate).     

Finding the best separation in situations of extremely low chromatographic resolution

Samples with a large number of compounds or similarities in their structure and polarity may yield insufficient chromatographic resolution. In such cases, however, finding conditions where the largest number of compounds appears sufficiently resolved can be still worthwhile. A strategy is here reported that optimises the resolution level of chromatograms in cases where conventional global criteria, such as the worst resolved peak pair or the product of elementary resolutions, are not able to detect any separation, even when most peaks are baseline resolved. The strategy applies a function based on the number of "well resolved" peaks, which are those that exceed a given threshold of peak purity. It is, therefore, oriented to quantify the success in the separation, and not the failure, as the conventional criteria do. The conditions that resolve the same amount of peaks are discriminated by either quantifying the partial resolution of those peaks that exceed the established threshold, or by improving the separation of peaks below it. The proposed approach is illustrated by the reversed-phase liquid chromatographic separation of a mixture of 30 ionisable and neutral compounds, using the acetonitrile content and pH as factors.     

Improved performance of comprehensive two-dimensional HPLC separation of traditional Chinese medicines by using a silica monolithic column and normalization of peak heights

Performance of comprehensive two-dimensional liquid chromatography system is greatly improved than we reported previously by using a silica monolithic column as for the second dimensional separation. Due to the increase of the elution speed on the second dimensional monolithic column, the first dimensional column efficiency and analysis rate can be greatly improved as comparing with conventionally second dimensional column. The developed system was applied to analysis of methanol extraction of two umbelliferae herbs Ligusticum chuanxiong Hort. and Angelica sinensis (Oliv.) Diels by using CN column as for the first dimensional separation and a silica monolithic ODS column for the second dimensional separation, and the obtained three-dimensional chromatograms were treated by normalization of peak heights with the value of the highest peak or setting a certain value using a software written in-house. It was observed that much more peaks for low-abundant components in TCM extract can clearly be detected here than we reported before, due to the large difference for the amount of components in TCMs' extract. With the above improvements in separation performance and data treatment, totally about 120 components in methanol extraction of Rhizoma chuanxiong and 100 in A. sinensis were separated with UV detection within 130 min. This result meant that both the number of peaks detected increase twice but the analysis time decrease twice if comparing with the previously reported result.     

Automatic program for peak detection and deconvolution of multi-overlapped chromatographic signals part II: peak model and deconvolution algorithms

Several interlinked algorithms for peak deconvolution by non-linear regression are presented. These procedures, together with the peak detection methods outlined in Part I, have allowed the implementation of an automatic method able to process multi-overlapped signals, requiring little user interaction. A criterion based on the evaluation of the multivariate selectivity of the chromatographic signal is used to auto-select the most efficient deconvolution procedure for each chromatographic situation. In this way, non-optimal local solutions are avoided in cases of high overlap, and short computation times are obtained in situations of high resolution. A new algorithm, fitting both the original signal and the second derivatives is proved to avoid local optima in intermediate coelution situations. This allows achieving the global optimum without the need of background knowledge by the user. A previously reported peak model, a Gaussian with a polynomial standard deviation whose complexity can be modulated to enhance the fitting quality, was applied. However, the original formulation was modified to account baseline outside the peak region. Also, the optimal model complexity was auto-selected via error propagation theory. The method is able to process simultaneously several related chromatograms. The software was tested with both simulated and experimental chromatograms obtained with monolithic silica columns.     

Pressure effects on resolution in ion mobility spectrometry

This paper explains the effect of pressure on separation factor, resolving power (defined based on a single peak), and resolution (defined based on two adjacent peaks) in ion mobility spectrometry. IMS spectra were recorded at various pressures ranging from 39 hPa (29 Torr) up to atmospheric pressure and various ion gates ranging from 50 to 225 μs. The results show that the IMS peaks shift perfectly linear with pressure so that separation factors remain unaffected by pressure. However, pressure has strong influence on resolving power and resolution. Reducing pressure at constant pulse width decreases the resolving power and resolution. On the other hand, the decrease in resolution can be compensated by shortening the ion pulse width since reducing pressure results in a higher ion current.     

Metrics of separation performance in chromatography. Part 1. Definitions and application to static analyses

Earlier introduced metrics of separation performance are described in a systematic way. After providing the definitions of the metrics suitable for a broad variety of applications, the study focuses on static analyses (isothermal GC, isocratic LC, etc.) and their general separation performance. Statistically expected number of resolved (adequately separated) single-component peaks is treated as the ultimate metric of general separation performance of chromatographic analysis. That number depends on the peak capacity of the analysis and the number of components in a test mixture. The peak capacity, in turn, depends on the separation capacity of a column and the lowest separation required by the data-analysis system for resolving poorly separated peaks. The separation capacity is a special case of a broader metric of the separation measure which is a function of column efficiency, solute separability, and the level of the solute interaction with a column stationary phase. The formulae for theoretical prediction of all these metrics for arbitrary pairs of peaks in static analyses are derived. To provide a better insight into the basic metrics of the separation performance, additional metrics such as the solute discrimination (relative difference in solute velocities), utilization of separability (solute discrimination per unit of their separability), specific separation (the separation per unit of separability), and others are defined and found for static analyses.     

The statistical overlap theory of chromatography using power law (fractal) statistics

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics.     

High-speed peak matching algorithm for retention time alignment of gas chromatographic data for chemometric analysis

A rapid retention time alignment algorithm was developed as a preprocessing utility to be used prior to chemometric analysis of large datasets of diesel fuel profiles obtained using gas chromatography (GC). Retention time variation from chromatogram-to-chromatogram has been a significant impediment against the use of chemometric techniques in the analysis of chromatographic data due to the inability of current chemometric techniques to correctly model information that shifts from variable to variable within a dataset. The alignment algorithm developed is shown to increase the efficacy of pattern recognition methods applied to diesel fuel chromatograms by retaining chemical selectivity while reducing chromatogram-to-chromatogram retention time variations and to do so on a time scale that makes analysis of large sets of chromatographic data practical. Two sets of diesel fuel gas chromatograms were studied using the novel alignment algorithm followed by principal component analysis (PCA). In the first study, retention times for corresponding chromatographic peaks in 60 chromatograms varied by as much as 300 ms between chromatograms before alignment. In the second study of 42 chromatograms, the retention time shifting exhibited was on the order of 10 s between corresponding chromatographic peaks, and required a coarse retention time correction prior to alignment with the algorithm. In both cases, an increase in retention time precision afforded by the algorithm was clearly visible in plots of overlaid chromatograms before and then after applying the retention time alignment algorithm. Using the alignment algorithm, the standard deviation for corresponding peak retention times following alignment was 17 ms throughout a given chromatogram, corresponding to a relative standard deviation of 0.003% at an average retention time of 8 min. This level of retention time precision is a 5-fold improvement over the retention time precision initially provided by a state-of-the-art GC instrument equipped with electronic pressure control and was critical to the performance of the chemometric analysis. This increase in retention time precision does not come at the expense of chemical selectivity, since the PCA results suggest that essentially all of the chemical selectivity is preserved. Cluster resolution between dissimilar groups of diesel fuel chromatograms in a two-dimensional scores space generated with PCA is shown to substantially increase after alignment. The alignment method is robust against missing or extra peaks relative to a target chromatogram used in the alignment, and operates at high speed, requiring roughly 1 s of computation time per GC chromatogram.     

An information-based computational technique for estimation of chromatographic peak purity

Assessment of the purity of chromatographic peaks is an important step in developing and validating purification procedures for complex mixtures. While curve-fitting techniques can be useful for determining the retention times and relative concentrations of the components of a chromatographic peak, their utility is limited by the lack of unambiguous criteria for determining the number of such components. In this work, we present a computational technique for analyzing chromatograms to estimate the number of components, their retention times, and their relative concentrations. In contrast to Fourier-transform-based techniques, the technique we present does not require manual peak identification. It is based on curve-fitting and uses the Akaike information criterion to estimate the number of components. Application of the technique to chromatograms obtained from size-exclusion and reverse-phase chromatography of test mixtures indicates that it is useful for the characterization of complex mixtures.     

Mutual peak matching in a series of HPLC–DAD mixture analyses

One of the largest challenges in high performance liquid chromatography (HPLC) method development is the necessity for tracking the movement of peaks as separation conditions are changed. Peak increments are then used to build a mathematical model capable of minimizing the number of experiments in an optimization circuit. Method optimization for an unknown mixture is, moreover, complicated by the absence of any a priori information on component properties and retention times when direct signal assignment is not possible. On the contrary, achievement of the maximum separation becomes an important factor for successful identification or quantitation. In this case, the optimization may be based on assigning peaks of the same component chosen from different experiments to each other. In other words, mutual peak matching between the HPLC runs is required.

A new method for mutual peak matching in a series of HPLC with diode array detector (HPLC–DAD) analyses of the same unknown mixture acquired at varying separation conditions has been developed. This approach, called mutual automated peak matching (MAP), does not require any prior knowledge of the mixture composition. Applying abstract factor analysis (AFA) and iterative key set factor analysis (IKSFA) on the augmented data matrix, the algorithm detects the number of mixture components and calculates the retention times of every individual compound in each of the input chromatograms. Every candidate component is then validated by target testing for presence in each HPLC run to provide quantitative criteria for the detection of “missing” peaks and non-analyte components as well as confirming successful matches. The matching algorithm by itself does not perform full curve resolution. However, its output may serve as a good initial estimate for further modeling. A common set of UV-Vis spectra of pure components can be obtained, as well as their corresponding concentration profiles in separate runs, by means of alternating least-square multivariate curve resolution (ALS MCR), resulting in reconstruction of overlapped peaks.

The algorithms were programmed in MATLAB^® and tested on a number of sets of simulated data. Possible ways to improve the stability of results, reduce calculation time, and minimize operator interaction are discussed. The technique can be used to optimize HPLC analysis of a complex mixture without preliminary identification of its components.     

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.     

离子色谱不对称色谱峰的处理

介绍了通过微分处理分辨离子色谱中不对称峰的方法。实验将Ｆ＾－、Ｃｌ＾－、Ａｃ＾－、ＮＯ２＾－、ＮＯ３＾－、ＰｈＣＯＯ＾－、ＳＣＮ＾－、柠檬酸根、水杨酸根、山梨酸根和葡萄糖酸根等常见离子按一定比例配合混合液,对出现的不对称峰进行微分处理,得到的导数谱图可进行峰高定量,收到了较好的效果。     

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.