Quantification of out-of-range peaks

Journal of Chemometrics, 2011

A method of noise filtering based on confidence interval evaluation is described. In the case of the approximation of a function, measured with error by a polynomial or other functions that allow estimation of the confidence interval, a minimal confidence interval is used as a criterion for the selection of the proper parameters of the approximating function. In the case of the polynomial approximation optimized parameters include the degree of the polynomial, the number of points (window) used for the approximation, and the position of the window center with respect to the approximated point. The Method is demonstrated using generated and measured chromatograms. The special considerations on confidence interval evaluation and quality of polynomial fit using noise properties of the 2 data array are discussed. The Method provides the lowest possible confidence interval for every data point.

Journal of Chromatography A, 2001

The problem of the appropriate choice of the function that describes a chromatographic peak is examined in combination with the deconvolution of overlapped peaks by means of the non-linear least-squares method. It is shown that the majority of the functions proposed in the literature to describe chromatographic peaks are not suitable for this purpose. Only the polynomial modified Gaussian function can describe almost every peak but it is mathematically incorrect unless it is redefined properly. Two new functions are proposed and discussed. It is also shown that the deconvolution of an overlapping peak can be done with high accuracy using a non-linear least-squares procedure, like Microsoft Solver, but this target is attained only if we use as fitted parameters the position of the peak maximum and the peak area (or height) of every component in the unresolved chromatographic peak. In case we use as fitted parameters all the parameters that describe each single peak enclosed in the multi-component peak, then Solver leads to better fits, which though do not correspond to the best deconvolution of the peak. Finally, it is found that Solver gives much better results than those of modern methods, like the immune and genetic algorithms.

1990

Various aspects of chromatographic peak quantitation and shape characterization are investigated in detail for single and overlapping chromatographic peaks. From the viewpoint of providing better quantitation of real chromatographic data while minimizing computational complexity, the results presented should be easily incorporated into existing routine chromatographic data analysis regimes. Three topics applicable to modem chromatographic data analysis are considered. First, progress in the application of the exponentially modified Gaussian (EMG) function to chromatography is reviewed. The review covers the following areas: (1) equations derived from the model, (2) studies of inherent errors in the quantitation of chromatographic peaks via use of the EMG model, (3) chromatographic applications since 1983 and (4) applications to flow injection analysis. The information discussed and the references included in this review should provide a valuable resource for those researchers consid...

Computer-assisted peak deconvolution on chromatograms obtained by GC separation of enantiomers of 1-chloro-2,2-dimethylaziridine on modified ␣-, ␤-, and ␥-cyclodextrin was used to determine the peak areas of enantiomers, prior Ž. Ž. to A , B and after the separation A , A. Both Gaussian as well as A, 0 B, 0 A B exponentially modified Gaussian functions were used to approximate the peak shapes in the deconvolution procedures. Determined peak areas were used in the calculation of the rate constants and energy barriers to enantiomerization. A comparison of energy barriers determined using the deconvolution of chromatograms with data published in the literature by classical kinetics shows differences within "5%.

Journal of chromatography. A, 2015

Lower order peak moments of individual peaks in heavily fused peak clusters can be determined by fitting peak models to the experimental data. The success of such an approach depends on two main aspects: the generation of meaningful initial estimates on the number and position of the peaks, and the choice of a suitable peak model. For the detection of meaningful peaks in multi-dimensional chromatograms, a fast data scanning algorithm was combined with prior resolution enhancement through the reduction of column and system broadening effects with the help of two-dimensional fast Fourier transforms. To capture the shape of skewed peaks in multi-dimensional chromatograms a formalism for the accurate calculation of exponentially modified Gaussian peaks, one of the most popular models for skewed peaks, was extended for direct fitting of two-dimensional data. The method is demonstrated to successfully identify and deconvolute peaks hidden in strongly fused peak clusters. Incorporation of ...

Separations

Selectivity in separation science is defined as the extent to which a method can determine the target analyte free of interference. It is the backbone of any method and can be enhanced at various steps, including sample preparation, separation optimization and detection. Significant improvement in selectivity can also be achieved in the data analysis step with the mathematical treatment of the signals. In this manuscript, we present a new approach that uses mathematical functions to model chromatographic peaks. However, unlike classical peak fitting approaches where the fitting parameters are optimized with a single profile (one-way data), the parameters are optimized over multiple profiles (two-way data). Thus, it allows high confidence and robustness. Furthermore, an iterative approach where the number of peaks is increased at each step until convergence is developed in this manuscript. It is demonstrated with simulated and real data that this algorithm is: (1) capable of mathemat...

Journal of Chromatography A, 2008

Resolution of overlapped chromatographic peaks is generally accomplished by modeling the peaks as Gaussian or modified Gaussian functions. It is possible, even preferable, to use actual single analyte input responses for this purpose and a nonlinear least squares minimization routine such as that provided by Microsoft Excel TM Solver can then provide the resolution. In practice, the quality of the results obtained varies greatly due to small shifts in retention time. I show here that such deconvolution can be considerably improved if one or more of the response arrays are iteratively shifted in time.

Journal of Chemical Information and Modeling, 2007

The result of our deconvolution technique applied to the size-exclusion chromatography test mixture is shown in Figure S1 and Table S1. In Figure S1c, we show the range of AIC scores found for various numbers of underlying peaks. We see that the best AIC score (the minimum score) is obtained when the number of peaks is four. In

… of Chromatography A, 2002

A new mathematical model for characterising skewed chromatographic peaks, which improves the previously reported polynomially modified Gaussian (PMG) model, is proposed. The model is a Gaussian based equation whose variance is a combined parabolic-Lorentzian function. The parabola accounts for the non-Gaussian shaped peak, whereas the Lorentzian function cancels the variance growth out of the elution region, which gives rise to a problematic baseline increase in the PMG model. The proposed parabolic-Lorentzian modified Gaussian (PLMG) model makes a correct description of peaks showing a wide range of asymmetry with positive and / or negative skewness. The new model is shown to give better fittingś than other models as the Li, log-normal or Pap-Papai models, which have a different mathematical basis. The model parameters are also related to peak properties as the skewness and kurtosis. The PLMG model is applied to the deconvolution of peaks in binary mixtures of structurally related compounds that are highly overlapped (retention times in min): oxytetracycline (9.00)-tetracycline (10.20), sulfathiazole (3.67)-sulfachloropyridazine (3.93), and sulfisoxazole (5.14)-sulfapyridine (5.24). The use of non-linear least-squares calibration in combination with the PLMG model gave superior results than the classical multiple linear least-squares and partial least-squares regressions. The proposed method takes into account run to run changes in retention time that occur along the injection of standards and samples, and the possible interactions that exist between the coeluting compounds. This decreases significantly the quantitation errors.

Journal of Chromatography A, 1989

that result from reversed-phase gradient elution often exhibit changes in band order when the gradient steepness is changed. This complicates the interpretation of the resulting separation, and prevents the application of computer simulation for method development.