Statistical moment techniques sort out distorted peaks

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  • Published: Mar 20, 2019
  • Author: Ryan De Vooght-Johnson
  • Channels: Laboratory Informatics / Chemometrics & Informatics
thumbnail image: Statistical moment techniques sort out distorted peaks

Assuming peaks are Gaussian can lead to misleading calculations

Calculations involving peak parameters, usually carried out by a variety of software packages, typically assume peaks have a perfect, ‘Gaussian’ shape. However, the examination of real-life chromatograms shows that distorted non-Gaussian peaks are common. Examples include the ‘tailing’ peaks seen with the HPLC of primary amines and the narrow ‘Eiffel tower’ peaks often seen with chiral HPLC columns. Assuming Gaussian peak shapes in calculations can give rise to very inaccurate values for parameters such as column efficiency. Various algorithms have been devised to deal with distorted peaks, but few are generally applicable.

The Arlington and Chicago scientists developed a better way to deal with peak parameters by using statistical moment analysis. This method makes no assumptions about peak shape, relying solely on the obtained chromatographic data along with peak start and end points.

Moment analysis used for peak calculations

Statistical moments were linked to peak parameters: the ‘zeroth’ moment (M0) to the peak area, the first moment (M1) to the average retention time and the second moment (M2) to the peak variance. Peak skew was related to the second (M2) and third moment (M3) by the formula: peak skew = M3/M23/2. The various moments were linked to the integrals of the appropriate function for each of them. The integrals were determined using the trapezoidal rule and Simpson’s rule. These numerical integration methods were shown to be superior to the often-used rectangular integration rule.

The authors attached an Excel template to the paper for the moment calculations. Raw data, in the form of signal and time, are entered, along with start and end times for the peaks of interest. The software supports up to ten peaks with a data limit of less than 10,000 data points per peak. The authors state that accurate estimation of the correct start and end points for each peak is important for the moment method to work correctly. The time for the software to run was given as between 15 and 30 sec, depending on the size of the data files.

The Excel template was tested against commercial software using model data, giving essentially the same results for the peak moments after integration using the trapezoidal rule and Simpson’s rule. In addition, a real-life UHPLC run was carried out using 5-methyl-5-phenylhydantoin on a chiral SPP teicoplanin column, with methanol as the eluting solvent. A methanol blank was injected to obtain a baseline. Values for the plate count and peak resolution from commercial software were shown to be far too high, by 128% and 74%, respectively, by comparison to the calculated moments using the Excel template.

The authors also discussed the application of moments to peaks distorted due to overloading, a frequent occurrence in preparative systems where overloading is usually necessary to obtain adequate yields with a reasonable number of injections. Overloading of main peaks is also a common result of trying to quantify trace impurities.

New Excel template enables straightforward calculations using peak moments

Although peak moments have previously been used, the new Excel template makes their application easier for the average analyst, enabling accurate calculations to be carried out with non-Gaussian peaks. The paper shows the importance of thinking about the mathematics underlying the software packages typically used with chromatography instruments. Just because a package produces a figure to ten significant figures, it does not mean it is at all accurate unless the underlying mathematical assumptions are valid.

Related Links

Misra, S., Wahab, M., Patel, D. et al. (2019). The utility of statistical moments in chromatography using trapezoidal and Simpson's rules of peak integration. Journal of Separation Science doi: 10.1002/jssc.201801131

Morton, D., Young, C. (1995). Analysis of peak profiles using statistical moments. Journal of Chromatographic Science 33 (9): 514-524.

Wikipedia, Moment (mathematics)

Article by Ryan De Vooght-Johnson

The views represented in this article are solely those of the author and do not necessarily represent those of John Wiley and Sons, Ltd.

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