Gradient design for liquid chromatography using multi-scale optimization

doi:10.1016/j.chroma.2017.12.040

2018-01-01

Sergio López-Ureña

J.R. Torres‐Lapasió *

Rosa Donat

M.C. García‐Álvarez‐Coque

DOI：10.1016/j.chroma.2017.12.040

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摘要

En 中文

In reversed phase-liquid chromatography, the usual solution to the general elution problem is the application of gradient elution with programmed changes of organic solvent (or other properties). A correct quantification of chromatographic peaks in liquid chromatography requires well resolved signals in a proper analysis time. When the complexity of the sample is high, the gradient program should be accommodated to the local resolution needs of each analyte. This makes the optimization of such situations rather troublesome, since enhancing the resolution for a given analyte may imply a collateral worsening of the resolution of other analytes. The aim of this work is to design multi-linear gradients that maximize the resolution; while fulfilling some restrictions: all peaks should be eluted before a given maximal time, the gradient should be flat or increasing, and sudden changes close to eluting peaks are penalized. Consequently, an equilibrated baseline resolution for all compounds is sought. This goal is achieved by splitting the optimization problem in a multi-scale framework. In each scale kappa, an optimization problem is solved with N-kappa approximate to 2(kappa) variables that are used to build the gradients. The N-kappa variables define cubic splines written in terms of a B-spline basis. This allows expressing gradients as polygonals of M points approximating the splines. The cubic splines are built using subdivision schemes, a technique of fast generation of smooth curves, compatible with the multi-scale framework. Owing to the nature of the problem and the presence of multiple local maxima, the algorithm used in the optimization problem of each scale kappa should be global, such as the pattern-search algorithm. The multi-scale optimization approach is successfully applied to find the best multi-linear gradient for resolving a mixture of amino acid derivatives. (C) 2017 Elsevier B.V. All rights reserved.

Keyword:

Liquid chromatography

Multi-linear gradients

Cubic splines

Resolution

Multi-scale optimization