Artificial neural networks for computer-aided modelling and optimisation in micellar electrokinetic chromatography

doi:10.1016/S0021-9673(99)00634-2

Journal of Chromatography A

Volume 850, Issues 1–2, 30 July 1999, Pages 345-353

https://doi.org/10.1016/S0021-9673(99)00634-2 Get rights and content

Abstract

The separation process in capillary micellar electrochromatography (MEKC) can be modelled using artificial neural networks (ANNs) and optimisation of MEKC methods can be facilitated by combining ANNs with experimental design. ANNs have shown attractive possibilities for non-linear modelling of response surfaces in MEKC and it was demonstrated that by combining ANN modelling with experimental design, the number of experiments necessary to search and find optimal separation conditions can be reduced significantly. A new general approach for computer-aided optimisation in MEKC has been proposed which, because of its general validity, can also be applied in other separation techniques.

Introduction

In micellar electrokinetic chromatography (MEKC), a surfactant is added to the mobile phase and the resultant micelles act as a pseudo stationary phase. The technique was developed by Terabe et al. [1]. MEKC is used for a great variety of analytes, particularly neutral compounds where the high efficiency of capillary electrophoresis (CE) separations can be applied. Recently, an extensive review on the separation of metal ions and metal-containing species by MEKC, including utilisation of metal ions in the separation of other species, has been published by Haddad et al. [2].

The explanation of migration behaviour in MEKC and the optimisation of separation is often difficult because there are many parameters that are known to influence the migration process and the mathematical description of these parameters can be quite complex. Various “hard” (i.e., physico-chemical) models for MEKC have been examined recently [3], [4], [5], [6], [7], [8], [9], [10]. If an appropriate model is chosen from those available, computer optimisation of composition of the background electrolyte can be performed and/or the migration behaviour of analytes can be predicted. In spite of the demonstrated success of this approach, the process can be very laborious if many parameters are involved because numerous experimental points are then necessary to derive the parameters of the model.

Over the last decade, increased attention has been paid to the applications of “soft” models in chemistry. Soft models can be defined as approaches in which an explicit mathematical model is neither formulated nor used. The prime example of such an approach is the use of artificial neural networks (ANNs). ANNs can be applied to various problems in chemistry as reviewed recently [11], [12] and to process different chemical information using association, classification, mapping, modelling, etc. In separation science, ANNs have already been used in CE [13], [14] and for the optimisation of chiral separations [12], [15]. A survey of the various approaches to optimisation of CE can be found in a recent review [16].

Büterhorn and Pyell [17] published a computer-aided optimisation of resolution in MEKC but neither a hard model nor an empirical model (equation) was used. ANNs have been applied for peak tracking in high-performance liquid chromatography (HPLC) optimisation [18], response surface modelling in HPLC optimisation [19], assessment of chromatographic peak purity [20], or for deconvolution of overlapping peaks [21]. Marengo et al. [22] studied the possibility of using ANNs to investigate the effect of five factors in ion-interaction chromatography and Sacchero et al. [23] have made a comparison of the prediction power between theoretical and neural-network models in ion-interaction chromatography. However, only in some publications [13], [14], [15] have attempts to achieve optimisation been performed, with ANNs normally being used only for modelling purposes. Recently, an extensive use of ANNs for modelling in ion chromatography has been presented [24]. The use of the combination of ANN and experimental design for optimisation has been first proposed in CE by Havel and co-workers [14], [15], [22]. Marengo et al. [22] also used ANNs and experimental design but only for decreasing the number of experiments for modelling purposes. Applications of experimental designs in CE have been recently reviewed by Altria et al. [25].

In this work the aims were to examine the modelling capabilities of the soft model-ANN approach in MEKC, with comparison to hard models, and the use of ANNs in combination with suitable experimental designs to facilitate the optimisation and/or prediction of electrophoretic mobilities in MEKC.

Section snippets

Theory of ANNs

While “hard” models in chemistry require formulae, mathematical equations and the knowledge or determination of the values of physico-chemical constants on which these equations are based, “soft” models (such as ANNs) consist only of arrays of simple activation units linked by weighted connections. The basic processing unit in an ANN is called a node or a simulated neuron [26]. A complete ANN is composed of multiple layers of neurons arranged so that each neuron in one layer is connected with

Data description and computation

The PDP ANN computational package [17] was used in this work with processing being performed on a Pentium-PC compatible computer. BP networks having three layers were created with this program and optimisation of the parameters for the networks was then carried out by systematically varying the values of the parameters until the “best” network performance was achieved.

Different data sets were used to study the applications of ANNs to the prediction of the best experimental conditions for MEKC

Results and discussion

The use ANNs for modelling in MEKC will be examined for several previously studied cases and the results of the ANN modelling approach will be compared to those of hard models reported for each case by Breadmore et al. [3]. Training and general application of the ANN will be considered using the slightly anionic complexes of HEDTC, with the more significantly charged complexes of CDTA then being used to apply the ANN procedures.

Conclusions

The migration behaviour and the overall resolution of analytes in MEKC can be modelled with ANNs. Migration behaviour of individual metal complexes could be modelled accurately using an ANN with three or more hidden neurons, but modelling of seven metal complexes simultaneously required seven hidden neurons. A new optimisation procedure based on a combination of experimental design and ANN was proposed and for a MEKC separation of seven metal–HEDTC complexes and eight metal–CDTA complexes it

Acknowledgements

A travel grant for J.H. from the Australian Department of Industry, Science and Tourism is gratefully acknowledged.

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¹: On leave at the University of Tasmania.

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Artificial neural networks for computer-aided modelling and optimisation in micellar electrokinetic chromatography

Abstract

Introduction

Section snippets

Theory of ANNs

Data description and computation

Results and discussion

Conclusions

Acknowledgements

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J. Chromatogr. A

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J. Chromatogr. A

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