Application of artificial neural networks for gradient elution retention modelling in ion chromatography

Gradient elution in ion chromatography (IC) offers several advantages: total analysis time can be significantly reduced, overall resolution of a mixture can be increased, peak shape can be improved (less tailing) and effective sensitivity can be increased (because there is little variation in peak shape). More importantly, it provides the maximum resolution per time unit. The aim of this work was the development of a suitable artificial neural network (ANN) gradient elution retention model that can be used in a variety of applications for method development and retention modelling of inorganic anions in IC. Multilayer perceptron ANNs were used to model the retention behaviour of fluoride, chloride, nitrite, sulphate, bromide, nitrate and phosphate in relation to the starting time of gradient elution and the slope of the linear gradient elution curve. The advantage of the developed model is the application of an optimized two-phase training algorithm that enables the researcher to make use of the advantages of first- and second-order training algorithms in one training procedure. This results in better predictive ability, with less time required for the calculations. The number of hidden layer neurons and experimental data points used for the training set were optimized in terms of obtaining a precise and accurate retention model with respect to minimization of unnecessary experimentation and time needed for the calculation procedures. This study shows that developed, ANNs are the method of first choice for retention modelling of inorganic anions in IC.     

Prediction of peptide retention times in reversed-phases high-performance liquid chromatography during linear gradient elution

The retention behavior of 100 peptides was studied during high-performance liquid chromatography on a C₁₈ column using aqueous trifluoroacetic acid as the mobile phase and acetonitrile as the mobile phase modifier in a linear gradient elution system. Retention times of the peptides were linearly related to the logarithm of the sum of Rekker's constants (R.F. Rekker, The Hydrophobic Fragmental Constant, Elsevier, Amsterdam, 1977, p. 301) for the constituent amino acid. Assuming this relationship, the best fit constants for this system were computed by non-linear multiple regression analysis. Using the new constants, it is possible to predict retention times for a wide variety of peptides at any slope of linear gradient, if the amino acid composition is known. It also enables accurate prediction of the retention time of peptides, whose amino acid composition in not known, after an analytical run with an alternate gradient.     

Optimization of artificial neural networks used for retention modelling in ion chromatography

The aim of this work is the development of an artificial neural network model, which can be generalized and used in a variety of applications for retention modelling in ion chromatography. Influences of eluent flow-rate and concentration of eluent anion (OH-) on separation of seven inorganic anions (fluoride, chloride, nitrite, sulfate, bromide, nitrate, and phosphate) were investigated. Parallel prediction of retention times of seven inorganic anions by using one artificial neural network was applied. MATLAB Neural Networks ToolBox was not adequate for application to retention modelling in this particular case. Therefore the authors adopted it for retention modelling by programming in MATLAB metalanguage. The following routines were written; the division of experimental data set on training and test set; selection of data for training and test set; Dixon's outlier test; retraining procedure routine; calculations of relative error. A three-layer feed forward neural network trained with a Levenberg-Marquardt batch error back propagation algorithm has been used to model ion chromatographic retention mechanisms. The advantage of applied batch training methodology is the significant increase in speed of calculation of algorithms in comparison with delta rule training methodology. The technique of experimental data selection for training set was used allowing improvement of artificial neural network prediction power. Experimental design space was divided into 8-32 subspaces depending on number of experimental data points used for training set. The number of hidden layer nodes, the number of iteration steps and the number of experimental data points used for training set were optimized. This study presents the very fast (300 iteration steps) and very accurate (relative error of 0.88%) retention model, obtained by using a small amount of experimental data (16 experimental data points in training set). This indicates that the method of choice for retention modelling in ion chromatography is the artificial neural network.     

Prediction of the chromatographic signal in gradient elution ion chromatography

This study describes the development of a signal prediction model in gradient elution ion chromatography. The proposed model is based on a retention model and generalized logistic peak shape function which guarantees simplicity of the model and its easy implementation in method development process. Extensive analysis of the model predictive ability has been performed for ion chromatographic determination of bromate, nitrite, bromide, iodide, and perchlorate, using KOH solutions as eluent. The developed model shows good predictive ability (average relative error of gradient predictions 1.94%). The developed model offers short calculation times as well as low experimental effort (only nine isocratic runs are used for modeling).     

Non-linear calibration functions in ion chromatography with suppressed conductivity detection using hydroxide eluents

The linearity of calibration curves in ion chromatography with suppressed conductivity detection using hydroxide eluents was investigated. Theoretical calibration curves were derived for strong electrolytes and weak monobasic acids and the results compared with experimental data. At low concentrations up to 1 micromol l(-1) the autoprotolysis of water induces left-curved calibration functions even for strong electrolytes like nitrate. The experimental data are best described by a quadratic function, the differences between linear and quadratic regression being up to 10%. At higher concentrations the calibration curves for strong electrolytes are linear. Due to incomplete dissociation, the calibration curves for weak mono- and dibasic acids show a right curvature. Thus, depending on the analyte and the concentration range of interest, analysts should carefully choose between a linear and a quadratic regression function.     

Prediction of protein retention at gradient elution conditions in ion-exchange chromatography.

This work presents a prediction procedure for protein retention in ion-exchange chromatography, where two linear gradient experiments of different length give the protein retention time at other linear gradients. The procedure predicts the retention time of early and late eluting proteins with similar precision and predictions by extrapolation deviate approximately 3% or less from the experimental retention times. By using the ionic strength, this procedure predicts protein retention times obtained with divalent ions in the eluent more accurately than a well-established procedure that uses the protein co-ion concentration.     

梯度淋洗离子色谱法测定烟草中的苹果酸、柠檬酸和阴离子

研究了用10mmol／L的NaOH溶液超声波提取,离子色谱法同时检测烟草中有机酸和阴离子的分析方法。采用美国Dionex公司DX-500型离子色谱仪,用H2O、5mmol／L NaOH和100mmol／L NaOH梯度淋洗,流速为1．5mL／min,成功地测定了烟草中的苹果酸、柠檬酸、NO3^-1、NO2^-、Cl^-、SO4^2-等成份。这些成分在检测条件下有良好的线性关系,相关系数r^2〉0．99,检出限为0．005～0．2mg／L,相对标准偏差为0．52％。9．14％,回收率为93．5％～107．7％;实验表明该方法具有分析时间短、线性范围宽、灵敏和准确、简单快速、试剂用量少等优点。     

Critical comparison of retention models for the optimisation of the separation of anions in ion chromatography: II. Suppressed anion chromatography using carbonate eluents

Seven theoretical retention models, namely the linear solvent strength model (using the dominant equilibrium approach and competing ion effective charge approach), the dual eluent species model, the Kuwamoto model, the extended dual eluent species model, the multiple species eluent/analyte model and the empirical end-points model, were used to describe the retention behaviour of anions in suppressed ion chromatography (IC). An extensive set of experimental retention data was gathered for 24 anions (fluoride, formate, bromate, chloride, hexanesulfonate, bromide, chlorate, nitrate, iodide, thiocyanate, perchlorate, sulfite, succinate, sulfate, tartrate, selenate, oxalate, tungstate, phthalate, molybdate, chromate, thiosulfate and phosphate) on a Dionex AS4A-SC column using carbonate eluents of varying concentration and HCO₃⁻:CO₃²⁻ ratios. Statistical comparison of the predicted and experimentally obtained retention factors showed that the performance of the theoretical models improved with the complexity of the model. However the empirical model (in which a linear relationship is assumed between the logarithm of retention factor and the logarithm of eluent strength, but the slope is determined empirically) gave the most consistent performance across the widest range of anions. The empirical end-points model was also shown to be the most satisfactory model due to its low knowledge requirements and easy solution. Compared with non-suppressed IC (see Part I), the retention behaviour in suppressed IC was found to be easier to model by all retention models.     

On-line pH modification of carbonate eluents using an electrolytic potassium hydroxide generator for ion chromatography

Classical gradient elution, based on the application of a gradient pump used for mixing two or more prepared eluent components in pre-determined concentrations, was replaced by a chromatography system equipped with an isocratic pump and an electrolytic KOH generator. The isocratic pump delivered a constant concentration eluent composed of pure hydrogencarbonate solution. Carbonate ions, the main component of carbonate/hydrogencarbonate-based eluents, were formed by titration of hydrogencarbonate with KOH formed on-line in the electrolytic KOH generator. By changing the concentration of electrolytically-generated KOH, the eluent composition could be changed from pure hydrogencarbonate to a carbonate/hydrogencarbonate buffer, and finally to a carbonate/hydroxide-based eluent. The described system was tested to achieve pH-based changes of retention behavior of phosphate under constant inflow eluent composition conditions.     

梯度淋洗-电导抑制离子色谱法同时测定果汁中26种有机酸和阴离子

通过对色谱柱类型、流速、柱温、pH值、淋洗液浓度等影响因素的研究,建立了多级梯度淋洗-电导抑制离子色谱同时测定果汁中26种有机酸和阴离子的分析方法。结果表明,当流速为1.00 mL/min、柱温为30℃、pH值为5.5~6.8时,26种组分的测定结果更准确。26种组分在0.02~10.0 mg/L范围内具有良好的线性关系（r均大于0.995）,检出限（S/N=3）为0.17~52.0 μg/L;在0.20~2.00 mg/L添加水平下的回收率为85.58%~108.86%,相对标准偏差为0.15%~7.65%（n=6）。该方法简便快速、灵敏度好、准确度高,适于果汁中26种组分的痕量分析。     

Prediction of programmed-temperature retention values of naphthas by artificial neural networks

It is proposed for the first time a method of prediction of the programmed-temperature retention times of components of naphthas in capillary gas chromatography using artificial neural networks. People are used to predict the programmed-temperature retention time using many formulas such as the integral formula, which requires that four parameters must be determined by calculation or experiments. However the results obtained by the formula are not so good to meet the demand of industry. In order to predict retention time accurately and conveniently, artificial neural networks using five-fold cross-validation and leave-20%-out methods have been applied. Only two parameters: density and isothermal retention index were used as input vectors. The average RMS error for predicted values of five different networks was 0.18, whereas the RMS error of predictions by the integral formula was 0.69. Obviously, the predictions by neural networks were much better than predictions by the formula, and neural networks need fewer parameters than the formula. So neural networks can successfully and conveniently solve the problem of predictions of programmed-temperature retention times, and provide useful data for analysis of naphthas in petrochemical industry.     

Evaluation of separation in gradient elution ion chromatography by combining several retention models and objective functions

In this work, three different methods for modeling of gradient retention were combined with several optimization objective functions in order to find the most appropriate combination to be applied in ion chromatography method development. The system studied was a set of seven inorganic anions (fluoride, chloride, nitrite, sulfate, bromide, nitrate, and phosphate) with a KOH eluent. The retention modeling methods tested were multilayer perceptron artificial neural network (MLP-ANN), radial-basis function artificial neural network (RBF-ANN), and retention model based on transfer of data from isocratic to gradient elution mode. It was shown that MLP retention model in combination with the objective function based on normalized retention difference product was the most adequate tool for optimization purposes.     

Optimisation of the separation of herbicides by linear gradient high performance liquid chromatography utilising artificial neural networks

An artificial neural network (ANN) was employed to model the chromatographic response surface for the linear gradient separation of 10 herbicides that are commonly detected in storm run-off water in agricultural catchments. The herbicides (dicamba, simazine, 2,4-D, MCPA, triclopyr, atrazine, diuron, clomazone, bensulfuron-methyl and metolachlor) were separated using reverse phase high performance liquid chromatography and detected with a photodiode array detector. The ANN was trained using the pH of the mobile phase and the slope of the acetonitrile/water gradient as input variables. A total of nine experiments were required to generate sufficient data to train the ANN to accurately describe the retention times of each of the herbicides within a defined experimental space of mobile phase pH range 3.0-4.8 and linear gradient slope 1-4% acetonitrile/min. The modelled chromatographic response surface was then used to determine the optimum separation within the experimental space. This approach allowed the rapid determination of experimental conditions for baseline resolution of all 10 herbicides. Illustrative examples of determination of these components in Milli-Q water, Sydney mains water and natural water samples spiked at 0.5-1 μg/L are shown. Recoveries were over 70% for solid-phase extraction using Waters Oasis^® HLB 6 cm³ cartridges.     

Prediction of peptide retention times in normal-phase liquid chromatography with only a single gradient run.

Previous studies of peptide separation by normal-phase liquid chromatography have shown a linear relationship between the logarithm of the capacity factor and the logarithm of the volume fraction of modifier in the mobile phase. This permitted the use of a model to predict isocratic and gradient retention times based on data obtained by two initial gradient runs. In the present study, chromatographic behavior of 25 peptides in normal-phase liquid chromatography with isocratic elution have been studied and a linear relationship between the slope (S) and intercept [log k(0)] was obtained. This relationship was combined with the algorithm of prediction reported in the previous paper. The prediction of peptide retention times with only a single experimental gradient retention data was investigated.     

Multi-criteria decision making development of ion chromatographic method for determination of inorganic anions in oilfield waters based on artificial neural networks retention model

This paper describes the development of ad hoc methodology for determination of inorganic anions in oilfield water, since their composition often significantly differs from the average (concentration of components and/or matrix). Therefore, fast and reliable method development has to be performed in order to ensure the monitoring of desired properties under new conditions. The method development was based on computer assisted multi-criteria decision making strategy. The used criteria were: maximal value of objective functions used, maximal robustness of the separation method, minimal analysis time, and maximal retention distance between two nearest components. Artificial neural networks were used for modeling of anion retention. The reliability of developed method was extensively tested by the validation of performance characteristics. Based on validation results, the developed method shows satisfactory performance characteristics, proving the successful application of computer assisted methodology in the described case study.