Chromatographic fingerprint-based analysis of extracts of green tea, lemon balm and linden: I. Development of global retention models without the use of standards.

We report here the improvement of a procedure to obtain global models, able to describe the retention behaviour of several sample components simultaneously. The reported global models include parameters that account for the general effects of column and solvent on retention and are common for all components, whereas other parameters are specific of each sample component. These models are fitted by alternate regression and offer a prediction performance comparable to individual retention models. The approach is suitable to samples of natural products including a large number of components in extremely diverse concentrations and in the absence of standards. Guidelines are given for the successful development of sample-oriented experimental designs (i.e. adapted to the elution of the components of the natural products), constituted by multi-linear gradients. These designs also facilitate peak tracking. The model proposed by Neue and Kuss to describe the retention was found to yield the best predictions. The approach is applied to the extracts of samples of green tea, lemon balm and linden, yielding excellent predictions of retention for selected components.

Multi-scale optimisation vs. genetic algorithms in the gradient separation of diuretics by reversed-phase liquid chromatography.

Multi-linear gradients are a convenient solution to get separation of complex samples by modulating carefully the gradient slope, in order to accomplish the local selectivity needs for each particular solute cluster. These gradients can be designed by trial-and-error according to the chromatographer experience, but this strategy becomes quickly inappropriate for complex separations. More evolved solutions imply the sequential construction of multi-segmented gradients. However, this strategy discards part of the search space in each step of the construction and, again, cannot deal properly with very complex samples. When the complexity is too large, the only valid alternative for finding the best gradient is the use of global search methods, such as genetic algorithms (GAs). Recently, a new global approach where the level of detail is increased along the search has been proposed, namely Multi-scale optimisation (MSO). In this strategy, cubic splines are applied to build intermediate curves to define any arbitrary solvent variation function. Subdivision schemes are used to generate the cubic splines and control their level of detail. The search was subjected to a number of restrictions, such as avoiding long elution and favouring a balanced peak distribution. The aim of this work is evaluating and comparing the results of GAs and MSO. Both approaches were tested with a set of 14 diuretics and probenecid, eluted with acetonitrile-water mixtures using a C18 column. Satisfactory baseline resolution was obtained with an analysis time of 15-16 min. We found that GAs optimisation offered results equivalent to those provided by MSO, when the penalisation parameters were included in the cost function.

Enhancement in the computation of gradient retention times in liquid chromatography using root-finding methods.

Gradient elution may provide adequate separations within acceptably short times in a single run, by gradually increasing the elution speed. Similarly to isocratic elution, chromatograms can be predicted under any experimental condition, through strategies based on retention models. The most usual approach implies solving an integral equation (i.e., the fundamental equation of gradient elution), which has an analytical solution only for certain combinations of retention model and gradient programme. This limitation can be overcome by using numerical integration, which is a universal approach although at the cost of longer computation times. In this work, several alternatives to improve the performance in the resolution of the integral equation are explored, which can be especially useful with multi-linear gradients. For this purpose, the application of several root-finding methods that include the Newton's and bisection searches is explored in three frameworks: isolated predictions, regression modelling problems using gradient training sets, and optimisation of multi-linear gradients. Significant reductions of computation times were obtained. The substitution of non-integrable retention models by Tchebyshev polynomial approximations, which are pre-calculated before solving the integral equation in optimisation problems, is also investigated.

Gradient design for liquid chromatography using multi-scale optimization.

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 κ, an optimization problem is solved with Nκ ≈ 2κ variables that are used to build the gradients. The Nκ 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 κ 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.

Assisted baseline subtraction in complex chromatograms using the BEADS algorithm.

The data processing step of complex signals in high-performance liquid chromatography may constitute a bottleneck to obtain significant information from chromatograms. Data pre-processing should be preferably done with little (or no) user supervision, for a maximal benefit and highest speed. In this work, a tool for the configuration of a state-of-the-art baseline subtraction algorithm, called BEADS (Baseline Estimation And Denoising using Sparsity) is developed and verified. A quality criterion based on the measurement of the autocorrelation level was designed to select the most suitable working parameters to obtain the best baseline. The use of a log transformation of the signal attenuated artifacts associated to a large disparity in signal size between sample constituents. Conventional BEADS makes use of trial-and-error strategies to set up the working parameters, which makes the process slow and inconsistent. This constitutes a major drawback in its successful application. In contrast, the assisted BEADS simplifies the setup, shortens the processing time and makes the baseline subtraction more reliable. The assisted algorithm was tested on several complex chromatograms corresponding to extracts of medicinal herbs analysed with acetonitrile-water gradients, and a mixture of sulphonamides eluted with acetonitrile gradients in the presence of the non-ionic surfactant Brij-35 under micellar conditions.