A simple optimization strategy based on Rs-minimum and information theory of chromatography

Summary A simple optimization method based on the well-known Rs-minimum method and on the information theory of FUMI Φ is proposed. Resolution (Rs), peak area and height (or width) are the only parameters necessary for the calculation of the information Φ and information flow ϑ. The most precise analysis can be selected as the chromatogram having maximal ϑ. Mobile phase composition, column length, flow rate, detection wavelength, amount of internal standard, etc. can be optimized by this method.     

Total chromatographic optimization (TOCO) I. Simultaneous optimization of many variables in liquid chromatography

Summary The following chromatographic variables are totally optimized based on the recently developed information theory of optimization: mobile phase composition, column length, flow rate, wavelength, and the amount of internal standard. The optimal internal standard is selected from among six candidates. Two types of optimal conditions (- and -optimals) are proposed: the -optimal is defined as the most precise analysis (the maximal ) while the -optimal is the most efficient (rapid) analysis (the maximal ). The observation times for the determination of an antipyretics mixture (three components) in liquid chromatography are ca. 50 s for the -optimal and ca. 8 min for the -optimal. The reliability of the - and -optimals is verified by experiments.     

Total chromatographic optimization (TOCO) II. Precision and efficiency of analysis

Summary A chromatographic system set at an operating condition takes its own precision and efficiency which are numerically described by the information called FUMI and the information flow , respectively. Optimization for a variable such as mobile phase composition draws a line in the - space. This paper demonstrates that optimization of different variables displays different patterns of lines in the - space. The variables examined here are mobile phase composition, column length, flow rate (velocity) and detection wavelength (or the amount of internal standard). Clear difference in the analytical roles of the variables can be known from the - plots.     

Information theory of optimization in chromatography: Optimum peak separation and dependency on peak area

Summary If a peak (j=2) moves along the time axis of a chromatogram with no change in the position ₁ of the other peak (j=1) or in areas A₁ and A₂, the optimum separation, _s, is defined as the resolution R_s which provides the maximum information, called FUMI, among all possible positions ₂ of the peak (₂₁). This paper demonstrates that optimum separation, _s, of chromatographic peaks critically depends on the peak areas. As the area ratio A₂/A₁ of overlapped peaks increases, greater separation (higher resolution R_s) is needed to obtain maximum information. The quantitative relationship between _s and A₂/A₁ is derived by computer simulation.     

Mathematical structure of chromatographic optimization based on information theory: II. Analytical role of chromatographic variables

Summary The influence of variables Z (mobile phase composition X, column length L, etc.) on chromatographic analysis is studied in terms of the two separate stages of the whole optimization process. In the first stage, peak separation is the central concern and the resolution R_s can be related to Shannon information _j of peak where C is a coefficient (>0). In the second stage, only chromatograms with no peak overlap are considered and R_s is not connected with _j. The analytical role of Z is evaluated by comparing the signs and magnitudes of the derivatives of the information, _j, and its transmission rate, _j, with respect to Z in both stages.     

Mathematical structure of chromatographic optimization based on information theory: I. Effect of mobile phase composition on precision

Summary The influence of mobile phase composition X on the precision of liquid-chromatographic analysis is interpreted in terms of the derivate of the mutual information for peak j with respect to X, d_j/dX. The sign and magnitude of d_j/dX depend on the operational conditions of X or on the details of chromatograms (e.g., resolutions R_s), but d_j/dX always indicates the direction of X toward more information _j. The sensitivity function s_j(=1/(k_j+1)) is examined on the basis of information theory. Optimization is formulated as a nonlinear programming problem.     

An expert system for the optimization of columns,operating conditions and instrumentation for high-pressure liquid chromatography

Summary Given the mobile and the stationary phase and values for the physical parameters such as temperature and pH, a separation can be optimized by varying the so-calledchromatographic parameters. These include the column dimensions, particle size, operating conditions (e.g. flow rate, attenuation) and instrumentation (e.g. detector cell, time constant). Optimization of the chromatographic parameters implies finding the best possible set of values, which we define as yielding (i) sufficient separation and (ii) sufficient sensitivity in (iii) the shortest possible time. Finding the best possible conditions (the global optimum) is very difficult for chromatographers in practice.An expert system is described that allows chromatographic optimization to be performed for isocratic separations. An initial chromatogram is required to consult the system. In return, the system provides a complete set of chromatographic parameters, which represents the global optimum within the limits set by the required resolution and signal-to-noise ratio specified by the user. The tolerated flow and pressure ranges, the volume of the available detector cells and the time constant of the detection system are constraints during the optimization. A separate module of the system concerns the sample preparation for pharmaceutical formulations in solid dosages and aqueous solutions.Prototype expert systems have been successfully implemented in the expert-system shell Knowledge Craft on a MicroVAX workstation.     

An expert system for the selection of criteria for selectivity optimization in high-pressure liquid chromatography

Summary Systematic procedures for the optimization of chromatographic selectivity require objective criteria to characterize the quality of separation in a chromatogram. Numerous criteria have been suggested. Different criteria yield different results and the choice will depend on a large number of factors. It is genuinely difficult to select the most suitable criterion in a particular situation. For these reasons, an expert system has been developed to assist chromatographers in the selection of optimization criteria. A structured representation of the required knowledge and its implementation in an expert-system shell are presented in this paper.     

Liquid chromatography of gramicidin

Summary A simple, selective method is described for separation of more than 10 gramicidin components on Spherisorb ODS B, 5 μm,250×4.6 mm I.D. column, maintained at 50°C. The mobile phase comprised methanol-water (71:29) at a flow rate of 1.0 mL min⁻¹. Detection was by UV at 282 nm. Valine gramicidins A, B and C were very well separated from the isoleucine gramicidins A, B and C. Four new gramicidin components were also resolved and their structures determined by liquid chromatography/ mass spectrometry. The names 10-methionine valine gramicidin C, 4-methionine valine gramicidin A, valine gramicidin A hydroxypropyl and isoleucine gramicidin A hydroxypropyl were proposed. Robustness of the liquid chromatography method was evaluated by performing a full factorial design experiment. The method also showed good repeatability, linearity and sensitivity.     

Resolution optimization in micellar electrokinetic chromatography using two different overlapping resolution mapping schemes

Summary An appropriate optimization strategy should be able to find good separation conditions in the shortest time with only a few experiments, to assure the baseline-separation of all components. In this paper, the use of two optimization schemes has been studied using 10 substituted benzene as model compounds. The triangular overlapping resolution mapping (ORM) scheme and cubic ORM scheme were compared to optimize the three relevant parameters-the concentration of surfactant, the concentration of HP-β-cyclodextrin and pH. By conducting experiments that span the maximum working range of the system, overall optimum conditions for separation can be obtained. To confirm the validity of the two ORM schemes, additional experiments using the predicted optimum conditions were performed. Finally, 10 substituted benzene compounds were completely separated within 20 min by both sets of optimized conditions.     

Optimizing separations in reversed-phase liquid chromatography by varying pH and solvent composition

Summary An interpretive optimization procedure in which pH can be one of the variables is presented with the emphasis on optimizing separations. When varying the pH in reversed-phase liquid chromatography the retention of ionogenic solutes will change. Thus, the selectivity between ionogenic and neutral solutes or between ionogenic solutes mutually can be optimized. However, pH also greatly affects the efficiency (plate count) and peak shape (asymmetry). Optimum selectivity (i.e. large differences in retention times) may be observed under conditions where peaks are broad and asymmetrical. Thus, it is essential to simultaneously consider retention, peak width and peak shape and their effects on separation (effective resolution) in pH-optimization studies. A procedure in which this is done is presented and applied to optimizing the separation of a synthetic mixture of selected pharmaceuticals. After initial experiments to establish the parameter space (boundaries for pH and binary methanol — water composition), twelve experiments are performed according to a 3×4 experimental design. At each loaction the retention, peak height, peak area and peak symmetry are recorded for each solute. These data are then used to build models for each of the four characteristics and for each solute. From this set of models the response surface, describing the quality of separation as a function of pH and composition, can be calculated. A variety of optimization criteria (quantifying quality of separation) can be used. The optimum corresponds to the highest point on the response surface.     

Preparative liquid chromatography

Summary Historically, liquid chromatography has been a preparative technique. Its applications have been limited, however, until a decade ago. The needs of modern chemical, pharmaceutical and biochemical industries have motivated this period of phenomenal growth which is being witnessed now. Novel packing materials, new packing technologies, and advancements in instrumentation and process technologies have appeared in rapid succession. Instruments using columns with diameters ranging from a few inches to a few feet, can be packed with efficiencies comparable or better than analytical columns having the same packing material. This permits the development of new applications covering a wide variety of problems. The empirical approach, followed until recently for the development of new applications, is being improved by insights derived from a better understanding of the theory of large concentration chromatography. With increased computer power and a greater comprehension of the theoretical aspects, a fundamental approach to design and optimization of the operating parameters is being developed. Investigation of the components of the cost of industrial production is also in its early stages. Historical trends, theoretical treatments, column technologies, operating modes and guidelines for optimization will be discussed and reviewed.     

Combined Kalman filtering and steepest descent minimization for quantitative analysis of unresolved misaligned chromatographic peaks. The resolution of alternariol and altenuisol mycotoxins in mixtures by HPLC

Summary The potential of a computational approach for the quantitative resolution of seriously overlapping chromatographic peaks when there is loss of collinearity between the pure component peaks and the mixture peak has been explored. The program makes iterative use of the Kalman filter algorithm for resolving the mixture peak with the component peaks aligned according to some values of the position parameters, and of a steepest descent minimization procedure to find the optimal alignment. This combined procedure has been applied to the quantitive resolution of the HPLC chromatograms of alternariol and altenuisol mycotoxins in synthetic mixtures and in real samples.     

Optimization of stepwise gradient elution in reversed-phase chromatography

Summary Equations describing multi-step gradient elution with a mobile phase of constant composition in each step were derived. These equations useful for calculating the retention volumes in both gradient HPLC and TLC were derived on the basis of the relationship between the isocratic capacity factor and the volume fraction of the organic modifier. The validity of the equations was experimentally verified in a LiChrosorbRP-18-water/methanol system for 11 methyl- and chlorobenzenes and phenols. A satisfactory agreement between the theoretical and experimental k′ values was found.     

Time optimization for routine separations,using high-speed microbore HPLC

Summary Algorithms for the time optimization of an HPLC separation are presented. Resolution, column performance, extra-column variance, capacity factor, and column length are incorporated into these algorithms. Extracolumn variance for a high-speed microbore system (1 mm i. d. column) was assessed using 2nd moment variance and a non-linear extrapolation of tubing length to zero. Extra-column variance, as a function of flowrate, was incorporated into the reduced operating curve of column performance. The use of empirical correction factors for column reproducibility and homogeneity are suggested. Cutting to an optimum length did not degrade column performance. These algorithms were applied to the optimization of a microbore assay for theophylline, in a simple xanthine mixture. Resulting total analysis times were reduced to 10seconds per sample, at a flowrate of 700l/min.     

Two-dimensional liquid chromatography of peptides: An optimization strategy

Summary An optimization strategy for the separation of a small number of peptides from a complex biological sample by two-dimensional liquid chromatography is presented. Ion-exchange chromatography is followed by reversed-phase separation. The ion-exchange separation is performed with a step gradient which admits a high sample load and simplifies instrumentation. The reversed-phase separation complements the first dimension with a different retention mechanism and higher resolution by linear gradient elution.Chromatographic theory is combined with experimental design to find separation conditions, for both dimensions, that allow the fastest gradient in the second dimension, giving short separation time, low detection limits and high load capacity. This is illustrated by the separation of a peptide from rat brain tissue, with a simple off-line arrangement. The strategy presented is useful in both analytical and preparative applications, and is widely applicable as it does not rely on special instrumentation or extensive knowledge of the sample.Dedicated to Professor Leslie S. Ettre on the occasion of his 70th birthday.     

Computerized optimization of gradient elution conditions with ternary solvent mobile phases in RPLC

Summary In this work, an optimization procedure for gradient RPLC separation, using ternary mobile phases, is described. This procedure requires eight preliminary experiments in gradient elution mode to predict the retention surface for each solute over the whole triangular space. This is followed by computerized calculations to determine the best ternary gradient elution profile with respect to both selectivity and analysis time. The efficiency of this procedure from the point of view of rapidity and of accuracy, is illustrated for the specific separation of twelve phenyl urea herbicides.     

Optimization of throughput in preparative column luquid chromatography by column overloading and partial fractionation of the effluent

Summary The criteria for the optimization of preparative chromatography are sample throughput and product purity. It is shown for column liquid chromatography that the throughput has been maximized for a given purity by column overloading and appropriate fractionation. The size and position of the fraction must be determined by chemical analysis, since overlapping peaks under overloading conditions are usually distorted compared to the peaks of the same amounts of pure compounds. With overloading of the column larger particles can be used as column packings without reduction of the separation effect.     

Retention and column efficiency in reversed phase liquid chromatography as a function of pH for optimization purposes

Summary The effects of pH on both the solute retention and the peak shape of ionogenic compounds are studied in order to propose accurate models for pH optimization purposes. Several mathematical models (theoretical and empirical) for describing the variation of the retention factor versus pH are compared within different pH ranges. Limits of such models used for optimizing the pH by requiring only 3 preliminary experimental runs, are discussed in terms of deviations (≤±5%) of predicted retention times from experimental retention times. An original procedure is developed for selecting the most convenient retention model, from a given set of three retention data. This set is also applied to modeling the variation of both peak width and peak asymmetry with mobile phase pH conditions. Such a procedure is demonstrated as helpful for the separation of ionogenic solutes by considering mobile phase pH as an additional variable that can be useful during optimization procedures.