Dissimilar or orthogonal reversed-phase chromatographic systems: A comparison of selection techniques

Developing an analytical separation procedure for an unknown mixture is a challenging issue. An important example is the separation and quantification of a new drug and its impurities. One approach to start method development is the screening of the mixture on dissimilar chromatographic systems, i.e. systems with large selectivity differences. After screening, the most suited system is retained for further method development. In a step prior to such strategy dissimilar chromatographic systems need to be selected. In this paper the performance of different chemometric selection approaches, described in the literature, was visually evaluated and compared. Additionally, orthogonal projection approach (OPA) was tested as another potential selection method. All techniques, including the OPA method, were able to select (a set of) dissimilar chromatographic systems and many similarities between the selections were observed. However, the Kennard and Stone algorithm performed best in selecting the most dissimilar systems in the earliest steps of the selection procedure. The generalized pairwise correlation method (GPCM) and the auto-associative multivariate regression trees (AAMRT) were also performing well. OPA and weighted pair group method using arithmetic averages (WPGMA) are less preferable.     

Determining orthogonal chromatographic systems prior to the development of methods to characterise impurities in drug substances

To define starting conditions for the development of methods to separate impurities from the active substance and from each other in drugs with an unknown impurity profile, the parallel application of generic orthogonal chromatographic systems could be useful. The possibilities to define orthogonal chromatographic systems were examined by calculation of the correlation coefficients between retention factors k for a set of 68 drugs on 11 systems, by visual evaluation of the selectivity differences, by using principal component analysis, by drawing color maps and evaluating dendrograms. A zirconia-based stationary phase coated with a polybutadiene (PBD) polymer and three silica-based phases (base-deactivated, polar-embedded and monolithic) were used. Besides the stationary phase, the influence of pH and of organic modifier, on the selectivity of a system were evaluated. The dendrograms of hierarchical clusters were found good aids to assess orthogonality of chromatographic systems. The PBD-zirconia phase/methanol/pH 2.5 system is found most orthogonal towards several silica-based systems, e.g. a base-deactivated C16 -amide silica/methanol/pH 2.5 system. The orthogonality was validated using cross-validation, and two other validation sets, i.e. a set of non-ionizable solutes and a mixture of a drug and its impurities.     

Quick prediction of the retention of solutes in 13 thin layer chromatographic screening systems on silica gel by classification and regression trees

The use of classification and regression trees (CART) was studied in a quantitative structure-retention relationship (QSRR) context to predict the retention in 13 thin layer chromatographic screening systems on a silica gel, where large datasets of interlaboratory determined retention are available. The response (dependent variable) was the rate mobility (RM) factor, while a set of atomic contributions and functional substituent counts was used as an explanatory dataset. The trees were investigated against optimal complexity (number of the leaves) by external validation and internal crossvalidation. Their predictive performance is slightly lower than full atomic contribution model, but the main advantage is the simplicity. The retention prediction with the proposed trees can be done without computer or even pocket calculator.     

Multivariate linear regression with missing values

This contribution presents and discusses an efficient algorithm for multivariate linear regression analysis of data sets with missing values. The algorithm is based on the insight that multivariate linear regression can be formulated as a set of individual univariate linear regressions. All available information is used and the calculations are explicit. The only restriction is that the independent variable matrix has to be non-singular. There is no need for imputation of interpolated or otherwise guessed values which require subsequent iterative refinement.     

Orthogonal signal correction, wavelet analysis, and multivariate calibration of complicated process fluorescence data

In this paper, multivariate calibration of complicated process fluorescence data is presented. Two data sets related to the production of white sugar are investigated. The first data set comprises 106 observations and 571 spectral variables, and the second data set 268 observations and 3997 spectral variables. In both applications, a single response, ash content, is modelled and predicted as a function of the spectral variables. Both data sets contain certain features making multivariate calibration efforts non-trivial. The objective is to show how principal component analysis (PCA) and partial least squares (PLS) regression can be used to overview the data sets and to establish predictively sound regression models. It is shown how a recently developed technique for signal filtering, orthogonal signal correction (OSC), can be applied in multivariate calibration to enhance predictive power. In addition, signal compression is tested on the larger data set using wavelet analysis. It is demonstrated that a compression down to 4% of the original matrix size — in the variable direction — is possible without loss of predictive power. It is concluded that the combination of OSC for pre-processing and wavelet analysis for compression of spectral data is promising for future use.     

A Matrix Based Indexing HDMR method for multivariate data modelling

Modelling multivariate data of real life problems from engineering, chemistry, physics, mathematics or other related sciences, in which function values are known only at arbitrarily distributed points of the problem domain, is an important and complicated issue since there exist mathematical and computational complexities in the analytical structure construction process coming from the multivariance. The Plain High Dimensional Model Representation (HDMR) method expresses a multivariate problem in terms of less-variate problems. In this work, a Matrix Based Indexing HDMR method is developed to make the Plain HDMR philosophy employable for the multivariate data partitioning process. This new method will have the ability of dealing with less-variate data sets by partitioning the given data set into univariate, bivariate and trivariate data sets. Interpolating these partitioned data sets will construct an approximate analytical structure as the model of the given multivariate data modelling problem.     

Dissimilar chromatographic systems to indicate and identify antioxidants from Mallotus species

The genus of Mallotus contains several species commonly used as traditional medicines in oriental countries. A data set containing 39 Mallotus samples, differing in species, cultivation conditions, harvest season and/or part of the plant was used to develop fingerprints on two dissimilar chromatographic systems. An exploratory analysis with principal component analysis (PCA) was performed on both data sets individually. The results were also combined to obtain additional information on the unknown samples included in the data set. Furthermore, the antioxidant activity of the samples was measured and modelled as a function of the fingerprints using the orthogonal projections to latent structures (O-PLS) technique. The regression coefficients of the models were studied to indicate the peaks potentially responsible for the antioxidant activity. The indicated peaks were analyzed and identified by HPLC coupled to mass spectrometry (HPLC-MS). Because of the complexity of biological samples, it was aspired to separate co-eluting components based on the significant difference in chromatographic selectivity on the dissimilar systems and consequently obtain additional, complementary information on the contribution of the individual components to the antioxidant activity. The results illustrate the potential use of dissimilar chromatographic systems. Several initially co-eluting compounds could be separated on the dissimilar system. The corresponding regression coefficients provided complementary information on the potential antioxidant activity of the separated compounds.     

Applications of maximum likelihood principal component analysis: incomplete data sets and calibration transfer

The application of a new method to the multivariate analysis of incomplete data sets is described. The new method, called maximum likelihood principal component analysis (MLPCA), is analogous to conventional principal component analysis (PCA), but incorporates measurement error variance information in the decomposition of multivariate data. Missing measurements can be handled in a reliable and simple manner by assigning large measurement uncertainties to them. The problem of missing data is pervasive in chemistry, and MLPCA is applied to three sets of experimental data to illustrate its utility. For exploratory data analysis, a data set from the analysis of archeological artifacts is used to show that the principal components extracted by MLPCA retain much of the original information even when a significant number of measurements are missing. Maximum likelihood projections of censored data can often preserve original clusters among the samples and can, through the propagation of error, indicate which samples are likely to be projected erroneously. To demonstrate its utility in modeling applications, MLPCA is also applied in the development of a model for chromatographic retention based on a data set which is only 80% complete. MLPCA can predict missing values and assign error estimates to these points. Finally, the problem of calibration transfer between instruments can be regarded as a missing data problem in which entire spectra are missing on the ‘slave’ instrument. Using NIR spectra obtained from two instruments, it is shown that spectra on the slave instrument can be predicted from a small subset of calibration transfer samples even if a different wavelength range is employed. Concentration prediction errors obtained by this approach were comparable to cross-validation errors obtained for the slave instrument when all spectra were available.     

A review of the main factors influencing the FT-IR-PLS abilities exemplified with petrochemical qualimetric applications

Quality control usually involves monitoring several variables directly related with industrial necessities using univariate tests. One powerful alternative is to link multivariate analytical techniques and multivariate chemometrics. In this way, Fourier Transform Infrared spectroscopy and Partial Least Squares regression are used to discuss and review several advantages and drawbacks encountered in using such combination in industrial facilities. Typical drawbacks are selection of data pretreatment, errors in reference methods, selection of calibration and validation sets and model-aging. This review is exemplified with petrochemical applications although other fields are also considered (mainly when dealing with data pretreatment).     

A review of the main factors influencing the FT-IR-PLS abilities exemplified with petrochemical qualimetric applications

Quality control usually involves monitoring several variables directly related with industrial necessities using univariate tests. One powerful alternative is to link multivariate analytical techniques and multivariate chemometrics. In this way, Fourier Transform Infrared spectroscopy and Partial Least Squares regression are used to discuss and review several advantages and drawbacks encountered in using such combination in industrial facilities. Typical drawbacks are selection of data pretreatment, errors in reference methods, selection of calibration and validation sets and model-aging. This review is exemplified with petrochemical applications although other fields are also considered (mainly when dealing with data pretreatment).     

Orthogonality and similarity within silica-based reversed-phased chromatographic systems

The starting point of this study was a current set of 32 chromatographic systems used to select initial conditions for method development to determine the impurity profile of a drug. The system exhibiting the best selectivity is then selected for further method development. In this current set eight silica-based phases are applied in conjunction with four mobile phases at different pH. In order to save time and resources, the possibilities for a meaningful subset selection were investigated. The most differing systems in terms of selectivity, in other words only the most orthogonal systems, need to be selected. Since the stationary phases are all silica-based, the selectivity differences are examined within a more homogeneous group than if, for instance, also zirconia- or polymer-based columns would be involved. To select the subset of systems also the best overall separation performances are taken into account. The selection is based both on the HPLC-DAD data of a generic set of 68 drugs, and on the LC-MS-DAD results for a mixture of 15 drugs, less different in structure. The orthogonality is evaluated using weighted-average-linkage dendrograms and color maps, both created from the Pearson-correlation coefficients r between normalized retention times r. The Derringer's desirability functions are applied to define the systems with the best overall separation performances. Proposals for different representative subsets of the initial 32 systems are made.     

Detection and quantification of cocoa butter equivalents in cocoa butter and plain chocolate by gas liquid chromatography of triacylglycerols

The development and in-house testing of a method for the detection and quantification of cocoa butter equivalents in cocoa butter and plain chocolate is described. A database consisting of the triacylglycerol profile of 74 genuine cocoa butter and 75 cocoa butter equivalent samples obtained by high-resolution capillary gas liquid chromatography was created, using a certified cocoa butter reference material (IRMM-801) for calibration purposes. Based on these data, a large number of cocoa butter/cocoa butter equivalent mixtures were arithmetically simulated. By subjecting the data set to various statistical tools, reliable models for both detection (univariate regression model) and quantification (multivariate model) were elaborated. Validation data sets consisting of a large number of samples (n = 4050 for detection, n = 1050 for quantification) were used to test the models. Excluding pure illipé fat samples from the data set, the detection limit was determined between 1 and 3% foreign fat in cocoa butter. Recalculated for a chocolate with a fat content of 30%, these figures are equal to 0.3-0.9% cocoa butter equivalent. For quantification, the average error for prediction was estimated to be 1.1% cocoa butter equivalent in cocoa butter, without prior knowledge of the materials used in the blend corresponding to 0.3% in chocolate (fat content 30%). The advantage of the approach is that by using IRMM-801 for calibration, the established mathematical decision rules can be transferred to every testing laboratory.     

Screening of macrocycles retention for microplanar analytical devices involving host-guest interactions and silica or octadecylsilica adsorbents

This paper reports planar chromatographic behavior and multivariate characterization of three types of macrocyclic compounds: cyclodextrins, calixarenes and macrocyclic antibiotics. Additionally two non-macrocyclic chemicals (estriol and pyrene) were analyzed as the reference retention markers. Target compounds were chromatographed using normal and reversed-phase systems and involving mono as well as binary water-organic liquids mobile phases based on methanol, ethanol and acetonitrile. Non-forced flow TLC/HPTLC elution was performed under isothermal (elevated temperature?=?303?K) and mobile phase vapor saturated conditions using 10?cm long glass plates positioned vertically inside temperature controlled Dewar type chambers. It is hoped that presented retention data, which were collected for the whole range of binary mobile phases compositions (0–100%) may be useful for designing of hybrid active layers for extraction, separation and detection systems involving host-guest interactions. Retention profiles were inspected using multivariate statistics (principal component analysis, PCA). Based on reported data various extraction and separation systems can be created where weak or strong interactions of macrocycles with chromatographic stationary phases or given micro device active supports should be expected. Particularly, studied macrocycles can be applied as selective additives for solid phase adsorption (SPE, SPME), microfluidic paper devices (μPAD) as well as micro-total analytical systems (μTAS), where bars formed active layers are fabricated.     

Optimisation of chromatographic separations by use of a chromatographic response function, empirical modelling and multivariate analysis

Summary The chiral separation of the drug substance R,S-oxybutynin chloride on a reversed phase HPLC system has been optimised by use of empirical modelling and multivariate analysis. The separation was characterised by a new chromatographic response function developed to modulate both quality of separation and retention time. The study includes a comparison between three different multivariate techniques (multi-layer feed-for-ward neural networks, multiple linear regression and partial least squares regression) of their capabilities to model the new chromatographic response function and predict its value for new experiments. It was indicated that the most accurate models were achieved with neural networks, although partial least squares regression could also be used to solve the problem since it gives the major directions for the optimal settings of the variables.