Statistical Methods for the Description and Prediction of Orthogonality for Two-Dimensional Liquid Chromatography (2D-LC)


Benjamin Place and Catherine Rimmer


With the development of commercially available instrumentation for two-dimensional liquid chromatography (2D-LC), recent research has been focused on the creation of analytical methods that exploit the analytical strength of the technique. 2D-LC methods are useful for the separation and quantification of compounds that are typically co-elute under a single dimension of separation. The focus of the current research at NIST is on method development for comprehensive 2D-LC for the analysis of Standard Reference Materials. In order to optimize the analytical performance of a 2D-LC method, the separation mechanism of each dimension must be as different as possible. The term ‘orthogonal’ is used to describe the degree of independence that each dimension of separation has from the other dimensions. Various statistical approaches have been used by other researchers in order to describe the orthogonality of a multidimensional chromatographic system, but there has yet to be consensus on what statistical parameter is best. These methods include geometric, correlation, and other chemometric tests that evaluate the differences and similarities between the retention times of multiple compounds in two dimensions.

To assist in the advancement of 2D-LC methods, as well as aid in interlaboratory comparisons of 2D-LC systems, a standard practice for the determination and prediction of orthogonality is necessary. An application, using the statistical program R, was developed to calculate the various orthogonal parameters of a list of retention times for a training set of compounds over separation methods that include different column stationary phase and mobile phase chemistries. From compound training sets used on an in-laboratory HPLC system, as well as other published training sets, the evaluation of the various statistical approaches will be presented. Each orthogonality statistic well describes the differences of retention times within a 2D-LC system, although most statistical parameters describe different aspects of orthogonality (e.g., linear correlation, clustering, and outliers). This finding suggests that there may not be a single statistic that embraces all aspects of orthogonality and therefore a combination of statistical tests may be best suited to define the orthogonality of a multidimensional chromatographic system. In addition, the impact of chromatographic parameters (e.g., mobile phase pH, mobile phase organic modifier, and stationary phase chemistry) on the orthogonality of a two-dimensional system will be discussed.