Impact of sample dimensionality on orthogonality metrics in comprehensive two-dimensional separations

Orthogonality is a key parameter in the evaluation of the performance of a 2D chromatography-based separation system. Two different perspectives on orthogonality are determined: the extent of the separation space utilized (global orthogonality) and the uniformity of the coverage of the separation space (local orthogonality). This work aims to elucidate the impact of sample dimensionality (the number of separation processes involved) on orthogonality evaluation through the use of descriptors from seven different algorithms utilizing mutually different properties of a chromatogram: Pearson correlation, conditional entropy, asterisk equations, convex hull, arithmetic mean (AN) and harmonic mean of the nearest neighbor, and geometric surface coverage (SC). Artificial chromatograms generated in silico and real GC × GC separations of diesel, plasma, and urine were used for the evaluation of orthogonality. The sample dimensionality has a deep effect on the orthogonality results of all approaches. The SC algorithm emerged as the best descriptor of local orthogonality samples of both low and high dimensionality, the AN algorithm on the global orthogonality of low-dimensionality samples. However, in the case of samples of high dimensionality, AN consistently indicated just the exploitation of the whole separation space; therefore, only local orthogonality is optimized by means of SC. Since no approach was able to monitor both global and local orthogonality as a single value, a new descriptor, ASCA, was developed. It combines the best global (AN) and local (SC) orthogonality algorithms by averaging, giving the same importance to data spread and crowding. ASCA thus provides the best estimation of orthogonality.