Orthogonal separations: Comparison of orthogonality metrics by statistical analysis

Twenty orthogonality metrics (OMs) derived from convex hull, information theory, fractal dimension, correlation coefficients, nearest neighbor distances and bin-density techniques were calculated from a diverse group of 47 experimental two-dimensional (2D) chromatograms. These chromatograms comprise two datasets; one dataset is a collection of 2D chromatograms from Peter Carr's laboratory at the University of Minnesota, and the other dataset is based on pairs of one-dimensional chromatograms previously published by Martin Gilar and coworkers (Waters Corp.). The chromatograms were pooled to make a third or combined dataset. Cross-correlation results suggest that specific OMs are correlated within families of nearest neighbor methods, correlation coefficients and the information theory methods. Principal component analysis of the OMs show that none of the OMs stands out as clearly better at explaining the data variance than any another OM. Principal component analysis of individual chromatograms shows that different OMs favor certain chromatograms. The chromatograms exhibit a range of quality, as subjectively graded by nine experts experienced in 2D chromatography. The subjective (grading) evaluations were taken at two intervals per expert and demonstrated excellent consistency for each expert. Excellent agreement for both very good and very bad chromatograms was seen across the range of experts. However, evaluation uncertainty increased for chromatograms that were judged as average to mediocre. The grades were converted to numbers (percentages) for numerical computations. The percentages were correlated with OMs to establish good OMs for evaluating the quality of 2D chromatograms. Certain metrics correlate better than others. However, these results are not consistent across all chromatograms examined. Most of the nearest neighbor methods were observed to correlate poorly with the percentages. However, one method, devised by Clark and Evans, appeared to work moderately well. Products of OMs show better correlation with the percentages than do single OMs. Product OMs that utilize one discretized metric paired with the convex hull relative area, which measures overall zone occupancy, perform well in determining the "best" chromatogram among both datasets and the combined dataset. A definition of chromatographic orthogonality is suggested that is based on maximizing the values of OMs or OM products. This optimization criterion suggests using the product of a global metric that measures the utilization of separation space (e.g., the convex hull relative area) and a local metric that measures peak spacing (e.g., the box-counting fractal dimension). The "best" column pairs for 2D chromatography are chosen by the product of these OMs.