Orthogonal separations: Comparison of orthogonality metrics by statistical analysis

Area of Science:

• Analytical Chemistry
• Chromatography
• Chemometrics

Background:

• Two-dimensional (2D) chromatography is a powerful separation technique.
• Assessing the orthogonality of 2D separations is crucial for method development and data interpretation.
• Existing orthogonality metrics (OMs) vary in their applicability and effectiveness.

Purpose of the Study:

• To evaluate a diverse set of twenty OMs for their ability to assess 2D chromatogram quality.
• To identify OMs that correlate well with expert subjective evaluations of chromatogram quality.
• To propose an optimized criterion for defining and selecting optimal column pairs in 2D chromatography.

Main Methods:

• Calculated twenty OMs from 47 experimental 2D chromatograms across three datasets.
• Utilized cross-correlation and principal component analysis (PCA) to analyze OM relationships and data variance.
• Correlated OMs with subjective quality grades assigned by nine chromatography experts.

Main Results:

• Specific OMs clustered within families (nearest neighbor, correlation coefficients, information theory).
• No single OM consistently explained data variance or outperformed others across all chromatograms.
• Product OMs, especially those combining global (convex hull relative area) and local (box-counting fractal dimension) metrics, showed strong correlation with expert grades.
• Expert evaluations showed high consistency for extreme quality chromatograms but increased uncertainty for average ones.

Conclusions:

• A novel definition of chromatographic orthogonality based on maximizing OM products is proposed.
• The product of global and local OMs provides a reliable method for selecting the "best" column pairs for 2D chromatography.
• This approach enhances the objective assessment of 2D separation quality.