Impact of sample dimensionality on orthogonality metrics in comprehensive two-dimensional separations Jaroslava J  a  cov  a a, b , Al  zb  eta Gardlo a, b , Jean-Marie D. Dimandja c , Tom  a  s Adam a, b , David Friedecký a, b, * a Laboratory of Metabolomics, Faculty of Medicine and Dentistry, Palacký University Olomouc, Hn evotínsk a 5, 779 00, Olomouc, Czech Republic b Department of Clinical Chemistry, University Hospital Olomouc, I. P. Pavlova 6, 779 00, Olomouc, Czech Republic c School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Dr. NW, 30313, Atlanta, United States highlights graphical abstract  The impact of sample dimensionality on orthogonality was evaluated.  Models generated in silico containing 2500 peaks and real separation ex- amples were used.  The best local and global orthogo- nality descriptors were identified.  ASCA, a combined local and global orthogonality descriptor, was defined and evaluated. article info Article history: Received 8 December 2018 Received in revised form 4 March 2019 Accepted 8 March 2019 Available online 12 March 2019 Keywords: Required dimensionality Global orthogonality Local orthogonality Combined descriptors Arithmetic mean of nearest neighbor Geometric surface coverage abstract 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 sep- aration 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 Abbreviations: (%O), orthogonality values in percentages; (2D), two-dimensional; (AE), asterisk equations approach; (AFID), alkali flame ionization detector; (AN), arithmetic mean of nearest neighbor approach; (ASCA), new combined orthogonality descriptor; (CE), conditional entropy approach; (ECD), electron capture detector; (EIC), extracted ion chromatogram; (GC  GC), two-dimensional gas chromatography; (GC  GC/MS), two-dimensional gas chromatography coupled to mass spectrometry; (HD), high-dimensional(ity); (HN), harmonic mean of nearest neighbor approach; (CH), convex hull; (LD), low-dimensional(ity); (m/z), mass to charge ratio; (MA), modeling approach; (MS), mass spectrometry; (NN), nearest neighbor approach; (O), orthogonality; (PC), Pearson correlation; (PCA), principal component analysis; (SC), geometric surface coverage; (TIC), total ion chromatogram; (WOSEL), scaling approach. * Corresponding author. Department of Clinical Chemistry, University Hospital Olomouc, I. P. Pavlova 6, 779 00, Olomouc, Czech Republic. E-mail address: david.friedecky@upol.cz (D. Friedecký). Contents lists available at ScienceDirect Analytica Chimica Acta journal homepage: www.elsevier.com/locate/aca https://doi.org/10.1016/j.aca.2019.03.018 0003-2670/© 2019 Elsevier B.V. All rights reserved. Analytica Chimica Acta 1064 (2019) 138e149