Assessment of the orthogonality in two-dimensional separation systems using criteria defined by the maximal information coefficient

A novel method based on the maximal information coefficient (MIC) is developed to assess the orthogonality of comprehensive two-dimensional separation systems. The proposed method is based on a modification of Marriott's method, which was previously reported in 2013. Marriott's method relies on the calculation of two separate parameters. The first term is Cpert which defines the peak coverage percent in separation space, and the second is Cpeaks which corresponds to 2-D distribution correlation of the peaks. Marriott's method for estimating the values of Cpeaks is based on the calculation of the coefficient of determination (R2) between the retention indices of the peaks. Herein, we present some examples where R2 is an inefficient way to estimate the values of Cpeaks. The results in this work illustrate that when there are either functional or non-functional local dependencies between the distributions of the peaks, R2 values fail to thoroughly estimate the values of Cpeaks. We proposed using the MIC instead of R2 to estimate the values of Cpeaks for orthogonality calculations. Simulations of comprehensive two-dimensional gas chromatograms were performed using the Abraham solvation parameter model in order to generate examples for orthogonality assessment. The results indicate that the suggested modifications in this work correct the shortcomings of Marriott's model, and the proposed equation accurately measures the column dependencies in 2-D separation systems.