Mutual information concept for evaluation of separation quality in hyphenated chromatographic measurements

Abstract

A new method for the evaluation of separation quality in hyphenated chromatographic measurements based on the information-theoretic concept of mutual information (MI) is developed. The MI values for the purest spectra selected using the simple-to-use interactive self-modeling mixture analysis (SIMPLISMA) and orthogonal projection approach (OPA) methods are calculated according to the differential information entropy (Shannon entropy). To calculate the MI values for more than two variables, the Kozachenko–Leonenko (KL) estimation of the Shannon entropy is used. The MI values of the purest spectra can reliably reflect the degree of peak overlap in the chromatographic direction. Herein, the developed method is employed on different simulated and real GC-MS and HPLC-DAD datasets (i.e., chromatographic segments and chromatographic fingerprints) to evaluate the potential of this new method. Inspection of the results showed that minimization of MI values is a good criterion for comprehensive evaluation of separation quality in hyphenated chromatographic measurements and to reach to the best chromatographic separation. Additionally, the performance of this method is compared with the previously developed overlap index (OVI) criterion and classical univariate criteria, such as ΣR_s and ΠR_s, which showed an improvement in all cases. As demonstrated by simulated and real chromatographic data, the MI index gives not only a comprehensive criterion for evaluation of separation quality, but also provides reliable information for the purity assessment of compounds of interest. Furthermore, the MI index can be used as a reliable criterion for multivariate optimization of hyphenated chromatographic measurements.