Improving the visualization of the Pareto-optimal front for the multi-response optimization of chromatographic determinations

Abstract

The paper shows tools to visualize and more easily interpret the effect that some experimental factors may exert on analytical responses of interest when optimization of several responses is needed. It is based on an adaptation of the parallel coordinate plot, a tool for graphical representation of points in multidimensional spaces that, theoretically and contrary to the usual Cartesian plots, does not have limits in the dimension of the points being depicted. The joint use of the Pareto-optimal solutions and their visualization allows a deeper knowledge about the problem at hand as well as the wise selection of the conditions of experimental factors for achieving specific goals about the responses. Although the methodology is for a general use, the procedure, its interpretation and usefulness is shown with several analytical cases in chromatography. The first one refers to the experimental conditions to obtain simultaneously the maximum allowable area for both the peak of the malachite green and its metabolite leucomalachite green in fish by liquid chromatography with tandem mass spectrometry detection (LC–MS/MS). The second one is about the simultaneous determination of steroid hormones estrone and 17-α-ethinylestradiol by gas chromatography–mass spectrometry (GC/MS). In the last case, the chromatographic separation by GC/MS of the diastereoisomers, α- and β-estradiol is needed taking into account that these hormones have the same mass fragments.