Chromatographic method verification by means of three-dimensional, multivariate visualization

Abstract

Using free-fatty-acid model systems, principal-component analysis as automated in Justice Innovations' Chrom Perfect and Echo Data's DataMax software was used to correlate, visualize, and verify the relationships of nine system-suitability parameters. Many-dimensional data were mapped by relaxing the usual 90° axes and by using non-orthogonal vectors. The arccosines of the correlation coefficients were used as the vector angles. Two types of matrices were non-orthogonally mapped: (1) chromatography system-suitability parameters as the vectors and chromatography components as the objects; (2) chromatography parameters for each component as the vectors and methods as the objects. The first type of matrix was found to be suitable for clustering similar chromatography parameters, for visualizing a single chromatogram, for comparing replicate results, and for verifying expected chromatography correlations. The second type of matrix had the same results as a chromatographic response function in that a chromatogram was reduced to a single value, or coordinate in the case of a non-orthogonal map. Practical applications include the visualization of multidetector, multiwavelength, multicolumn data. Two examples were demonstrated: (1) chromatography method evaluation by non-orthogonally mapping a 4 × 35 matrix representing resolution, theoretical plates, tailing factor, α, and capacity factor for a seven-component mixture; (2) identification of optimum concentration, time-course effects, and replicate reproducibility using a 180 × 6 matrix representing 180 multicomponent chromatograms. In each case, Echo Data's DataMax software was found to facilitate more rapid screening than currently possible by the use of computerized statistical analysis alone.