Mathematical chromatography solves the cocktail party effect in mixtures using 2D spectra and PARAFAC

The cocktail party effect in analytical chemistry refers to the ability to measure a complex mixture of analytes and to resolve the signals from a single analyte. We describe a new approach that we have coined mathematical chromatography, where data from complex spectra are resolved into pure-analyte information by so-called three-way modeling. Three-way analysis requires the addition of an extra dimension to the signals being acquired. Here, as an example, mathematical chromatography is applied to a series of diffusion-edited 2D NMR spectra of mixtures of glucose, maltose and maltotriose to demonstrate that it is possible to identify and to resolve individual components in highly overlapping 2D NMR spectra.