Lipari-Szabo mapping: A graphical approach to Lipari-Szabo analysis of NMR relaxation data using reduced spectral density mapping

In this paper, we explore connections between the Lipari-Szabo formalism and reduced spectral density mapping, and show how spectral density estimates can be associated with Lipari-Szabo parameters via a simple geometric construction which we call Lipari-Szabo mapping. This relationship can be used to estimate Lipari-Szabo parameters from spectral density estimates without the need for nonlinear optimization, and to perform 'model selection' in a graphical manner. The Lipari-Szabo map also provides insight into the Lipari-Szabo model, and allows us to determine when a given set of experimental spectral densities are inconsistent with the Lipari-Szabo formalism. Practical applications of Lipari-Szabo mapping in conjunction with more traditional analysis methods are discussed.