Diffusion-diffusion correlation spectroscopy in macroscopic anisotropic systems

Diffusion-Diffusion COrrelation SpectroscopY (DDCOSY) [1] was introduced to reveal local anisotropy through the observation of spin dynamics in macroscopically isotropic (powder-like) systems, by tracing molecular displacements in different spatial directions (typically in subsequent time intervals). While the displacement correlation tensor in the two time intervals has been explored in general [2] , its impacts on DDCOSY has not been studied so far. Furthermore, sDDCOSY (short-DDCOSY) was suggested as a variant of DDCOSY [3], which measures the two displacements instantaneously. While there is no displacement correlation tensor for sDDCOSY, the cross terms may impact on experimental results in a similar way.

In this work, we investigate the cross terms and displacement correlation tensor, their behavior in isotropic samples and develop means for suppressing or isolating their influences on final correlation results. We support our study by simulations using multiple correlation function [4] and random walk techniques in a three-dimensional confining domain. Furthermore, experiments on phantoms demonstrate the ability of our approach to study even macroscopically anisotropic systems, such as polymetric solutions, fibrous tissues and heterogeneous rocks. Moreover, the similarity of sDDCOSY and diffusion tensor imaging (DTI) [5] leads to the opportunity to obtain fractional anisotropy averaged over the entire sample via sDDCOSY experiments.