Localization regime in diffusion NMR: Theory and experiments

Nicolas Moutal; Kerstin Demberg; Denis S Grebenkov; Tristan Anselm Kuder

doi:10.1016/j.jmr.2019.06.016

Localization regime in diffusion NMR: Theory and experiments

J Magn Reson. 2019 Aug:305:162-174. doi: 10.1016/j.jmr.2019.06.016. Epub 2019 Jul 2.

Authors

Nicolas Moutal¹, Kerstin Demberg², Denis S Grebenkov³, Tristan Anselm Kuder⁴

Affiliations

¹ Laboratoire de Physique de la Matière Condensée, Ecole Polytechnique, CNRS, IP Paris, 91128 Palaiseau, France. Electronic address: nicolas.moutal@polytechnique.edu.
² Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany; Faculty of Physics and Astronomy, Heidelberg University, Heidelberg, Germany.
³ Laboratoire de Physique de la Matière Condensée, Ecole Polytechnique, CNRS, IP Paris, 91128 Palaiseau, France. Electronic address: denis.grebenkov@polytechnique.edu.
⁴ Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany.

PMID: 31295631
DOI: 10.1016/j.jmr.2019.06.016

Abstract

In this work we investigate the emergence of the localization regime for diffusion NMR in various geometries: inside slabs, inside cylinders and outside rods arranged on a square array. At high gradients, the transverse magnetization is strongly attenuated in the bulk, whereas the macroscopic signal is formed by the remaining magnetization localized near boundaries of the sample. As a consequence, the signal is particularly sensitive to the microstructure. The theoretical analysis relies on recent mathematical advances on the study of the Bloch-Torrey equation. Experiments were conducted with hyperpolarized xenon-129 gas in 3D-printed phantoms and show an excellent agreement with numerical simulations and theoretical predictions. Our mathematical arguments and experimental evidence indicate that the localization regime with a stretched-exponential decay of the macroscopic signal is a generic feature of diffusion NMR that can be observed at moderately high gradients in most NMR scanners.

Keywords: High gradients; Localization regime; PGSE.