Localization regime in diffusion NMR: theory and experiments

Nicolas Moutal (1) , Kerstin Demberg (2, 3) , Denis S Grebenkov (1) , Tristan Anselm Kuder (2)

1 LPMC - Laboratoire de physique de la matière condensée
2 DKFZ - German Cancer Research Center - Deutsches Krebsforschungszentrum [Heidelberg]
3 Universität Heidelberg [Heidelberg] = Heidelberg University

In this work we investigate the emergence of the localization regime for diffusion in various geometries: inside slabs, inside cylinders and around 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. Our 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.

Mots clés: Localization regime; High gradients; PGSE

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]; Biophysique [physics.bio-ph]; Chimie-Physique [physics.chem-ph]; Physique Numérique [physics.comp-ph]; Analyse de données, Statistiques et Probabilités [physics.data-an]

Nicolas Moutal, Kerstin Demberg, Denis S Grebenkov, Tristan Anselm Kuder. Localization regime in diffusion NMR: theory and experiments. Journal of Magnetic Resonance, In press, 305, pp.162-174. ⟨10.1016/j.jmr.2019.06.016⟩. ⟨hal-02343853⟩