The localization regime in a nutshell

TL;DR

This paper explains the universal non-Gaussian signal behavior in high-gradient diffusion MRI, linking it to boundary symmetry breaking and advocating for non-perturbative analysis to improve microstructural imaging.

Contribution

It provides a rigorous description of the localization regime in diffusion MRI, highlighting its origin and limitations of traditional methods, and suggests new imaging approaches.

Findings

Non-Gaussian signal decay is a universal feature of the Bloch-Torrey equation.

Localization regime arises from symmetry breaking at reflecting boundaries.

Limitations of perturbative techniques are identified, promoting non-perturbative methods.

Abstract

High diffusion-sensitizing magnetic field gradients have been more and more often applied nowadays to achieve a better characterization of the microstructure. As the resulting spin-echo signal significantly deviates from the conventional Gaussian form, various models have been employed to interpret these deviations and to relate them with the microstructural properties of a sample. In this paper, we argue that the non-Gaussian behavior of the signal is a generic universal feature of the Bloch-Torrey equation. We provide a simple yet rigorous description of the localization regime emerging at high extended gradients and identify its origin as a symmetry breaking at the reflecting boundary. We compare the consequent non-Gaussian signal decay to other diffusion NMR regimes such as slow-diffusion, motional-narrowing and diffusion-diffraction regimes. We emphasize limitations of conventional perturbative techniques and advocate for non-perturbative approaches which may pave a way to new imaging modalities in this field.