Diffusion MRI/NMR at high gradients: challenges and perspectives

TL;DR

This paper explores the challenges and recent advances in understanding high-gradient diffusion MRI/NMR signals, emphasizing the spectral analysis of the Bloch-Torrey operator and its implications for microstructure probing.

Contribution

It introduces a spectral decomposition approach using the Bloch-Torrey operator to analyze signal decay at high gradients, revealing new microstructural insights.

Findings

Signal decay follows a stretched-exponential form at high gradients.

Eigenmodes are localized near boundary points, enhancing boundary sensitivity.

Extracellular space signals deviate from Gaussian behavior at high gradients.

Abstract

We discuss some challenges and recent advances in understanding the macroscopic signal formation at high non-narrow magnetic field gradients at which both the narrow pulse and the Gaussian phase approximations fail. The transverse magnetization and the resulting signal are fully determined by the spectral properties of the non-selfadjoint Bloch-Torrey operator which incorporates the microstructure of a sample through boundary conditions. Since the spectrum of this operator is known to be discrete for isolated pores, the signal can be decomposed onto the eigenmodes of the operator that yields the stretched-exponential decay at high gradients and long times. Moreover, the eigenmodes are localized near specific boundary points that makes the signal more sensitive to the boundaries and thus opens new ways of probing the microstructure. We argue that this behavior is much more general than earlier believed, and should also be valid for unbounded and multi-compartmental domains. In particular, the signal from the extracellular space is not Gaussian at high gradients, in contrast to the common assumption of standard fitting models.