The localization regime in a nutshell.

Area of Science:

• Physics
• Chemistry
• Materials Science

Background:

• High diffusion-sensitizing magnetic field gradients are increasingly used for microstructure characterization.
• Spin-echo signals in these conditions deviate from Gaussian behavior, necessitating advanced interpretation models.

Purpose of the Study:

• To demonstrate that non-Gaussian signal behavior is a universal feature of the Bloch-Torrey equation under high gradients.
• To describe the localization regime and its origin in symmetry breaking.
• To compare this regime with other diffusion NMR regimes.

Main Methods:

• Theoretical analysis of the Bloch-Torrey equation under high magnetic field gradients.
• Description of the emerging localization regime and its symmetry-breaking origin.
• Comparison of non-Gaussian signal decay with established diffusion NMR regimes.

Main Results:

• The non-Gaussian behavior of spin-echo signals is a generic, universal feature of the Bloch-Torrey equation.
• A localization regime emerges at high extended gradients due to symmetry breaking at reflecting boundaries.
• Limitations of perturbative techniques are highlighted, advocating for non-perturbative approaches.

Conclusions:

• Non-Gaussian signal decay under high gradients is a fundamental aspect of diffusion MRI.
• Understanding this behavior is crucial for accurate microstructural characterization.
• Non-perturbative methods may enable novel diffusion MRI modalities.