Experimental determination of pore shapes using phase retrieval from q-space NMR diffraction

TL;DR

This paper introduces a phase retrieval method in q-space NMR diffusion imaging to reconstruct arbitrary pore shapes without direct phase measurements, validated through simulations and experiments.

Contribution

It develops a novel phase retrieval algorithm for NMR pore imaging that simplifies experimental procedures and enables shape reconstruction of complex pores.

Findings

Successful phase retrieval from simulated data with noise

Validation with phantom experiments using hyperpolarized xenon gas

Reconstruction of arbitrary pore shapes without prior shape knowledge

Abstract

This paper presents a novel approach on solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method, which allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical q-space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here, the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.