Nuclear magnetic resonance diffusion pore imaging: Experimental phase detection by double diffusion encoding

Diffusion pore imaging in the presence of extraporal water

Diffusion-weighted imaging (DWI) is a powerful, non-invasive tool which is widely used in clinical routine. Mostly, apparent diffusion coefficient maps are acquired, which cannot be related directly to cellular structure. More recently it was shown that DWI is able to reconstruct pore shapes using a specialized magnetic field gradient scheme so that cell size distributions may be obtained. So far, artificial systems have been used for experimental demonstration without extraporal signal components and relatively low gradient amplitudes. The aim of this study was to investigate the feasibility of diffusion pore imaging in the presence of extraporal fluids and to develop correction methods for the effects arising from extraporal signal contributions. Monte Carlo simulations and validation experiments on a 14.1 T NMR spectrometer equipped with a dedicated diffusion probe head were performed. Both by using a filter gradient approach suppressing extraporal signal components as well as by using post-processing methods relying on the Gaussian phase approximation, it was possible to reconstruct pore space functions in the presence of extraporal fluids with little to no deviations from the expectations. These results may be a significant step towards application of diffusion pore imaging to biological samples.

Stimulated echo double diffusion encoded imaging of closed pores: Influence and removal of unbalanced terms

Nuclear magnetic resonance (NMR) diffusion pore imaging has been proposed to study the shape of arbitrary closed pores filled with an NMR-detectable medium by use of nonclassical diffusion encoding schemes. Potential applications can be found in biomedical imaging and porous media research. When studying non-point-symmetric pores, NMR signals with nonvanishing imaginary parts arise containing the pore shape information, which is lost for classical diffusion encoding schemes. Key limitations are the required high magnetic field gradient amplitudes and T2 relaxation while approaching the diffusion long-time limit. To benefit from the slower T1 decay, we demonstrate the feasibility of diffusion pore imaging with stimulated echoes using Monte Carlo simulations and experiments with hyperpolarized xenon-129 gas in well-defined geometries and show that the necessary complex-valued signals can be acquired. Analytical derivation of the stimulated echo double diffusion encoded signal was performed to investigate the effect of the additionally arising undesired terms on the complex phase information. These terms correspond to signals arising for spin-echo sequences with unbalanced gradients. For most possible applications, the unbalanced terms can be neglected. If non-negligible, selection of the appropriate signal component using a phase cycling scheme was demonstrated experimentally. Using stimulated echoes may be a step towards application of diffusion pore imaging to larger pores with gradient amplitudes available today in preclinical systems.

Nano-metering of Solvated Biomolecules Or Nanoparticles from Water Self-Diffusivity in Bio-inspired Nanopores

Taking inspiration from the structure of diatom algae frustules and motivated by the need for new detecting strategies for emerging nanopollutants in water, we analyze the potential of nanoporous silica tablets as metering devices for the concentration of biomolecules or nanoparticles in water. The concept relies on the different diffusion behavior that water molecules exhibit in bulk and nanoconfined conditions, e.g., in nanopores. In this latter situation, the self-diffusion coefficient of water reduces according to the geometry and surface properties of the pore and to the concentration of suspended biomolecules or nanoparticles in the pore, as extensively demonstrated in a previous study. Thus, for a given pore-liquid system, the self-diffusivity of water in nanopores filled with biomolecules or nanoparticles provides an indirect measure of their concentration. Using molecular dynamics and previous results from the literature, we demonstrate the correlation between the self-diffusion coefficient of water in silica nanopores and the concentration of proteins or nanoparticles contained therein. Finally, we estimate the time required for the nanoparticles to fill the nanopores, in order to assess the practical feasibility of the overall nano-metering protocol. Results show that the proposed approach may represent an alternative method for assessing the concentration of some classes of nanopollutants or biomolecules in water.

Localization regime in diffusion NMR: Theory and experiments

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

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

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that 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.