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.

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.

Temperature and concentration calibration of aqueous polyvinylpyrrolidone (PVP) solutions for isotropic diffusion MRI phantoms.

To use the "apparent diffusion coefficient" (Dapp) as a quantitative imaging parameter, well-suited test fluids are essential. In this study, the previously proposed aqueous solutions of polyvinylpyrrolidone (PVP) were examined and temperature calibrations were obtained. For example, at a temperature of 20°C, Dapp ranged from 1.594 (95% CI: 1.593, 1.595) µm2/ms to 0.3326 (95% CI: 0. 3304, 0.3348) µm2/ms for PVP-concentrations ranging from 10% (w/w) to 50% (w/w) using K30 polymer lengths. The temperature dependence of Dapp was found to be so strong that a negligence seems not advisable. The temperature dependence is descriptively modelled by an exponential function exp(c2 (T - 20°C)) and the determined c2 values are reported, which can be used for temperature calibration. For example, we find the value 0.02952 K-1 for 30% (w/w) PVP-concentration and K30 polymer length. In general, aqueous PVP solutions were found to be suitable to produce easily applicable and reliable Dapp-phantoms.

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

Diffusion pore imaging is an extension of diffusion-weighted nuclear magnetic resonance imaging enabling the direct measurement of the shape of arbitrarily formed, closed pores by probing diffusion restrictions using the motion of spin-bearing particles. Examples of such pores comprise cells in biological tissue or oil containing cavities in porous rocks. All pores contained in the measurement volume contribute to one reconstructed image, which reduces the problem of vanishing signal at increasing resolution present in conventional magnetic resonance imaging. It has been previously experimentally demonstrated that pore imaging using a combination of a long and a narrow magnetic field gradient pulse is feasible. In this work, an experimental verification is presented showing that pores can be imaged using short gradient pulses only. Experiments were carried out using hyperpolarized xenon gas in well-defined pores. The phase required for pore image reconstruction was retrieved from double diffusion encoded (DDE) measurements, while the magnitude could either be obtained from DDE signals or classical diffusion measurements with single encoding. The occurring image artifacts caused by restrictions of the gradient system, insufficient diffusion time, and by the phase reconstruction approach were investigated. Employing short gradient pulses only is advantageous compared to the initial long-narrow approach due to a more flexible sequence design when omitting the long gradient and due to faster convergence to the diffusion long-time limit, which may enable application to larger pores.