Comment on "Magnetic resonance imaging by synergistic diffusion-diffraction patterns"

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.

1D and 2D diffusion pore imaging on a preclinical MR system using adaptive rephasing: Feasibility and pulse sequence comparison

Diffusion pore imaging (DPI) has recently been proposed as a means to acquire images of the average pore shape in an image voxel or region of interest. The highly asymmetric gradient scheme of its sequence makes it substantially demanding in terms of the hardware of the NMR system. The aim of this work is to show the feasibility of DPI on a preclinical 9.4T animal scanner. Using water-filled capillaries with an inner radius of 10μm, four different variants of the DPI sequence were compared in 1D and 2D measurements. The pulse sequences applied cover the basic implementation using one long and one temporally narrow gradient pulse, a CPMG-like variant with multiple refocusing RF pulses as well as two variants splitting up the long gradient and distributing it on either side of the refocusing pulse. Substantial differences between the methods were found in terms of signal-to-noise ratio, contrast, blurring, deviations from the expected results and sensitivity to gradient imperfections. Each of the tested sequences was found to produce characteristic gradient mismatches dependent on the absolute value, direction and sign of the applied q-value. Read gradients were applied to compensate these mismatches translating them into time shifts, which enabled 1D DPI yielding capillary radius estimations within the tolerances specified by the manufacturer. For a successful DPI application in 2D, a novel gradient amplitude adaption scheme was implemented to correct for the occurring time shifts. Using this adaption, higher conformity to the expected pore shape, reduced blurring and enhanced contrast were achieved. Images of the phantom's pore shape could be acquired with a nominal resolution of 2.2μm.

NMR-based diffusion lattice imaging

Nuclear magnetic resonance (NMR) diffusion experiments are widely employed as they yield information about structures hindering the diffusion process, e.g., about cell membranes. While it has been shown in recent articles that these experiments can be used to determine the shape of closed pores averaged over a volume of interest, it is still an open question how much information can be gained in open well-connected systems. In this theoretical work, it is shown that the full structure information of connected periodic systems is accessible. To this end, the so-called "SEquential Rephasing by Pulsed field-gradient Encoding N Time intervals" (SERPENT) sequence is used, which employs several diffusion encoding gradient pulses with different amplitudes. Two two-dimensional solid matrices that are surrounded by an NMR-visible medium are considered: a hexagonal lattice of cylinders and a rectangular lattice of isosceles triangles.

Effects of pore-size and shape distributions on diffusion pore imaging by nuclear magnetic resonance

In medical imaging and porous media research, NMR diffusion measurements are extensively used to investigate the structure of diffusion restrictions such as cell membranes. Recently, several methods have been proposed to unambiguously determine the shape of arbitrary closed pores or cells filled with an NMR-visible medium by diffusion experiments. The first approach uses a combination of a long and a short diffusion-weighting gradient pulse, while the other techniques employ short gradient pulses only. While the eventual aim of these methods is to determine pore-size and shape distributions, the focus has been so far on identical pores. Thus, the aim of this work is to investigate the ability of these different methods to resolve pore-size and orientation distributions. Simulations were performed comparing the various pore imaging techniques employing different distributions of pore size and orientation and varying timing parameters. The long-narrow gradient profile is most advantageous to investigate pore distributions, because average pore images can be directly obtained. The short-gradient methods suppress larger pores or induce a considerable blurring. Moreover, pore-shape-specific artifacts occur; for example, the central part of a distribution of cylinders may be largely underestimated. Depending on the actual pore distribution, short-gradient methods may nonetheless yield good approximations of the average pore shape. Furthermore, the application of short-gradient methods can be advantageous to differentiate whether pore-size distributions or intensity distributions, e.g., due to surface relaxation, are predominant.

Magnetic-resonance pore imaging of nonsymmetric microscopic pore shapes

Imaging of the microstructure of porous media such as biological tissue or porous solids is of high interest in health science and technology, engineering and material science. Magnetic resonance pore imaging (MRPI) is a recent technique based on nuclear magnetic resonance (NMR) which allows us to acquire images of the average pore shape in a given sample. Here we provide details on the experimental design, challenges, and requirements of MRPI, including its calibration procedures. Utilizing a laser-machined phantom sample, we present images of microscopic pores with a hemiequilateral triangular shape even in the presence of NMR relaxation effects at the pore walls. We therefore show that MRPI is applicable to porous samples without a priori knowledge about their pore shape and symmetry. Furthermore, we introduce "MRPI mapping," which combines MRPI with conventional magnetic resonance imaging (MRI). This enables one to resolve microscopic pore sizes and shapes spatially, thus expanding the application of MRPI to samples with heterogeneous distributions of pores.

Diffusion pore imaging by hyperpolarized xenon-129 nuclear magnetic resonance

While NMR diffusion measurements are widely used to derive parameters indirectly related to the microstructure of biological tissues and porous media, direct imaging of pore shapes would be of high interest. Here we demonstrate experimentally that complexly shaped closed pores can be imaged by diffusion acquisitions. Collecting the signal from the whole sample eliminates the problem of vanishing signal at increasing resolution of conventional NMR imaging. This approach may be used to noninvasively obtain structural information inaccessible so far such as pore or cell shapes, cell density, or axon integrity.

Shemesh, Westin, and Cohen reply

A Reply to the comment by Valerij G. Kiselev and Dmitry S. Novikov.