Novel pore size-controlled, susceptibility matched, 3D-printed MRI phantoms

PURPOSE

We report the design concept and fabrication of MRI phantoms, containing blocks of aligned microcapillaires that can be stacked into larger arrays to construct diameter distribution phantoms or fractured, to create a "powder-averaged" emulsion of randomly oriented blocks for vetting or calibrating advanced MRI methods, that is, diffusion tensor imaging, AxCaliber MRI, MAP-MRI, and multiple pulsed field gradient or double diffusion-encoded microstructure imaging methods. The goal was to create a susceptibility-matched microscopically anisotropic but macroscopically isotropic phantom with a ground truth diameter that could be used to vet advanced diffusion methods for diameter determination in fibrous tissues.

METHODS

Two-photon polymerization, a novel three-dimensional printing method is used to fabricate blocks of capillaries. Double diffusion encoding methods were employed and analyzed to estimate the expected MRI diameter.

RESULTS

Susceptibility-matched microcapillary blocks or modules that can be assembled into large-scale MRI phantoms have been fabricated and measured using advanced diffusion methods, resulting in microscopic anisotropy and random orientation.

CONCLUSION

This phantom can vet and calibrate various advanced MRI methods and multiple pulsed field gradient or diffusion-encoded microstructure imaging methods. We demonstrated that two double diffusion encoding methods underestimated the ground truth diameter.

Correlating the Diffusion of Water to Performance in Model Reverse Osmosis Polyamides with Controlled Crosslink Densities

We systematically reduce the cross-link density of a PA network based on m-phenylene diamine by substituting a fraction of the trifunctional trimesoyl chloride cross-linking agent with a difunctional isophthaloyl analog that promotes chain extension, in order to elucidate robust design cues for improving the polyamide (PA) separation layer in reverse osmosis (RO) membranes for desalination. Thin films of these model PA networks are fully integrated into a composite membrane and evaluated in terms of their water flux and salt rejection. By incorporating 15 mol % of the difunctional chain extender, we reduce the cross-link density of the network by a factor of two, which leads to an 80 % increase in the free or unreacted amine content. The resulting swelling of the PA network in liquid water increases by a factor of two accompanied by a 30 % increase in the salt passage through the membrane. Surprisingly, this leads to a 30 % decrease in the overall permeance of water through the membrane. This conundrum is resolved by quantifying the microscopic diffusion coefficient of water inside the PA network with quasi-elastic neutron scattering. In the highest and lowest cross-link density networks, water shows strong signatures of confined diffusion. At short length scales, the water exhibits a translational diffusion that is consistent with the jump-diffusion mechanism. This translational diffusion coefficient is approximately five times slower in the lowest cross-linked density network, consistent with the reduced water permeance. This is interpreted as water molecules interacting more strongly with the increased free amine content. Over longer length scales the water diffusion is confined, exhibiting mobility that is independent of length scale. The length scales of confinement from the quasi-elastic neutron scattering experiments at which this transition from confined to translational diffusion occurs is on the order of (5 to 6) Å, consistent with complementary X-ray scattering, small angle neutron scattering, and positron annihilation lifetime spectroscopy measurements. The confinement appears to come from heterogeneities in the average inter-atomic distances, suggesting that diffusion occurs by water bouncing between chains and occasionally sticking to the polar functional groups. The results obtained here are compared with similar studies of water diffusion through both rigid porous silicates and ion exchange membranes, revealing robust design cues for engineering high-performance RO membranes.

A single-shot measurement of time-dependent diffusion over sub-millisecond timescales using static field gradient NMR

Time-dependent diffusion behavior is probed over sub-millisecond timescales in a single shot using a nuclear magnetic resonance static gradient time-incremented echo train acquisition (SG-TIETA) framework. The method extends the Carr-Purcell-Meiboom-Gill cycle under a static field gradient by discretely incrementing the π-pulse spacings to simultaneously avoid off-resonance effects and probe a range of timescales (50-500 µs). Pulse spacings are optimized based on a derived ruleset. The remaining effects of pulse inaccuracy are examined and found to be consistent across pure liquids of different diffusivities: water, decane, and octanol-1. A pulse accuracy correction is developed. Instantaneous diffusivity, Dinst(t), curves (i.e., half of the time derivative of the mean-squared displacement in the gradient direction) are recovered from pulse accuracy-corrected SG-TIETA decays using a model-free log-linear least squares inversion method validated by Monte Carlo simulations. A signal-averaged 1-min experiment is described. A flat Dinst(t) is measured on pure dodecamethylcyclohexasiloxane, whereas decreasing Dinst(t) is measured on yeast suspensions, consistent with the expected short-time Dinst(t) behavior for confining microstructural barriers on the order of micrometers.

Unexpected Diffusion Anisotropy of Carbon Dioxide in the Metal-Organic Framework Zn2(dobpdc)

Metal-organic frameworks are promising materials for energy-efficient gas separations, but little is known about the diffusion of adsorbates in materials featuring one-dimensional porosity at the nanoscale. An understanding of the interplay between framework structure and gas diffusion is crucial for the practical application of these materials as adsorbents or in mixed-matrix membranes, since the rate of gas diffusion within the adsorbent pores impacts the required size (and therefore cost) of the adsorbent column or membrane. Here, we investigate the diffusion of CO2 within the pores of Zn2(dobpdc) (dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) using pulsed field gradient (PFG) nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations. The residual chemical shift anisotropy for pore-confined CO2 allows PFG NMR measurements of self-diffusion in different crystallographic directions, and our analysis of the entire NMR line shape as a function of the applied field gradient provides a precise determination of the self-diffusion coefficients. In addition to observing CO2 diffusion through the channels parallel to the crystallographic c axis (self-diffusion coefficient D∥ = (5.8 ± 0.1) × 10-9 m2 s-1 at a pressure of 625 mbar CO2), we unexpectedly find that CO2 is also able to diffuse between the hexagonal channels in the crystallographic ab plane (D⊥ = (1.9 ± 0.2) × 10-10 m2 s-1), despite the walls of these channels appearing impermeable by single-crystal X-ray crystallography and flexible lattice MD simulations. Observation of such unexpected diffusion in the ab plane suggests the presence of defects that enable effective multidimensional CO2 transport in a metal-organic framework with nominally one-dimensional porosity.