The measurement of diffusion and flow in polymer solutions using dynamic NMR microscopy

Use of high-resolution MRI for investigation of fluid flow and global permeability in a material with interconnected porosity

We present a multi-scale experimental approach designed to improve the investigation of both localized and global fluid flow in biomaterials with randomly interconnected porosity. Coralline hydroxyapatite (ProOsteon 500 from Interpore-Cross), having a relatively well-defined porosity, was used as an in vitro model of typical bone architecture. Axial fluid velocity profiles within the pores of a cylindrical hydroxyapatite sample were characterized using high-resolution MRI in conjunction with the measurement of global flow and associated permeability based on the Darcy-type relationship. Assuming Newtonian fluid behaviour, image analysis permitted computation of local porosity, intra-pore fluid shear, and visualization of flow heterogeneity within the sample. These results may benefit applications in biomaterials for the evaluation of factors influencing bony incorporation in porous scaffolds and on porous implant and bone surfaces. Normal and diseased biological tissues are also clinical relevant applications.

Two-dimensional PFG NMR for encoding correlations of position, velocity, and acceleration in fluid transport

A generalized approach to obtain two-dimensional maps of spatial particle coordinates and their derivatives with respect to time by PFG-NMR employing multiple gradient pulses is presented. A sequence of n magnetic field gradient pulses makes it possible, after independent stepping of each pulse and subsequent Fourier transformation, to plot the spin density distribution in coordinate space at n times and along the respective directions of the gradient pulses. In particular, two gradient pulses of effective area k(1) and k(2) separated by a time interval Delta lead to a plot of the combined two-time probability density, W(2)(r(1), 0; r(2), Delta), to find a particle at a coordinate r(1) at t = 0 and at r(2) at t = Delta. A conventional experiment for measuring transport properties by simultaneous stepping of the gradients under the condition k(1) = -k(2) is equivalent to a projection onto the secondary diagonal in the [r(1), r(2)] plot. The main diagonal represents an average position between the two timepoints t = 0 and t = Delta, so that a rotation of the coordinate plot by an angle of 45 degrees allows one to correlate the displacement R = r(2) - r(1) with the averaged position r parallel to the gradient direction. While an average velocity during the time interval Delta can be defined as &vmacr; = R/Delta, an extension toward acceleration and higher order derivatives is straightforward by modification of the pulse sequence. We discuss this concept by application to flow through a circular and a narrowing pipe (confusor), respectively, the experimental results of which are compared to numerical simulations. Copyright 2000 Academic Press.

"One-shot" velocity microscopy: NMR imaging of motion using a single phase-encoding step

The use of the pulsed gradient spin-echo sequence in NMR microscopy enables the measurement of molecular translational motion and simultaneous construction of velocity and self-diffusion images, a technique that has been termed dynamic NMR microscopy. In this method the PGSE contrast gradient is stepped in a fourth dimension (q space) and so is inherently inefficient. Provided that one is prepared to sacrifice some of the additional information provided by the multiple PGSE gradient approach, it is possible to construct a velocity image alone by means of a single PGSE phase-encoding step. We illustrate applications of this method in which a signal from the stationary spins is nulled by the use of both gradient phase cycling and a final "z-storage" rf pulse. The limits to velocity resolution are around 10 microns s-1 in free water but can be considerably smaller for molecules with a low self-diffusion coefficient. We demonstrate this method in a study of water capillary flow at 12 microns transverse pixel resolution, extending the velocity range by employing a four-quadrant analysis method. This method is also used to measure vascular transport in a living plant and find a flow rate of around 45 microns s-1.