Statistics of highly heterogeneous flow fields confined to three-dimensional random porous media.

We present a strong relationship between the microstructural characteristics of, and the fluid velocity fields confined to, three-dimensional random porous materials. The relationship is revealed through simultaneously extracting correlation functions R_{uu}(r) of the spatial (Eulerian) velocity fields and microstructural two-point correlation functions S_{2}(r) of the random porous heterogeneous materials. This demonstrates that the effective physical transport properties depend on the characteristics of complex pore structure owing to the relationship between R_{uu}(r) and S_{2}(r) revealed in this study. Further, the mean excess plot was used to investigate the right tail of the streamwise velocity component that was found to obey light-tail distributions. Based on the mean excess plot, a generalized Pareto distribution can be used to approximate the positive streamwise velocity distribution.

Effects of pulmonary inhalation on hyperpolarized krypton-83 magnetic resonance T1 relaxation.

The (83)Kr magnetic resonance (MR) relaxation time T(1) of krypton gas in contact with model surfaces was previously found to be highly sensitive to surface composition, surface-to-volume ratio, and surface temperature. The work presented here explored aspects of pulmonary (83)Kr T(1) relaxation measurements in excised lungs from healthy rats using hyperpolarized (hp) (83)Kr with approximately 4.4% spin polarization. MR spectroscopy without spatial resolution was applied to the ex vivo lungs that actively inhale hp (83)Kr through a custom designed ventilation system. Various inhalation schemes were devised to study the influence of anatomical dead space upon the measured (83)Kr T(1) relaxation times. The longitudinal (83)Kr relaxation times in the distal airways and the respiratory zones were independent of the lung inhalation volume, with T(1) = 1.3 s and T(1) = 1.0 s, depending only on the applied inhalation scheme. The obtained data were highly reproducible between different specimens. Further, the (83)Kr T(1) relaxation times in excised lungs were unaffected by the presence of up to 40% oxygen in the hp gas mixture. The results support the possible importance of (83)Kr as a biomarker for evaluating lung function.

Rapid analysis of non-uniformly sampled pulsed field gradient data for velocity estimation.

Bretthorst's recent generalization of the Lomb-Scargle periodogram shows that a sufficient statistic for frequency estimation from non-uniformly, but simultaneously sampled quadrature data is equivalent to the FFT of those data with the missing samples replaced by zeros. We have applied this concept to the rapid analysis of pulsed field gradient MRI data which have been non-uniformly sampled in the velocity encoding wave vector q. For a small number of q samples, it is more computationally efficient to calculate the periodogram directly rather than using the FFT algorithm with a large number of zeros. The algorithm we have implemented for finding the peak of the generalized periodogram is simple and robust; it involves repeated apodization and grid searching of the periodogram until the desired velocity resolution is achieved. The final estimate is refined by quadratic interpolation. We have tested the method for fully developed Poiseuille flow of a Newtonian fluid and have demonstrated substantial improvement in the precision of velocity measurement achievable in a fixed acquisition time with non-uniform sampling. The method is readily extendible to multidimensional data. Analysis of a 256 by 256 pixel image with 8 q samples and an effective velocity resolution of better than 1/680 of the Nyquist range requires approximately 1 minute computation time on a 400 MHz SUN Ultrasparc II processor.