Hydrodynamic dispersion in ß-lactoglobulin gels measured by PGSE NMR.

The displacement scale dependent molecular dynamics of solvent water molecules flowing through [Formula: see text] -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.

Erratum to: Hydrodynamic dispersion in ß-lactoglobulin gels measured by PGSE NMR.

The displacement scale dependent molecular dynamics of solvent water molecules flowing through ß-lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.

A PGSE study of propane gas flow through model porous bead packs.

We present a study of the probability density for molecular displacements of gas flowing through bead packs. The three bead packs to be described are composed of polydispersed porous PVC particles, 500 microm glass spheres, and 300 microm polystyrene spheres. A range of velocities (1 cm s(-1) to 1 m s(-1)) and observation times (3-500 ms), hence transport distances, are presented. For comparison we also measure the propagators for water flow in the polystyrene sphere pack. The exchange time between the moving and the stagnant portions of the flow is a strong function of the diffusion coefficient of the fluid. Comparing the propagators between water and propane flowing in similar porous media makes this clear. The gas propagators, for flowing and diffusing molecules, consistently show a feature at the average pore diameter. This feature has previously been observed for similar Peclet number studies in smaller monodispersed bead packs using liquids, but is now demonstrated for larger beads with gas. We analyze and discuss these propagators in the physically intuitive propagator space and also in the well-understood Fourier q space. The extension of NMR PGSE experiments to gas systems allows flow and diffusion information to be obtained over a wider range of length and time scales than with liquids, and also for a new range of physical environments and systems. Interactions between stochastic and deterministic motion are fundamental to the theoretical description of transport in porous media, and the time and length scale dependences are central to an understanding of the resultant dispersive motion.

Taylor dispersion and molecular displacements in Poiseuille flow.

We have used pulsed gradient spin echo (PGSE) NMR to measure longitudinal displacements of octane molecules undergoing Poiseuille flow in a 150 microm diameter pipe, accessing time scales which approach the Taylor dispersion limit. We monitor the change in displacement distribution which occurs as molecules undergoing Brownian motion sample an increasing proportion of the ensemble of streamlines, observing the effects of wall collisions and the gradual transition of the propagator from Poiseuille to Taylor-Aris behavior. The further use of a double PGSE sequence allows the direct measurement of the stochastic part of the motion alone.

Generalised calculation of NMR imaging edge effects arising from restricted diffusion in porous media.

The theoretical problem of how to describe apparent image spin density under conditions of restricted diffusion, given any general gradient sequence, is intrinsically complex. Here we demonstrate a simple approach to calculating the signal and the corresponding density in nuclear magnetic resonance (NMR) imaging experiments by means of an impulse-propagator method based on matrix multiplication. The multiplication scheme bears a natural and straightforward relationship to the k-space sampling, while the matrices themselves are calculated from the eigenmodes of the pore diffusion equation. Good agreement is found between theoretical predictions and the results of micro-imaging experiments on water trapped in rectangular pores whose walls are spaced by 100 microns along the read direction.

A three-dimensional NMR imaging scheme utilizing doubly resonant gradient coils.

A 3DFT gradient-echo technique has been developed which, in conjunction with series-resonant gradient-coil circuits, can produce three-dimensional NMR images with an echo time of less than 100 microseconds. The method involves a read-gradient waveform composed of two sinusoids of different frequencies. This is an improvement on previous imaging sequences using a single sinusoid where only half of k space was sampled and where the second half was calculated using conjugate symmetry. The inaccuracies involved in the necessary "cut and paste" of k space inevitably lead to artifacts in the final image. The important features of the new method are that with suitable phase encoding all octants of k space are sampled, the RF pulse is applied when the gradients are all zero, and the echo forms when the gradient is essentially constant. This method will allow more extensive application of solid imaging techniques to biological samples in vivo.

Physical determinants of bronchial mucosal folding.

It has recently been proposed, on the basis of a theoretical analysis, that the folding of the mucosa provides a significant component of airway stiffness. The model predicted that the stiffness of an airway was directly related to the number of epithelial folds that developed. In this study we examine the possibility that the folding pattern is determined by the physical requirements that the folding membrane must stay within the boundary of the smooth muscle wall, that the submucosal mass is constant, and that the strain energy of the folding membrane is the minimum possible within the geometric constraints. Model predictions are compared with morphometric data from the noncartilaginous airways of 17 sheep lungs. The data are in agreement with our predictions, which are based on the assumption that the folding membrane thickness is proportional to the submucosal thickness (in a fully dilated airway). The outcome of this analysis is that the increase in intrinsic stiffness of the folding membrane resulting from the increased thickness outweighs the decrease in stiffness conferred by the fewer folds required by the thicker submucosa. It is suggested that the increase in folding membrane thickness observed in asthma could be viewed as a protective mechanism that tends to reduce hyperresponsiveness.

Tensile stiffness of ovine tracheal wall.

The epithelial folding that occurs during bronchoconstriction requires that the pressure on the muscle side of the folding membrane be greater than that on the lumen side. The pressure required for a given level of folding depends on the elastic properties of the tissue and on the geometry of the folding. To quantify the elastic properties, uniaxial tensile stiffness of the tracheal inner wall of nine sheep was measured in two directions: parallel to the tracheal axis and circumferentially. The tissue showed anisotropic behavior, being approximately three times stiffer longitudinally than circumferentially. Histological examination showed that collagen in the lamina propria was randomly arranged, whereas there were straight elastin fibers aligned with the tracheal axis. This observation could explain the observed elastic anisotropy. Mechanical removal of the epithelium had no effect on tensile stiffness. It was also found that the tissue was under tension in situ. When a strip was excised, its length decreased by > or = 30%. After allowing for the systematic errors inherent in this experiment, the in situ circumferential tensile stiffness is estimated to be > or = 20 kPa. If the equivalent tissue in the bronchioles has the same tensile stiffness as that in the trachea, the forces required to fold the membrane are significant at small transbronchial pressure differences and increase in the presence of membrane thickening such as that seen in asthma.