The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

Measurement of the diffusion of multiple nuclei in restricted spaces by pulsed field gradient NMR

In this study, the restricted diffusion of a solvent, anion, and cation in an electrolyte solution was measured by pulsed field gradient (PFG) NMR for ¹H, ¹⁹F, and ⁷Li nuclei. Further, the time dependences of the diffusion coefficients were measured for a 1 M LiPF₆ electrolyte solution in porous polyethylene, which has pores with sizes of tens of micrometers. The decreasing ratio of the diffusion coefficients of the solvent, cation, and anion based on the diffusion time can be scaled similarly for each diffusion distance. The experimentally obtained time dependences of the diffusion coefficients of the solvent, anion, and cation agreed with the results of the analytical equation with the same structural parameters. Furthermore, the abovementioned experimental results were produced via Monte Carlo simulation in the same model-restricted structure for the solvent, anion, and cation. Based on PFG-NMR, it can be concluded that the solvent, anion, and cation exhibit the same restricted diffusion behavior in polyethylene pores measuring tens of micrometers. It was confirmed that measuring the time dependences of the diffusion coefficients via PFG-NMR with multiple nuclei is effective for studying the diffusion mechanisms of electrolyte solutions in restricted spaces.

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.

Matrix-assisted DOSY

The analysis of mixtures by NMR spectroscopy is challenging. Diffusion-ordered NMR spectroscopy enables a pseudo-separation of species based on differences in their translational diffusion coefficients. Under the right circumstances, this is a powerful technique; however, when molecules diffuse at similar rates separation in the diffusion dimension can be poor. In addition, spectral overlap also limits resolution and can make interpretation challenging. Matrix-assisted diffusion NMR seeks to improve resolution in the diffusion dimension by utilising the differential interaction of components in the mixture with an additive to the solvent. Tuning these matrix-analyte interactions allows the diffusion resolution to be optimised. This review presents the background to matrix-assisted diffusion experiments, surveys the wide range of matrices employed, including chromatographic stationary phases, surfactants and polymers, and demonstrates the current state of the art.

A 4D hyperspherical interpretation of q-space

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space.

Velocity distributions in confined flows of some complex fluids: sequence, sample and hardware issues

The present work addresses the problem of using Pulsed Field Gradient (PFG) experiments to measure velocity probability density functions and/or distributions in restricted flows, without being subjected to the blurring due to diffusive molecular motions. It especially focuses on two important classes of complex yield-stress fluids, i.e. water based colloidal suspensions or polymeric gels, and concentrated emulsions. Taking into account the many constraints owing to fluid diffusive properties, flow rate, hardware characteristics and pore size, it is found that the existence of suitable and optimised sequence parameters can be discussed in a graphical way. To do so, it also shown that Murday and Cotts formula describing diffusion inside emulsion droplets can be efficiently approximated by means of a set of asymptotic expressions. Different tuning regimes are identified for both kind of fluids, highlighting the influence of each of the various constraints on measuring possibilities. A method is given to build quantitative diagrams indicating pore sizes and flow rates allowing pure velocity assessment for a given fluid and Nuclear Magnetic Resonance (NMR) hardware. Measurements are found to be mainly constrained by fluid self-diffusivity and microstructure at low flow rates, and hardware characteristics at high flow rates. Although high gradient strengths can be made necessary to decrease achievable velocities and pore sizes in some specific cases, low gradient systems turn out suitable in many situations thanks to optimised sequence tuning. Due to their larger size, the latter also appear to offer the widest variety of workable experimental conditions. The use of these results is finally exemplified on the practical case of an emulsion flow in a model porous system.

Time-dependent diffusion in skeletal muscle with the random permeable barrier model (RPBM): application to normal controls and chronic exertional compartment syndrome patients

The purpose of this work was to carry out diffusion tensor imaging (DTI) at multiple diffusion times Td in skeletal muscle in normal subjects and chronic exertional compartment syndrome (CECS) patients and analyze the data with the random permeable barrier model (RPBM) for biophysical specificity. Using an institutional review board approved HIPAA-compliant protocol, seven patients with clinical suspicion of CECS and eight healthy volunteers underwent DTI of the calf muscle in a Siemens MAGNETOM Verio 3 T scanner at rest and after treadmill exertion at four different T(d) values. Radial diffusion values λ(rad) were computed for each of seven different muscle compartments and analyzed with RPBM to produce estimates of free diffusivity D(0), fiber diameter a, and permeability κ. Fiber diameter estimates were compared with measurements from literature autopsy reference for several compartments. Response factors (post/pre-exercise ratios) were computed and compared between normal controls and CECS patients using a mixed-model two-way analysis of variance. All subjects and muscle compartments showed nearly time-independent diffusion along and strongly time-dependent diffusion transverse to the muscle fibers. RPBM estimates of fiber diameter correlated well with corresponding autopsy reference. D(0) showed significant (p < 0.05) increases with exercise for volunteers, and a increased significantly (p < 0.05) in volunteers. At the group level, response factors of all three parameters showed trends differentiating controls from CECS patients, with patients showing smaller diameter changes (p = 0.07), and larger permeability increases (p = 0.07) than controls. Time-dependent diffusion measurements combined with appropriate tissue modeling can provide enhanced microstructural specificity for in vivo tissue characterization. In CECS patients, our results suggest that high-pressure interfiber edema elevates free diffusion and restricts exercise-induced fiber dilation. Such specificity may be useful in differentiating CECS from other disorders or in predicting its response to either physical therapy or fasciotomy.

A novel approach to interpretation of the time-dependent self-diffusion coefficient as a probe of porous media geometry

This article presents a new approximation describing fluid diffusion in porous media. Time dependence of the self-diffusion coefficient D(t) in the permeable porous medium is studied based on the assumption that diffusant molecules move randomly. An analytical expression for time dependence of the self-diffusion coefficient was obtained in the following form: D(t)=(D0-D∞)exp(-D0t/λ)+D∞, where D0 is the self-diffusion coefficient of bulk fluid, D∞ is the asymptotic value of the self-diffusion coefficient in the limit of long time values (t→∞), λ is the characteristic parameter of this porous medium with dimensionality of length. Applicability of the solution obtained to the analysis of experimental data is shown. The possibility of passing to short-time and long-time regimes is discussed.

Magnetic resonance diffusion and relaxation characterization of water in the unfrozen vein network in polycrystalline ice and its response to microbial metabolic products

Polycrystalline ice, as found in glaciers and the ice sheets of Antarctica, is a low porosity porous media consisting of a complicated and dynamic pore structure of liquid-filled intercrystalline veins within a solid ice matrix. In this work, Nuclear Magnetic Resonance measurements of relaxation rates and molecular diffusion, useful for probing pore structure and transport dynamics in porous systems, were used to physically characterize the unfrozen vein network structure in ice and its response to the presence of metabolic products produced by V3519-10, a cold tolerant microorganism isolated from the Vostok ice core. Recent research has found microorganisms that can remain viable and even metabolically active within icy environments at sub-zero temperatures. One potential mechanism of survival for V3519-10 is secretion of an extracellular ice binding protein that binds to the prism face of ice crystals and inhibits ice recrystallization, a coarsening process resulting in crystal growth with ice aging. Understanding the impact of ice binding activity on the bulk vein network structure in ice is important to modeling of frozen geophysical systems and in development of ice interacting proteins for biotechnology applications, such as cryopreservation of cell lines, and manufacturing processes in food sciences. Here, we present the first observations of recrystallization inhibition in low porosity ice containing V3519-10 extracellular protein extract as measured with Nuclear Magnetic Resonance and Magnetic Resonance Imaging.

Bessel Fourier Orientation Reconstruction (BFOR): an analytical diffusion propagator reconstruction for hybrid diffusion imaging and computation of q-space indices

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA).

Chromatographic NMR with size exclusion chromatography stationary phases

Chromatographic NMR describes the use of stationary phases or solvent additives, such as polymers, to modify the diffusion properties of analyte molecules and thereby improve the observed resolution in the diffusion domain. This paper demonstrates similar ideas using size exclusion chromatographic media and characterises the changes in the observed diffusion coefficient using a series of polymer molecular weight reference standards of known polydispersity. The results are interpreted in terms of a simple description of the size exclusion phenomena.

Empirical time dependence of liquid self-diffusion coefficient in porous media

A new method of finding experimental time dependence of the self-diffusion coefficient D(t) for fluid in the porous media is proposed. We investigate the time-dependent self-diffusion coefficient D(t) of random walkers in permeable porous media. D(t) is measured in pulse field gradient (PFG) experiments with fluid-saturated porous media of randomly packed spherical glass beads. In absence of the specific interactions between pore walls and a fluid we show that D(t) = (D(0) - D(∞))exp(-F√(D(0)t)/d) + D(∞), where D(0) is the diffusion constant in a bulk fluid, D(∞) is the asymptotical value of the diffusion coefficient for long diffusion times (t→∞), d is the bead diameter and F is the constant characterizing the geometry (the size and shape) pores.

Characterization of cerebral white matter properties using quantitative magnetic resonance imaging stains

The image contrast in magnetic resonance imaging (MRI) is highly sensitive to several mechanisms that are modulated by the properties of the tissue environment. The degree and type of contrast weighting may be viewed as image filters that accentuate specific tissue properties. Maps of quantitative measures of these mechanisms, akin to microstructural/environmental-specific tissue stains, may be generated to characterize the MRI and physiological properties of biological tissues. In this article, three quantitative MRI (qMRI) methods for characterizing white matter (WM) microstructural properties are reviewed. All of these measures measure complementary aspects of how water interacts with the tissue environment. Diffusion MRI, including diffusion tensor imaging, characterizes the diffusion of water in the tissues and is sensitive to the microstructural density, spacing, and orientational organization of tissue membranes, including myelin. Magnetization transfer imaging characterizes the amount and degree of magnetization exchange between free water and macromolecules like proteins found in the myelin bilayers. Relaxometry measures the MRI relaxation constants T1 and T2, which in WM have a component associated with the water trapped in the myelin bilayers. The conduction of signals between distant brain regions occurs primarily through myelinated WM tracts; thus, these methods are potential indicators of pathology and structural connectivity in the brain. This article provides an overview of the qMRI stain mechanisms, acquisition and analysis strategies, and applications for these qMRI stains.

A mixed basis approach in the SGP-limit

A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s(2)) time, where s denotes the number of boundary elements. Several approximate eigenvalues and eigenfunctions to the diffusion operator are retrieved. The method is applied to 1D and 2D systems with Neumann boundary conditions.

Recent advances in diffusion MRI modeling: Angular and radial reconstruction

Recent advances in diffusion magnetic resonance image (dMRI) modeling have led to the development of several state of the art methods for reconstructing the diffusion signal. These methods allow for distinct features to be computed, which in turn reflect properties of fibrous tissue in the brain and in other organs. A practical consideration is that to choose among these approaches requires very specialized knowledge. In order to bridge the gap between theory and practice in dMRI reconstruction and analysis we present a detailed review of the dMRI modeling literature. We place an emphasis on the mathematical and algorithmic underpinnings of the subject, categorizing existing methods according to how they treat the angular and radial sampling of the diffusion signal. We describe the features that can be computed with each method and discuss its advantages and limitations. We also provide a detailed bibliography to guide the reader.

Deriving time-dependent diffusion and relaxation rate in porous systems using eigenfunctions of the Laplace operator

Porous systems are investigated using eigendecomposition of the Laplace matrix. Three parameters; tortuosity, surface-to-pore volume ratio and relaxation rate are derived from the eigenvalue spectrum of the Laplace matrix and connected to the parameters in the Padé approximation, an expression often used to describe the time-dependent diffusion coefficient in porous systems. The Padé length is identified for systems with large pore to connector volume ratio. The results are compared with simulations.

Resolution enhancement in MRI of laser polarized 3He by control of diffusion

Diffusion of atoms or molecules in presence of magnetic field gradients not only attenuates the NMR signal but also leads to distortions close to restricting boundaries. This phenomenon is most evident in imaging with laser polarized (LP) noble gases. Diffusion of gases can be manipulated, however, by admixing inert gases of different molecular weight. In this work we analyze the effect of mixing LP-(3)He with SF(6) on the image quality of a phantom consisting of an arrangement of capillaries with different diameters. Admixing buffer gases of higher molecular weight changes the contrast and offers a means to record images with high spatial and time resolution. Additionally we demonstrate how distortions due to edge enhancement can be reduced even for long timed MRI-sequences.

Simulation and experimental verification of the diffusion in an anisotropic fiber phantom

Diffusion weighted magnetic resonance imaging enables the visualization of fibrous tissues such as brain white matter. The validation of this non-invasive technique requires phantoms with a well-known structure and diffusion behavior. This paper presents anisotropic diffusion phantoms consisting of parallel fibers. The diffusion properties of the fiber phantoms are measured using diffusion weighted magnetic resonance imaging and bulk NMR measurements. To enable quantitative evaluation of the measurements, the diffusion in the interstitial space between fibers is modeled using Monte Carlo simulations of random walkers. The time-dependent apparent diffusion coefficient and kurtosis, quantifying the deviation from a Gaussian diffusion profile, are simulated in 3D geometries of parallel fibers with varying packing geometries and packing densities. The simulated diffusion coefficients are compared to the theory of diffusion in porous media, showing a good agreement. Based on the correspondence between simulations and experimental measurements, the fiber phantoms are shown to be useful for the quantitative validation of diffusion imaging on clinical MRI-scanners.

Studying porous materials with krypton-83 NMR spectroscopy

This report is the first review of (83)Kr nuclear magnetic resonance as a new and promising technique for exploring the surfaces of solid materials. In contrast to the spin I = 1/2 nucleus of (129)Xe, (83)Kr has a nuclear spin of I = 9/2 and therefore possesses a nuclear electric quadrupole moment. Interactions of the quadrupole moment with the electronic environment are modulated by surface adsorption processes and therefore affect the (83)Kr relaxation rate and spectral lineshape. These effects are much more sensitive probes for surfaces than the (129)Xe chemical shielding and provide unique insights into macroporous materials in which the (129)Xe chemical shift is typically of little diagnostic value. The first part of this report reviews the effect of quadrupolar interactions on the (83)Kr linewidth in zeolites and also the (83)Kr chemical shift behavior that is distinct from that of its (129)Xe cousin in some of these materials. The second part reviews hyperpolarized (hp) (83)Kr NMR spectroscopy of macroporous materials in which the longitudinal relaxation is typically too slow to allow sufficient averaging of thermally polarized (83)Kr NMR signals. The quadrupolar-driven T(1) relaxation times of hp (83)Kr in these materials are sensitive to surface chemistry, surface-to-volume ratios, coadsorption of other species on surfaces, and surface temperature. Thus, (83)Kr T(1) relaxation can provide information about surfaces and chemical processes in macroscopic pores and can generate surface-sensitive contrast in hp (83)Kr MRI.

Measurement of hyperpolarized gas diffusion at very short time scales

We present a new pulse sequence for measuring very-short-time-scale restricted diffusion of hyperpolarized noble gases. The pulse sequence is based on concatenating a large number of bipolar diffusion-sensitizing gradients to increase the diffusion attenuation of the MR signal while maintaining a fundamentally short diffusion time. However, it differs in several respects from existing methods that use oscillating diffusion gradients for this purpose. First, a wait time is inserted between neighboring pairs of gradient pulses; second, consecutive pulse pairs may be applied along orthogonal axes; and finally, the diffusion-attenuated signal is not simply read out at the end of the gradient train but is periodically sampled during the wait times between neighboring pulse pairs. The first two features minimize systematic differences between the measured (apparent) diffusion coefficient and the actual time-dependent diffusivity, while the third feature optimizes the use of the available MR signal to improve the precision of the diffusivity measurement in the face of noise. The benefits of this technique are demonstrated using theoretical calculations, Monte-Carlo simulations of gas diffusion in simple geometries, and experimental phantom measurements in a glass sphere containing hyperpolarized (3)He gas. The advantages over the conventional single-bipolar approach were found to increase with decreasing diffusion time, and thus represent a significant step toward making accurate surface-to-volume measurements in the lung airspaces.

Enhanced (13)C PFG NMR for the study of hydrodynamic dispersion in porous media

PFG NMR methods are frequently used as a means of probing both coherent and incoherent molecular motions of fluids contained within heterogeneous porous media. The time scale over which molecular displacements can be probed in a conventional PFG NMR experiment is limited by the relaxation characteristics of (1)H - the nucleus that is typically observed. In multiphase systems, due to its sensitivity to susceptibility gradients and interactions with surfaces,(1)H signal is frequently characterized by rapid T(1) and T(2) relaxation. In this work, a heteronuclear approach to PFG NMR is demonstrated which allows the study of molecular displacement over extended time scales (and, consequently, length scales) by exploiting the longer relaxation time of (13)C. The method presented employs the DEPT technique of polarization transfer in order to enhance both the sensitivity and efficiency of (13)C detection. This hybrid coherence transfer PFG technique has been used to acquire displacement propagators for flow through a bead pack with an observation time of up to 35 s.

Exploring the surface permeability of nanoporous particles by pulsed field gradient NMR

A new method to determine the surface permeability of nanoporous particles is proposed. It is based on the comparison of experimental data on tracer exchange and intracrystalline molecular mean square displacements as obtained by the PFG NMR tracer desorption technique with the corresponding solutions of the diffusion equation via dynamical Monte Carlo simulations. The method is found to be particularly sensitive in the "intermediate" regime, when the influence of intracrystalline diffusion and surface resistances of the nanoporous crystal on molecular transport are comparable and the conventional method fails. As an example, the surface permeabilities of two samples of zeolite NaCaA with different crystal sizes are determined with methane, as a probe molecule, at room temperature.

Temporal diffusion spectroscopy: theory and implementation in restricted systems using oscillating gradients

The theory of temporal diffusion spectra is reviewed. In contrast to q-space spectroscopy, which measures the displacement spectrum of spins in a spatial domain, the spectral density of the velocity correlation function (VCF) in the temporal domain is considered. It is demonstrated that casting diffusion in this domain may facilitate measurements of microscopic geometry and the decomposition of the diffusion signal into components due to disperse flow and restricted diffusion. An oscillating gradient (OG) method of diffusion spectroscopy was developed and implemented. Microscopic pore sizes, surface-to-volume ratios (S/Vs), and diffusion path tortuosities were extracted from model systems using this method. Cases are discussed in which this type of experiment may allow the characterization of pore geometry when spatial domain experiments fail. OGs may be combined with imaging sequences to map complex patterns of diffusion and flow. Moreover, scalar apparent diffusion coefficient (ADC) measurements in complex biological systems may be subtly dependent on specific pulse sequence parameters. Thus, scalar ADC measurements using gradient pulses with different frequency spectra may give different results. Conversely, the frequency dependence of motion-sensitizing gradient pulses may be exploited to deduce the origin of ADC changes.

Controlling diffusion of3He by buffer gases: A structural contrast agent in lung MRI

PURPOSE

To study the influence of admixing inert buffer gases to laser-polarized (3)He in terms of resulting diffusion coefficients and the consequences for image contrast and resolution.

MATERIALS AND METHODS

The diffusion coefficient of (3)He was altered by admixing buffer gases of various molecular weights ((4)He, N(2), and SF(6)). The influence of the pulse sequence and the diffusion coefficient on the appearance of MRI of (laser-polarized) gases was analyzed by comparison of basic theoretical concepts with demonstrative experiments.

RESULTS

Excellent agreement between theoretical description and observed signal in simple gradient echoes was observed. A maximum signal gain can be predicted and was experimentally validated. Images acquired under such conditions revealed improved resolution. The nature and concentration of the admixed gas defines a structural threshold for the observed apparent diffusion coefficient (ADC) as demonstrated with diffusion-weighted MRI on a pig's lung flooded with suitable gas mixtures.

CONCLUSION

A novel procedure is proposed to control the diffusion coefficient of gases in MRI by admixture of inert buffer gases. Their molecular mass and concentration enter as additional parameters into the equations that describe structural contrast. This allows for setting a structural threshold up to which structures contribute to the image. For MRI of the lung this enables images of very small structural elements (alveoli) only, or in the other extreme, all airways can be displayed with minimal signal loss due to diffusion.

Diffusion-weighted MRI of the lung with hyperpolarized helium-3: a study of reproducibility

PURPOSE

To determine the reproducibility of several parameters of the ADC measurement by calculating the scan-to-scan intrasubject variability.

MATERIALS AND METHODS

Measurements were performed using a gradient-echo sequence with a bipolar gradient for diffusion weighting (b=3.89 sec/cm2). Five patients with pulmonary emphysema, and six healthy-lung volunteers were included in the study. Images were acquired after inspiration of 3He during a single inspiratory breath-hold. To assess the reproducibility, the measurement was performed twice (time between measurements=20 minutes) without repositioning the subjects. Analysis was performed on the basis of region-of-interest (ROI) analysis and global lung ADC histograms.

RESULTS

The mean ADC of a ROI varied by 5.1% between two measurements for volunteers and by 6.1% for patients. In the global evaluation, the 75th percentile demonstrated the best reproducibility (2%), while other parameters showed variations up to 12%. Only the variation of the standard deviation (SD) and the measure of homogeneity of the ADC map showed a significant difference between patients and volunteers.

CONCLUSION

Diffusion-weighted imaging (DWI) is a well-reproducible method for assessing the lung microstructure.

Probing short length scales with restricted diffusion in a static gradient using the CPMG sequence

We experimentally verify a new method of extracting the surface-to-volume ratio (S/V) of porous media with diffusion NMR. In contrast to the widely used pulsed field gradient (PFG) technique, which employs the stimulated echo coherence pathway, we use here the direct Carr-Purcell-Meiboom-Gill (CPMG) path. Even for high echoes, which exhibit ample attenuation due to diffusion in the field gradient, the relevant ruler length for the direct pathway is fixed by the diffusion length during a single inter-pulse spacing. The direct path, therefore, is well suited for probing shorter length scales than is possible with the conventional approach. In our experiments in a low-field static-gradient system, the direct CPMG pathway was found to be sensitive to structure an order of magnitude smaller than accessible with the stimulated-echo pathway.

Feasibility of diffusion-NMR surface-to-volume measurements tested by calculations and computer simulations

It has been demonstrated previously that the surface-to-volume ratio S/V can be determined from the derivative of the time-dependent diffusion coefficient D(t), in the limit t --> 0. Several questions arise concerning the practicality of determining S/V by NMR. In particular, how large are the errors generated by (1) working outside the t --> 0 limit and (2) measuring D outside the b --> 0 limit, both for narrow and full-width gradient pulses? Here b is gamma2G2delta2Delta for narrow pulses and gamma2G2t3/12 for broad pulses. These questions are addressed by random-walk computer simulations and numerical calculations in geometries relevant to small-airways of lung. The results demonstrate that one can work well outside the t --> 0 and b --> 0 limits, provided 10-20% accuracy in the measured S/V is sufficient. Emphasis is placed on the useful range of times t for which NMR determinations of lung S/V are feasible.

Investigating 3He diffusion NMR in the lungs using finite difference simulations and in vivo PGSE experiments

Finite difference simulations have been used to model (3)He gas diffusion in simulated lung tissue. The technique has the advantage that a wide range of structural models and diffusion-sensitizing gradient waveforms can be investigated, for which analytical methods would otherwise be virtually impossible. Results from simulations and in vivo pulsed-gradient-spin-echo (PGSE) experiments show that the apparent diffusion coefficient (ADC) is a function of diffusion time and gradient strength, and suggests diffusion is locally anisotropic. The simulations have been compared to recent work on an analytical model that characterizes lung tissue as a series of independent cylinders. The results presented may have clinical implications for (3)He ADC measurements in assessing lung diseases such as chronic-obstructive-pulmonary-disease.

Exploring lung function with hyperpolarized129Xe nuclear magnetic resonance

With the use of polarization-transfer pulse sequences and hyperpolarized (129)Xe NMR, gas exchange in the lung can be measured quantitatively. However, harnessing the inherently high sensitivity of this technique as a tool for exploring lung function requires a fundamental understanding of the xenon gas-exchange and diffusion processes in the lung, and how these may differ between healthy and pathological conditions. Toward this goal, we employed NMR spectroscopy and imaging techniques in animal models to investigate the dependence of the relative xenon gas exchange rate on the inflation level of the lung and the tissue density. The spectroscopic results indicate that gas exchange occurs on a time scale of milliseconds, with an average effective diffusion constant of about 3.3 x 10(-6)cm(2)/s in the lung parenchyma. Polarization-transfer imaging pulse sequences, which were optimized based on the spectroscopic results, detected regionally increased gas-exchange rates in the lung, indicative of increased tissue density secondary to gravitational compression. By exploiting the gas-exchange process in the lung to encode physiologic parameters, these methods may be extended to noninvasive regional assessments of lung-tissue density and the alveolar surface-to-volume ratio, and allow lung pathology to be detected at an earlier stage than is currently possible.

Effects of finite-width pulses in the pulsed-field gradient measurement of the diffusion coefficient in connected porous media

We analytically compute the apparent diffusion coefficient D(app) for an open restricted geometry, such as an extended porous medium, for the case of a pulsed-field gradient (PFG) experiment with finite-width pulses. In the short- and long-time limits, we give explicit, model-independent expressions that correct for the finite duration of the pulses and can be used to extract the pore surface-to-volume (S/V) ratio as well as the tortuosity. For all times, we compute D(app) using a well-established model form of the actual time-dependent diffusion coefficient D(t) that can be obtained from an ideal narrow-pulse PFG. We compare D(app) and D(t) and find that, regardless of pulse widths and geometry-dependent parameters, the two quantities deviate by less than 20%. These results are in sharp contrast with the studies on closed geometries [J. Magn. Reson. A 117 (1995) 209], where the effects of finite gradient-pulse widths are large. The analytical results presented here can be easily adapted for different pulse protocols and time sequences.

Validation of diffusion spectrum magnetic resonance imaging with manganese-enhanced rat optic tracts and ex vivo phantoms

Diffusion spectrum imaging (DSI) has been demonstrated to resolve crossing axonal fibers by mapping the probability density function of water molecules diffusion at each voxel. However, the accuracy of DSI in defining individual fiber orientation and the validity of Fourier relation under finite gradient pulse widths are not assessed yet. We developed an ex vivo and an in vivo model to evaluate the error of DSI with gradient pulse widths being relatively short and long, respectively. The ex vivo model was a phantom comprising sheets of parallel capillaries filled with water. Sheets were stacked on each other with capillaries crossed at 45 degrees or 90 degrees. High-resolution T2-weighted images (T2WI) of the phantom served as a reference for the orientation of intersecting capillaries. In the in vivo model, manganese ions were infused into rats' optic tracts. The optic tracts were enhanced on T1-weighted images (T1WI) and served as a reference for the tract orientation. By comparing DSI with T2WI, the deviation angles between the primary orientation of diffusion spectrum and the 90 degrees and 45 degrees phantoms were 1.19 degrees +/- 4.82 degrees and -0.71 degrees +/- 4.91 degrees, respectively. By comparing DSI with the T1WI of rat optic tracts, the deviation angle between primary orientation of diffusion spectrum and optic tracts was -0.41 degrees +/- 6.18 degrees. In addition, two sequences of DSI using short and long gradient pulses were performed in a rat brain. The bias of the primary orientation between these two sequences was approximately 10 degrees. In conclusion, DSI can resolve crossing fiber orientation accurately. The effect of finite gradient pulse widths on the primary orientation is not critical.

Applications of controlled-flow laser-polarized xenon gas to porous and granular media study

We report initial NMR studies of continuous flow laser-polarized xenon gas, both in unrestricted tubing, and in a model porous media. The study uses Pulsed Gradient Spin Echo-based techniques in the gas-phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients. Pulsed Gradient Echo studies of continuous flow laser-polarized xenon gas in unrestricted tubing indicate clear diffraction minima resulting from a wide distribution of velocities in the flow field. The maximum velocity experienced in the flow can be calculated from this minimum, and is seen to agree with the information from the complete velocity spectrum, or motion propagator, as well as previously published images. The susceptibility of gas flows to parameters such as gas mixture content, and hence viscosity, are observed in experiments aimed at identifying clear structural features from echo attenuation plots of gas flow in porous media. Gas-phase NMR scattering, or position correlation flow-diffraction, previously clearly seen in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack is not so clear in experiments using a different gas mixture. A propagator analysis shows most gas in the sample remains close to static, while a small portion moves through a presumably near-unimpeded path at high velocities.

Modified oscillating gradient pulses for direct sampling of the diffusion spectrum suitable for imaging sequences

A variation of the oscillating gradient spin echo method had been developed, which isolates temporal frequencies of the dephasing spectrum. This allows sampling of the diffusion spectrum, the Fourier transform of the velocity correlation function (VCF). It has been shown that restriction and flow alter this function in ways that can be mathematically characterized, yielding quantitative information on restriction geometry and flow parameters. It is demonstrated that in many systems of interest, dispersion of velocity will produce a peak in the VCF spectrum near omega=0, while restricted diffusion will manifest itself in the spectrum at higher frequencies. The method, therefore, may be useful for decoupling their effects on the apparent diffusion coefficient (ADC), as well as in revealing the physics of both phenomena. This method has been implemented in model systems of packed beads, yielding data consistent with theoretical models of restricted diffusion spectra and data from one previous study. The method may have significant application to biology and medicine, as well as the study of transport phenomena in porous media and complex flow.

Diffusion NMR methods applied to xenon gas for materials study

We report initial NMR studies of (i) xenon gas diffusion in model heterogeneous porous media and (ii) continuous flow laser-polarized xenon gas. Both areas utilize the pulsed gradient spin-echo (PGSE) techniques in the gas phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients--a brief overview of this area is provided in the Introduction. The heterogeneous or multiple-length scale model porous media consisted of random packs of mixed glass beads of two different sizes. We focus on observing the approach of the time-dependent gas diffusion coefficient, D(t) (an indicator of mean squared displacement), to the long-time asymptote, with the aim of understanding the long-length scale structural information that may be derived from a heterogeneous porous system. We find that D(t) of imbibed xenon gas at short diffusion times is similar for the mixed bead pack and a pack of the smaller sized beads alone, hence reflecting the pore surface area to volume ratio of the smaller bead sample. The approach of D(t) to the long-time limit follows that of a pack of the larger sized beads alone, although the limiting D(t) for the mixed bead pack is lower, reflecting the lower porosity of the sample compared to that of a pack of mono-sized glass beads. The Pade approximation is used to interpolate D(t) data between the short- and long-time limits. Initial studies of continuous flow laser-polarized xenon gas demonstrate velocity-sensitive imaging of much higher flows than can generally be obtained with liquids (20-200 mm s-1). Gas velocity imaging is, however, found to be limited to a resolution of about 1 mm s-1 owing to the high diffusivity of gases compared with liquids. We also present the first gas-phase NMR scattering, or diffusive-diffraction, data, namely flow-enhanced structural features in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack.