Yi-Qiao Song

Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions

We present an efficient algorithm to solve a class of two- and 2.5-dimensional (2-D and 2.5-D) Fredholm integrals of the first kind with a tensor product structure and nonnegativity constraint on the estimated parameters of interest in an optimization framework. A zeroth-order regularization functional is used to incorporate a priori information about the smoothness of the parameters into the problem formulation. We adapt the Butler-Reeds-Dawson (1981) algorithm to solve this optimization problem in three steps. In the first step, the data are compressed using singular value decomposition (SVD) of the kernels. The tensor-product structure of the kernel is exploited so that the compressed data is typically a thousand fold smaller than the original data. This size reduction is crucial for fast optimization. In the second step, the constrained optimization problem is transformed to an unconstrained optimization problem in the compressed data space. In the third step, a suboptimal value of the smoothing parameter is chosen by the BRD method. Steps 2 and 3 are iterated until convergence of the algorithm. We demonstrate the performance of the algorithm on simulated data.

Enhancement of Solution NMR and MRI with Laser-Polarized Xenon

Optical pumping with laser light can be used to polarize the nuclear spins of gaseous xenon-129. When hyperpolarized xenon-129 is dissolved in liquids, a time-dependent departure of the proton spin polarization from its thermal equilibrium is observed. The variation of the magnetization is an unexpected manifestation of the nuclear Overhauser effect, a consequence of cross-relaxation between the spins of solution protons and dissolved xenon-129. Time-resolved magnetic resonance images of both nuclei in solution show that the proton magnetization is selectively perturbed in regions containing spin-polarized xenon-129. This effect could find use in nuclear magnetic resonance spectroscopy of surfaces and proteins and in magnetic resonance imaging.

Determining multiple length scales in rocks

Carbonate reservoirs in the Middle East are believed to contain about half of the worlds oil. The processes of sedimentation and diagenesis produce in carbonate rocks microporous grains and a wide range of pore sizes, resulting in a complex spatial distribution of pores and pore connectivity. This heterogeneity makes it difficult to determine by conventional techniques the characteristic pore-length scales, which control fluid transport properties. Here we present a bulk-measurement technique that is non-destructive and capable of extracting multiple length scales from carbonate rocks. The technique uses nuclear magnetic resonance to exploit the spatially varying magnetic field inside the pore space itself—a ‘fingerprint’ of the pore structure. We found three primary length scales (1–100u2009µm) in the Middle-East carbonate rocks and determined that the pores are well connected and spatially mixed. Such information is critical for reliably estimating the amount of capillary-bound water in the rock, which is important for efficient oil production. This method might also be used to complement other techniques for the study of shaly sand reservoirs and compartmentalization in cells and tissues.

Effects of diffusion on magnetic resonance imaging of laser-polarized xenon gas

Molecular diffusion during the application of magnetic field gradients can distort magnetic resonance images. A systematic characterization of these distortions in one dimension was performed using highly spin-polarized xenon gas. By varying the strength of the applied gradient and the geometric dimension of the sample, the evolution of these image distortions between the regimes of strong and weak diffusion was observed. These results are compared with numerical simulations. By directly measuring the displacement distribution of the polarized xenon atoms, it is shown that in the weak-diffusion regime the image distortions originate from the restricted diffusive motion near the sample boundaries, in agreement with previous theoretical work. Additionally, it is shown that the effects of diffusion can be utilized to enhance the contrast between the boundaries and bulk in the images of polarized gas samples, and thus may be exploited as a means of boundary detection in such systems.

Determining the resolution of Laplace inversion spectrum

In experiments involving decaying signals, it is often desirable to analyze the data as a sum of exponential decays using the Laplace inversion method. However, Laplace inversion is an ill-conditioned problem, and it is difficult to ascertain the stability of the reconstruction method and resolution of the resulting spectrum. This paper provides an easily computed approximate bound of the resolution and offers guidelines on how to design experiments to improve the spectral resolution.

High-field cross polarization NMR from laser-polarized xenon to surface nuclei

A method for NMR investigations of surface nuclei using cross polarization from optically polarized xenon (OPCP) is described. We find this methodology results in enhancement factors of approximately 103 upon application to surface protons. The dynamics of129Xe transfer to protons is examined in some detail, including the time, temperature, and multiple contact dependences of signal intensities. Furthermore, we discuss the sensitivity of the transfer process to spatial diffusion. Finally, we report on application of the OPCP experiment to a low total surface area sample.

High-resolution MRI of internal field diffusion-weighting in trabecular bone

Trabecular bone structure is known to play a crucial role in the overall strength, and thus fracture risk, of such areas of the skeleton as the vertebrae, spine, femur, tibiae, or radius. Several MR methods devoted to probing this structure depend upon the susceptibility difference between the solid bone matrix and the intervening fluid/marrow/fat, usually in the context of a linewidth (1/T2′) measurement or mapping technique. A recently demonstrated new approach to this system involves using internal gradients to encode diffusion weighting, and extracting structural information (e.g., surface‐to‐volume ratio) from the resulting signal decay. This contrast method has been demonstrated in bulk measurements on cleaned, water‐saturated bovine trabecular bone samples. In the present work, microscopic imaging (0.156u2009mm in‐plane resolution) is performed in order to spatially resolve this contrast on the trabecular level, and confirm its interpretation for the bulk measurements. It is found that the local rate of decay due to diffusion in the internal field (DDIF) is maximal close to the trabecular surfaces. The overall decay rate in a lower resolution scan probes the abundance of these surfaces, and provides contrast beyond that found in conventional proton density weighted or T1‐weighted imaging. Furthermore, a microscopic calculation of internal field distributions shows a qualitative distinction between the structural sensitivities of DDIF and T2′. DDIF contrast is highly localized around trabecular walls than is the internal field itself, making it a less sensitive but more specific measure of such important properties as trabecular number. Copyright

SQUID detected NMR of laser-polarized xenon at 4.2 K and at frequencies down to 200 Hz

Abstract A spectrometer based on a dc SQUID (superconducting quantum interference device) was used to record nuclear magnetic resonance signals from laser-polarized 129 Xe at 4.2 K and at frequencies ranging from about 200 Hz to 110 kHz in magnetic fields varying from about 0.02 to 9 mT. The 129 Xe resonance linewidths were found to increase with increasing magnetic field, and, at a given field, to increase with higher 129 Xe concentration. The spin-lattice relaxation times were observed to decrease from ∼ 8000 s at 5 mT to ∼ 2000 s at fields below 0.05 mT. Such long relaxation times make possible a variety of spin polarization transfer experiments.

Acceleration of multi-dimensional propagator measurements with compressed sensing.

NMR can probe the microstructures of anisotropic materials such as liquid crystals, stretched polymers and biological tissues through measurement of the diffusion propagator, where internal structures are indicated by restricted diffusion. Multi-dimensional measurements can probe the microscopic anisotropy, but full sampling can then quickly become prohibitively time consuming. However, for incompletely sampled data, compressed sensing is an effective reconstruction technique to enable accelerated acquisition. We demonstrate that with a compressed sensing scheme, one can greatly reduce the sampling and the experimental time with minimal effect on the reconstruction of the diffusion propagator with an example of anisotropic diffusion. We compare full sampling down to 64× sub-sampling for the 2D propagator measurement and reduce the acquisition time for the 3D experiment by a factor of 32 from ∼80 days to ∼2.5 days.

Broadband CPMG sequence with short composite refocusing pulses

We demonstrate that CPMG sequences with phase-modulated refocusing pulses of the same duration as the standard 180° pulses can generate echo trains with significantly increased amplitudes compared to the standard CPMG sequence in the case when there is a large range of Larmor frequencies across the sample. The best performance is achieved with symmetric phase-alternating (SPA) composite refocusing pulses of the form α-yβ+yα-y. In comparison to standard 180° pulses, we show that with SPA refocusing pulses with α≈27° and β≈126°, it is possible to double the signal-to-noise ratio without increasing the total pulse duration or power consumption of the refocusing pulses. The increased bandwidth of these pulses more than compensates for the decrease in performance in the vicinity of resonance. To achieve the full benefit of the broadband nature of the SPA pulses in a CPMG sequence, it is necessary to combine these refocusing pulses with a broadband excitation pulse. When it is not possible to use a short, high amplitude excitation pulse, we show that phase-alternating (PA) excitation pulses are suitable for this purpose. We present a detailed analysis of the underlying spin dynamics of these new pulse sequences and confirm the simulations with experiments. We show that for samples with T1/T2>1, the new sequences in grossly inhomogeneous fields do not only generate echoes with an increased amplitude, but also with an increased decay time. Finally, we analyze the diffusion properties and show quantitatively that the broadband sequences have a substantially higher diffusion sensitivity compared with the standard CPMG sequence.