Quantitative single point imaging with compressed sensing

Mapping of fatty acid composition with free-breathing MR spectroscopic imaging and compressed sensing

Nonalcoholic fatty liver disease (NAFLD) is a growing health problem, and a major challenge in NAFLD management is identifying which patients are at risk of progression to more serious disease. Simple measurements of liver fat content are not strong predictors of clinical outcome, but biomarkers related to fatty acid composition (ie, saturated vs. unsaturated fat) may be more effective. MR spectroscopic imaging (MRSI) methods allow spatially resolved, whole-liver measurements of chemical composition but are traditionally limited by slow acquisition times. In this work we present an accelerated MRSI acquisition based on spin echo single point imaging (SE-SPI), which, using appropriate sampling and compressed sensing reconstruction, allows free-breathing acquisition in a mouse model of fatty liver disease. After validating the technique's performance in oil/water phantoms, we imaged mice that had received a normal diet or a methionine and choline deficient (MCD) diet, some of which also received supplemental injections of iron to mimic hepatic iron overload. SE-SPI was more resistant to the line-broadening effects of iron than single-voxel spectroscopy measurements, and was consistently able to measure the amplitudes of low-intensity spectral peaks that are important to characterizing fatty acid composition. In particular, in the mice receiving the MCD diet, SE-SPI showed a significant decrease in a metric associated with unsaturated fat, which is consistent with the literature. This or other related metrics may therefore offer more a specific biomarker of liver health than fat content alone. This preclinical study is an important precursor to clinical testing of the proposed method. MR-based quantification of fatty acid composition may allow for improved characterization of non-alcoholic fatty liver disease. A spectroscopic imaging method with appropriate sampling strategy allows whole-liver mapping of fat composition metrics in a free-breathing mouse model. Changes in metrics like the surrogate unsaturation index (UIs) are visible in mice receiving a diet which induces fat accumulation in the liver, as compared to a normal diet; such metrics may prove useful in future clinical studies of liver disease.

Applications of magnetic resonance imaging in chemical engineering

While there are many techniques to study phenomena that occur in chemical engineering applications, magnetic resonance imaging (MRI) receives increasing scientific interest. Its non-invasive nature and wealth of parameters with the ability to generate functional images and contrast favors the use of MRI for many purposes, in particular investigations of dynamic phenomena, since it is very sensitive to motion. Recent progress in flow-MRI has led to shorter acquisition times and enabled studies of transient phenomena. Reactive systems can easily be imaged if NMR parameters such as relaxation change along the reaction coordinate. Moreover, materials and devices can be examined, such as batteries by mapping the magnetic field around them.

Identification of sampling patterns for high-resolution compressed sensing MRI of porous materials: 'learning' from X-ray microcomputed tomography data

There exists a strong motivation to increase the spatial resolution of magnetic resonance imaging (MRI) acquisitions so that MRI can be used as a microscopy technique in the study of porous materials. This work introduces a method for identifying novel data sampling patterns to achieve undersampling schemes for compressed sensing MRI (CS-MRI) acquisitions, enabling 3D spatial resolutions of 17.6 µm to be achieved. A data-driven learning approach is used to derive k-space undersampling schemes for 3D MRI acquisitions from 3D X-ray microcomputed tomography (µCT) datasets acquired at a higher spatial resolution than can be acquired using MRI. The performance of the new sampling approach was compared to other, well-established sampling strategies using simulated MRI data obtained from high-resolution µCT images of rock core plugs. These simulations were performed for a range of different k-space sampling fractions (0.125-0.375) using images of Ketton limestone. The method was then extended to consideration of imaging Estaillades limestone and Fontainebleau sandstone. The results show that the new sampling approach performs as well as or better than conventional variable density sampling and without need for time-consuming parameter optimisation. Further, a bespoke sampling pattern is produced for each rock type. The novel undersampling strategy was employed to acquire 3D magnetic resonance images of a Ketton limestone rock at spatial resolutions of 35 and 17.6 µm. The ability of the k-space sampling scheme produced using the new approach in enabling reconstruction of the pore space characteristics of the rock was then demonstrated by benchmarking against the pore space statistics obtained from high-resolution µCT data. The MRI data acquired at 17.6 µm resolution gave excellent agreement with the pore size distribution obtained from the X-ray microcomputed tomography dataset, while the pore coordination number distribution obtained from the MRI data was slightly skewed to lower coordination numbers. This approach provides a method of producing a k-space undersampling pattern for MRI acquisition at a spatial resolution for which a fully sampled acquisition at that spatial resolution would be impractically long. The approach can be easily extended to other CS-MRI techniques, such as spatially resolved flow and relaxation time mapping. LAY DESCRIPTION: Magnetic resonance imaging (MRI) is widely used to study the microstructure of, and fluid transport phenomena in porous media relevant for engineering applications. A major application is the study of water and hydrocarbon transport in porous sedimentary rocks, which typically have pore sizes smaller than 100 µm. The spatial resolution of routine MRI acquisitions, however, is limited to several hundred µm due to the relatively low sensitivity of the magnetic resonance method. Therefore, there exists a strong motivation to increase the spatial resolution of MRI by one to two orders of magnitude to be able to study these rocks at a pore scale. This work reports the initial step towards achieving this. Three-dimensional images of rock pore structure are acquired at both 35 and 17.6 µm spatial resolution. In ongoing work, these methods are now being incorporated into magnetic resonance velocity imaging methods, thereby enabling imaging of both pore structure and hydrodynamics at these much higher spatial resolutions than were hitherto possible. Although X-ray microcomputed tomography (µCT) produces high spatial resolution images, it is far more limited in being able to spatially map transport processes (i.e. flow) in porous media. This work reports a strategy for accelerating the image acquisition time such that sufficient signal-to-noise ratio (SNR) is achieved to increase the spatial resolution, that is, the voxel size within which there is sufficient SNR within the resulting image. To achieve this, a technique known as compressed sensing is used which exploits undersampling of the acquired data relative to the standard fully sampled image. In MRI, data are acquired in so-called k-space and Fourier transformed to yield the real space image. The challenge, when undersampling, is to optimise the specific points in k-space that are acquired because these will influence the quality of the resulting image. This work reports a straightforward, robust strategy for identifying the optimal sets of k-space points to acquire. The method introduced uses simulated MRI images calculated from high-resolution µCT images of the rocks of interest, from which optimised MRI sampling patterns are obtained. The method does not require any optimisation of parameters for its implementation, which is a significant advantage compared to other strategies. Moreover, we show that the pore space characteristics of the acquired MRI images are in excellent agreement with the same characteristics obtained from a high-resolution µCT image.

In Situ Chemically-Selective Monitoring of Multiphase Displacement Processes in a Carbonate Rock Using 3D Magnetic Resonance Imaging

Accurate monitoring of multiphase displacement processes is essential for the development, validation and benchmarking of numerical models used for reservoir simulation and for asset characterization. Here we demonstrate the first application of a chemically-selective 3D magnetic resonance imaging (MRI) technique which provides high-temporal resolution, quantitative, spatially resolved information of oil and water saturations during a dynamic imbibition core flood experiment in an Estaillades carbonate rock. Firstly, the relative saturations of dodecane (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{o}})$$\end{document}So) and water (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{w}})$$\end{document}Sw), as determined from the MRI measurements, have been benchmarked against those obtained from nuclear magnetic resonance (NMR) spectroscopy and volumetric analysis of the core flood effluent. Excellent agreement between both the NMR and MRI determinations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{o}}$$\end{document}So and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{w}}$$\end{document}Sw was obtained. These values were in agreement to 4 and 9% of the values determined by volumetric analysis, with absolute errors in the measurement of saturation determined by NMR and MRI being 0.04 or less over the range of relative saturations investigated. The chemically-selective 3D MRI method was subsequently applied to monitor the displacement of dodecane in the core plug sample by water under continuous flow conditions at an interstitial velocity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.27\times 10^{-6}\,\hbox {m}\,\hbox {s}^{-1}$$\end{document}1.27×10-6ms-1 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.4\,\hbox {ft}\,\hbox {day}^{-1})$$\end{document}0.4ftday-1). During the core flood, independent images of water and oil distributions within the rock core plug at a spatial resolution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.31\,\hbox {mm}\times 0.39\,\hbox {mm} \times 0.39\,\hbox {mm}$$\end{document}0.31mm×0.39mm×0.39mm were acquired on a timescale of 16 min per image. Using this technique the spatial and temporal dynamics of the displacement process have been monitored. This MRI technique will provide insights to structure–transport relationships associated with multiphase displacement processes in complex porous materials, such as those encountered in petrophysics research.

MRI of chemical reactions and processes

As magnetic resonance imaging (MRI) can spatially resolve a wealth of molecular information available from nuclear magnetic resonance (NMR), it is able to non-invasively visualise the composition, properties and reactions of a broad range of spatially-heterogeneous molecular systems. Hence, MRI is increasingly finding applications in the study of chemical reactions and processes in a diverse range of environments and technologies. This article will explain the basic principles of MRI and how it can be used to visualise chemical composition and molecular properties, providing an overview of the variety of information available. Examples are drawn from the disciplines of chemistry, chemical engineering, environmental science, physics, electrochemistry and materials science. The review introduces a range of techniques used to produce image contrast, along with the chemical and molecular insight accessible through them. Methods for mapping the distribution of chemical species, using chemical shift imaging or spatially-resolved spectroscopy, are reviewed, as well as methods for visualising physical state, temperature, current density, flow velocities and molecular diffusion. Strategies for imaging materials with low signal intensity, such as those containing gases or low sensitivity nuclei, using compressed sensing, para-hydrogen or polarisation transfer, are discussed. Systems are presented which encapsulate the diversity of chemical and physical parameters observable by MRI, including one- and two-phase flow in porous media, chemical pattern formation, phase transformations and hydrodynamic (fingering) instabilities. Lastly, the emerging area of electrochemical MRI is discussed, with studies presented on the visualisation of electrochemical deposition and dissolution processes during corrosion and the operation of batteries, supercapacitors and fuel cells.

Fast imaging of laboratory core floods using 3D compressed sensing RARE MRI

Three-dimensional (3D) imaging of the fluid distributions within the rock is essential to enable the unambiguous interpretation of core flooding data. Magnetic resonance imaging (MRI) has been widely used to image fluid saturation in rock cores; however, conventional acquisition strategies are typically too slow to capture the dynamic nature of the displacement processes that are of interest. Using Compressed Sensing (CS), it is possible to reconstruct a near-perfect image from significantly fewer measurements than was previously thought necessary, and this can result in a significant reduction in the image acquisition times. In the present study, a method using the Rapid Acquisition with Relaxation Enhancement (RARE) pulse sequence with CS to provide 3D images of the fluid saturation in rock core samples during laboratory core floods is demonstrated. An objective method using image quality metrics for the determination of the most suitable regularisation functional to be used in the CS reconstructions is reported. It is shown that for the present application, Total Variation outperforms the Haar and Daubechies3 wavelet families in terms of the agreement of their respective CS reconstructions with a fully-sampled reference image. Using the CS-RARE approach, 3D images of the fluid saturation in the rock core have been acquired in 16min. The CS-RARE technique has been applied to image the residual water saturation in the rock during a water-water displacement core flood. With a flow rate corresponding to an interstitial velocity of vi=1.89±0.03ftday(-1), 0.1 pore volumes were injected over the course of each image acquisition, a four-fold reduction when compared to a fully-sampled RARE acquisition. Finally, the 3D CS-RARE technique has been used to image the drainage of dodecane into the water-saturated rock in which the dynamics of the coalescence of discrete clusters of the non-wetting phase are clearly observed. The enhancement in the temporal resolution that has been achieved using the CS-RARE approach enables dynamic transport processes pertinent to laboratory core floods to be investigated in 3D on a time-scale and with a spatial resolution that, until now, has not been possible.

3D single point imaging with compressed sensing provides high temporal resolution R 2* mapping for in vivo preclinical applications

OBJECTIVE

Purely phase-encoded techniques such as single point imaging (SPI) are generally unsuitable for in vivo imaging due to lengthy acquisition times. Reconstruction of highly undersampled data using compressed sensing allows SPI data to be quickly obtained from animal models, enabling applications in preclinical cellular and molecular imaging.

MATERIALS AND METHODS

TurboSPI is a multi-echo single point technique that acquires hundreds of images with microsecond spacing, enabling high temporal resolution relaxometry of large-R ₂* systems such as iron-loaded cells. TurboSPI acquisitions can be pseudo-randomly undersampled in all three dimensions to increase artifact incoherence, and can provide prior information to improve reconstruction. We evaluated the performance of CS-TurboSPI in phantoms, a rat ex vivo, and a mouse in vivo.

RESULTS

An algorithm for iterative reconstruction of TurboSPI relaxometry time courses does not affect image quality or R ₂* mapping in vitro at acceleration factors up to 10. Imaging ex vivo is possible at similar acceleration factors, and in vivo imaging is demonstrated at an acceleration factor of 8, such that acquisition time is under 1 h.

CONCLUSIONS

Accelerated TurboSPI enables preclinical R ₂* mapping without loss of data quality, and may show increased specificity to iron oxide compared to other sequences.

Optimal sampling with prior information of the image geometry in microfluidic MRI

Recent advances in MRI acquisition for microscopic flows enable unprecedented sensitivity and speed in a portable NMR/MRI microfluidic analysis platform. However, the application of MRI to microfluidics usually suffers from prolonged acquisition times owing to the combination of the required high resolution and wide field of view necessary to resolve details within microfluidic channels. When prior knowledge of the image geometry is available as a binarized image, such as for microfluidic MRI, it is possible to reduce sampling requirements by incorporating this information into the reconstruction algorithm. The current approach to the design of the partial weighted random sampling schemes is to bias toward the high signal energy portions of the binarized image geometry after Fourier transformation (i.e. in its k-space representation). Although this sampling prescription is frequently effective, it can be far from optimal in certain limiting cases, such as for a 1D channel, or more generally yield inefficient sampling schemes at low degrees of sub-sampling. This work explores the tradeoff between signal acquisition and incoherent sampling on image reconstruction quality given prior knowledge of the image geometry for weighted random sampling schemes, finding that optimal distribution is not robustly determined by maximizing the acquired signal but from interpreting its marginal change with respect to the sub-sampling rate. We develop a corresponding sampling design methodology that deterministically yields a near optimal sampling distribution for image reconstructions incorporating knowledge of the image geometry. The technique robustly identifies optimal weighted random sampling schemes and provides improved reconstruction fidelity for multiple 1D and 2D images, when compared to prior techniques for sampling optimization given knowledge of the image geometry.

Magnetic resonance signal moment determination using the Earth's magnetic field

We demonstrate a method to manipulate magnetic resonance data such that the moments of the signal spatial distribution are readily accessible. Usually, magnetic resonance imaging relies on data acquired in so-called k-space which is subsequently Fourier transformed to render an image. Here, via analysis of the complex signal in the vicinity of the centre of k-space we are able to access the first three moments of the signal spatial distribution, ultimately in multiple directions. This is demonstrated for biofouling of a reverse osmosis (RO) membrane module, rendering unique information and an early warning of the onset of fouling. The analysis is particularly applicable for the use of mobile magnetic resonance spectrometers; here we demonstrate it using an Earth's magnetic field system.

Ultrashort echo time (UTE) imaging using gradient pre-equalization and compressed sensing

Ultrashort echo time (UTE) imaging is a well-known technique used in medical MRI, however, the implementation of the sequence remains non-trivial. This paper introduces UTE for non-medical applications and outlines a method for the implementation of UTE to enable accurate slice selection and short acquisition times. Slice selection in UTE requires fast, accurate switching of the gradient and r.f. pulses. Here a gradient "pre-equalization" technique is used to optimize the gradient switching and achieve an effective echo time of 10μs. In order to minimize the echo time, k-space is sampled radially. A compressed sensing approach is used to minimize the total acquisition time. Using the corrections for slice selection and acquisition along with novel image reconstruction techniques, UTE is shown to be a viable method to study samples of cork and rubber with a shorter signal lifetime than can typically be measured. Further, the compressed sensing image reconstruction algorithm is shown to provide accurate images of the samples with as little as 12.5% of the full k-space data set, potentially permitting real time imaging of short T2(*) materials.

Multiscale reconstruction algorithm for compressed sensing

Compressed sensing (CS) method has attracted increasing attention owing to providing a novel insight for signal and image processing technology. Acquiring high-quality reconstruction results plays a crucial role in successful applications of CS method. This paper presents a multiscale reconstruction model that simultaneously considers the inaccuracy properties on the measurement data and the measurement matrix. Based on the wavelet analysis method, the original inverse problem is decomposed into a sequence of inverse problems, which are solved successively from the largest scale to the original scale. An objective functional, that integrate the beneficial advantages of the least trimmed sum of absolute deviations (LTA) estimation and the combinational M-estimation, is proposed. An iteration scheme that incorporates the advantages of the homotopy method and the evolutionary programming (EP) algorithm is designed for solving the proposed objective functional. Numerical simulations are implemented to validate the feasibility of the proposed reconstruction method.

Spatially resolved D-T(2) correlation NMR of porous media

Within the past decade, 2D Laplace nuclear magnetic resonance (NMR) has been developed to analyze pore geometry and diffusion of fluids in porous media on the micrometer scale. Many objects like rocks and concrete are heterogeneous on the macroscopic scale, and an integral analysis of microscopic properties provides volume-averaged information. Magnetic resonance imaging (MRI) resolves this spatial average on the contrast scale set by the particular MRI technique. Desirable contrast parameters for studies of fluid transport in porous media derive from the pore-size distribution and the pore connectivity. These microscopic parameters are accessed by 1D and 2D Laplace NMR techniques. It is therefore desirable to combine MRI and 2D Laplace NMR to image functional information on fluid transport in porous media. Because 2D Laplace resolved MRI demands excessive measuring time, this study investigates the possibility to restrict the 2D Laplace analysis to the sum signals from low-resolution pixels, which correspond to pixels of similar amplitude in high-resolution images. In this exploratory study spatially resolved D-T2 correlation maps from glass beads and mortar are analyzed. Regions of similar contrast are first identified in high-resolution images to locate corresponding pixels in low-resolution images generated with D-T2 resolved MRI for subsequent pixel summation to improve the signal-to-noise ratio of contrast-specific D-T2 maps. This method is expected to contribute valuable information on correlated sample heterogeneity from the macroscopic and the microscopic scales in various types of porous materials including building materials and rock.

Low-field permanent magnets for industrial process and quality control

In this review we focus on the technology associated with low-field NMR. We present the current state-of-the-art in low-field NMR hardware and experiments, considering general magnet designs, rf performance, data processing and interpretation. We provide guidance on obtaining the optimum results from these instruments, along with an introduction for those new to low-field NMR. The applications of lowfield NMR are now many and diverse. Furthermore, niche applications have spawned unique magnet designs to accommodate the extremes of operating environment or sample geometry. Trying to capture all the applications, methods, and hardware encompassed by low-field NMR would be a daunting task and likely of little interest to researchers or industrialists working in specific subject areas. Instead we discuss only a few applications to highlight uses of the hardware and experiments in an industrial environment. For details on more particular methods and applications, we provide citations to specialized review articles.

Phase reconstruction from velocity-encoded MRI measurements--a survey of sparsity-promoting variational approaches

In recent years there has been significant developments in the reconstruction of magnetic resonance velocity images from sub-sampled k-space data. While showing a strong improvement in reconstruction quality compared to classical approaches, the vast number of different methods, and the challenges in setting them up, often leaves the user with the difficult task of choosing the correct approach, or more importantly, not selecting a poor approach. In this paper, we survey variational approaches for the reconstruction of phase-encoded magnetic resonance velocity images from sub-sampled k-space data. We are particularly interested in regularisers that correctly treat both smooth and geometric features of the image. These features are common to velocity imaging, where the flow field will be smooth but interfaces between the fluid and surrounding material will be sharp, but are challenging to represent sparsely. As an example we demonstrate the variational approaches on velocity imaging of water flowing through a packed bed of solid particles. We evaluate Wavelet regularisation against Total Variation and the relatively recent second order Total Generalised Variation regularisation. We combine these regularisation schemes with a contrast enhancement approach called Bregman iteration. We verify for a variety of sampling patterns that Morozov's discrepancy principle provides a good criterion for stopping the iterations. Therefore, given only the noise level, we present a robust guideline for setting up a variational reconstruction scheme for MR velocity imaging.

Faster imaging with a portable unilateral NMR device

Unilateral NMR devices are important tools in various applications such as non-destructive testing and well logging, but are not applied routinely for imaging, primarily because B0 inhomogeneity in these scanners leads to a relatively low signal and requires use of the slow single point imaging scan scheme. Enabling high quality, fast imaging could make this affordable and portable technology practical for various imaging applications as well as for new applications that are not yet feasible with MRI technology. The goal of this work was to improve imaging times in a portable unilateral NMR scanner. Both Compressed Sensing and Fast Spin Echo were modified and applied to fit the unique characteristics of a unilateral device. Two printed phantoms, allowing high resolution images, were scanned with both methods and compared to a standard scan and to a low pass scan to evaluate performance. Both methods were found to be feasible with a unilateral device, proving ways to accelerate single point imaging in such scanners. This outcome encourages us to explore how to further accelerate imaging times in unilateral NMR devices so that this technology might become clinically applicable in the future.

Velocity field measurements in sedimentary rock cores by magnetization prepared 3D SPRITE

A time-efficient MRI method suitable for quantitative mapping of 3-D velocity fields in sedimentary rock cores, and granular samples is discussed. The method combines the 13-interval Alternating-Pulsed-Gradient Stimulated-Echo (APGSTE) scheme and three-dimensional Single Point Ramped Imaging with T(1) Enhancement (SPRITE). Collecting a few samples near the q-space origin and employing restricted k-space sampling dramatically improves the performance of the imaging method. The APGSTE-SPRITE method is illustrated through mapping of 3-D velocity field in a macroscopic bead pack and heterogeneous sandstone and limestone core plugs. The observed flow patterns are consistent with a general trend for permeability to increase with the porosity. Domains of low permeability obstruct the flow within the core volume. Water tends to flow along macroscopic zones of higher porosity and across zones of lower porosity.

Rapid 3D-imaging of phosphocreatine recovery kinetics in the human lower leg muscles with compressed sensing

The rate of phosphocreatine (PCr) resynthesis following physical exercise is an accepted index of mitochondrial oxidative metabolism and has been studied extensively with unlocalized (31)P-MRS methods and small surface coils. Imaging experiments using volume coils that measure several muscles simultaneously can provide new insights into the variability of muscle function in healthy and diseased states. However, they are limited by long acquisition times relative to the dynamics of PCr recovery. This work focuses on the implementation of a compressed sensing technique to accelerate imaging of PCr resynthesis following physical exercise, using a modified three-dimensional turbo-spin-echo sequence and principal component analysis as sparsifying transform. The compressed sensing technique was initially validated using 2-fold retrospective undersampling of fully sampled data from four volunteers acquired on a 7T MRI system (voxel size: 1.6 mL, temporal resolution: 24 s), which led to an accurate estimation of the mono-exponential PCr resynthesis rate constant (mean error <6.4%). Acquisitions with prospective 2-fold acceleration (temporal resolution: 12 s) demonstrated that three-dimensional mapping of PCr resynthesis is possible at a temporal resolution that is sufficiently high for characterizing the recovery curve of several muscles in a single measurement.

On the utility of spectroscopic imaging as a tool for generating geometrically accurate MR images and parameter maps in the presence of field inhomogeneities and chemical shift effects

Lack of spatial accuracy is a recognized problem in magnetic resonance imaging (MRI) which severely detracts from its value as a stand-alone modality for applications that put high demands on geometric fidelity, such as radiotherapy treatment planning and stereotactic neurosurgery. In this paper, we illustrate the potential and discuss the limitations of spectroscopic imaging as a tool for generating purely phase-encoded MR images and parameter maps that preserve the geometry of an object and allow localization of object features in world coordinates. Experiments were done on a clinical system with standard facilities for imaging and spectroscopy. Images were acquired with a regular spin echo sequence and a corresponding spectroscopic imaging sequence. In the latter, successive samples of the acquired echo were used for the reconstruction of a series of evenly spaced images in the time and frequency domain. Experiments were done with a spatial linearity phantom and a series of test objects representing a wide range of susceptibility- and chemical-shift-induced off-resonance conditions. In contrast to regular spin echo imaging, spectroscopic imaging was shown to be immune to off-resonance effects, such as those caused by field inhomogeneity, susceptibility, chemical shift, f(0) offset and field drift, and to yield geometrically accurate images and parameter maps that allowed object structures to be localized in world coordinates. From these illustrative examples and a discussion of the limitations of purely phase-encoded imaging techniques, it is concluded that spectroscopic imaging offers a fundamental solution to the geometric deficiencies of MRI which may evolve toward a practical solution when full advantage will be taken of current developments with regard to scan time reduction. This perspective is backed up by a demonstration of the significant scan time reduction that may be achieved by the use of compressed sensing for a simple phantom.

Two-dimensional T2 distribution mapping in rock core plugs with optimal k-space sampling

Spin-echo single point imaging has been employed for 1D T(2) distribution mapping, but a simple extension to 2D is challenging since the time increase is n fold, where n is the number of pixels in the second dimension. Nevertheless 2D T(2) mapping in fluid saturated rock core plugs is highly desirable because the bedding plane structure in rocks often results in different pore properties within the sample. The acquisition time can be improved by undersampling k-space. The cylindrical shape of rock core plugs yields well defined intensity distributions in k-space that may be efficiently determined by new k-space sampling patterns that are developed in this work. These patterns acquire 22.2% and 11.7% of the k-space data points. Companion density images may be employed, in a keyhole imaging sense, to improve image quality. T(2) weighted images are fit to extract T(2) distributions, pixel by pixel, employing an inverse Laplace transform. Images reconstructed with compressed sensing, with similar acceleration factors, are also presented. The results show that restricted k-space sampling, in this application, provides high quality results.

Quantification of superparamagnetic iron oxide with large dynamic range using TurboSPI

This work proposes the use of TurboSPI, a multi-echo single point imaging sequence, for the quantification of labeled cells containing moderate to high concentrations of iron oxide contrast agent. At each k-space location, TurboSPI acquires several hundred time points during a spin echo, permitting reliable relaxation rate mapping of large-R(2)(∗) materials. An automatic calibration routine optimizes image quality by promoting coherent alignment of spin and stimulated echoes throughout the multi-echo train, and this calibration is sufficiently robust for in vivo applications. In vitro relaxation rate measurements of SPIO-loaded cervical cancer cells exhibit behavior consistent with theoretical predictions of the static dephasing regime in the spin echo case; the relaxivity measured with TurboSPI was 10.47±2.3 s(-1)/mG, comparable to the theoretical value of 10.78 s(-1)/mG. Similar measurements of micron-sized iron oxide particles (0.96 μm and 1.63 μm diameter) show a reduced relaxivity of 8.06±0.68 s(-1)/mG and 7.13±0.31 s(-1)/mG respectively, indicating that the static dephasing criterion was not met. Nonetheless, accurate quantification of such particles is demonstrated up to R(2)(∗)=900 s(-1), with a potentially higher upper limit for loaded cells having a more favorable R(2)('):R(2) ratio. Based on the cells used in this study, reliable quantification of cells loaded with 10 pg of iron per cell should be possible up to a density of 27 million cells/mL. Such quantification will be of crucial importance to the development of longitudinal monitoring for cellular therapy and other procedures using iron-labeled cells.

MR imaging of ore for heap bioleaching studies using pure phase encode acquisition methods

Various MRI techniques were considered with respect to imaging of aqueous flow fields in low grade copper ore. Spin echo frequency encoded techniques were shown to produce unacceptable image distortions which led to pure phase encoded techniques being considered. Single point imaging multiple point acquisition (SPI-MPA) and spin echo single point imaging (SESPI) techniques were applied. By direct comparison with X-ray tomographic images, both techniques were found to be able to produce distortion-free images of the ore packings at 2 T. The signal to noise ratios (SNRs) of the SESPI images were found to be superior to SPI-MPA for equal total acquisition times; this was explained based on NMR relaxation measurements. SESPI was also found to produce suitable images for a range of particles sizes, whereas SPI-MPA SNR deteriorated markedly as particles size was reduced. Comparisons on a 4.7 T magnet showed significant signal loss from the SPI-MPA images, the effect of which was accentuated in the case of unsaturated flowing systems. Hence it was concluded that SESPI was the most robust imaging method for the study of copper ore heap leaching hydrology.

Two-dimensional T2 distribution mapping in porous solids with phase encode MRI

Two pure phase encode MRI sequences, CPMG-prepared SPRITE and spin-echo SPI with compressed sensing, for two-dimensional (2-D) T2 distribution mapping have been presented. The sequences are 2-D extensions of their 1-D predecessors previously described and are intended for studying processes in porous solids and other samples with short relaxation times whenever 2-D T2 maps are preferable to simple 1-D profiling. The sequences were tested on model samples and natural water-saturated rocks, in a low field MRI instrument. 2-D spin-echo SPI and CPMG-SPRITE demonstrate a similar performance, enabling measurement of T2 down to 1-2 ms. Both experiments are time consuming (up to 2-2.5 h sample dependent). As such, they can be recommended mostly for measurement during steady state conditions or when studying relatively slow dynamic processes (e.g. enhanced oil recovery, cement paste hydration, curing rubber, infiltration of paramagnetic ions).

Accelerating multi-echo T2 weighted MR imaging: analysis prior group-sparse optimization

This works addresses the problem of reconstructing multi-echo T2 weighted MR images from partially sampled K-space data. Previous studies in reconstructing MR images from partial samples of the K-space used Compressed Sensing (CS) techniques to exploit the spatial correlation of the images (leading to sparsity in transform domain). Such techniques can be employed to reconstruct the individual T2 weighted images. However, in the current context, the different images are not independent; they are images of the same cross section, and hence are highly correlated. In this work, we not only exploit the spatial correlation within the image, but also the correlation between the images to achieve even better reconstruction results. For individual MR images, CS based techniques lead to a sparsity promoting optimization problem in a transform domain. In this paper, we show how to extend the same framework in order to incorporate correlation between images leading to group sparsity promoting optimization. Group sparsity promoting optimization is popularly formulated as a synthesis prior problem. The synthesis prior formulation for group sparsity leads to superior reconstruction results compared to ordinary sparse reconstruction. However, in this paper we show that when group sparsity is framed as an analysis prior problem the reconstruction results are even better for proper choice of the sparsifying transform. An interesting observation of this work is that when the same sampling pattern is used to sample the K-space for all the T2 weighted echoes, group sparsity does not yield any noticeable improvement, but when different sampling patterns are used for different echoes, our proposed group sparsity promoting formulation yields significant improvement (in terms of Normalized Mean Squared Error) over previous CS based techniques.

Application of compressed sensing to in vivo 3D ¹⁹F CSI

This study shows how applying compressed sensing (CS) to (19)F chemical shift imaging (CSI) makes highly accurate and reproducible reconstructions from undersampled datasets possible. The missing background signal in (19)F CSI provides the required sparsity needed for application of CS. Simulations were performed to test the influence of different CS-related parameters on reconstruction quality. To test the proposed method on a realistic signal distribution, the simulation results were validated by ex vivo experiments. Additionally, undersampled in vivo 3D CSI mouse datasets were successfully reconstructed using CS. The study results suggest that CS can be used to accurately and reproducibly reconstruct undersampled (19)F spectroscopic datasets. Thus, the scanning time of in vivo(19)F CSI experiments can be significantly reduced while preserving the ability to distinguish between different (19)F markers. The gain in scan time provides high flexibility in adjusting measurement parameters. These features make this technique a useful tool for multiple biological and medical applications.

Feasibility of high temporal resolution breast DCE-MRI using compressed sensing theory

PURPOSE

To investigate the feasibility of high temporal resolution breast DCE-MRI using compressed sensing theory.

METHODS

Two experiments were designed to investigate the feasibility of using reference image based compressed sensing (RICS) technique in DCE-MRI of the breast. The first experiment examined the capability of RICS to faithfully reconstruct uptake curves using undersampled data sets extracted from fully sampled clinical breast DCE-MRI data. An average approach and an approach using motion estimation and motion compensation (ME/MC) were implemented to obtain reference images and to evaluate their efficacy in reducing motion related effects. The second experiment, an in vitro phantom study, tested the feasibility of RICS for improving temporal resolution without degrading the spatial resolution.

RESULTS

For the uptake-curve reconstruction experiment, there was a high correlation between uptake curves reconstructed from fully sampled data by Fourier transform and from undersampled data by RICS, indicating high similarity between them. The mean Pearson correlation coefficients for RICS with the ME/MC approach and RICS with the average approach were 0.977 +/- 0.023 and 0.953 +/- 0.031, respectively. The comparisons of final reconstruction results between RICS with the average approach and RICS with the ME/MC approach suggested that the latter was superior to the former in reducing motion related effects. For the in vitro experiment, compared to the fully sampled method, RICS improved the temporal resolution by an acceleration factor of 10 without degrading the spatial resolution.

CONCLUSIONS

The preliminary study demonstrates the feasibility of RICS for faithfully reconstructing uptake curves and improving temporal resolution of breast DCE-MRI without degrading the spatial resolution.

Reducing data acquisition times in phase-encoded velocity imaging using compressed sensing

We present a method for accelerating the acquisition of phase-encoded velocity images by the use of compressed sensing (CS), a technique that exploits the observation that an under-sampled signal can be accurately reconstructed by utilising the prior knowledge that it is sparse or compressible. We present results of both simulated and experimental measurements of liquid flow through a packed bed of spherical glass beads. For this system, the best image reconstruction used a spatial finite-differences transform. The reconstruction was further improved by utilising prior knowledge of the liquid distribution within the image. Using this approach, we demonstrate that for a sampling fraction of approximately 30% of the full k-space data set, the velocity can be recovered with a relative error of 11%, which is below the visually detectable limit. Furthermore, the error in the total flow measured using the CS reconstruction is <3% for sampling fractions > or = 30%. Thus, quantitative velocity images were obtained in a third of the acquisition time required using conventional imaging. The reduction in data acquisition time can also be exploited in acquiring images at a higher spatial resolution, which increases the accuracy of the measurements by reducing errors arising from partial volume effects. To illustrate this, the CS algorithm was used to reconstruct gas-phase velocity images at a spatial resolution of 230 microm x 230 microm. Images at this spatial resolution are prohibitively time-consuming to acquire using full k-space sampling techniques.