Optimal k-space sampling for single point imaging of transient systems

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.

Quasi-Random Single-Point Imaging Using Low-Discrepancy $k$ -Space Sampling

Magnetic resonance imaging of short relaxation time spin systems has been a widely discussed topic with serious clinical applications and led to the emergence of fast imaging ultra-short echo-time sequences. Nevertheless, these sequences suffer from image blurring, due to the related sampling point spread function and are highly prone to imaging artefacts arising from, e.g., chemical shifts or magnetic susceptibilities. In this paper, we present a concept of spherical quasi-random single-point imaging. The approach is highly accelerateable, due to intrinsic undersampling properties and capable of strong metal artefact suppression. Imaging acceleration is achieved by sampling of quasi-random points in -space, based on a low-discrepancy sequence, and a combination with non-linear optimization reconstruction techniques [compressed sensing (CS)]. The presented low-discrepancy trajectory shows ideal noise like undersampling properties for the combination with CS, leading to denoised images with excellent metal artefact reduction. Using eightfold undersampling, acquisition time of a few minutes can be achieved for volume acquisitions.

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.

Restricted k-space sampling in pure phase encode MRI of rock core plugs

In the study of rock core plugs with multidimensional MRI, the samples are of a regular cylindrical shape that yields well defined intensity distributions in reciprocal space. The high intensity k-space points are concentrated in the central region and in specific peripheral regions. A large proportion of the k-space points have signal intensities that are below the noise level. These points can be zero-filled instead of being collected experimentally. k-space sampling patterns that collect regions of high intensity signal while neglecting low intensity regions can be naturally applied to a wide variety of pure phase encoding measurements, such as T2 mapping SESPI, hybrid-SESPI and SPRITE, since all imaging dimensions can be under-sampled. With a shorter acquisition time, as fewer experimental data points are required, the RF and gradient duty cycles are reduced, while the image SNR is improved.

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.

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.

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.

Towards inherently distortion-free MR images for image-guided radiotherapy on an MRI accelerator

In MR-guided interventions, it is mandatory to establish a solid relationship between the imaging coordinate system and world coordinates. This is particularly important in image-guided radiotherapy (IGRT) on an MRI accelerator, as the interaction of matter with γ-radiation cannot be visualized. In conventional acquisitions, off-resonance effects cause discrepancies between coordinate systems. We propose to mitigate this by using only phase encoding and to reduce the longer acquisitions by under-sampling and regularized reconstruction. To illustrate the performance of this acquisition in the presence of off-resonance phenomena, phantom and in vivo images are acquired using spin-echo (SE) and purely phase-encoded sequences. Data are retrospectively under-sampled and reconstructed iteratively. We observe accurate geometries in purely phase-encoded images for all cases, whereas SE images of the same phantoms display image distortions. Regularized reconstruction yields accurate phantom images under high acceleration factors. In vivo images were reconstructed faithfully while using acceleration factors up to 4. With the proposed technique, inherently undistorted images with one-to-one correspondence to world coordinates can be obtained. It is a valuable tool in geometry quality assurance, treatment planning and online image guidance. Under-sampled acquisition combined with regularized reconstruction can be used to accelerate the acquisition while retaining geometrical accuracy.

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).

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.

Quantitative single point imaging with compressed sensing

A novel approach with respect to single point imaging (SPI), compressed sensing, is presented here that is shown to significantly reduce the loss of accuracy of reconstructed images from under-sampled acquisition data. SPI complements compressed sensing extremely well as it allows unconstrained selection of sampling trajectories. Dynamic processes featuring short T2* NMR signal can thus be more rapidly imaged, in our case the absorption of moisture by a cereal-based wafer material, with minimal loss of image quantification. The absolute moisture content distribution is recovered via a series of images acquired with variable phase encoding times allowing extrapolation to time zero for each image pixel and the effective removal of T2* contrast.