Faculty Bibliography

NMR relaxometry can provide information about the relaxation of the magnetization in different tissues, increasing our understanding of molecular dynamics and biochemical composition in biological systems. In general, tissues have complex and heterogeneous structures composed of multiple pools. As a result, bulk magnetization returns to its original state with different relaxation times, in a multicomponent relaxation. Recovering the distribution of relaxation times in each voxel is a difficult inverse problem; it is usually unstable and requires long acquisition time, especially on clinical scanners. MRI can also be viewed as an inverse problem, especially when compressed sensing (CS) is used. The solution of these two inverse problems, CS and relaxometry, can be obtained very efficiently in a synergistically combined manner, leading to a more stable multicomponent relaxometry obtained with short scan times. In this paper, we will discuss the details of this technique from the viewpoint of inverse problems.

PURPOSE/OBJECTIVE:) mapping of knee cartilage. METHODS:-mapping of knee cartilage, including spatio-temporal finite differences, wavelets, dictionary from principal component analysis, and exponential decay models, and also low rank and low rank plus sparse models (L+S). Complex-valued fitting was used and Marchenko-Pastur principal component analysis filtering also tested. RESULTS:mapping, with median normalized absolute deviation below 10% up to AF of 6. CONCLUSION/CONCLUSIONS:mapping of knee cartilage, being it is a good alternative to Cartesian sampling for reducing scan time and/or improving image and mapping quality. The methods exponential decay models, spatio-temporal finite differences, and low rank obtained the best results for radial sampling patterns.

BACKGROUND:Quantification of dynamic biomechanical strain in articular cartilage in vivo; in situ using noninvasive MRI techniques is desirable and may potentially be used to assess joint pathology. PURPOSE/OBJECTIVE:To demonstrate the use of static mechanical loading and continuous 3D-MRI acquisition of the human knee joint in vivo to measure the strain in the tibiofemoral articular cartilage. STUDY TYPE/METHODS:Prospective. SUBJECTS/METHODS:Five healthy human volunteers (four women, one man; age 25.6 ± 1.7) underwent MRI at rest, under static mechanical loading condition, and during recovery. FIELD STRENGTH/SEQUENCE/UNASSIGNED:A field strength of 3T was used. The sequence used was 3D-continuous golden angle radial sparse parallel (GRASP) MRI and compressed sensing (CS) reconstruction. ASSESSMENT/RESULTS:Tibiofemoral cartilage deformation maps under loading and during recovery were calculated using an optical flow algorithm. The corresponding Lagrangian strain was calculated in the articular cartilage. STATISTICAL TESTS/UNASSIGNED:Range of displacement and strain in each subject, and the resulting mean and standard deviation, were calculated. RESULTS:During the loading condition, the cartilage displacement in the direction of loading ranged from a minimum of -673.6 ± 121.9 μm to a maximum of 726.5 ± 169.5 μm. Corresponding strain ranged from a minimum of -7.0 ± 4.2% to a maximum of 5.4 ± 1.6%. During the recovery condition, the cartilage displacement in the same direction reduced to a minimum of -613.0 ± 129.5 μm and a maximum of 555.7 ± 311.4 μm. The corresponding strain range reduced to a minimum of -1.6 ± 7.5% to a maximum of 4.2 ± 2.6%. DATA CONCLUSION/UNASSIGNED:This study shows the feasibility of using static mechanical loading with continuous GRASP-MRI acquisition to measure the strain in the articular cartilage. By measuring strain during the loading and recovery phases, dynamic strain information in the articular cartilage might be able to be investigated. LEVEL OF EVIDENCE/METHODS:2 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019.

An improvement of the monotone fast iterative shrinkage-thresholding algorithm (MFISTA) for faster convergence is proposed. Our motivation is to reduce the reconstruction time of compressed sensing problems in magnetic resonance imaging. The proposed modification introduces an extra term, which is a multiple of the proximal-gradient step, into the so-called momentum formula used for the computation of the next iterate in MFISTA. In addition, the modified algorithm selects the next iterate as a possibly-improved point obtained by any other procedure, such as an arbitrary shift, a line search, or other methods. As an example, an arbitrary-length shift in the direction from the previous iterate to the output of the proximal-gradient step is considered. The resulting algorithm accelerates MFISTA in a manner that varies with the iterative steps. Convergence analysis shows that the proposed modification provides improved theoretical convergence bounds, and that it has more flexibility in its parameters than the original MFISTA. Since such problems need to be studied in the context of functions of several complex variables, a careful extension of FISTA-like methods to complex variables is provided.

PURPOSE/OBJECTIVE:parameters (short and long relaxation times and corresponding fractions) comparable to fully sampled scans. METHODS:parameter estimation was also tested. RESULTS:Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative median normalized absolute deviation (MNAD) around 10%. Some sparsifying transforms, such as low rank with spatial finite difference (L + S SFD), spatiotemporal finite difference (STFD), and exponential dictionaries (EXP) significantly improved this performance, reaching MNAD below 15% with AF up to 10, when spatial filtering was used. CONCLUSION/CONCLUSIONS:mapping of knee cartilage with CS is feasible. The best results were obtained by STFD, EXP, and L + S SFD regularizers combined with spatial prefiltering. These 3 CS methods performed satisfactorily on synthetic phantom as well as in vivo knee cartilage for AFs up to 10, with median error below 15%.

Model-based image reconstruction has improved contrast and spatial resolution in imaging applications such as magnetic resonance imaging and emission computed tomography. However, these methods have not succeeded in pulse-echo applications like ultrasound imaging due to the typical assumption of a finite grid of possible scatterer locations in a medium⁻an assumption that does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit, that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of two-dimensional ultrasound imaging with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.

More than a decade after the introduction of compressed sensing (CS) in MRI, researchers are still working on ways to translate it into different research and clinical applications. The greatest advantage of CS in MRI is the reduced amount of k-space data needed to reconstruct images, which can be exploited to reduce scan time or to improve spatial resolution and volumetric coverage. Efficient data acquisition using CS is extremely important for compositional mapping of the musculoskeletal system in general and knee cartilage mapping techniques in particular. High-resolution quantitative information about tissue biochemical composition could be obtained in just a few minutes using CS MRI. However, in order to make this goal a reality, some issues still need to be addressed. In this article we review the current state of the art of CS methods for rapid compositional mapping of knee cartilage. Specifically, data acquisition strategies, image reconstruction algorithms, and data fitting models are discussed. Different CS studies for T₂ and T_1ρ mapping of knee cartilage are reviewed, with illustrative results. Future directions, opportunities, and challenges of rapid compositional mapping techniques are also discussed.

PURPOSE/OBJECTIVE:relaxation times. METHODS:parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included. RESULTS:fitting. CONCLUSION/CONCLUSIONS:error of 6.5%.