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PURPOSE: To compare different optimization approaches for choosing the spin-lock times (TSLs), in spin-lattice relaxation time in the rotating frame (T(1ρ)) mapping. METHODS: Optimization criteria for TSLs based on Cramér-Rao lower bounds (CRLB) are compared with matched sampling-fitting (MSF) approaches for T(1ρ) mapping on synthetic data, model phantoms, and knee cartilage. The MSF approaches are optimized using robust methods for noisy cost functions. The MSF approaches assume that optimal TSLs depend on the chosen fitting method. An iterative non-linear least squares (NLS) and artificial neural networks (ANN) are tested as two possible T(1ρ) fitting methods for MSF approaches. RESULTS: All optimized criteria were better than non-optimized ones. However, we observe that a modified CRLB and an MSF based on the mean of the normalized absolute error (MNAE) were more robust optimization approaches, performing well in all tested cases. The optimized TSLs obtained the best performance with synthetic data (3.5–8.0% error), model phantoms (1.5–2.8% error), and healthy volunteers (7.7–21.1% error), showing stable and improved quality results, comparing to non-optimized approaches (4.2–13.3% error on synthetic data, 2.1–6.2% error on model phantoms, 9.8–27.8% error on healthy volunteers). CONCLUSION: A modified CRLB and the MSF based on MNAE are robust optimization approaches for choosing TSLs in T(1ρ) mapping. All optimized criteria allowed good results even using rapid scans with 2 TSLs when a complex-valued fitting is done with iterative NLS or ANN.

Quantitative MRI can detect early biochemical changes in cartilage; however, the conventional techniques only measure one parameter (e.g., Tsub1/sub, Tsub2/sub, and Tsub1ρ/sub) at a time while also being comparatively slow. We implemented a 3D magnetic resonance fingerprinting (3D-MRF) technique for simultaneous, volumetric mapping of Tsub1/sub, Tsub2/sub, and Tsub1ρ/subin knee articular cartilage in under 9 min. It is evaluated on 11 healthy volunteers (mean age: 53 ± 9 years), five mild knee osteoarthritis (OA) patients (Kellgren-Lawrence (KL) score: 2, mean age: 60 ± 4 years), and the National Institute of Standards and Technology (NIST)/International Society for Magnetic Resonance in Medicine (ISMRM) system phantom. Proton density image, and Tsub1/sub, Tsub2,/subTsub1ρ/subrelaxation times, and Bsub1/subsup+/supwere estimated in the NIST/ISMRM system phantom as well as in the human knee medial and lateral femur, medial and lateral tibia, and patellar cartilage. The repeatability and reproducibility of the proposed technique were assessed in the phantom using analysis of the Bland-Altman plots. The intrasubject repeatability was assessed with the coefficient of variation (CV) and root mean square CV (rmsCV). The Mann-Whitney U test was used to assess the difference between healthy subjects and mild knee OA patients. The Bland-Altman plots in the NIST/ISMRM phantom demonstrated an average difference of 0.001% ± 015%, 1.2% ± 7.1%, and 0.47% ± 3% between two scans from the same 3-T scanner (repeatability), and 0.002% ± 015%, 0.62% ± 10.5%, and 0.97% ± 14% between the scans acquired on two different 3-T scanners (reproducibility) for Tsub1/sub, Tsub2/sub, and Tsub1ρ/sub, respectively. The in vivo knee study showed excellent repeatability with rmsCV less than 1%, 2%, and 1% for Tsub1/sub, Tsub2/sub, and Tsub1ρ/sub, respectively. Tsub1ρ/subrelaxation time in the mild knee OA patients was significantly higher (p lt; 0.05) than in healthy subjects. The proposed 3D-MRF sequence is fast, reproducible, robust to Bsub1/subsup+/supinhomogeneity, and can simultaneously measure the Tsub1/sub, Tsub2/sub, Tsub1ρ/sub, and Bsub1/subsup+/supvolumetric maps of the knee joint in a single scan within a clinically feasible scan time.

Quantitative MRI can detect early biochemical changes in cartilage, but its bilateral use in clinical routines is challenging. The aim of this prospective study was to demonstrate the feasibility of magnetic resonance fingerprinting for bilateral simultaneous T(1), T(2), and T(1ρ) mapping of the hip joint. The study population consisted of six healthy volunteers with no known trauma or pain in the hip. Monoexponential T(1), T(2), and T(1ρ) relaxation components were assessed in femoral lateral, superolateral, and superomedial, and inferior, as well as acetabular, superolateral, and superomedial subregions in left and right hip cartilage. Aligned ranked nonparametric factorial analysis was used to assess the side’s impact on the subregions. Kruskal–Wallis and Wilcoxon tests were used to compare subregions, and coefficient of variation to assess repeatability. Global averages of T(1) (676.0 ± 45.4 and 687.6 ± 44.5 ms), T(2) (22.5 ± 2.6 and 22.1 ± 2.5 ms), and T(1ρ) (38.2 ± 5.5 and 38.2 ± 5.5 ms) were measured in the left and right hip, and articular cartilage, respectively. The Kruskal–Wallis test showed a significant difference between different subregions’ relaxation times regardless of the hip side (p < 0.001 for T(1), p = 0.012 for T(2), and p < 0.001 for T(lρ)). The Wilcoxon test showed that T(1) of femoral layers was significantly (p < 0.003) higher than that for acetabular cartilage. The experiments showed excellent repeatability with CV(rms) of 1%, 2%, and 4% for T(1), T(2), and T(1ρ,) respectively. It was concluded that bilateral T(1), T(2), and T(1ρ) relaxation times, as well as B(1)(+) maps, can be acquired simultaneously from hip joints using the proposed MRF sequence.

Purpose To use golden-angle radial sampling and compressed sensing (CS) for accelerating mono- and biexponential 3D spin-lattice relaxation time in the rotating frame (T1ρ ) mapping of knee cartilage. Methods Golden-angle radial stack-of-stars and Cartesian 3D-T1ρ -weighted knee cartilage datasets (n = 12) were retrospectively undersampled by acceleration factors (AFs) 2-10. CS-based reconstruction using 8 different sparsifying transforms were compared for mono- and biexponential T1ρ -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 Most CS methods performed well for an AF of 2, with relative median normalized absolute deviation below 10% for monoexponential and biexponential mapping. For monoexponential mapping, radial sampling obtained a median normalized absolute deviation below 10% up to AF of 10, while Cartesian obtained this level of error only up to AF of 4. Radial sampling was also better with biexponential T1ρ mapping, with median normalized absolute deviation below 10% up to AF of 6. Conclusion Golden-angle radial acquisitions combined with CS outperformed Cartesian acquisitions for 3D-T1ρ 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.

In this study we use undersampled MRI acquisition methods to obtain accelerated 3D mono and biexponential spin–lattice relaxation time in the rotating frame (T1ρ) mapping of knee cartilage, reducing the usual long scan time. We compare the accelerated T1ρ maps obtained by deep learning-based variational network (VN) and compressed sensing (CS). Both methods were compared with spatial (S) and spatio-temporal (ST) filters. Complex-valued fitting was used for T1ρ parameters estimation. We tested with seven in vivo and six synthetic datasets, with acceleration factors (AF) from 2 to 10. Median normalized absolute deviation (MNAD), analysis of variance (ANOVA), and coefficient of variation (CV) were used for analysis. The methods CS-ST, VN-S, and VN-ST performed well for accelerating monoexponential T1ρ mapping, with MNAD around 5% for AF = 2, which increases almost linearly with the AF to an MNAD of 13% for AF = 8, with all methods. For biexponential mapping, the VN-ST was the best method starting with MNAD of 7.4% for AF = 2 and reaching MNAD of 13.1% for AF = 8. The VN was able to produce 3D-T1ρ mapping of knee cartilage with lower error than CS. The best results were obtained by VN-ST, improving CS-ST method by nearly 7.5%.

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 Use compressed sensing (CS) for 3D biexponential spin-lattice relaxation time in the rotating frame (T1ρ ) mapping of knee cartilage, reducing the total scan time and maintaining the quality of estimated biexponential T1ρ parameters (short and long relaxation times and corresponding fractions) comparable to fully sampled scans. Methods Fully sampled 3D-T1ρ -weighted data sets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared for biexponential T1ρ -mapping of knee cartilage, including temporal and spatial wavelets and finite differences, dictionary from principal component analysis (PCA), k-means singular value decomposition (K-SVD), exponential decay models, and also low rank and low rank plus sparse models. Synthetic phantom (N = 6) and in vivo human knee cartilage data sets (N = 7) were included in the experiments. Spatial filtering before biexponential T1ρ 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 Accelerating biexponential 3D-T1ρ 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%.

Purpose To evaluate the feasibility of using compressed sensing (CS) to accelerate 3D-T1ρ mapping of cartilage and to reduce total scan times without degrading the estimation of T1ρ relaxation times. Methods Fully sampled 3D-T1ρ datasets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared, including finite differences, temporal and spatial wavelets, learned transforms using principal component analysis (PCA) and K-means singular value decomposition (K-SVD), explicit exponential models, low rank and low rank plus sparse models. Spatial filtering prior to T1ρ parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included. Results Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative T1ρ error lower than 4.5%. Some sparsifying transforms, such as spatiotemporal finite difference (STFD), exponential dictionaries (EXP) and low rank combined with spatial finite difference (L+S SFD) significantly improved this performance, reaching average relative T1ρ error below 6.5% on T1ρ relaxation times with AF up to 10, when spatial filtering was used before T1ρ fitting, at the expense of smoothing the T1ρ maps. The STFD achieved 5.1% error at AF = 10 with spatial filtering prior to T1ρ fitting. Conclusion Accelerating 3D-T1ρ mapping of cartilage with CS is feasible up to AF of 10 when using STFD, EXP or L+S SFD regularizers. These three best CS methods performed satisfactorily on synthetic phantom and in vivo knee cartilage for AFs up to 10, with T1ρ error of 6.5%.

Miniaturization is a major challenge in fabricating medical microrobots designed to operate inside the human body. Current microrobots lack an adequate embedded communication system to transmit sensory data due to a shortage of power. In this paper, we propose a communication method, using the susceptibility effect in MRI, to overcome the size and power constraints in microrobots. The proposed method relies on a binary communication scheme in the form of a frequency alteration in the electrical current circulating along a miniature coil embedded in a microrobot. The frequency of the electrical current could be regulated by a predetermined sensory threshold input implemented in the microrobot. Such a frequency provides information on the level of sensory information gathered by the microrobot, and it is determined using single-shot EPI-GE MR images. The proposed method is independent of the microrobot’s position and orientation. Moreover, the experiments showed that MRI is sensitive enough to detect the change in magnetic field if we scaled the coil to an appropriate size for embedding into the microrobot. The proposed method could potentially apply to microrobots for monitoring and mapping specific physiological conditions within the body.

Visualization of small blood vessels feeding tumor sites provides important information on the tumors and their microenvironment. This information plays an important role in targeted drug therapies using magnetic gradients. However, capabilities of current clinical imaging modalities may be insufficient to resolve complex microvascular networks. The purpose of this study is to map the vascular network, 3D, based on the magnetic susceptibility contrast.Magnetic particles induce an inhomogeneity in the MRI's magnetic field in an order much larger than their real size. This is an approach to compensate the spatial resolution insufficiency of a clinical MR scanner. Micron-sized agglomerations of magnetite nanoparticles were injected in a 3D phantom vascular network, and a fast multislice, multiacquisition MR sequence was applied to track the agglomerations along their trajectories. The experiment was performed twice for two different imaging planes: coronal and transversal. The susceptibility artifact in the images indicated the presence and the position of the agglomerations. The calculated positions through multiple images were assembled to build up the 3D distribution of the vascular network.The calculated points were compared with the centerline of the channels, extracted from the 3D reference image, to determine the absolute measurement error. The mean error was measured to be approximately half of the pixel's size. It was found that the positioning error on the axis perpendicular to the imaging slice was nearly twice as high as on the imaging plane axes due to the slice thickness. In order to compensate for the lack of resolution on the perpendicular axis, the reconstruction was performed using a combination of coronal and transversal data. The combination of the coordinates led to a significant decrease in the mean measurement error at each segment in the vascular network (p0.001).A method for 3D reconstruction of a microvascular network based on the susceptibility contrast in MRI and using a clinical scanner and a commercial receiver coil was proposed. The method presents a novel approach for reconstruction of vascular networks using the susceptibility effect. The proposed method may be applied to resolve vascular networks at a micrometric scale.

The purpose of this study was to demonstrate the feasibility of biexponential T1ρ relaxation mapping of human knee cartilage in vivo. A three-dimensional, customized, turbo-flash sequence was used to acquire T1ρ-weighted images from healthy volunteers employing a standard 3-T MRI clinical scanner. A series of T1ρ-weighted images was fitted using monoexponential and biexponential models with two- and four-parametric non-linear approaches, respectively. Non-parametric Kruskal–Wallis and Mann–Whitney U-statistical tests were used to evaluate the regional relaxation and gender differences, respectively, with a level of significance of P = 0.05. Biexponential relaxations were detected in the cartilage of all volunteers. The short and long relaxation components of T1ρ were estimated to be 6.9 and 51.0 ms, respectively. Similarly, the fractions of short and long T1ρ were 37.6% and 62.4%, respectively. The monoexponential relaxation of T1ρ was 32.6 ms. The experiments showed good repeatability with a coefficient of variation (CV) of less than 20%. A biexponential relaxation model showed a better fit than a monoexponential model to the T1ρ relaxation decay in knee cartilage. Biexponential T1ρ components could potentially be used to increase the specificity to detect early osteoarthritis by the measurement of different water compartments and their fractions.