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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.

Purpose To implement a novel technique for simultaneous, quantitative multiparametric mapping of the knee articular cartilage. Methods A novel MR fingerprinting pulse sequence is proposed and implemented for simultaneous measurements of proton density, T1 , T2, and T1 ρ relaxation times at 3T. The repeatability and reproducibility of the proposed technique were assessed in model phantoms. Institutional review board-approved MR fingerprinting imaging sequence was performed on healthy volunteers and patients with mild knee osteoarthritis. The Wilcoxon test was used to compare healthy controls and patients. The intra- and intersubject repeatability were assessed with coefficient of variation and the RMS coefficient of variation, respectively RESULTS: The Bland-Altman plots demonstrated an average difference of 4.67 ms, -0.09 ms, and 0.05 ms between 2 scans in the same scanner; and 9.68 ms, 0.29 ms, and -0.72 ms between the scans acquired on 2 different scanners for T1 , T2 , and T1 ρ , respectively. The in vivo knee study showed excellent repeatability with RMS coefficient of variation less than 3%, 6%, and 5% for T1 , T2 , and T1 ρ , respectively. The Wilcoxon test showed a significant difference between control and mild osteoarthritis patients for T1 (P = .04), T2 (P = .01), and T1 ρ (P = .02) relaxation time in medial tibial cartilage, as well as for T2 relaxation time (P = .02) in medial femoral cartilage. Conclusion The proposed MRF sequence is fast and can simultaneously measure the T1 , T2 , T1 ρ , and B 1 + maps in a single scan. It is able to discriminate between mild osteoarthritis patients and healthy volunteers.

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 develop a 3D sequence for T1ρ relaxation mapping using radial volumetric encoding (3D-T1ρ -RAVE) and to evaluate the multi relaxation components in the liver of healthy controls and chronic liver disease (CLD) patients. METHODS Fat saturation and T1ρ preparation modules were followed by a train of gradient-echo acquisitions and T1 restoration delay. The series of T1ρ -weighted images were fitted using mono-exponential, bi-exponential, and stretched-exponential models. The repeatability and reproducibility of the proposed technique were evaluated on National Institute of Standards and Technology phantom by calculating the coefficient of variation between test-retest scans on the same scanner and between two different 3T scanners, respectively. Mann-Whitney U-test was performed to assess differences in T1ρ components among patients (n = 3) and a control group (n = 10). RESULTS The phantom study showed an error of 8.9% and 11.5% in mono T2 relaxation time measurement relative to the reference on 2 different scanners. The coefficient of variation for test-retest scans performed on the same scanner was 5.7% and 2.4% for scans performed on 2 scanners. The comparison between healthy controls and CLD patients showed a significant difference (P < .05) in mono relaxation time (P = .002), stretched-exponential relaxation parameter (P = .04). The Akaike information criteria C criterion showed 2.53 ± 0.9% (2.3 ± 0.3% for CLD) of the voxels are bi-exponential while in 65.3 ± 5.8% (81.2 ± 0.06% for CLD) of the liver voxels, the stretched-exponential model was preferred. CONCLUSION The 3D-T1ρ -RAVE sequence allows volumetric, multicomponent T1ρ assessment of the liver during free breathing and can distinguish between healthy volunteers and CLD patients.

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.

PURPOSE: To develop a novel MR-fingerprinting pulse sequence that is insensitive to B(1)(+) and B(0) imperfections for simultaneous T(1), T(2,) and T(1ρ) relaxation mapping. METHODS: We implemented a totally-balanced-spin-lock (TB-SL) module to encode T(1ρ) relaxation into an existing MRF framework that encoded T(1) and T(2). The spin-lock module utilized two 180° pulses with compensatory phases to reduce T(1ρ) sensitivity to B(1) and B(0) inhomogeneities. We compared T(1ρ) measured using TB-SL MRF in Bloch simulations, model agar phantoms, and in-vivo experiments to those with a self-compensated spin-lock preparation module (SC-SL). TB-SL MRF repeatability was evaluated in maps acquired in the lower leg skeletal muscle of 12 diabetic peripheral neuropathy patients scanned two times each during visits separated by ~30 days. RESULTS: The phantom relaxation times measured with TB-SL and SC-SL MRF were in good agreement with reference values in regions with low B(1) inhomogeneities. Compared to SC-SL, TB-SL MRF showed in experiments greater robustness against severe B(1) inhomogeneities and in Bloch simulations greater robustness against B(1) and B(0). We measured with TB-SL MRF average of T(1)=950.1±28.7ms, T(2)=26.0±1.2ms, and T(1ρ)=31.7±3.2ms in skeletal muscle across patients. Bland-Altman analysis demonstrated low bias between TB-SL and SC-SL MRF and between TB-SL MRF maps acquired in two visits. The coefficient of variation was less than 3% for all measurements. CONCLUSION: The proposed TB-SL MRF sequence is fast and insensitive to B(1)(+) and B(0) imperfections. It can simultaneously map T(1), T(2), T(1ρ), and B(1)(+) in a single scan and could potentially be used to study muscle composition.

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.

Background In addition to the articular cartilage, osteoarthritis (OA) affects several other tissues such as tendons, ligaments, and subchondral bone. T1ρ relaxation study of these short T2 tissues may provide a more comprehensive evaluation of OA. Purpose To develop a 3D spin-lattice relaxation in the rotating frame (T1ρ ) prepared zero echo time (ZTE)-based pointwise encoding time reduction with radial acquisition (3D-T1ρ -PETRA) sequence for relaxation mapping of semisolid short-T2 tissues on a clinical 3 T scanner. Study type Prospective. Population Phantom, two bovine whole knee joint and Achilles tendon specimens, 10 healthy volunteers with no known inflammation, trauma or pain in the knee or ankle. Field strength/sequence A customized PETRA sequence to acquire fat-suppressed 3D T1ρ -weighted images tissues with semisolid short T2 / T 2 * relaxation times in the knee and ankle joints at 3 T. Assessment Mono- and biexponential T1ρ relaxation components were assessed in the patellar tendon (PT), anterior cruciate ligament (ACL), posterior cruciate ligament (PCL), and Achilles tendon (AT). Statistical tests Kruskal-Wallis with post-hoc Dunn's test for multiple pairwise comparisons. Results Phantom and ex vivo studies showed the feasibility of T1ρ relaxation mapping using the proposed 3D-T1ρ -PETRA sequence. The in vivo study demonstrated an averaged mono-T1ρ relaxation of (median [IQR]) 15.9 [14.5] msec, 23.6 [9.4] msec, 17.4 [7.4] msec, and 5.8 [10.2] msec in the PT, ACL, PCL, and AT, respectively. The bicomponent analysis showed the short and long components (with their relative fractions) of 0.65 [1.0] msec (46.9 [15.3]%) and 37.3 [18.4] msec (53.1 [15.3]%) for PT, 1.7 [2.1] msec (42.5 [12.5]%) and 43.7 [17.8] msec (57.5 [12.5]%) for ACL, and 1.2 [1.9] msec (42.6 [14.0]%) and 27.7 [14.7] msec (57.3 [14.0]%) for PCL and 0.4 [0.02] msec (58.8 [13.3]%/) and 31.3 [10.8] msec (41.2 [13.3]%) for AT. Statistically significant (P ≤ 0.05) differences were observed in the mono- and biexponential relaxation between several regions. Data conclusion The 3D-T1ρ -PETRA sequence allows volumetric, isotropic (0.78 × 0.78 × 0.78 mm), biexponential T1ρ assessment with corresponding fractions of the tissues with semisolid short T2 / T 2 * . Level of evidence 2 Technical Efficacy Stage: 1 J. Magn. Reson. Imaging 2019;50:1207-1218.

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%.

Background The progressive loss of hyaline articular cartilage due to osteoarthritis (OA) changes the functional and biochemical properties of cartilage. Measuring the T1 ρ along with the morphological assessment can potentially be used as noninvasive biomarkers in detecting early-stage OA. To correlate the biochemical and morphological data, submillimeter isotropic resolution for both studies is required. Purpose To implement a high spatial resolution 3D-isotropic-MRI sequence for simultaneous assessment of morphological and biexponential T1 ρ relaxometry of human knee cartilage in vivo. Study type Prospective. Population Ten healthy volunteers with no known inflammation, trauma, or pain in the knee. Field strength/sequence Standard FLASH sequence and customized Turbo-FLASH sequence to acquire 3D-isotropic-T1 ρ-weighted images on a 3T MRI scanner. Assessment The mean volume and thickness along with mono- and biexponential T1 ρ relaxations were assessed in the articular cartilage of 10 healthy volunteers. Statistical tests Nonparametric rank-sum tests. Bland-Altman analysis and coefficient of variation. Results The mean monoexponential T1 ρ relaxation was 40.7 ± 4.8 msec, while the long and short components were 58.2 ± 3.9 msec and 6.5 ± 0.6 msec, respectively. The mean fractions of long and short T1 ρ relaxation components were 63.7 ± 5.9% and 36.3 ± 5.9%, respectively. Statistically significant (P ≤ 0.03) differences were observed in the monoexponential and long components between some of the regions of interest (ROIs). No gender differences between biexponential components were observed (P > 0.05). Mean cartilage volume and thickness were 25.9 ± 6.4 cm3 and 2.2 ± 0.7 mm, respectively. Cartilage volume (P = 0.01) and thickness (P = 0.03) were significantly higher in male than female participants across all ROIs. Bland-Altman analysis showed agreement between two morphological methods with limits of agreement between -1000 mm3 and +1100 mm3 for volume, and -0.78 mm and +0.46 mm for thickness, respectively. Data conclusion Simultaneous assessment of morphological and multicomponent T1 ρ relaxation of knee joint with 0.7 × 0.7 × 0.7 mm isotropic spatial resolution is demonstrated in vivo. Comparison with a standard method showed that the proposed technique is suitable for assessing the volume and thickness of articular cartilage. Level of evidence 2 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2018;48:1707-1716.

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%.

Purpose To evaluate biexponential T2 relaxation mapping of human knee cartilage in vivo in clinically feasible scan times. Materials and Methods T2-weighted magnetic resonance (MR) images were acquired from eight healthy volunteers using a standard 3T clinical scanner. A 3D Turbo-Flash sequence was modified to enable T2-weighted imaging with different echo times. Series of T2-weighted images were fitted using mono- and biexponential models with two- and four-parametric nonlinear approaches, respectively. Results Biexponential relaxation of T2 was detected in the knee cartilage in five regions of interest in all eight healthy volunteers. Short/long relaxation components of T2 were estimated to be 8.27 ± 0.68 / 45.35 ± 3.79 msec with corresponding fractions of 41.3 ± 1.1% / 58.6 ± 4.6%, respectively. The monoexponential relaxation of T2 was measured to be 26.9 ± 2.27 msec. The experiments showed good repeatability with coefficient of variation root mean square (CVrms) < 18% in all regions. The only difference in gender was observed in medial tibial cartilage, where the biexponential T2 in female volunteers was significantly higher compared to male volunteers (P = 0.014). Significant differences were observed in T2 relaxation between different regions on interest. Conclusion Biexponential relaxation of T2 was observed in the human knee cartilage in vivo. The short and long components are thought to be related to the tightly bound and loosely bound macromolecular water compartments. These preliminary results of biexponential T2 analysis could potentially be used to increase the specificity for detection of early osteoarthritis by measuring different water compartments and their fractions. Level of Evidence: 1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017.

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.

Recently, Ultra-wide band signals have become attractive for their particular advantage of having high spatial resolution and good penetration ability which makes them suitable in medical applications. One of these applications is wireless detection of heart rate and respiration rate. Two hypothesis of static environment and fixed patient are considered in the method presented in previous literatures which are not valid for long term monitoring of ambulant patients. In this article, a new method to detect the respiration rate of a moving target is presented. The first algorithm is applied to the simulated and experimental data for detecting respiration rate of a fixed target. Then, the second algorithm is developed to detect respiration rate of a moving target. The proposed algorithm uses correlation for body movement cancellation, and then detects the respiration rate based on energy in frequency domain. The results of algorithm prove an accuracy of 98.4 and 97% in simulated and experimental data, respectively.