Optimization of spin-lock times for T1ρ mapping of human knee cartilage with bi- and stretched-exponential models

Abstract

Two optimization criteria based on Cramér-Rao Bounds are compared between each other and with non-optimized schedules for T1ρ mapping using synthetic data, model phantoms, and in-vivo knee cartilage. The curve fitting is done on complex-valued data using an iterative Nonlinear Least Squares (NLS) approach. The optimization criteria are compared based on the Mean Normalized Absolute Error (MNAE) and variance of the estimated parameters. The optimized spin-lock time (TSL) schedules provided improved results over the non-optimized schedules for all cases that were tested. The simulations showed that optimized schedules can reach the same precision and reduce acquisition times by 16.5 min (42%) for the bi-exponential model, and 6.6 min (22%) for the stretched-exponential model. In the model phantoms experiments, the bi-exponential MNAE was reduced from 0.47 to 0.36, while stretched-exponential from 0.28 to 0.20 with a Modified Cramér-Rao Lower Bound (MCRLB). In-vivo knee cartilage experiments show a reduction in bi-exponential MNAE from 0.47 to 0.31, and stretched-exponential from 0.047 to 0.039. The optimized spin-lock times criteria reduced the error in all cases, being more significant in the synthetic data and model phantoms. The optimized TSL schedules can be either used to improve the quality of parameter maps or reduce scan time.

Updates on Compositional MRI Mapping of the Cartilage: Emerging Techniques and Applications

“…While it is known that two T 1ρ ‐weighted images are the minimum necessary for T 1ρ mapping, this study showed that the right choice of the TSLs could improve image quality and parameter estimation, obtaining results better than if three or more nonoptimized TSLs were chosen. The CRLB approach to choosing the TSLs was extended to bi‐exponential and stretched‐exponential T 1ρ mapping, showing that nearly the same quality can be obtained using half of the number of TSLs if they were optimized 70 …”

“…The CRLB approach to choosing the TSLs was extended to bi-exponential and stretchedexponential T 1ρ mapping, showing that nearly the same quality can be obtained using half of the number of TSLs if they were optimized. 70 Efficient use of phase-cycling acquisitions in magnetization-prepared angle-modulated partitioned k-space spoiled GRE snapshots (MAPSS) sequences was proposed. 71 To reduce the T 1 contamination that affects the precision of cartilage T 1ρ mapping, MAPSS required essentially two acquisitions with the same TSLs, one regular and the other with phase cycling.…”

Age and Gender‐Dependence of Single‐and Bi‐Exponential T1ρ MR Parameters in Knee Ligaments

“…The 3D‐PETRA‐ T 1 ρ weighted images were acquired with a spin‐lock frequency of 500 Hz and spin‐lock times (TSLs): 0, 0.2, 2.6, 12.9, 12.9, and 30 msec. These TSL values were chosen using previously described optimization experiments 22,23 . Fat suppression and T 1 ρ preparation modules were applied at every 26 readouts to minimize acquisition time.…”

“…These TSL values were chosen using previously described optimization experiments. 22,23 Fat suppression and T 1ρ preparation modules were applied at every 26 readouts to minimize acquisition time. The acquisition parameters were as follows: repetition time (TR)/echo time (TE) = 5 msec/0.07 msec, field of view = 200 Â 200 mm 2 , flip angle = 6 , matrix size = 256 Â 256 Â 256, thickness = 0.78 mm, voxel size = 0.78 Â 0.78 Â 0.78 mm 2 , receiver bandwidth = 399 Hz/px, T 1 recovery delay =500 msec, number of radial spokes = 8000, number of segments =350, number of readouts in each segment = 26, and number of Cartesian sample points = 1419.…”