Optimization of spin-lock times for T_1ρ mapping of human knee cartilage with bi- and stretched-exponential models

Two optimization criteria based on Cramér-Rao Bounds are compared between each other and with non-optimized schedules for T_1ρ 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.