On the selection of sampling points for myocardial T₁ mapping

Purpose To provide a method for the optimal selection of sampling points for myocardial T₁ mapping, and to evaluate how this selection affects the precision. Theory The Cramér-Rao lower bound on the variance of the unbiased estimator was derived for the sampling of the longitudinal magnetization curve, as a function of T₁, signal-to-noise ratio, and noise mean. The bound was then minimized numerically over a search space of possible sampling points to find the optimal selection of sampling points. Methods Numerical simulations were carried out for a saturation recovery-based T₁ mapping sequence, comparing the proposed point selection method to a uniform distribution of sampling points along the recovery curve for various T₁ ranges of interest, as well as number of sampling points. Phantom imaging was performed to replicate the scenarios in numerical simulations. In vivo imaging for myocardial T₁ mapping was also performed in healthy subjects. Results Numerical simulations show that the precision can be improved by 13-25% by selecting the sampling points according to the target T₁ values of interest. Results of the phantom imaging were not significantly different than the theoretical predictions for different sampling strategies, signal-to-noise ratio and number of sampling points. In vivo imaging showed precision can be improved in myocardial T₁ mapping using the proposed point selection method as predicted by theory. Conclusion The framework presented can be used to select the sampling points to improve the precision without penalties on accuracy or scan time. Magn Reson Med 73:1741-1753, 2015.