Formulas for Determining the Recovery Times for Optimal Two-Point Saturation–Recovery Measurement of the MR Longitudinal Relaxation Rate

Abstract

The saturation-recovery method is a frequently used NMR/MRI technique for the measurement of the longitudinal relaxation rate R 1 . Under noise influence, the accuracy and the precision of the measurement outcome depend on the selection of the recovery times. This work seeks to determine the optimal recovery-time selection when the total scan time is constrained. A Monte Carlo computational method was used to simulate the noise-influenced distribution of the R 1 measurement for various combinations of the two recovery times and to find the combination that produces the minimal standard deviation. Using the sum of recovery times (SRT) as the total scan time, mathematical formulas are derived from the simulation covering the SRT range of [0.05T 1 , 15T 1 ]. The formulas describe the relationship between the SRT, the optimal accuracy and precision, and the recovery-time selection, and reproduce the results for the cases previously validated with experiments. In clinical application, the scan time is limited by the scan subject's tolerance in the scanner and the time that can be allocated to the measurement in a scan session. These formulas provide a practical way to evaluate the trade-offs between precision and the scan time in scan planning.