An intrinsic efficiency measure for quantitative MRI applicable to transient and steady-state sequences

Purpose: This study proposes an efficiency metric to quantify the performance of quantitative MRI methods based on their intrinsic ability to extract information about tissue parameters. The metric can be used to both optimize and compare sequences. Here we compare steady-state sequences with transient measurement methods such as magnetic resonance fingerprinting (MRF). Theory and Methods: Under a regime of unbiased parameter estimates, an intrinsic efficiency metric $\eta$ was derived for fully-sampled experiments, which quantifies the information per square root of time that is extracted about a tissue parameter. Several steady-state and transient gradient echo based qMRI methods for joint T1 and T2 mapping were optimized to maximize $\eta$ and then compared. The impact of under-sampling was also evaluated, assuming incoherent aliasing that is treated as noise by parameter estimation. Phantom and in-vivo validations of the efficiency metric were also performed. Results: Transient methods such as MRF can be up to 3.5 times more efficient than steady-state methods, when spatial under-sampling is ignored. If incoherent aliasing is treated as noise during least-squares parameter estimation, the efficiency is reduced in proportion to the SNR of the data, with reduction factors of 5 often seen for practicable SNR levels. Phantom and in-vivo validations showed a very good agreement between the theoretical and experimentally predicted efficiency. Conclusion: This work presents and validates a metric to optimize and compare the performance of qMRI methods. Transient methods were found to be intrinsically more efficient than steady-state methods, however the effect of spatial under-sampling significantly erodes this advantage.