Optimized quantification of spin relaxation times in the hybrid state

Abstract

Purpose: The optimization and analysis of spin ensemble trajectories in the hybrid state-a state in which the direction of the magnetization adiabatically follows the steady state while the magnitude remains in a transient state.

Methods: Numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for ${\text{T}}_1$ -encoding, ${\text{T}}_2$ -encoding, and their weighted sum, respectively, followed by a comparison between the Cramér-Rao bounds obtained with our optimized spin-trajectories, Look-Locker sequences, and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain.

Results: After a nonrecurring inversion segment on the southern half of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern hemisphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance ${\text{T}}_1$ - and ${\text{T}}_2$ -encoding still result in near optimal signal-to-noise efficiency for each relaxation time. Thus, the second parameter can be encoded at virtually no extra cost.

Conclusions: We provided new insights into the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We found that joint acquisitions of ${\text{T}}_1$ and ${\text{T}}_2$ in the hybrid state are substantially more efficient than sequential encoding techniques.

Keywords: HSFP; MRF; SSFP; optimal control; parameter mapping; quantitative MRI.