  To realize Quantitative MRI (QMRI) with clinically acceptable scan time,
acceleration factors achieved by conventional parallel imaging techniques are
often inadequate. Further acceleration is possible using model-based
reconstruction. We propose a theoretical metric called TEUSQA: Time Efficiency
for UnderSampled QMRI Acquisitions to inform sequence design and sample pattern
optimisation. TEUSQA is designed for a particular class of reconstruction
techniques that directly estimate tissue parameters, possibly using prior
information to regularize the estimation. TEUSQA can be used to evaluate
undersampling patterns for multi-contrast QMRI sequences targeting any tissue
parameter. To verify the time efficiency predicted by TEUSQA, we performed
Monte Carlo simulations and an accelerated parameter mapping with two sequences
(Inversion prepared fast spin echo for T1 and T2 mapping and 3D GRASE for T2
and B0 inhomogeneity mapping). Using TEUSQA, we assessed several ways to
generate undersampling patterns in silico, providing insight into the relation
between sample distribution and time efficiency for different acceleration
factors. The time efficiency predicted by TEUSQA was within 15 % of that
observed in the Monte Carlo simulations and the prospective acquisition
experiment. The assessment of undersampling patterns showed that a class of
good patterns could be obtained by low-discrepancy sampling. We believe that
TEUSQA offers a valuable instrument for developers of novel QMRI sequences
pushing the boundaries of acceleration to achieve clinically feasible
protocols. Finally, we applied a time-efficient undersampling pattern selected
using TEUSQA for a 32-fold accelerated scan to map T1 and T2 mapping of a
healthy volunteer.
