  Purpose: To develop a free-breathing myocardial T1 mapping technique using
inversion-recovery (IR) radial fast low-angle shot (FLASH) and calibrationless
motion-resolved model-based reconstruction. Methods: Free-running
(free-breathing, retrospective cardiac gating) IR radial FLASH is used for data
acquisition at 3T. First, to reduce the waiting time between inversions, an
analytical formula is derived that takes the incomplete T1 recovery into
account for an accurate T1 calculation. Second, the respiratory motion signal
is estimated from the k-space center of the contrast varying acquisition using
an adapted singular spectrum analysis (SSA-FARY) technique. Third, a
motion-resolved model-based reconstruction is used to estimate both parameter
and coil sensitivity maps directly from the sorted k-space data. Thus,
spatiotemporal total variation, in addition to the spatial sparsity
constraints, can be directly applied to the parameter maps. Validations are
performed on an experimental phantom, eleven human subjects, and a young
landrace pig with myocardial infarction. Results: In comparison to an IR
spin-echo reference, phantom results confirm good T1 accuracy when reducing the
waiting time from five seconds to one second using the new correction. The
motion-resolved model-based reconstruction further improves precision compared
to the spatial regularization-only reconstruction. Aside from showing that a
reliable respiratory motion signal can be estimated using modified SSA-FARY, in
vivo studies demonstrate that dynamic myocardial T1 maps can be obtained within
two minutes with good precision and repeatability. Conclusion: Motion-resolved
myocardial T1 mapping during free-breathing with good accuracy, precision and
repeatability can be achieved by combining inversion-recovery radial FLASH,
self-gating and a calibrationless motion-resolved model-based reconstruction.
