  T1 mapping is a quantitative magnetic resonance imaging (qMRI) technique that
has emerged as a valuable tool in the diagnosis of diffuse myocardial diseases.
However, prevailing approaches have relied heavily on breath-hold sequences to
eliminate respiratory motion artifacts. This limitation hinders accessibility
and effectiveness for patients who cannot tolerate breath-holding. Image
registration can be used to enable free-breathing T1 mapping. Yet, inherent
intensity differences between the different time points make the registration
task challenging. We introduce PCMC-T1, a physically-constrained deep-learning
model for motion correction in free-breathing T1 mapping. We incorporate the
signal decay model into the network architecture to encourage
physically-plausible deformations along the longitudinal relaxation axis. We
compared PCMC-T1 to baseline deep-learning-based image registration approaches
using a 5-fold experimental setup on a publicly available dataset of 210
patients. PCMC-T1 demonstrated superior model fitting quality (R2: 0.955) and
achieved the highest clinical impact (clinical score: 3.93) compared to
baseline methods (0.941, 0.946 and 3.34, 3.62 respectively). Anatomical
alignment results were comparable (Dice score: 0.9835 vs. 0.984, 0.988). Our
code and trained models are available at https://github.com/eyalhana/PCMC-T1.
