Self-supervised reconstruction framework via motion- and physics-informed learning for four-dimensional magnetic resonance fingerprinting.

Four-dimensional magnetic resonance fingerprinting (4DMRF) provides multi-parametric and motion-resolved tissue property quantification, promising to enhance the precision of liver cancer radiotherapy. However, its clinical translation is hindered by prolonged reconstruction time. Deep learning acceleration is fundamentally constrained by the lack of ground-truth 4D data. To this end, we propose SS-4DMRF, the first self-supervised reconstruction framework for 4DMRF, to reconstruct motion-resolved tissue maps without using supervised image labels. SS-4DMRF features a core temporal low-rank-constrained registration (TelReg) network for precise motion modeling. It leverages the intrinsic low-rank compressibility of respiratory motion and is directly self-supervised by the original highly undersampled k-space data and the derived subspace images. Motion-resolved tissue maps are reconstructed using a motion-informed compensation approach via a physics-informed pattern matching (PiPM) network. PiPM network incorporates novel multi-scale Swin Transformers with Bloch-equation-guided subspace denoising to achieve high-fidelity tissue quantification. SS-4DMRF was validated on digital phantom (n=30) and in vivo liver cancer patient (n=33) datasets. Compared to state-of-the-art 4DMRF methods, SS-4DMRF demonstrated superior tissue quantification and motion measurement accuracy. It achieved significantly reduced NRMSE in 4D tissue property quantification and improved inter-phase structural repeatability in 4D motion characterization (Paired Student's t-tests, p<0.001). The measured tumor motion trajectory presented strong Peason correlation with motion reference (r=0.939±0.057). Crucially, SS-4DMRF achieves this dual improvement in accuracy with a 10-fold acceleration in reconstruction time compared with conventional 4DMRF methods. By enabling rapid, precise, and motion-resolved quantitative imaging, SS-4DMRF advances the precision of liver cancer radiotherapy and establishes a clinically feasible platform for abdominal quantitative MRI in oncology.