One Frame, Full Heartbeat: ECG-Free 4D Cardiac Cine MRI Synthesis via Radial-Decomposed Flow Matching

Cine cardiovascular magnetic resonance (CMR) captures the cardiac cycle as a four-dimensional (4D) sequence, but standard acquisition requires electrocardiogram (ECG) gating and repeated breath holds. Visual realism alone does not establish accurate patient-specific ejection fraction (EF) or ventricular volumes. We present PhaseFlow3D, a generative framework that synthesizes a complete 4D cine sequence from a single end-diastolic (ED) three-dimensional (3D) volume without ECG. To capture asymmetric systolic and diastolic dynamics, it represents the cardiac cycle as a piecewise linear phase anchored at ED and end-systolic (ES) time points. At inference, a population-level canonical template supplies this phase without patient-specific temporal information. A phase-conditioned rectified flow model generates a cardiac motion trajectory in latent space. Radial Contraction Decomposition converts each latent state into a 3D displacement field, combining a physics-informed radial component for centripetal myocardial contraction with an image-conditioned residual for rotation and out-of-plane motion. Each frame is generated by directly warping the ED volume, bypassing variational autoencoder decoding. On the combined ACDC and M&Ms benchmark, PhaseFlow3D achieves the lowest EF mean absolute error, the only positive left-ventricular volume-curve R2, and the best distributional quality among compared methods. Ablations confirm each component's contribution. Downstream evaluations demonstrate the utility of the synthesized sequences and displacement fields for segmentation, pathology classification, label propagation, and myocardial strain analysis.