RIVER: Relational 4D Gaussian Reconstruction from Ultra-Sparse Dynamic Projections

Ultra-sparse dynamic digital subtraction angiography (DSA) couples angular undersampling with temporal contrast variation. Representative radiative Gaussian models predict attenuation through per-primitive queries, leaving vascular neighborhood dependencies implicit. We introduce RIVER, a relational 4D Gaussian representation in which neighboring primitives explicitly condition the forward attenuation model. A coverage graph supports broad message propagation, while a confidence graph selects structurally supported relations for regularization. Directional-state stabilization and transport-inspired, segment, and tubular priors complement this relational representation without interpreting its latent states as calibrated hemodynamic quantities. Across ten private clinical acquisitions and two public acquisitions, RIVER improves projection fidelity most clearly under severe sparsity: at ten views, private-cohort PSNR increases from 29.76 to 31.40 dB over the strongest compared baseline. On the private cohort, registered 3D evaluation yields lower Hausdorff distances, while CD, clDice, and projection-domain perceptual gains are not uniformly improved. Capacity, self-context, neighbor-context, and priors-only controls distinguish the tested contributions of forward communication and auxiliary regularization. Mechanism diagnostics further show that broad message coverage coexists with selective structural participation. These results support explicit inter-primitive conditioning as a representation bias for ultra-sparse dynamic vascular reconstruction.