Accurate mixed-dimensional modeling of cerebral hemodynamics depends on defining a topologically consistent vascular domain from Time-of-Flight MRA data. However, noise and resolution limits frequently cause signal dropouts, particularly near the resolution limit, resulting in disconnected networks that prevent the robust discretization required for coupled PDE analysis. To bridge the gap between raw volumetric data and simulation-ready domains, we propose Network Inpainting via Optimal Transport (NIOT). This variational framework embeds physical priors directly into the reconstruction by using a branch-inducing functional from Optimal Transport theory. This term enforces the formation of efficient, ramified structures, effectively repairing topological defects. We present results on high-resolution real scans (characterized by 0.5mm cubic resolution and approximately 20 million voxels), demonstrating the recovery of connectivity essential for subsequent flow simulations. The proposed method not only restores the topological integrity of the vascular network but also provides a mathematically rigorous foundation for generating mixed-dimensional meshes suitable for advanced biomedical applications.