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For studying vascular structures in 4D biomedical imaging, it is of great importance to automatically determine the velocity of flow in video sequences, for example blood flow in vessel networks. In this thesis new optimal transport models focusing on direction and segmentation are investigated to find an accurate displacement between two density distributions. By incorporating fluid dynamics constraints, one can obtain a realistic description of the displacement. With an a-priori given segmentation of the network structure, transport models can be improved. However, a segmentation is not always known beforehand. Therefore, in this work a joint segmentation-optimal transport model has been described. Other contributions are the ability of the model to allow for inflow or outflow and the incorporation of anisotropy in the displacement cost. For the problem, a convex variational method has been used and primal-dual proximal splitting algorithms have been implemented. Existence of a solution of the model has been proved. The framework has been applied to synthetic vascular structures and real data, obtained from a collaboration with the applied mathematics and the hospital in Cambridge.