A newly developed imaging technique called light-sheet laser microscopy imaging can visualize the detailed 3D structures of capillaries. Capillaries form complicated network structures in the obtained data, and this makes it difficult to model vessel structures by existing methods that implicitly assume simple tree structures for blood vessels. To cope with such dense capillaries with network structures, we propose to track the flow of blood vessels along a base-axis using a multiple-object tracking framework. We first track multiple blood vessels in cross-sectional images along a single axis to make the trajectories of blood vessels, and then connect these blood vessels to reveal their entire structures. This framework is efficient to track densely distributed vessels since it uses only a single cross-sectional plane. The network structure is then generated in the post-processing by connecting blood vessels on the basis of orientations of the trajectories. The results of experiments using a challenging real data-set demonstrate the efficacy of the proposed method, which are capable of modeling dense capillaries.