In this paper, we present a relational-tubular (ReTu ) deformable model for segmenting a complex and the entire tubular network structure with branches in close proximity of each other. Specifically, we incorporate a priori knowledge of the target anatomy structure as well as the spatial relationship between branches to reduce possible segmentation errors due to the effects of a variety of imaging artifacts and noise. To get more robust description of the data properties than a simple 3D edge map, a new data energy functional is proposed based on testing the volumetric density within the model cross-sections. The deformation process is formulated as a two-stage procedure:tubular medial axis deformation and tubular surface deformation. The efficiency of this approach is demonstrated by our experiments which show that satisfactory quantifications of the entire zebrafish vasculature recorded from the fluorescence confocal microscope. The experiments also demonstrate the robustness of our deformable model in the presence of complex tissue structure that adhered to the vessel branches.