Vessel segmentation in 2D/3D images is crucial for accurate computer-assisted diagnosis and preoperative planning. However, due to noise, complex topology, and low contrast with the background, previous segmentation algorithms are prone to missing some segments of vessels and generating breakpoints in the segmentation maps, resulting in discontinuities in the extracted centerline. In this paper, to preserve the correct topology in the segmentation maps, we propose an innovative connectivity-preserving dice (coDice) loss function. coDice is calculated by comparing the local regions connected to a common seed point in both the predicted and ground-truth segmentation. Extending this, we also propose three types of seed generation strategies that can be used in conjunction with the proposed coDice loss. Preliminary experiments on both 2D and 3D images show that the proposed coDice loss can improve segmentation accuracy and region connectivity in tubular structure segmentation.