Background: The accurate automated extraction of brain vessel centerlines from Computed tomographic angiography (CTA) images plays an important role in diagnosing and treating cerebrovascular diseases such as stroke. Despite its significance, this task is complicated by the complex cerebrovascular structure and heterogeneous imaging quality. Purpose: This study aims to develop and validate a segmentation-assisted framework designed to improve the accuracy and efficiency of brain vessel centerline extraction from CTA images. We streamline the process of lumen segmentation generation without additional annotation effort from physicians, enhancing the effectiveness of centerline extraction. Methods: The framework integrates four modules: (1) pre-processing techniques that register CTA images with a CT atlas and divide these images into input patches, (2) lumen segmentation generation from annotated vessel centerlines using graph cuts and robust kernel regression, (3) a dual-branch topology-aware UNet (DTUNet) that optimizes the use of the annotated vessel centerlines and the generated lumen segmentation via a topology-aware loss (TAL) and its dual-branch structure, and (4) post-processing methods that skeletonize and refine the lumen segmentation predicted by the DTUNet. Results: An in-house dataset derived from a subset of the MR CLEAN Registry is used to evaluate the proposed framework. The dataset comprises 10 intracranial CTA images, and 40 cube CTA sub-images with a resolution of (Formula presented.) voxels. Via five-fold cross-validation on this dataset, we demonstrate that the proposed framework consistently outperforms state-of-the-art methods in terms of average symmetric centerline distance (ASCD) and overlap (OV). Specifically, it achieves an ASCD of 0.84, an (Formula presented.) of 0.839, and an (Formula presented.) of 0.885 for intracranial CTA images, and obtains an ASCD of 1.26, an (Formula presented.) of 0.779, and an (Formula presented.) of 0.824 for cube CTA sub-images. Subgroup analyses further suggest that the proposed framework holds promise in clinical applications for stroke diagnosis and treatment. Conclusions: By automating the process of lumen segmentation generation and optimizing the network design of vessel centerline extraction, DTUnet achieves high performance without introducing additional annotation demands. This solution promises to be beneficial in various clinical applications in cerebrovascular disease management.