Vascular segmentation is a critical task in clinical medical image processing and a prerequisite for accurately diagnosing vascular-related diseases. The development of automated segmentation methods is challenged by internal variability in vessel representations. Recently, topology guidance has shown potential for capturing semantically consistent representations. However, current topology-guided methods lack modeling of global-to-local dependencies. This limitation forces latent representations subject to a trade-off between learning global topology and local geometries within the vascular network. In this paper, we propose a Bayesian-based topology-guided (BayeTopo) learning approach to capture global-to-local dependencies. It introduces a prior that explicitly models local geometry as a probability conditioned on global topology within topology-sensitive regions of the vascular network. We further implement a topology-guided diffusion model to optimize the conditional probability. It gradually infers local geometry from the restored global topology with multi-scale noise, enabling rich global-to-local representations. Then, an inhomogeneous diffusion process is involved, where noise initially accumulates in topology-sensitive regions before achieving uniformity. It ensures an orderly degradation of information from global topology to local geometry, thereby enabling effective global-to-local supervision. Extensive experiments on six datasets, involving three types of vascular networks under four imaging modalities, demonstrate the superior performance and generalization capability of our method compared to previous topology-guided learning and diffusion-based models. A series of case studies further validates the effectiveness of our designs in enhancing semantic consistency within local vascular regions, thereby improving topological accuracy.

As a leading global cause of mortality, coronary ischemia requires accurate diagnostics for effective management. The combining coronary angiography with fractional flow reserve (FFR) offers structural and functional assessment of coronary stenosis to guide revascularization. However, traditional FFR measurements are invasive, requiring pressure wire placement. Image-based FFR estimation methods integrate vascular morphology with biomechanics but face challenges in modelling the complex fluid-structure interaction (FSI) of coronary flow and vessel walls. Therefore, we propose a physics-guided variational domain progressing method (PVDPM) for non-invasive FFR estimation through FSI system. PVDPM employs the principle of virtual work to model FSI system. This approach can improve the modelling of interdependent physical processes, enabling accurate FFR estimation based on coronary angiography-derived vascular morphology. The PVDPM demonstrates 91% accuracy in clinical datasets and offers solution for diagnosing coronary ischemia based on coronary angiography.