MARVEL: Universal Murray's Law-informed Vessel Tree Segmentation and Topology Estimation
Authors: Yi Zhou, Thiara Sana Ahmed, Jacqueline Chua, Meng Wang, Qinrong Zhang, Alejandro F. Frangi, Huazhu Fu, Jun Cheng, +2 more
Abstract
Vascular circulation follows fundamental biophysical principles that optimize mass transport and metabolic energy expenditure, which can be effectively modeled by Murray's law. However, contemporary deep learning methods for vascular segmentation often neglect these biophysical constraints. This leads to physiologically implausible branching and misclassification vascular trees, rendering. These automated segmentation results are unreliable unreliable for downstream clinical tasks such as blood flow simulation or disease quantification. In this paper, we introduce MARVEL (Universal MurrAy's law-infoRmed Vessel sEgmentation and topoLogy estimation), a backbone-agnostic framework that integrates biophysical priors into vascular tree extraction. MARVEL combines per-pixel supervision with explicit radius predictions to enforce local bifurcation constraints derived from an empirical width-exponent mapping. We implement these constraints as differentiable regularizers during training to guide models toward physiologically consistent reconstructions. We evaluate MARVEL on eight public datasets across multiple vascular modalities and segmentation backbones. Results demonstrate MARVEL's superior performance in segmentation accuracy, topological consistency, and physiological plausibility. By converting segmented masks into graph-based hemodynamic simulations, we demonstrate that MARVEL preserves the subtle pathological narrowing and topological connectivity required to distinguish hypertensive from normotensive eyes. Results show that MARVEL significantly improves the classification of hypertension via arteriovenous pressure differences in the eye (p < 0.001), outperforming baseline models in both topological consistency and clinical predictive value.
Accurate pulmonary vessel segmentation remains challenging due to the sparse, tortuous, and multi-scale nature of vascular structures, where small branches are easily lost and topology integrity is difficult to preserve under voxel-wise supervision. Existing deep segmentation models primarily optimize binary masks, lacking explicit geometric constraints, thus struggling to recover continuous tubular morphology and fine vascular connectivity. In this study, we introduce MorVess, a morphology-aware segmentation framework that integrates differentiable geometric priors with large-scale foundation model adaptation to achieve fine-grained vascular parsing. MorVess jointly predicts vessel masks, distance maps, and thickness maps, providing explicit supervision for vascular boundaries, centerline consistency, and smooth diameter transitions. A lightweight 2.5D adapter bridges 3D spatial context and 2D SAM representations, while a global-local fusion block aggregates multi-level semantics and geometric cues for high-fidelity topology reconstruction. Across two challenging pulmonary CT benchmarks, MorVess delivers superior Dice, clDice, and HD95 scores, substantially improving small-vessel recovery and global connectivity. These results demonstrate that embedding geometric intelligence into pretrained vision models offers a principled and scalable pathway toward precise vessel analysis and clinically reliable structural quantification. Our source code is available at https://github.com/MaoFuyou/MorVess.
Blood vessel segmentation is a core task in medical image analysis for the care of vascular diseases and surgical planning, yet the challenges of providing expert vascular annotations pose a major obstacle for the progress of related deep learning techniques. To address this, we propose VesselSim, a two-stage framework for universal 3D blood vessel segmentation that eliminates the need for real annotated data during training. First, we introduce a stochastic, geometry-driven vascular simulation framework that models recursive branching, curvature-controlled growth, and collision-aware topology, followed by domain-randomized intensity synthesis to generate 16,500 anatomically plausible 3D angiographic volumes. Second, a 3D U-Net is trained solely on this synthetic data. To bridge the domain gap from synthetic to real images at inference time, we introduce a test-time adaptation strategy via a self-supervised mask reconstruction decoder, enabling adaptation to unseen clinical scans without prior domain knowledge. We evaluate VesselSim in a zero-shot setting on multiple real-world datasets spanning MR and CT across several anatomical regions, including the brain and kidneys. Despite being trained exclusively on synthetic data, VesselSim achieves performance competitive with state-of-the-art vascular segmentation foundation models. These findings suggest that learning vessel geometry from synthetic tubular structures is effective for robust cross-domain generalization, substantially reducing the reliance on acquired medical imaging data and more importantly, expert annotations.
Blood vessel segmentation and -tracing are essential tasks in many medical imaging applications. Although numerous methods exist, the prevailing segment-then-fix paradigm is fundamentally limited regarding its suitability for modeling the task of complete and topologically accurate vascular network reconstruction. Here, we propose an approach to extract topologically more accurate vascular graphs from 3D image data, building upon highly successful ideas from the related biomedical tasks of cell segmentation and -tracking. Our approach first predicts voxel-wise vessel direction vectors joint with standard vessel segmentation masks. Second, to extract the vascular graph from these predictions, we introduce a direction-vector-guided extension of the TEASAR algorithm. Our approach achieves state-of-the-art performance on three benchmark datasets, spanning both synthetic and real imagery. We further demonstrate the applicability of our approach to challenging 3D micro-CT scans of rat heart vasculature. Finally, we propose meaningful and interpretable measures of topological error, namely false splits and false merges for graphs. Overall, our approach substantially improves the topological accuracy of reconstructed vascular graphs, being able to separate closely apposed vessel segments and handle multiple vascular trees within a single volume.
Rajalakshmi Palaniappan, Christoph Karg, Nemesio Navarro-Arambula +4