MARVEL: Universal Murray's Law-informed Vessel Tree Segmentation and Topology Estimation

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.