Physics-encoded neural network via multi-scale tree-structured graph representation for assessing cardiovascular hemodynamics

Hemodynamic assessment is crucial for understanding cardiovascular disease mechanisms and accurate diagnosis. Deep learning with prior physical knowledge holds promise for hemodynamic modelling. However, existing approaches struggle to assess hemodynamics across various cardiovascular systems due to geometric heterogeneity and imbalance learning from competing physical constraints. We propose a multi-scale tree-structured physics-encoded graph neural network for hemodynamic assessment across various cardiovascular systems. We introduce a multi-scale tree-structured graph representation (MTGR) that hierarchically decomposes vascular systems. This enables adaptive geometric modelling while maintaining physiological consistency. Building on MTGR, we propose a physics-encoded computational decoupling paradigm: (1) intra-segment hemodynamic computation within continuous vessel regions and (2) inter-segment hemodynamic coupling at bifurcation nodes. This decoupling paradigm efficiently combines knowledge of morphology and physics. With physics-encoded framework, we achieve the network training with label-free data. Experimental results on coronary and pulmonary arteries validate our framework’s superior generalization across diverse vascular topologies while preserving clinically interpretable physics. The excellent accuracy in predicting functionally significant stenosis demonstrates that this novel methodology has the potential to contribute to the development of innovative diagnostic and treatment strategies in the field of cardiovascular medicine.