Relational Anatomical Supervision for Accurate 3D Multi-Chamber Cardiac Mesh Reconstruction

Accurate reconstruction of multi-chamber cardiac anatomy from medical images is a cornerstone for patient-specific modeling, physiological simulation, and interventional planning. However, current reconstruction pipelines fundamentally rely on surface-wise geometric supervision and model each chamber in isolation, resulting in anatomically implausible inter-chamber violations despite apparently favorable overlap or distance metrics. In this work, we propose a relational anatomical supervision framework for multi-chamber cardiac mesh reconstruction by introducing a Mesh Interrelation Enhancement (MIE) loss. The proposed formulation explicitly encodes spatial relationships between cardiac structures into a differentiable occupancy-based objective, thereby transforming qualitative anatomical rules into quantitative geometric supervision. We further establish violation-aware evaluation metrics to directly quantify inter-chamber structural correctness, revealing systematic limitations of commonly used geometric measures such as Dice and Chamfer distance. Extensive experiments on multi-center CT data, densely sampled MR data, and two independent external cohorts, including a highly heterogeneous congenital heart disease population, demonstrate that the proposed method consistently suppresses clinically critical boundary violations by up to 83\%, while maintaining competitive volumetric accuracy and achieving superior surface fidelity. Notably, the proposed relational supervision generalizes robustly across imaging modalities, centers, and pathological conditions, even under severe anatomical deformation. These results demonstrate that distance-based supervision alone is insufficient to guarantee anatomically faithful reconstruction, and that explicit enforcement of multi-structure anatomical relations provides a principled and robust pathway toward reliable patient-specific cardiac modeling.