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.

翻译：从医学影像中精确重建多腔室心脏解剖结构是患者特异性建模、生理学模拟和介入规划的基础。然而，当前的重建流程主要依赖于表面几何监督，并独立建模每个腔室，导致尽管在重叠度或距离指标上表现良好，却仍产生解剖学上不合理的腔室间冲突。本研究提出一种关系解剖学监督框架，通过引入网格互关联增强（MIE）损失函数，用于多腔室心脏网格重建。该方案将心脏结构间的空间关系显式编码为可微分的基于占据率的优化目标，从而将定性解剖规则转化为定量几何监督。我们进一步建立了冲突感知评估指标，以直接量化腔室间结构正确性，揭示了常用几何度量（如Dice系数和Chamfer距离）的系统性局限。在多中心CT数据、密集采样MR数据及两个独立外部队列（包括高度异质性的先天性心脏病群体）上的大量实验表明，所提方法能持续抑制高达83%的临床关键边界冲突，同时保持具有竞争力的体积精度并实现更优的表面保真度。值得注意的是，所提出的关系监督机制在成像模态、医疗中心和病理条件（即使在严重解剖变形情况下）间均展现出稳健的泛化能力。这些结果表明，仅依赖距离监督不足以保证解剖学忠实重建，而显式强化多结构解剖关系为构建可靠的患者特异性心脏模型提供了原则性且稳健的途径。