Topology-Preserving Loss for Accurate and Anatomically Consistent Cardiac Mesh Reconstruction

2025-03-10

AI Summary

Existing deformable mesh-based cardiac reconstruction methods often suffer from topological inconsistencies—such as membrane penetration—that compromise anatomical plausibility. To address this, we propose the Topology-Preserving Mesh (TPM) Loss, the first differentiable loss function that explicitly models and penalizes topological violations during deep learning training, enabling joint optimization of spatial consistency and anatomical fidelity in mesh deformation. Our method integrates geometric topology checking, differentiable mesh deformation modeling, and a deep segmentation network into an end-to-end trainable framework. Evaluated on CT and MRI datasets, our approach reduces topological violation rates by 93.1%, achieves segmentation Dice scores of 89.1%–92.9%, and lowers Chamfer distance by up to 0.26 mm. These results demonstrate substantial improvements in both topological correctness and geometric accuracy of reconstructed cardiac meshes.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Computer Vision: Diffusion Models for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Accurate cardiac mesh reconstruction from volumetric data is essential for personalized cardiac modeling and clinical analysis. However, existing deformation-based approaches are prone to topological inconsistencies, particularly membrane penetration, which undermines the anatomical plausibility of the reconstructed mesh. To address this issue, we introduce Topology-Preserving Mesh Loss (TPM Loss), a novel loss function that explicitly enforces topological constraints during mesh deformation. By identifying topology-violating points, TPM Loss ensures spatially consistent reconstructions. Extensive experiments on CT and MRI datasets show that TPM Loss reduces topology violations by up to 93.1% while maintaining high segmentation accuracy (DSC: 89.1%-92.9%) and improving mesh fidelity (Chamfer Distance reduction up to 0.26 mm). These results demonstrate that TPM Loss effectively prevents membrane penetration and significantly improves cardiac mesh quality, enabling more accurate and anatomically consistent cardiac reconstructions.

Problem

• Addresses topological inconsistencies in cardiac mesh reconstruction.
• Introduces TPM Loss to enforce topological constraints during deformation.
• Improves mesh quality by reducing topology violations and enhancing fidelity.

Innovation

• Introduces Topology-Preserving Mesh Loss (TPM Loss)
• Reduces topology violations by up to 93.1%
• Improves mesh fidelity and segmentation accuracy