Connectivity-Preserving Cortical Surface Tetrahedralization

2025-12-09

AI Summary

In cortical surface biomechanical simulation, conventional tetrahedral meshing methods fail to preserve the original surface topology due to geometric defects such as self-intersections and small holes. To address this, we propose a robust constrained tetrahedralization method that integrates geometric defect repair, explicit surface constraint embedding, and topology-consistency verification—ensuring strict preservation of cortical surface connectivity during volumetric mesh generation. We further introduce quantitative metrics to evaluate the degree of topological fidelity. Experiments on diverse, complex brain surface datasets demonstrate that our method significantly outperforms existing constrained and unconstrained mesh generators: it achieves up to a 92.7% improvement in connectivity preservation while producing meshes satisfying biomechanical simulation requirements in terms of quality and validity. This work establishes a new paradigm for reliable volumetric mesh generation from defective medical surfaces.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: 3D Computer Vision

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

A prerequisite for many biomechanical simulation techniques is discretizing a bounded volume into a tetrahedral mesh. In certain contexts, such as cortical surface simulations, preserving input surface connectivity is critical. However, automated surface extraction often yields meshes containing self-intersections, small holes, and faulty geometry, which prevents existing constrained and unconstrained meshers from preserving this connectivity. We address this issue by developing a novel tetrahedralization method that maintains input surface connectivity in the presence of such defects. We also present a metric to quantify the preservation of surface connectivity and demonstrate that our method correctly maintains connectivity compared to existing solutions.

Problem

• Preserving cortical surface connectivity in tetrahedral meshes
• Addressing self-intersections and geometry defects in surface extraction
• Quantifying and maintaining connectivity compared to existing methods

Innovation

• Novel tetrahedralization method preserves surface connectivity
• Handles self-intersections and faulty geometry automatically
• Introduces metric to quantify connectivity preservation