Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Area of Science:

• Orthopaedic Biomechanics
• Computational Mechanics
• Medical Imaging and Simulation

Background:

• Musculoskeletal finite element analysis (FEA) is crucial for orthopaedic biomechanics research.
• Generating volumetric meshes, particularly hexahedral meshes, is a significant bottleneck in FEA.
• Current multi-block hexahedral meshing approaches require manual placement of building blocks, hindering automation.

Purpose of the Study:

• To investigate the potential of Gaussian curvature analysis for automating building block structure generation.
• To develop an algorithm for automatic multi-block hexahedral mesh generation in musculoskeletal FEA.
• To overcome the manual limitations in defining building blocks for complex geometries.

Main Methods:

• Developed the Automated Building Block Algorithm, integrating differential geometry, combinatorics, statistical analysis, and computer science.
• Utilized Gaussian curvature analysis to guide the automatic generation of building block structures.
• Applied the algorithm to a dataset of 29 diverse bone geometries.

Main Results:

• Successfully generated a usable hexahedral mesh for all 29 tested bone geometries.
• Demonstrated the algorithm's capability to automatically create building block structures without prior information.
• Validated the effectiveness of Gaussian curvature analysis in this automated meshing process.

Conclusions:

• The Automated Building Block Algorithm significantly advances the automation of building block definition for hexahedral meshing.
• This method offers a robust solution for generating meshes in musculoskeletal FEA, reducing manual effort and time.
• Gaussian curvature analysis is a viable approach for automating complex mesh generation tasks in biomechanics.