From computed tomography to finite element space: A unified bone material mapping strategy

Area of Science:

• Biomechanics
• Computational modeling
• Medical imaging

Background:

• Finite element models (FEM) of bone often use spatially varying mechanical properties derived from quantitative computed tomography (QCT) bone density data.
• Accurately and efficiently mapping voxel-based density data to FEM meshes is crucial for reliable bone modeling.

Purpose of the Study:

• To develop and evaluate novel discretization variants for mapping bone density data to finite element meshes.
• To compare the performance of continuous and discontinuous finite element methods against existing nodal and element approaches.

Main Methods:

• Formulated density projection in least-squares terms.
• Discretized the projection using continuous and discontinuous variants of the finite element method (FEM).
• Compared proposed FEM variants with established nodal and element formulations.

Main Results:

• The discontinuous zero-order FEM variant demonstrated superior accuracy (L2 norm, energy distance) and efficiency.
• This variant effectively preserves density spectrum at edges while maintaining low computational cost.
• Differences in implementation, computational cost, and spectral preservation between continuous and discontinuous FEM were highlighted.

Conclusions:

• The discontinuous zero-order FEM variant is the most advantageous for mapping bone density to FEM meshes.
• This method provides a more accurate and computationally efficient approach compared to existing methods.
• The findings offer improved capabilities for finite element analysis of bone mechanical properties.