Numerical errors and uncertainties in finite-element modeling of trabecular bone

Area of Science:

• Biomechanics
• Computational Modeling
• Materials Science

Background:

• Micromechanical finite-element models (FEM) are crucial for interpreting biomechanical test results.
• A systematic analysis of numerical errors and uncertainties in FEM for bone is lacking.

Purpose of the Study:

• To investigate the sensitivity of calculated elastic moduli in human L1 vertebra FEM to resolution, boundary conditions, and material property variations.
• To identify optimal FEM parameters for accurate biomechanical analysis.

Main Methods:

• Finite-element models of human L1 vertebrae were created.
• Sensitivity analyses were performed for mesh resolution (voxel size), boundary conditions, and Poisson's ratio.
• Results were compared against mechanical testing data.

Main Results:

• Discretization of bone architecture led to an underestimation of elastic moduli by approximately 20% at 20 microm resolution.
• A cancellation of errors was observed between discretization softening and hexahedral element bending resistance.
• Eight-node cubic elements, matching image voxel size, yielded the most accurate results (<5% error at 20 microm).
• Uncertainties in grip conditions during mechanical testing were comparable in magnitude to systematic differences between testing methods.

Conclusions:

• Optimized FEM, utilizing eight-node cubic elements at resolutions matching image voxels, can achieve high accuracy in calculating bone elastic moduli.
• Discretization errors and grip condition uncertainties significantly impact absolute modulus calculations but have less effect on relative moduli.
• FEM provides a valuable tool for biomechanical analysis, but careful consideration of numerical errors and experimental uncertainties is essential.