A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress

Area of Science:

• Biomechanics
• Materials Science
• Orthopedics

Background:

• Trabecular bone's complex architecture significantly influences its mechanical properties.
• Accurate prediction of bone stiffness and stress distribution is crucial for understanding bone health and disease.

Purpose of the Study:

• To introduce and validate a homogenization sampling procedure for calculating effective trabecular bone stiffness.
• To determine individual trabecula level stress and strain energy density based on bone architecture.

Main Methods:

• Developed a homogenization sampling procedure using 3D digitized images of 53 trabecular bone specimens.
• Converted 3D images into 3D finite element meshes with each voxel as an 8-node isoparametric brick element.
• Employed an element-by-element preconditioned conjugate gradient (EBEPCG) program to solve finite element equations.

Main Results:

• Predicted effective stiffness correlated well with experimental results (R2 > 0.73), though slightly underestimated values.
• The procedure showed lower average absolute errors (31-38%) compared to regression fits (49-150%).
• Trabecular stress varied widely (-200 to +300 times continuum prediction), with tensile and compressive stresses arising from continuum compression.

Conclusions:

• The homogenization sampling procedure reliably predicts the impact of trabecular bone architecture on effective stiffness.
• The method provides accurate trabecular tissue stress and strain estimates for whole bone loading.
• Significant variations in tissue-level stresses and strains were observed compared to continuum-level predictions.