[Wolff's law-based continuum topology optimization method and its application in biomechanics]

Area of Science:

• Biomechanics
• Computational modeling
• Materials science

Context:

• Cancellous bone's complex microstructure influences its mechanical properties.
• Accurate simulation of bone mass distribution is crucial for understanding skeletal health and disease.
• Existing methods may not fully capture the intricate relationship between microstructure and macro-scale properties.

Purpose:

• To develop a new computational method for simulating cancellous bone mass distribution.
• To integrate bone remodeling into a topology optimization framework using finite element analysis (FEA).
• To utilize fabric tensors to represent bone microstructure and constitutive properties.

Summary:

• The presented method models bone remodeling as topology optimization of a continuum structure.
• Fabric tensor invariants quantify effective volume fraction and relative density.
• A reference strain interval identifies the final structure topology, simulating biomechanical strain dead zones.

Impact:

• Successfully simulated vertebral coronal plane shapes and proximal femur mass distributions (2D and 3D).
• Validated the method's feasibility and accuracy by comparing numerical results with published literature.
• Provides a novel computational tool for researchers in biomechanics and bone tissue engineering.