A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method.

Area of Science:

• Biomechanics
• Computational Biology
• Biomedical Engineering

Background:

• Bone remodeling is a complex cellular process regulating bone density in response to stimuli.
• Understanding bone adaptation to mechanical loading is crucial for skeletal health.

Purpose of the Study:

• To numerically describe bone remodeling using a novel 2D biomechanical model.
• To investigate bone adaptation to loading regimes, including bone resorption.

Main Methods:

• Developed a novel 2D biomechanical model with unique parameters for bone and cellular density.
• Implemented automatic boundary recognition for spatial control of remodeling.
• Integrated a meshless approach, the Radial Point Interpolation Method (RPIM).
• Mimicked mechanical transduction to osteoclasts and osteoblasts based on strain energy density (SED).

Main Results:

• The model successfully simulates bone's adaptation to loading, leading to changes in apparent density.
• Bone cells' signaling pathways were shown to be dependent on strain energy density (SED).
• The model demonstrated bone's ability to reach an equilibrium state, optimizing structure for applied loads.

Conclusions:

• The novel 2D biomechanical model provides a simplified yet effective approach to simulating bone remodeling.
• This model has potential for high-quality solutions in understanding bone adaptation and optimizing skeletal structures.