Growth of a long bone cross section - A 2D phase-field model

Area of Science:

• Biomechanics
• Mathematical Biology
• Cell Biology

Background:

• Mammal long bone growth is influenced by mechanical forces.
• Understanding bone remodeling in response to exercise is crucial for skeletal health.

Purpose of the Study:

• To model the effects of mechanical loading on mammal long bone growth.
• To investigate bone reshaping and growth rates under different loading conditions.

Main Methods:

• Utilized a Ginzburg-Landau partial differential equation system.
• Employed a phase variable to track material properties during bone evolution.
• Solved the partial differential equation numerically using the finite element method.

Main Results:

• A critical load threshold was identified, below which bone resorption occurs.
• Three distinct loading intervals were defined, each resulting in different patterns of bone growth and resorption.
• Results for bending around a fixed axis showed good agreement with experimental data from turkeys.

Conclusions:

• Mechanical loading significantly influences bone remodeling, affecting both size and shape.
• The model provides a framework for understanding exercise-induced bone changes.
• Specific loading patterns can lead to either bone loss or increased bone mass.