The thermodynamic driving force for bone growth and remodelling: a hypothesis

Area of Science:

• Biomechanics
• Materials Science
• Solid Mechanics

Background:

• Bone exhibits complex mechanical and electrical properties, including piezoelectricity and piezomagnetism.
• Bone's structure is heterogeneous and undergoes continuous remodelling and growth.
• Cosserat (micropolar) elasticity accounts for the material microstructure's influence on mechanical response.

Purpose of the Study:

• To derive the Eshelby stress tensor for bone modeled as an inhomogeneous piezoelectric and piezomagnetic Cosserat medium.
• To identify the configurational force driving structural transformations in bone.
• To investigate the thermodynamic basis of bone remodelling and growth.

Main Methods:

• Derivation of the Eshelby stress (static energy momentum) tensor.
• Analysis of the divergence of the tensor to determine configurational forces.
• Application of a thermodynamic approach to relate forces to phase and structural transformations.

Main Results:

• The divergence of the Eshelby stress tensor represents the configurational force acting on bone's material gradients and defects.
• This force is identified as the thermodynamic driver for bone remodelling and growth.
• Driving force terms are proportional to stress, with quadratic terms dominating at heterogeneities.
• Inertial forces indicate that the rate of loading is significant.

Conclusions:

• Bone remodelling and growth are thermodynamically driven by configurational forces within a piezoelectric, piezomagnetic Cosserat framework.
• Both tensile and compressive loading stimulate growth, particularly at heterogeneities.
• The rate of mechanical loading is a critical factor in bone's adaptive response.