Determination of the geometry of the RVE for cancellous bone by using the effective complex shear modulus

Area of Science:

• Biomechanics
• Computational Material Science
• Medical Imaging Analysis

Background:

• Cancellous bone exhibits complex microstructural heterogeneity.
• Accurate determination of bone's geometrical properties is crucial for understanding its mechanical behavior.
• Existing methods for bone characterization have limitations in capturing microstructural details.

Purpose of the Study:

• To apply the inverse homogenization method for determining the geometrical properties of cancellous bone.
• To develop an extended Marquardt-Levenberg method capable of identifying global minima in optimization.
• To model cancellous bone as a biphasic viscoelastic medium.

Main Methods:

• Utilized a combination of the extended Marquardt-Levenberg method and multiscale finite element method.
• Employed gradient-based optimization strategies integrated with numerical homogenization.
• Modeled bone using three representative volume elements, simulating isotropic and anisotropic behavior.

Main Results:

• Successfully determined main geometrical properties of trabeculae from effective shear modulus data.
• Demonstrated the capability of the extended Marquardt-Levenberg method to distinguish global from local minima.
• Validated the multiscale finite element method for modeling heterogeneous microstructures like cancellous bone.

Conclusions:

• The inverse homogenization method provides a robust framework for characterizing cancellous bone geometry.
• The enhanced optimization strategy effectively handles complex, multi-modal objective functions.
• This approach offers a pathway for more accurate in silico analysis of bone mechanics and disease progression.