The cancellous bone multiscale morphology-elasticity relationship.

Area of Science:

• Biomechanics
• Materials Science
• Orthopedics

Background:

• Cancellous bone exhibits complex multiscale architecture influencing its mechanical properties.
• Understanding the relationship between microstructural anisotropy and macroscopic behavior is crucial for bone mechanics.
• Existing models often simplify the complex interplay between trabecular structure and material response.

Purpose of the Study:

• To analyze the effective properties of cancellous bone across micro and meso scales.
• To establish multiscale relationships between representative volume element properties and trabecular trajectory orientation.
• To develop a multiaxial failure surface for cancellous bone.

Main Methods:

• Microscale analysis of representative volume elements.
• Mesoscale statistical analysis of trabecular trajectory orientation using fabric and trajectory orientation tensors.
• Stochastic interpolation for fitting scatter data (elastic modulus, trajectory orientation, apparent density).
• Least squares fitting with Nelder-Mead simplex for elasticity tensor estimation.
• Modified super-ellipsoid for constructing and interpolating the multiaxial failure surface.

Main Results:

• Established multiscale connections between microstructural anisotropy and mechanical properties.
• Quantified the relationship between fabric tensor and trajectory orientation tensor.
• Successfully fitted experimental data and estimated engineering constants.
• Developed a predictive multiaxial failure surface for cancellous bone.

Conclusions:

• The study provides a multiscale framework for understanding cancellous bone mechanics.
• The developed methods enable accurate prediction of bone effective properties and failure behavior.
• This research contributes to improved modeling of bone tissue and potential applications in personalized medicine and implant design.