Analogy of strain energy density based bone-remodeling algorithm and structural topology optimization

Area of Science:

• Biomechanics
• Computational Engineering
• Orthopedic Research

Background:

• Bone morphology is influenced by internal mechanical loads, a concept studied computationally since the 1970s.
• The strain energy density (SED) approach, proposed by Huiskes et al., models bone adaptation based on density changes relative to strain thresholds.
• Topology optimization, a structural optimization technique, has also been applied to simulate bone remodeling by iteratively distributing material.

Purpose of the Study:

• To compare the strain energy density-based bone remodeling algorithm (biomechanical approach) with the compliance-based structural topology optimization method (mechanical approach).
• To analyze the mathematical formulations, numerical challenges, and solution behaviors of these two distinct computational methods.
• To quantitatively assess the similarities, differences, and convergence of solutions through numerical case studies.

Main Methods:

• Comparative analysis of mathematical formulations for SED-based bone remodeling and compliance-based topology optimization.
• Implementation of two numerical case studies to simulate bone adaptation under mechanical loads.
• Quantitative evaluation of solution convergence and numerical behaviors for both approaches.

Main Results:

• The study demonstrates both similarities and differences between the SED-based and topology optimization methods in simulating bone remodeling.
• Numerical case studies provide insights into the practical application and performance of each approach.
• Quantitative analysis of solution convergence highlights the distinct characteristics of each method.

Conclusions:

• The research provides a quantitative comparison of two prominent computational methods for bone remodeling simulation.
• Understanding the mathematical and numerical nuances of these approaches aids in selecting appropriate methods for biomechanical and prosthetic design analyses.
• This work contributes to more accurate computational modeling of bone adaptation to mechanical stimuli.