Changes in the Fabric and Compliance Tensors of Cancellous Bone due to Trabecular Surface Remodeling, Predicted by a Digital Image-based Model

Abstract

Fabric and compliance tensors of a cube of cancellous bone with a complicated three-dimensional trabecular structure were obtained for trabecular surface remodeling by using a digital image-based model combined with a large-scale finite element method. Using mean intercept length and a homogenization method, the fabric and compliance tensors were determined for the trabecular structure obtained in the computer remodeling simulation. The tensorial quantities obtained indicated that anisotropic structural changes occur in cancellous bone adapting to the compressive loading condition. There were good correlations between the fabric tensor, bone volume fraction, and compliance tensor in the remodeling process. The result demonstrates that changes in the structural and mechanical properties of cancellous bone are essentially anisotropic and should be expressed by tensorial quantities.

Keywords:

• Computational biomechanics
• Cancellous bone
• Trabecular structure
• Bone remodeling
• Adaptation
• Digital image-based model

Acknowledgements

The support of the Special Postdoctoral Researchers Program at The Institute of Physical and Chemical Research (RIKEN) is gratefully acknowledged. This work was financially supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The authors thank Dr Scott J. Hollister and Dr Steven A. Goldstein of the Orthopaedic Research Laboratories at the University of Michigan for providing bone data and helpful comments, and Mr Shuntaro Yamazaki of RIKEN for providing the tool used to visualize the trabecular structure in Fig. 1.