A new numerical concept for modeling hydroxyapatite in human cortical bone

Abstract

This research presents a new modelling procedure which allows the computation of the physical properties of the human cortical bone, considered as a strongly heterogeneous medium consisting of bony architecture and the physical properties of the two basic components: the collagen and the hydroxyapatite (Hap). The numerical simulations are based on the homogenisation theory, however, since the size of the Hap crystals are small compared to the size of a collagen stick, a new entity (the elementary volume of mineral content (EVMC)) is defined at the nanoscopic scale. This model permits the testing of all the possible structural configurations that may be present and suggests that the anisotropy of the bone is not only induced by the haversian structure but by the properties of the Hap crystals and their special organisation.

Keywords:

• Cortical bone
• Homogenisation theory
• Numerical simulation
• Hydroxyapatite
• Mechanical properties

Acknowledgements

This study has been supported by the CNRS (“Programme Matériaux, n 43”).