Multi-scale analysis of bone

In this paper we review our multi-scale analysis of bone. First, we characterize the bone organ experimentally at several structural levels: the macroscale (whole bone), the mesoscale (trabecular bone represented as a porous network and cortical bone represented as collection of osteons in an interstitial bone), the microscale (single trabecula or single osteon), the sub-microscale (single lamella), and the nanoscale (apatite crystals and collagen fibrils), as shown in Fig. 1. More specifically, we study the hierarchical structure of bone using scanning electron microscopy (SEM), transmission electron microscopy (TEM), second harmonic generation (SHG) microscopy, computed tomography (CT) and micro-computed tomography (micro-CT), the composition using Fourier transform infrared micro-spectroscopy (FTIR-MS), and mechanical properties using compression and tension tests, and micro- and nano-indentation techniques. Then, we model bone theoretically at each structural level in a hierarchical way. The modeling techniques include analytical micromechanics theories and simulations involving a finite element method. We compare our theoretical results on elastic moduli and strengths at different scales with mechanical property measurements. Such experimentally-based multi-scale predictive computational model can be used to assess of bone quality, including the diagnosis of bone diseases such as osteoporosis. Secondly, it provides a more complete understanding of the complex phenomena taking place in bone during fracture.