**7. Conclusion**

In this study, three 3D FE model for each nano-scopic struc- ture of bone ultrastructure (MCM, MCF and MCFR) were proposed. Different numerical simulations were performed to identify the apparent behavior for each structure (global homogenized) and to identify the corresponding apparent mechanical properties. The proposed 3D geometric models were used to perform para- metric studies to see the influence of geometrical and mechanical properties of the elementary constituents (HA crystals, TC molecules and cross-links) on the equivalent properties. In a second step, a multiscale approach using neural networks was developed. This approach uses the results of the finite element analysis for the training phase. It allows us to generalize the results obtained by finite element and do the transition between the different scale levels. The results were compared and vali- dated by other studies from the literature and a good agreement was observed. This hybrid multiscale approach allows deter- mining quickly (a few seconds) the mechanical equivalent properties as a function of the entered parameters. Here the method was only used to determine the elastic properties but can be approved to identify mechanical equivalent properties related to fracture behavior.

Otherwise, the proposed bone remodeling model can be enriched by the integration of transduction processes in addition to cellular activities and the explicit integration of the effects of RANKL/RANK/OPG regulation. It would also be useful to study the behavior of the bone remodeling model on heterogeneous 2D and 3D femurs. The scenarios (age, sex, physical activities, etc.) illustrated in this study are not exhaustive and others (medication, calcium content, etc.) can be incorporated.

### **Nomenclature**

