Simulation on the structure and growth of vertebra

At present there is only linear rate equation of bone remodeling to quantitatively describe bone's self-optimization or self-adaptation. By combining it with FEM bone structure can be predicated. In literature several authors simulated internal bone architectures inside the real external shapes. But few results simulated on bone external shape have been reported. The aim of this paper was to simulate the external shape and internal structure of vertebra and its growth. A new high order nonlinear rate equation of bone remodeling combining with FEM was adopted in a uniform square plate, in which we imported topology optimization in engineering. We also measured the external shape and internal structure of the cross-section of the third lumber. The results simulated are consistent with practical measure in both external shape and internal structure. In old stage, its shape is more concave than that in young stage and its trabecular bone is disposed along the principal stresses, i. e, along vertical direction. The trabecular bone in old stage is merely much looser. Whether we can say it that by combining this self-optimizing equation with FEM, not only can we simulate and predict the external shape and internal structure of bone, but also simulate its growth with topology-optimization idea. In particular the simulation on bone external shape has been accomplished, thus the simulation on bone growth can become possible.