The application of topology optimization on the quantitative description of the external shape of bone structure.

The aim of this paper was to introduce the idea of topology optimization in engineering to the simulation of bone morphology. The external shape of bone structure was predicted with the quantitative bone functional adaptation theory. The high-order nonlinear equation of bone remodeling proposed by Zhu et al. (J. Biomech. 35(7)(2002)951) combining with the finite element method was adopted to a rectangular design domain, which occupies a larger space than the external shape of bone structure. It was at this point we imported the idea of topology optimization in engineering. The proximal femur was used here as an example, whose external shape and internal density distribution were simultaneously simulated quantitatively to validate that the external shape of bone structure could be successfully predicted in this way. Then the growth of vertebral body from young to old was simulated numerically in its coronal section to discuss the significance of the prediction of external shape. The study in this paper provides computational basis for further studies on osteophyte formation, osteoporosis, osteoarthritis, bone growth and even bone evolution, etc.