Abstract

It is widely known that trabecular bones of vertebrates are constantly being remodeled in response to the corresponding local stresses and strains. This is called Wolff's law. On the other hand, it has yet to be understood how the outer shape of a vertebrae bone is formed. In this study, based on the observation of zebrafish vertebrae bones, we hypothesize that a vertebrae bone is composed of the two regions: one is formed a priori, while the other is formed a posteriori against external loading like trabecular bones. Assuming that Wolff's law can be expansively applied to the formation of the outer shape of a vertebrae bone, we introduce a mathematical model using topology optimization. We apply the mathematical model to simulating the zebrafish vertebrae bone growth. Numerical results show the proposed model can capture the basic feature of vertebrae bone, while there remain some discrepancies between the calculated shape and the measured shape.