In the vertebral body (VB), the load carrying and transmitting function is primarily performed by the cortical VB. Hence, we have modelled the cortical VB as a hyperboloid shell whose geometry and composition are made up of its generators. This paper analyses the forces in the VB generators due to compression, bending and torsional loadings. The unique feature of the hyperboloid geometry is that all the loadings are transmitted as axial forces in the generators. This makes the VB a high-strength structure. Furthermore, because the cortical VB material is primarily made up of its generators (through which all the loadings are transmitted axially), it also makes the VB an intrinsically lightweight structure.We then analyse for the optimal hyperboloid shape and geometry by minimizing the sum of the forces in the hyperboloid VB generators with respect to the hyperboloid shape parameter (angle β between pairs of generators). The value of β is determined to be 26.5◦, which closely matches with the in vivo geometry of the VB based on its magnetic resonance imaging scan. In other words, for the hyperboloid shape parameter β = 26.5◦, the VB generators’ forces are minimal so as to enable it to bear maximal amounts of loadings. In this way, we have demonstrated that the VB is an intrinsically, functionally optimal structure.
axial force, bending, toque, generators, hyperboloid, optimal structure, shape parameter, stress
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