Biomechanics of lumbar vertebrae as a functionally optimal structure.

In this paper, we demonstrate that the spinal vertebral body (VB) remodels (as per Wolf's law) such that its shape and dimensions enable it to be a light-weight high-strength structure. The VB is modeled as a hyperboloid shell, whose generators are shown to sustain (and transmit) all the loadings on the VB as axial forces. Upon minimizing the sum of the forces in the hyperboloid VB generators with respect to its shape parameters theta (the angle between pairs of generators), we obtain the optimal shape-dimensions of the VB which corresponds to its measured shape-dimensions. This parameter theta is deemed to be the prime shape parameter of the hyperboloid VB.