Sensitivity of Vertebral Compressive Strength to Endplate Loading Distribution

The sensitivity of vertebral body strength to the distribution of axial forces along the endplate has not been comprehensively evaluated. Using quantitative computed tomography-based finite element models of 13 vertebral bodies, an optimization analysis was performed to determine the endplate force distributions that minimized (lower bound) and maximized (upper bound) vertebral strength for a given set of externally applied axial compressive loads. Vertebral strength was also evaluated for three generic boundary conditions: uniform displacement, uniform force, and a nonuniform force distribution in which the interior of the endplate was loaded with a force that was 1.5 times greater than the periphery. Our results showed that the relative difference between the upper and lower bounds on vertebral strength was $14.2±7.0%$$(mean±SD)$. While there was a weak trend for the magnitude of the strength bounds to be inversely proportional to bone mineral density ($R2=0.32$, $p=0.02$), both upper and lower bound vertebral strength measures were well predicted by the strength response under uniform displacement loading conditions ($R2=0.91$ and $R2=0.99$, respectively). All three generic boundary conditions resulted in vertebral strength values that were statistically indistinguishable from the loading condition that resulted in an upper bound on strength. The results of this study indicate that the uncertainty in strength arising from the unknown condition of the disc is dependent on the condition of the bone (whether it is osteoporotic or normal). Although bone mineral density is not a good predictor of strength sensitivity, vertebral strength under generic boundary conditions, i.e., uniform displacement or force, was strongly correlated with the relative magnitude of the strength bounds. Thus, explicit disc modeling may not be necessary.