Shear stress distribution in the trabeculae of human vertebral bone

The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r2>0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r2=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r2=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV = A + B exp(-x/C)]. The COV of the stress was higher for low volume fraction tissue (<0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading.