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 m odels. The goal was to test the hypothesis that average trabecular von Mise s stress is correlated to the maximum trabecular level von Mises stress, Th e hypothesis was proposed to explain the close experimental correlation bet ween apparent strength and stiffness of human cancellous bone tissue. A thr ee-parameter Weibull function described the probability distribution of the estimated von Mises stress (r(2)>0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r(2)=0.63) sup porting the hypothesis that average and maximum magnitude stress would be c orrelated. The coefficient of variation (COV) of the von Mises stress was n onlinearly related to apparent compressive strength, apparent stiffness, an d bone volume fraction (adjusted r(2)=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 weakn ess of low volume fraction tissue and suggesting that stress variation is b etter controlled in higher volume fraction tissue. We propose that the aver age stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading. (C) 2000 Biomedical Engineering Society. [S0090-6964(00)00910-3].