Linear microcracks and diffuse damage (staining over a broad region) are two types of microscopic damage known to occur in vivo in human vertebral trabecular bone. These damage types might be associated with vertebral failure. Using microcomputed tomography and finite element analysis for specimens of cancellous bone, we estimated the stresses in the trabeculae of human vertebral tissue for inferosuperior loading. Microdamage was quantified histologically. The density of in vivo linear microcracks was, but the diffuse damage area was not, related to the estimates of von Mises stress distribution in the tissue. In vivo linear microcrack density increased with increasing coefficient of variation of the trabecular von Mises stress and with increasing average trabecular von Mises stress generated per superoinferior apparent axial stress. Nonlinear increase in linear crack density, similar to the increase of the coefficient of variation of trabecular shear stresses, with decreasing bone stiffness and bone volume fraction suggests that damage may accumulate rather rapidly in diseases associated with low bone density due to the dramatic increase of shear stresses in the tissue.
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.
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