Not only stiffness, but also yield strength of the trabecular structure determined by non-linear µFE is best predicted by bone volume fraction and fabric tensor

Abstract

The micro-architecture of cancellous bone is considered a major determinant of the fracture risk. Yet, if morphometry tells about alterations of the trabecular network, its elastic behaviour is best described by bone volume fraction (BV/TV) and the fabric tensor, which gives the anisotropy of the trabecular structure. This remains to be proven for yield strength, the onset of bone failure. The microstructure of 126 samples extracted from femoral heads of two female subjects was evaluated on micro-computed tomography scans via 25 structural indices. Parameters such as plate and rod decomposition via ITS and textural analyses by ISV, similar to the trabecular bone score, were also examined. The degree of collinearity between indices was assessed. The indices considered sufficiently independent were included in multi-linear regression models predicting stiffness or yield strength measured via nonlinear micro finite element analyses. The models’ accuracy was checked and the contributions of all explanatory variables to the prediction were compared. Our results show that BV/TV alone explained most of the predicted yield strength (76%) and stiffness (89%). BV/TV together with the fabric tensor explained more than 98% of both measures! The fabric tensor also had a larger impact on yield strength (23%) than on the stiffness predictions (9%). On the other hand, the predictive value of the other independent factors (Tb.Th.SD, Tb.Sp.SD, rTb.Th, RR.Junc.D, ISV) was negligible (<1%). In conclusion, just as stiffness, yield strength of femoral trabecular bone is also best explained by BV/TV and trabecular anisotropy, the latter being even more relevant in its post-elastic behaviour.