Improved prediction of rat cortical bone mechanical behavior using composite beam theory to integrate tissue level properties

Tissue level characteristics of bone can be measured by nanoindentation and microspectroscopy, but are challenging to translate to whole bone mechanical behavior in this hierarchically structured material. The current study calculated weighted section moduli from microCT attenuation values based on tissue level relationships (Zlin,a and Zlin,b) between mineralization and material properties to predict whole bone mechanical behavior. Zlin,a was determined using the equation of the best fit linear regression between indentation modulus from nanoindentation and mineral:matrix ratio from Raman spectroscopy. To better represent the modulus of unmineralized tissue, a second linear regression with the intercept fixed at 0 was used to calculate Zlin,b. The predictive capability of the weighted section moduli calculated using a tissue level relationship was compared with average tissue level properties and weighted section moduli calculated using an apparent level relationship (Zexp) between Young's Modulus and mineralization. A range of bone mineralization was created using vitamin D deficiency in growing rats. After 10 weeks, left femurs were scanned using microCT and tested to failure in 3 point bending. Contralateral limbs were used for co-localized tissue level mechanical properties by nanoindentation and compositional measurements by Raman microspectroscopy. Vitamin D deficiency reduced whole bone stiffness and strength by ∼35% and ∼30%, respectively, but only reduced tissue mineral density by ∼10% compared with Controls. Average tissue level properties did not correlate with whole bone mechanical behavior while Zlin,a, Zlin,b, and Zexp predicted 54%, 66%, and 80% of the failure moment respectively. This study demonstrated that in a model for varying mineralization, the composite beam model in this paper is an improved method to extrapolate tissue level data to macro-scale mechanical behavior.