An improved method to assess torsional properties of rodent long bones

Torsion is an important testing modality commonly used to calculate structural properties of long bones. However, the effects of size and geometry must be excluded from the overall structural response in order to compare material properties of bones of different size, age and species. We have developed a new method to analyze torsional properties of bones using actual cross-sectional information and length-wise geometrical variations obtained by micro-computed topographic (microCT) imaging. The proposed method was first validated by manufacturing three rat femurs through rapid prototyping using a plastic with known material properties. The observed variations in calculated torsional shear modulus of the hollow elliptical model of mid-shaft cross-section (Ekeland et al.), multi-prismatic model of five true cross-sections (Levenston et al.) and multi-slice model presented in this study were 96%, -7% and 6% from the actual properties of the plastic, respectively. Subsequently, we used this method to derive relationships expressing torsional properties of rat cortical bone as a function of muCT-based bone volume fraction or apparent density over a range of normal and pathologic bone densities. Results indicate that a regression model of shear modulus or shear strength and bone volume fraction or apparent density described at least 81% of the variation in torsional properties of normal and pathologic bones. Coupled with the structural rigidity analysis technique introduced by the authors, the relationships reported here can provide a non-invasive tool to assess fracture risk in bones affected by pathologies and/or treatment options.