Comprehensively characterizing heterogeneous and transversely isotropic properties of femur cortical bones

Comprehensive characterization of the transversely isotropic mechanical properties of long bones along both the longitudinal and circumferential gradients is crucial for developing accurate mathematical models and studying bone biomechanics. In addition, mechanical testing to derive elastic, plastic, and failure properties of bones is essential for modeling plastic deformation and failure of bones. To achieve these, we machined a total of 336 cortical specimens, including 168 transverse and 168 longitudinal specimens, from four different quadrants of seven different sections of 3 bovine femurs. We conducted three-point bending tests of these specimens at a loading rate of 0.02 mm/s. Young's modulus, yield stress, tangential modulus, and effective plastic strain for each specimen were derived from correction equations based on classical beam theory. Our statistical analysis reveals that the longitudinal gradient has a significant effect on the Young's modulus, yield stress, and tangential modulus of both longitudinal and transverse specimens, whereas the circumferential gradient significantly influences the Young's modulus, yield stress, and tangential modulus of transverse specimens only. The differences in Young's modulus and yield stress between longitudinal specimens from different sections are greater than 40%, whereas those between transverse specimens are approximately 30%. The Young's modulus and yield stress of transverse specimens in the anterior quadrant were 18.81%/15.46% and 18.34%/14.88% higher than those in the posterior and lateral quadrants, respectively. There is no significant interaction between the longitudinal gradient and the circumferential gradient. Considering the transverse isotropy, it is crucial to consider loading direction when investigating the impact of circumferential gradients in the anterior, lateral, medial, and posterior directions. Our findings indicate that the conventional assumption of homogeneity in simulating the cortical bone of long bones may have limitations, and researchers should consider the anatomical position and loading direction of femur specimens for precise prediction of mechanical responses.