Anisotropy of Young's modulus of human tibial cortical bone

Abstract

The anisotropy of Young's modulus in human cortical bone was determined for all spatial directions by performing coordinate rotations of a 6 by 6 elastic stiffness matrix. The elastic stiffness coefficients were determined experimentally from ultrasonic velocity measurements on 96 samples of normal cortical bone removed from the right tibia of eight human cadavers. The following measured values were used for our analysis: c11 = 19.5 GPa, c22 = 20.1 GPa, c33 = 30.9 GPa, c44 = 5.72 GPa, c55 = 5.17 GPa, c66 = 4.05 GPa, c23 = 12.5 GPa. The remaining coefficients were determined by assuming that the specimens possessed at least an orthorhombic elastic symmetry, and further assuming that c13 = c23 c12 = c11 - 2c66. Our analysis revealed a substantial anisotropy in Young's modulus in the plane containing the long axis of the tibia, with maxima of 20.9 GPa parallel to the long axis, and minima of 11.8 GPa perpendicular to this axis. A less pronounced anisotropy was observed in the plane perpendicular to the long axis of the tibia. To display our results for the full three-dimensional anisotropy of cortical bone, a closed surface was used to represent Young's modulus in all spatial directions.