The relationship between the mechanical anisotropy of human cortical bone tissue and its microstructure

Orthopedics research has made significant advances in the areas of biomechanics, bone implants and bone substitute materials. However, to date there is no definitive model to explain the structure-property relationships in bone as a material to enable better implant designs or to develop a true biomechanical analog of bone. The objective of this investigation was to establish a relationship between the elastic anisotropy of cortical bone tissue and its microstructure. Ultrasonic wave propagation was used to measure stiffness coefficients for specimens sectioned along the length of a human femur. The elastic constants were orthotropic and varied with anatomical location. Stiffness coefficients were generally largest at the midshaft and stiffness anisotropy ratios were largest at the distal and proximal ends. Stiffness coefficients were shown to be correlated as a power law relation to apparent density, but anisotropy ratios were not. These tests were run on four additional human femurs to assess the influence of phenotypes as an exploratory investigation. For the current sample size, it was found that in fact these differences do exist, but the causes are and will remain unknown. Certainly, a much larger sample size is needed in order to state definitive conclusions about the phenotypic variation. Texture analysis was performed on selected samples to measure the orientation distribution of the bone mineral crystals. Inverse pole figures showed that bone mineral crystals had a preferred crystallographic orientation, coincident with the long axis of the femur, which is its principal loading direction. The degree of preferred orientation was represented in Multiples of a Random Distribution (MRD), and correlated to the anisotropy ratios. Variation in elastic anisotropy was shown to be primarily due to the bone mineral orientation. The results found in this work can be used to incorporate anisotropy into structural analysis for bone as a material.