The relative influence of apatite crystal orientations and intracortical porosity on the elastic anisotropy of human cortical bone

Elastic anisotropy exhibits spatial inhomogeneity in human cortical bone, but the structural origins of anatomic variation are not well understood. In this study, the elastic anisotropy of human cortical bone was predicted using a specimen-specific multiscale model that investigated the relative influence of apatite crystal orientations and intracortical porosity. The elastic anisotropy of cortical bone specimens from the diaphysis of human femora was measured by ultrasonic wave propagation as the ratio of elastic constants in the longitudinal/radial (L/R) and longitudinal/circumferential (L/C) anatomic specimen axes. Experimental measurements of elastic constants exhibited orthotropy, with greater anisotropy in the L/R plane compared to the L/C plane. Model predictions included (1) a micromechanical model accounting for the effects of apatite crystal orientations, (2) a voxel-based finite element model accounting for the effects of intracortical porosity, and (3) a combined model accounting for both effects. The combined model provided the most accurate predictions of elastic anisotropy in both the L/R and L/C plane, with less than 10% mean error. The micromechanical model alone was able to accurately predict elastic anisotropy in the L/C plane, but predicted transverse isotropy. The finite element model alone grossly underestimated elastic anisotropy in both the L/R and L/C planes, but was able to predict orthotropy. Therefore, the results of this study suggest that the dominant and less variable transverse isotropy of human cortical bone, reflected by L/C, is governed primarily by apatite crystal orientations, while the more subtle and variable orthotropy, reflected by the difference between L/R and L/C, is governed primarily by intracortical porosity. Moreover, the combined model may be useful to investigate other structure-function relationships or in place of current numerical models, for example, in the study of bone adaptation and metabolic bone disease.