Misalignment Error in Cancellous Bone Apparent Elastic Modulus Depends on Bone Volume Fraction and Degree of Anisotropy

Cancellous bone is an anisotropic structure with architectural and mechanical properties that vary due to both skeletal site and disease state. This anisotropy means that, in order to accurately and consistently measure the mechanical properties of cancellous bone, experiments should be performed along the primary mechanical axis (PMA), that is, the orientation in which the mechanical properties are at their maximum value. Unfortunately, some degree of misalignment will always be present, and the magnitude of the resulting error is expected to be architecture dependent. The goal of this work is to quantify the dependence of the misalignment error, expressed in terms of change in apparent elastic modulus (⁠$ΔE$⁠), on both the bone volume fraction (BV/TV) and the degree of anisotropy (DA). Finite element method (FEM) models of bovine cancellous bone from five different skeletal sites were created at 5 deg and $20 deg$ from the PMA determined for each region. An additional set of models was created using image dilation/erosion steps in order to control for BV/TV and better isolate the effect of DA. Misalignment error was found to increase with increasing DA and decreasing BV/TV. At $5 deg$ misaligned from the PMA, error is relatively low (<5%) in all cases but increases to 8–24% error at $20 deg$⁠. These results suggest that great care is needed to avoid introducing misalignment error into experimental studies, particularly when studying regions with high anisotropy and/or low bone volume fraction, such as vertebral or osteoporotic bone.