Since the turn of the century, investigators have been documenting the ability of cancellous bone to align itself in such a way as to most effectively support the loads to which it is exposed. The fundamental contribution of this work is to build upon the existing bone remodeling formulations--which do not account for trabecular alignment--to include directional material behavior. This takes the form of two evolution equations for the fourth rank stiffness tensor which supplements the existing evolution equation for the apparent density, each with its respective advantages and disadvantages. Neither approach requires the introduction of additional intermediate morphological measures beyond the density.

In both cases, no assumptions of material symmetry were employed. By preserving a completely general formulation, predicted regional symmetries (e.g., orthotropy, transverse isotropy, or isotropy) result from adaptation and not modeling assumptions. Furthermore, by requiring the anisotropic formulation to reduce to the isotropic formulation in specific cases, the anisotropic formulation can be cast entirely in terms of the parameters which describe the isotropic formulation. This avoids the introduction of any new degrees-of-freedom to the model which would otherwise require estimation and verification.

Although this work is theoretical in nature, computational implementations were applied to a two dimensional model of the proximal femur with encouraging preliminary results. The predicted density distributions using the new formulations match well with observations and with that predicted with the isotropic formulation, indicating that in situations where changes in density alone are of concern, anisotropy might be ignored (at least in the proximal femur). The directional normal stiffnesses are also in agreement with observations of cancellous bone anisotropic stiffness measurements. This phenomenological approach promises to be quite valuable in clinically relevant situations where the directional response is important.