ADAPTIVE BONE REMODELING INCORPORATING SIMULTANEOUS DENSITY AND ANISOTROPY CONSIDERATIONS

Over 100 years ago, Wolff hypothesized that cancellous bone altered bo th its apparent density and trabecular orientation in response to mech anical loads. A mathematical counterpart of this principle is derived by adding a remodeling rule for the rate-of-change of the full anisotr opic stiffness tensor (all 21 independent terms) to the density rate-o f-change rule adapted from an existing isotropic theory. As a result, anisotropy and density patterns develop such that the local stiffness tensor is optimal for the given series of applied loadings. The method does not rely on additional morphological measures of trabecular orie ntation. Furthermore, assumptions of material symmetry are not require d, and any observed regions of orthotropy, transverse isotropy, or iso tropy are a result entirely of the functional adaptation of the bone a nd not the consequence of a modeling assumption. This approach has bee n implemented with the finite element method and applied to a two-dime nsional model of the proximal femur with encouraging results. (C) 1997 Elsevier Science Ltd.