Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement

Abstract

In this work, a new model for internal anisotropic bone remodelling is applied to the study of the remodelling behaviour of the proximal femur before and after total hip replacement (THR). This model considers bone remodelling under the scope of a general damage-repair theory following the principles of continuum damage mechanics. A “damage-repair” tensor is defined in terms of the apparent density and Cowin's “fabric tensor”, respectively, associated with porosity and directionality of the trabeculae. The different elements of a thermodynamically consistent damage theory are established, including resorption and apposition criteria, evolution law and rate of remodelling. All of these elements were introduced and discussed in detail in a previous paper (Garcı́a, J. M., Martinez, M. A., Doblaré, M., 2001. An anisotrophic internal–external bone adaptation model based on a combination of CAO and continuum damage mechanics technologies. Computer Methods in Biomechanics and Biomedical Engineering 4(4), 355–378.), including the definition of the proposed mechanical stimulus and the qualitative properties of the model. In this paper, the fundamentals of the proposed model are briefly reviewed and the computational aspects of its implementation are discussed. This model is then applied to the analysis of the remodelling behaviour of the intact femur obtaining densities and mass principal values and directions very close to the experimental data. The second application involved the proximal femoral extremity after THR and the inclusion of an Exeter prosthesis. As a result of the simulation process, some well-known features previously detected in medical clinics were recovered, such as the stress yielding effect in the proximal part of the implant or the enlargement of the cortical layer at the distal part of the implant. With respect to the anisotropic properties, bone microstructure and local stiffness are known to tend to align with the stress principal directions. This experimental fact is mathematically proved in the framework of this remodelling model and clearly shown in the results corresponding to the intact femur. After THR the degree of anisotropy decreases tending, specifically in the proximal femur, to a more isotropic behaviour.