Assessment of mechanical variables best describing bone remodelling responses based on their correlation with bone density

Abstract

Density distribution in bones can be estimated using bone remodelling models (BRM) and applying daily normal loads to assess the stress/strain state to which the bone is subjected. These models locally relate a certain mechanical stimulus, derived from the stress/strain state, directly to bone density or to its variation over time. The background of this idea is Frost’s Mechanostat Theory, which states that overloading states tend to increase bone density and disuse states tend to decrease it. Different variables have been proposed in the literature to measure the mechanical stimulus. Strain energy density (SED) and stresses have been commonly used as mechanical stimuli, but to date their use has not been justified with convincing arguments. In this paper we have selected several variables derived from stress and strain tensors and correlated them with the distribution of bone density in the femur of 13 elderly women to conclude which would be most appropriate for use as a mechanical stimulus in a BRM. We have performed this correlation analysis for six different activities: walking normally, fast walking, stair ascent, stair descent, rising from and sitting on a chair, and jumping in place. Musculoskeletal models were used to estimate joint reaction and muscle forces of each individual for each activity. These were applied to the corresponding finite element model of the femur to obtain stress and strain tensors at each point. The variables proposed as mechanical stimulus and derived from these tensors were correlated to the actual density obtained for each individual from CT-scans. Our results show that stress variables are the best correlated with density. In contrast, the correlations of SED are very weak, so it is not a good candidate for mechanical stimulus. Strains are also weakly correlated to density, but in this case because their distribution across the femur is rather uniform. This is in agreement with the Mechanostat Theory which states that bone reacts to load changes by changing its stiffness so to keep strains in a certain interval. Consequently, a plausible choice for a remodelling criterion could be keeping that strain uniformity.