Effect of modeling method on prediction of cortical bone strength adaptation under various loading conditions

The ability to numerically simulate the effects of different loading conditions on the strength adaptation of a bone can be a valuable tool in understanding the relationship between the strength of a bone and its mechanical environment. Because significant strength changes may result from alterations in the profile of the surface of cortical bone, many computational models of bone strength adaptation have been developed to predict load-induced shape modifications. To gain insight into the effects of the modeling methods used for these predictions, the resulting changes to the surface profile of an initially circular cylinder were compared for a number of computational modeling methods. Models based on strain tensor, von Mises stress, and strain energy density were examined under various loading conditions including axial, bending, torsional, and surface forces as well as combinations of these basic loading modes. The differences between the use of a singular reference value and the use of a range of reference values to drive the magnitude of the local shape changes were investigated. Trends in the strain distributions were analyzed. The comparisons performed indicated that, despite the high sensitivity to the values of the model parameters used under the applied loading modes, with the proper selection of these parameters, the diverse methods studied yielded quite similar predictions of the bone's shape changes, and thus, strength adaptations.