The process of adaptive bone remodeling can be described mathematically and simulated with a self-optimizing finite element method (FEM) model. The aim of this study was to understand the effect of the basic remodeling rule on the bone density distribution of the proximal femur affected by the muscle loadings and the hip joint contact forces during normal gait (walking). The basic remodeling rule, which is an objective function for an optimization process relative to external load, was applied to predict the bone density. The purpose of the process is to obtain a constant value for the strain energy per unit bone mass, by adapting density modeling. The precise solution is dependent on the magnitude and direction of loads, loading rate, initial conditions and the parameters in the remodeling rule. In this study, we applied adaptive bone density remodeling under both static and dynamic loading conditions. In the static case, the forces at different phases in the gait cycle were statically applied as boundary conditions. The density distributions from these loadings were averaged to find the density distribution in the proximal femur. Three different initial densities were considered to investigate the effect of initial conditions. The influence of different parameters and functions on the density distribution and its convergence rate was also investigated. Furthermore, effect of changing of muscle loading and hip joint contact forces on resultant mass and density distribution of proximal femur was studied. In the dynamic approach, the forces of different phases of gait cycle were applied during different gait cycle’s times of 1.27 second (slow speed), 1.11 second (normal speed), 1.01 second (moderately fast speed), and 0.83 second (very fast speed). Although the results of bone density adaptations in both approaches were comparable with an example of an actual bone density distribution of the femoral head, neck and the proximal femoral shaft; the converged density distribution in the static approach was smoother and more realistic. It was shown that by applying more loading conditions through the gait cycle the converged density distribution is smoother. The resultant density distribution was more comparable with actual proximal femur compared to past studies.
Computational Analysis of Bone Remodeling in the Proximal Tibia Under Electrical Stimulation Considering the Piezoelectric Properties
