Different approaches of remodeling of bone to predict bone density distribution of proximal femur

Bone remodeling is a life long process where bone is removed from the skeleton (bone resorption) and new bone is formed. Remodeling responds to muscle and joint contacts forces. As a result, bone is added where needed and removed where not required. Therefore, bone remodeling results in creating different bone density distribution.;An imbalance in the regulation of bone remodeling, resorption and formation, results in many metabolic bone diseases, such as osteoporosis. Therefore, better understanding of bone remodeling procedure helps to prevent these kinds of diseases.;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. In the dynamic approach, the forces of different phases of gait cycle were applied during different gait cycle's period 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. The resultant density distribution was more comparable with actual proximal femur compared to past studies.;In addition to above investigations, a new efficient method for simulating the bone remodeling procedure was developed. This method was based on the trajectorial architecture theory of optimization and employs a beam-like frame for bone. The beams in the model were subjected to external loads including the hip joint contact force and muscular forces at the attachment sites of the muscles to the bone. The stress in the beams was calculated and the beams with high stresses were identified. The initial beams were modified by introducing new beams wherever the stress exceeded a prescribed value; each beam undergoing a high stress was replaced by several new beams by adding new nodes around it. Introduction of these new beams to the structure, which was constructed according to an arithmetic mean formula, strengthen the structure and reduced the stress within the respective zone. The triangle containing the critical beam was replaced by a shell element where it was filled up with these beams. The beams with low stress were identified too. They were eliminated if their stress was lower than a critical stress. This procedure was repeated for several steps. Convergence was achieved when there were no critical beams remaining or they have been converted to the shell elements. This method was used to study the 2D shape of proximal femur in the frontal plane and provided results that were consistent with DEXA data. The proposed method exhibited capability similar to more complicated conventional nonlinear algorithms, however, with a much higher convergence rate and lower computational costs.