Abstract
BackgroundThe resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior.ResultsThe purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration elastic-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the finite element method algorithm to investigate the effect of the damage.ConclusionThe results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading.
Highlights
Bone is the main constituent of the skeletal system enable to maintain substantially the shape of the body; to protect the internal organs; to store minerals and lipids; to participate in blood cell production; and to assist body movements by transmitting the force of muscular contraction from one part to another [1].As a living tissue, bone is able to optimize its structure by redistributing its density under the influence of external forces
Elastic-damaged bone remodeling theory The femur can be remodeled in response to external loads to give greater bone matrix in regions that are subjected to higher levels of stress
Where: ρmin the minimal density corresponding to the reabsorbed bone ρmax the maximal density of cortical bone let ρ0 denote the initial bone density we introduce the evolution law of the damage suggested by Martin [7,20] through the equation: D 1⁄4 D0: efd t
Summary
Bone is the main constituent of the skeletal system enable to maintain substantially the shape of the body; to protect the internal organs; to store minerals and lipids; to participate in blood cell production; and to assist body movements by transmitting the force of muscular contraction from one part to another [1].As a living tissue, bone is able to optimize its structure by redistributing its density under the influence of external forces. The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior. Elastic-damaged bone remodeling theory The femur can be remodeled in response to external loads to give greater bone matrix in regions that are subjected to higher levels of stress. These external loads induce changes in the mechanical fields and damage to the femur, such as macro cracks or micro cracks [14,15]
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