Dependence of Elastic Properties of Human Femoral Cortical Bone on Porosity

Abstract

Hip fracture is one of the most serious and common health problems among elderly which may lead to permanent disability or death. Hip fracture commonly occurs in the femoral bone, the major bone in the hip joint. Microscopic age-related changes in the structure of cortical bone is one of the factors that is considered to be partially responsible for the increase of fracture risk in elderly. It is of great interest to develop a predictable model of such fractures for the aging population in preparation of a suitable therapy. These micro structural changes influence mechanical properties and, therefore, behavior of bone and are critical to understand risk and mechanics of fracture of bone. Correlation between cortical bone strength and porosity, as a microscopic structural factor, has been examined frequently as a function of age and/or porosity. These studies have investigated the effect of porosity experimentally and have not studied the effect of porosity independently from other structural factors such as bone mineral density. In this study effect of porosity on elastic properties of human femoral cortical bone was studied independently using finite element analysis assuming transversely isotropic behavior in terms of elastic properties with the axis of elastic properties along the longitudinal axis of femur shaft. In this study, published standard mechanical tests for transversely isotropic materials were simulated using finite element computer simulation on models with different porosities. The developed finite element model utilized material properties based on the best fit regression in previously published articles. Pores’ size, shape and distribution were also modeled based on previous experimental studies. The finite element model, in general, predicted behavior of five independent elastic mechanical properties, namely, longitudinal Young’s modulus, transverse poisson’s ratio, transverse shear modulus, transverse Young’s modulus and longitudinal poisson’s ratio, as a function of porosity. Furthermore, effect of porosity on the elastic properties across various age groups was investigated using published data on age-related changes in bone porosity. Mathematical models based on Finite Element Analysis results have been developed using linear least square regression. These models show negative linear relationship between studied elastic properties of human femoral cortical bone and porosity. The Finite Element Analysis results compared well with the previously published experimental data. Furthermore, the results obtained show the elastic properties as functions of age for females and males. The predicted values for elastic properties are lower for men compared to women of age 20 to 40 years old. However, after the age of 44, elastic properties of femoral cortical bone for men are higher than women. The Finite Element Model developed in this study will help to create a clinical bone model for the prediction of fracture risk or the selection of suitable therapy in orthopedic surgery.