Using a Truss-Inspired Model with the Uniform Strength Optimization Theory to Predict Spongy Bone Geometry in Proximal Femur

Abstract

This paper presents a new naïve approach for simulating bone remodeling process. It is based on the uniform strength theory of optimization and employs a truss-like model for bone. The truss was subjected to external loads including 5 point loads simulating the hip joint contact forces and 3 muscular forces at the attachment sites of the muscles to the bone and the rest are reactions of ligaments. The strain in the links was calculated and the links with high strains were identified. The initial truss is modified by introducing new links wherever the strain exceeds a prescribed or critical value. The critical value was assumed to be equal to an average of the absolute value of strains in the initial model. Each link which undergoes a high strain is replaced by several new links by adding new nodes around it using Delaunay method. Introducing the new links to the truss, which is conducted according to a weighted arithmetic mean formula, will strengthen the structure and reduce the strain within the respective zone. This procedure was repeated for several times. Convergence was achieved when there were no critical links remaining. This method was used to study the 2D shape of proximal femur in the frontal plane and provided results which are in a fairly good agreement with CT image of the human proximal femur.