Spatial Distribution of Material Properties in Load Bearing Femur as Characterized by Evolutionary Structural Optimization

Abstract

This works aims to simulate bone formation under natural loading using evolutionary structural optimization. Unlike material elimination by hard-kill approach applied previously, the current presentation implements material replacement defined as soft-kill method. A numerical analysis platform was developed and finite element model of sheep femur was constructed using computer tomography data. Quadruple material properties governing soft medullary canal, cancellous as well as plexiform and haversian cortical structures were considered as the main material constituents of the femur. An iterative algorithm was designed for determining the spatial distribution of these tissue types throughout the femur. The model initially started with a homogenous plexiform design and iteratively converged to a final state with heterogeneous density profile, nearly similar to a natural femur. The inefficient regions were gradually changed with mechanically lower grade and lighter tissues and thus the final construct had the least weight but still supported the load. The convergence was achieved successfully. . The tissue types were distributed in a mechanically optimum fashion to counteract the applied forces. The resulting internal material assignments provided insights into the structural remodeling of femur within the context of Wolff’s law. . Using the developments, bone formation can be simulated numerically under different mechanical loading conditions. Such investigations may provide useful information about the vulnerability of bone as its material properties change with osteoporosis or the fracture risk as a result of malfunction in muscles attached to the femur.