Mechanics and material properties of the femoral head : from microstructure to continuum modelling

Abstract

The principal goal of this thesis was to determine an appropriate set of elastic constants to be used for modelling the femoral head. A survey of the distribution of density and compressive stiffness was conducted using 5 femoral heads. Compressive moduli were calculated in the Superoinferior (SΓ), mediolateral (ML) and anteroposterior (AP) directions from the stiffness data. The architecture of the structurally important medial group femoral head cancellous bone was studied in a procedure that involved serial sectioning of bone in which individual sections were photographed and digitised. The analysis demonstrated that the medial group bone plates of the femur are very closely aligned with the 16° inferolaterally directed Load Line in walking. Other directions of alignment are AP and ML which are also orthogonal to SL The SI direction was the Stiffest of the three followed by AP and ML. Cellular models with geometric properties similar to the medial group cancellous bone were formulated. The constants calculated using one of these models, based on a tetrakaidecahedral unit cell compared favourably with other modelling and experimental studies in the literature and have provided an insight into how compressive and shear moduli and Poisson's ratios might be interrelated for this bone. It was determined that a small change in plate architecture can result in a very big change in stiffnesses and that shear moduli and Poisson's ratios are directionally dependent. A three-dimensional continuum finite element model of the femoral head and neck was developed. After comprehensive convergence testing this finite element model was used to evaluate the importance of material symmetry assumptions on stress/strain solution data. Stress/strain data calculated using the tetrakaidecahedral cellular model material constants was compared with corresponding results using a set of constants for a significantly denser isotropic foam of similar longitudinal stiffness. While highlighting the importance of a realistic material description for strain calculations transverse to the load direction, the results suggest that a femoral architecture based on the tetrakaidecahedral cancellous bone model will maintain a similar stress and IongitudinaI strain field with an economy of material.