STRESS DISTRIBUTION WITHIN THE HEAD AND NECK OF THE FEMUR

Abstract

Introduction: Since the mid-1800’s it has been believed that the human femur functions in a similar way to a crane in which the distal end is fixed and body weight is applied to the femoral head (Meyer, 1867, Williams, 1995). This results in tension in the lateral femoral shaft and in the so-called ‘principal tensile system’ of trabeculae while, compression is found in the medial shaft and in the ‘principal compressive system’. Most studies have concentrated on the shaft to find ways of avoiding these tensile stresses and recognised that the inclusion of muscle forces is essential in any realistic modelling. The state of stress in the proximal femur has not been satisfactorily resolved, though a minority view is that muscle forces put all of the trabeculae into compression (Strange, 1965). Our hypothesis is that the majority of the proximal femur is in compression and that the so-called ‘principal tensile system’ functions as an arch, transferring compressive stresses to the diaphysis.

Methods: To begin to test this, we have developed a 2D finite element (FE) model of the femur. The distal end was constrained and a force of half body weight, representing two-legged stance and negligible muscle forces, was applied to a representation of the acetabulum. The material properties used were 17 GPa for cortical bone, and 100–400 MPa for cancellous bone, with a higher modulus assigned to areas of greater apparent density. The model was meshed, using eight-node quadrilateral elements, and solved using ANSYS 8.0 software (ANSYS, Inc., USA). Recognising that the joint capsule is a substantial structure, ligamentous forces were included by spring-like link elements. Contact elements were used between the femoral head and acetabulum.

Results: In the absence of the capsular ligaments, stresses in the proximal femur were similar to those predicted by the crane model, i.e. corresponding to the traditional description of tensile and compressive trabeculae. The inclusion of ligamentous forces resulted in compressive stresses being generated over most of the proximal femur. When the denser trabecular systems were given a higher modulus the stresses become focused along the arch of the horizontal trabeculae.

Discussion: This study shows that inclusion of ligamentous forces results in compressive stresses being generated in the proximal femur and transmitted through the arch-like structure of trabeculae. It is notable that the capsular ligaments are thick and strong and are aligned with the femoral neck. Also, though ignored in this study, some of the major muscle groups have a significant component lying in the same direction. These result in a considerable force pressing the femoral head into the acetabulum and compressive stresses in most of the head and neck. This makes best use of the mechanical properties of bone, which functions better in compression than tension (Cowin, 2001), and avoids tensile forces in the diaphysis.