Compression or tension? The stress distribution in the proximal femur

Abstract

Background: Questions regarding the distribution of stress in the proximal human femur have never been adequately resolved. Traditionally, by considering the femur in isolation, it has been believed that the effect of body weight on the projecting neck and head places the superior aspect of the neck in tension. A minority view has proposed that this region is in compression because of muscular forces pulling the femur into the pelvis. Little has been done to study stress distributions in the proximal femur. We hypothesise that under physiological loading the majority of the proximal femur is in compression and that the internal trabecular structure functions as an arch, transferring compressive stresses to the femoral shaft.

Methods: To demonstrate the principle, we have developed a 2D finite element model of the femur in which body weight, a representation of the pelvis, and ligamentous forces were included. The regions of higher trabecular bone density in the proximal femur (the principal trabecular systems) were assigned a higher modulus than the surrounding trabecular bone. Two-legged and one-legged stances, the latter including an abductor force, were investigated.

Results: The inclusion of ligamentous forces in two-legged stance generated compressive stresses in the proximal femur. The increased modulus in areas of greater structural density focuses the stresses through the arch-like internal structure. Including an abductor muscle force in simulated one-legged stance also produced compression, but with a different distribution.

Conclusion: This 2D model shows, in principle, that including ligamentous and muscular forces has the effect of generating compressive stresses across most of the proximal femur. The arch-like trabecular structure transmits the compressive loads to the shaft. The greater strength of bone in compression than in tension is then used to advantage. These results support the hypothesis presented. If correct, a better understanding of the stress distribution in the proximal femur may lead to improvements in prosthetic devices and an appreciation of the effects of various surgical procedures affecting load transmission across the hip.

Figure 1

The human hip joint. Radiograph of the human proximal femur and acetabulum in which the two main systems of trabeculae (group 1 and 2) are indicated. These are traditionally known as the principle tensile and compressive trabeculae respectively, a questionable nomenclature.

Figure 2

Finite element model of the hip. Finite element model of the proximal femur and acetabulum. Spring elements join the two components and represent the capsular ligaments. The model is fixed at the top and loaded through the base of the femur. Also shown with an asterisk is the link-element used to apply the abductor force in the model representing one-legged stance. Red: modulus 17 GPa Blue: modulus 400 MPa Turquoise: modulus 100 MPa.

Figure 3

Two-legged stance. The distribution of principal stresses as the tension in the spring elements is increased. The length and direction of the arrows show the relative magnitude and direction of compression, in blue, and tension, in red. (a) Without spring elements, showing generation of tension in the group 1 trabeculae. Increasing the initial strain to (b) 2.5%, (c) 5% and (d) 10% shows how the stresses become compressive throughout the proximal femur and focussed into the arch of the group 1 trabeculae.

Figure 4

One-legged stance. The distribution of principal stresses in a model of one-legged stance with spring elements at a prestrain of 5%, a vertical force of body weight applied to the femur and an abductor force of three times body weight. The lengths and directions of the arrows show the relative magnitudes and directions of compression, in blue, and tension, in red.