Determination of Bone and Joint Loads

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Determination of Bone and Joint Loads from Bone Density Distributions

Kenneth J Fischer, MS; Marc E Levenston, MS; Chris R Jacobs, PhD; Dennis R Carter, PhD; Dianna D Cody, PhD (Henry Ford Hospital, Detroit, MI)

Significance - Over 100,000 total hip replacements are performed each year in the United States. The proportion of revision surgeries is increasing. As people live longer, implants such as total joint replacements will need improved endurance. Better implant designs could significantly reduce the need for many revision surgeries.

Problem - Adverse changes in bone density and structure following total joint replacement lead to loosening and eventual failure of the implants. Computer simulations of bone remodeling have been developed to guide the development of implant designs to reduce adverse changes in the bone. Since the loading conditions greatly affect the simulations, accurate estimates of the loads are essential.

Background - Bone, like muscle, becomes more dense and strong when subjected to increased loads and becomes more porous and weak when loads are reduced. These adaptations occur through a process called bone remodeling.

Our research group developed a theory and approach to bone remodeling simulations that has been shown to reproduce natural bone density distributions. Simulations have reproduced the natural bone densities of the metacarpal, the proximal femur, and the acetabulum. The theory states that the local bone tissue will change its density, according to the loads, to achieve a specific level of mechanical stimulus - the attractor stress stimulus. In a mature bone, nearly all bone tissue should be at the same mechanical stress stimulus, with little net change in density.

Hypothesis - Because the structure of a bone is influenced by the loading conditions, its geometry and internal density distribution must contain information about its loading conditions. By adjusting the loads on a bone model to achieve a constant (attractor) stress stimulus, we should be able to determine appropriate and accurate loads for the bone.

Approach - The first step is to develop a finite element mesh with the external geometry of the bone (Figure 1). Then the density distribution (Figure 2) is mapped into the model. Numerous plausible loads are selected, based on our knowledge of anatomy and joint kinematics, and the complete normalized stress distribution is calculated for each. Final selected loads will be a combination of these normalized loads.

Figure 1. Finite element mesh.

Figure 2. Quantitative CT data.

Within a nonlinear optimization procedure, the local stress stimulus is calculated and compare to the attractor stress stimulus. Each load magnitude is iteratively updated until the global stress stimulus error is minimized. Important loads have a large magnitude, whereas incorrect or unimportant loads have negligible magnitude. These estimated loads are evaluated by using them in a bone remodeling simulation. Accurate loads should reproduce the actual bone density distribution in the remodeling simulation.

Progress - This load determination method has undergone several stages of testing. Initial tests used an idealized bone-end model and showed that, under the most ideal conditions, the procedure is very accurate. The load determination method was also tested with an existing model on the more complex geometry of the proximal femur, which has multiple loading sites.

Figure 3. Estimated loads and the density distribution generated with them.

The load determination method was recently applied to a set of quantitative radiographic (CT) data for the proximal femur. A finite element mesh (Figure 1) matching the geometry of the coronal CT data (Figure 2) was developed. Eight dominant load cases were determined. In Figure 3, each arrow on the head of the femur represents a parabolic pressure distribution. Each arrow on the greater trochanter represents a constant traction. The density distribution of Figure 3, produced by the estimated loads, has similar general structures as that of Figures 2, but the details are different. Thus, more work is needed to develop the procedure. Still, the results are promising, and we continue to improve the load determination method.

Republished from the 1994 Rehabilitation R&D Center Progress Report. For current information about this project, contact Dennis R Carter.