## An efficient approach for modeling hip joint contact

Bearbeitung: | M.Sc. Kristin Fietz, Prof. Dr.-Ing Undo Nackenhorst |

Förderung durch: | This research is supported by the German Research Foundation under Grant NA 330/6-1. |

**Motivation and Goal**

Although osteoarthritis is the major cause for artificial joint replacement in developed countries the reasons and early progress of this degenerative joint disease remain partly unknown. The most widely accepted theory is that too high cartilage stresses alter the nutrition processes and therefore lead to cartilage degeneration. The aim of this project is to compute cartilage pressures and related nutrient transport under physiological loading in order to contribute to a better understanding of synovial joint contact, especially in the hip joint.

Different daily activities have to be computed in order to cover the physiological range of motion and loading. From www.orthoload.com load data is available for situations like walking, stair climbing, etc. Large relative motions of femoral head and pelvis have to be handled in the model.

**Modeling approach for bone**

The cartilage stresses are strongly influenced by the joint geometry, therefore the bones of the hip joint are included in the model.

The reconstruction of the 3D geometries of the pelvic bone and of the femoral head from CT-data (available from the Visible Human Project) is sketched in figure 1 (left), the resulting finite element model is shown in figure 1 (right).

Bone is considered to be linear elastic in the project. The Young's modulus of each element corresponds to the bone density. The bone density distribution is estimated from the Hounsfield unit values from the CT-data which is mapped onto the finite element mesh. In figure 2 the resulting density distribution is shown for some model planes in comparison to corresponding CT-images.

Figure 1: Reconstruction of bone geometries from CT-data (left); Three dimensional finite element model of the hip joint (right)

Figure 2: Comparison of CT-data and projected bone density

**Modeling approach for cartilage**

For the cartilage modeling we cooperate with project partners from the Institute of Applied Mechanics of the University of Stuttgart. The cartilage layers will be modeled as a fluid saturated porous medium using Taylor-Hood-elements.

**Modeling approach for the synovial fluid in the synovial gap**

The cartilage layers are separated by a thin fluid film which provides low friction contact conditions. In the model a midsurface between the cartilage layers represents the fluid film geometry. This midsurface concept provides an efficient remeshing procedure in each joint position. The midsurface is generated by orthogonal projection which is illustrated in figure 3. In figure 4 the resulting midsurface element with variable thickness is shown. On the curved midsurface the Reynolds equation is solved.

Figure 3: Midsurface generation by orthogonal projection

Figure 4: Midsurface element with variable thickness

**Contact Algorithm**

The interaction between the porous cartilage layers and the synovial fluid between them is solved by a staggered strategy which is depicted in figure 5. Starting with an initial cartilage geometry the initial midsurface with the initial thickness distribution is constructed. In each iterative step the pressure distribution and corresponding velocities in the synovial gap are obtained from solving the Reynolds equation. From the pressure distribution contact forces acting on the cartilage layers are computed. With these contact forces as Neumann boundary conditions the solid problem is solved for the cartilage displacements which lead to an updated thickness distribution and a new fluid solution. This way the fluid and solid fields are solved in turn until equilibrium is reached.

Figure 5: Staggered Contact Algorithm

**Project Partners**

- Institute of Applied Mechanics, University of Stuttgart
- Labor für Biomechanik und Biomaterialien,

Orthopädische Klinik der Medizinischen Hochschule Hannover - Sektion für experimentelle Radiologie, Universitätsklinikum Tübingen