Keywords: computer tomography scans, marching cubes algorithm, finite element model, loosening and migration of cementless acetabular cup, pelvis, UHMW-PE wear, contact stresses.

The loosening and migration of the femoral component or the cementless acetabular cup into the pelvic bone belong to the most serious therapeutic complications arising from several months to years after the operation. The reason for this phenomenon has been neither sufficiently explained nor the influence of the primary and secondary fixation has been assessed. Clinical practice considers the achievement of maximum primary fixation as optimum.

The aseptic loosening of the cup is possibly influenced by two mechanical factors: UHMW-PE wear and initial cancellous bone stresses. Wear is removal of material from surface that is caused by relative motion of articulating surfaces under applied load when the contact stresses exceed the strength of the material. For estimation of the wear volume FE models of the individual component were constructed and loaded by a load corresponding to the normal gait cycle. Another important factor influencing the migration is the cancellous bone stress field. Therefore the question whether the growing bone stresses around the implant body and threads do not result in subsequent reduction of secondary fixation, remains still open.

For the finite element analysis we built a three-dimensional model based on data obtained from Computer Tomography (CT) scans. For the construction of the pelvis geometry a standard procedure including a semi-automatic tissue segmentation was used. We used traditional intensity based segmentation relying on the fact, that pixels representing the same tissue are clustered around a mean characteristic value. The scans were taken in 1 mm slices in 512 512 pixel resolution. A treshold procedure combined with repetitive application of Gaussian filter was used combined with removal islands (removing regions of tissue smaller then specified value) semi-automatic removal of misclassified tissue etc. After the pelvic tissue is segmented a surface reconstruction using a generalized marching cubes algorithm (MCA) was used to identify the inner and outer surface describing the pelvic bone. Since the MCA [1] produces very large number of triangles describing the surface a decimating algorithm follows [2]. After the reduction of the triangles Delaunay 3-D triangulation that enables us to fill the volume with tetrahedral elements was applied.

The geometry of the acetabular cups was designed directly in ANSYS and imported to the database file containing the geometry of the pelvis generated from the CT images. The volume of the cementless acetabular cup was subtracted from the volume of the pelvis. Than new mesh of the pelvic bone was created to reflect the original that one created by the direct generation method. After the Boolean operation the total number of elements in the dense model was more than 110 000. Between the surfaces of the metal backing of the acetabular component and the opening in the pelvis contact elements were defined. The contact elements were defined as surface-to-surface with large sliding taken into account. The material properties assigned to the cancellous bone were calculated using the Hounsfield values of apparent density values of corresponding tissue obtained from CT scanning. The loading data were taken from the work of Bergmann et al. [3].

It was found that the contact stress is influenced not only by the cyclic loading, component thickness and the polyethylene strength but that the most important factor influencing the magnitude of the contact stress is the bearing conformity. For this reason we conducted several FE parametric studies taking this factor into account. We also tried different contact algorithms and come to a conclusion that for the correct estimation of the UHMW-PE wear it is necessary to use face-to-face contact elements with large sliding. The commonly used node-to-node contact elements are the least computationally expensive, but underestimate the total wear volume.

Acknowledgement

The research has been supported by the research fund MSM 212600025 of the Ministry of Education, Youth and Sports of the Czech Republic and by the research plan AV0Z 2071913 of the Academy of Sciences of the Czech Republic.

1

Lorensen, W.E., Cline, H.E., "Marching Cubes: A High Resolution 3D Surface Construction Algorithm", Computer Graphics, vol. 21, 163-169, 1987. doi:10.1145/37402.37422

2

Schroeder, W.J., Zarge, J., Lorensen, W.E., "Decimation of Triangle Meshes, Computer Graphics", vol. 26, no. 2, 65-70, 1992. doi:10.1145/142920.134010

3

Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A., Strauss, J., Duda, G.N., "Hip contact forces and gait patterns from routine activities", Journal of Biomechanics, vol. 34, 859-871, 2001. doi:10.1016/S0021-9290(01)00040-9

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