Keywords: hemiarthroplasty, hip joint replacement, pelvis, finite element model, numerical modelling, migration.

Hip hemiarthroplasty, or arthroplasty, is a surgical procedure in which the diseased parts of the hip joint are removed and replaced with new, artificial parts. These artificial parts are called the prosthesis. The goals of hip hemiarthroplasty surgery are to improve mobility by relieving pain and to improve the function of the hip joint. The hip is essentially a ball and socket joint, linking the "ball" at the head of the femur with the cup-shaped "socket" in the pelvic bone. If the surgery is a "hemiarthroplasty", the only bone replaced with a prosthetic device is the head of the femur. The most common reason that people have hip hemiarthroplasty surgery is the wearing down of the hip joint that results from osteoarthritis. Other conditions, such as rheumatoid arthritis, avascular necrosis, injury, and bone tumours also may lead to the breakdown of the hip joint and the need for hip replacement surgery. The greatest problem of the hemiarthroplasty is the migration of the replacement head which is observable after couple of months in all cases of the after-surgery of patients [1]. There are two dominant directions of the replacement head migration: median migration into the pelvis minor or migration in acetabular lambrum direction.

The finite element (FE) method was used for stress analysis in the pelvic bone with the head of the hip joint replacement. Three-dimensional geometrical model of the pelvic bone were generated from a sequence of 240 computer tomography slices using a generalized marching cubes algorithm (MCA) and segmentation procedures [2]. Since the MCA produces a very large number of triangles describing the surface a decimating algorithm [3] as follows. The whole high-resolution finite element model is composed of the geometrical models of the pelvis and the head of the replacement [4]. Modelling and all simulations are carried out using the ANSYS FE package [5]. Elements representing cancellous bone are created using quadratic tetrahedral elements SOLID187.

The FE model of pelvic bone was developed to assess the influence of selected parameters on the implant migration. The material of the FE model consists of the cancellous bone of the pelvis and steel of the replacement. Material properties of the cancellous bone were taken from the literature and as well from experiments carried out at the Institute of Theoretical and Applied Mechanics. Material with lower value of Young's modulus was chosen for the FE model to get the most unfavourable situation. There are two important input parameters for stress analysis: the CE (centre-edge) angle representing the shape of acetabulum and the direction of the femoral replacement loading. Boundary conditions were represented by the fixity of all surfaces within the area close to the acetabulum. The loading resultants intersects the centre of the replacement head. The computational model was solved in four loading steps with loading direction -45^o and -10^o from the pelvis and 0^o (vertical loading) and 10^o into the pelvis.

The total displacements and values of the first and the third principal stresses were used as reference magnitudes. Results showed the importance of a well-developed acetabulum reducing extreme values of cancellous bone stresses. The way the artificial femoral implant fits influences the direction of the loading force. When the prosthesis is fitted higher in comparison with the intact head the muscles on the lateral side is prestressed and the resultant force is deflected from the vertical direction laterally. On the other hand when the replacement head is fitted lower the result is the opposite. The replacement head is fitted correctly, when its centre is 1-3 mm under the greater trochanter. Also the coxa vara and coxa valga positions have the significant influence on the loading of the hip joint.

The stresses and displacement fields show that the primary migration of the replacement head followed the direction of loading. Decreasing of the CE angle and increasing of the loading direction angle concentrate the stress to the acetabular lambrum area. This very unfavourable situation probably initiates the migration; therefore the natal predispositions of the acetabular CE angle and the higher fitted prostheses have a significant influence on the migration.

1

J. Bartonícek, "After surgery clinical report", Orthopaedic Clinics, Third Faculty of Medicine, Charles University in Prague, 2005.

2

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

3

W.J. Schroeder, J. Zarge and W.E. Lorensen, "Decimation of Triangle Meshes", Computer Graphics, 26, 65-70, 1992. doi:10.1145/142920.134010

4

O. Jiroušek, "Development of finite element models from CT scans for the use in biomechanics", Reviews of results and the set of selected publications achieved on IBM RS 6000/SP, Czech Technical University in Prague, 2001.

5

J. Vycichl and O. Jiroušek, "Contact analysis of acetabular cup and pelvic bone", in Proceedings of 13rd ANSYS User´s Meeting, J. Stárek (Editor), SVS FEM Brno, Prerov, 2005.

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