FEM analysis aimed at characterizing the mechanical behavior of the stem of a hip prosthesis inserted inside a femur.
The following article is an extract from a project carried out for the course of Advanced Techniques for the Design of Prosthetic Devices. Held for Medical Engineering at the University of Rome Tor Vergata.
Authors: Mastrofini Alessandro & Muscedere Erica
Total Hip Arthtoplasty
Total hip replacement surgery consists in the complete replacement of the coxofemoral joint. The operation, often referred to as THA (Total Hip Arthroplasty) consists in the replacement of the damaged parts of the joint (head of the femur and acetabular cavity). So the implants are typically modular, ie they are assembled at the time of surgery to best adapt to the anatomy of the individual patient. The heart of the prosthesis is the joint subjected to movement, typically it is composed of cobalt-chromium alloys, ceramic or couplings with plastic materials. The shaft, the head and the acetabular cavity are often made of stainless steel or titanium alloy [1]. In this case, a titanium alloy stem (Ti-6Al-4V) and a Nylon 12 capsule are considered.
Mechanical properties
To best perform the FEM analysis it is necessary to consider the mechanical properties of the bone. Although microscopically it is a highly porous and non-homogeneous structure, it is possible to consider homogenized macroscopic properties. A fragile elastic behavior of the isotropic type is considered, therefore Young’s modulus, Poisson’s ratio and ultimate stress are considered by the literature.
Given the great variability of biological tissues it is necessary to make some considerations.
As reported in fig. 1a human bone is affected by a great variability of mechanical properties. This variability is certainly present from individual to individual but also within the same bone. The cortical bone is typically more compact and rigid, while the trabecular bone is less dense and typically less rigid. In particular bone areas subjected to very high mechanical stress, the trabecular bone increases in density and tends to arrange itself along the load lines (Fig. 1b) and this gives the bone significantly higher strength and stiffness.
The femoral neck is cut and the stem is inserted inside. This causes a densification of the trabecular bone both due to bone remodeling and due to the addition of bone cement during the operating procedure. Overall, the upper area of the femur, around the prosthesis, will have a behavior more similar to that of compact bone [10].
| Material | E [GPa] | ν | σy [MPa] | ρ [Kg/m3] |
|---|---|---|---|---|
| Cortical bone | 20.0 | 0.38 | 168 | 1908 |
| Trabecular bone | 14.0 | 0.38 | 70 | 1178 |
| Shell – Nylon 12 [11] | 4.90 | 0.393 | 50 | 1310 |
| Stem – Ti-6Al-4V | 104.8 | 0.31 | 827 | 4428 |
Tab 1: Mechanical properties of the used materials
CAD design
Before implementing finite element simulation it is necessary to have a CAD model of the objects of interest. In this case we started from the model of the prosthesis and from a scan of a femur as a mesh.
For the prosthesis it was sufficient to separate the capsule from the stem by correctly associating the material. For the bone, modeling is slightly more complex. The first step was to switch from a mesh to a solid body in Solidworks through Geomagic.
Subsequently it was decided to insert a scaled copy inside, representing the trabecular part. Although this worked at the CAD level, it led to many problems at the level of FEM analysis. This is partly due to the great precision of Geomagic which returns a solid body full of details that, for the type of analysis in question, could also be overlooked. But these details on the external surface lead to a slight densification of the mesh in some points, if the same volume is used for the trabecular bone, this complication would also be added for the generation of contacts between the two.
Approximate geometries
An approximate solution, even if fully satisfactory, was to reconstruct the trabecular part by simplifying the previously introduced scaled copy. In addition to the computational complexity (less than 1/10 of the time is required), this approximation also makes it possible to better cope with the lack of data on the morphology of the canal inside the bone and reflects the natural bone distribution due to continuous remodeling.
Then a loft geometry was created, suitably centered on the femoral axis, by means of circumferences such as to approximate the scaled copy of the femur. All in compliance with the volume ratios between trabecular and cortical bone [12].
The upper part of the femur was filled with a predominance of cortical bone following the information in the literature for which the trabecular bone in that area has mechanical properties more similar to cortical bone. The materials have been defined by adding their properties in table 1.
For the CAD model of the bone there are two configurations: default, containing what is described, and Forzamento, described in the specific shrink fit test.
Analisi FEM
In order to analyze the behavior of the prosthesis-femur system subjected to a vertical force of 1000 N and a horizontal force of 100 N, applied to the head of the prosthesis, two areas of the sphere were separated using the Split Line function, referring to the part of prosthesis theoretically placed on the hip.
The system was assembled together by placing the prosthesis with its axis parallel to the vertical axis.
The various parts that make up the bone and the prostheses were considered to be united: in particular, a contact was made between components between the trabecular bone, the cortical bone and the stem of the prosthesis.
The femur was constrained with an interlock at the level of the cut on the shaft (inferior surface).
Therefore, the Von Mises criterion was used to analyze the resulting strains, considered in the literature to be one of the best for evaluating bone fractures [3]. The yield stresses were considered as a limit, however it is necessary to keep in mind that the trabecular bone will not respond with a fragile fracture but will undergo densification. Both types of bone respond to high levels of stress through remodeling which leads to increased mechanical properties.
For the simulation with vertical load, the load of 1000 N was placed parallel to the axis of the prosthesis.
The detailed results are shown in fig . 6 and fig. 7.
For the simulation with horizontal load, the load of 100 N was placed orthogonal to the axis of the prosthesis.
The detailed results are shown in fig . 8 and fig. 9.
Conclusions
In all simulations the materials are far from critical stress.
In the case of vertical load the safety factor remains higher than 1 for all materials . Only in some points of the trabecular bone does the safety factor drop beyond the critical threshold indicating that the yield stress has been exceeded (Fig. 6c).
This is not worrying for two reasons: the limit stress is however localized in limited areas and, from a clinical point of view, is an indication of a subsequent bone remodeling which will lead to an improvement in the mechanical properties of the bone and a better osseointegration of the prosthesis.
In conclusion, a flexion of the femur is observed with a maximum displacement of 1,849 mm at the level of the prosthesis head (fig. 7a). Even lower stress levels are observed for horizontal loading. The materials are all far from the yield point. From the simulations it is evident that the femur is mechanically stressed in a large part of the interface with the prosthesis and this is an indication of a possible good osseointegration.
Stress on the femur
The least stressed part is the area of the greater trochanter both in the case of vertical and horizontal loading. Therefore, based on the results obtained, this area may require further investigation to avoid the problems of bone resorption typical of hip prostheses.
On the basis of the applied loads, a greater response of the material to a vertical load is observed compared to a horizontal stress. Furthermore, this also makes evident the stress that falls on the neck of the prosthesis. Although it is far from the yield point, it still suffers from a higher stress than the other areas of the prosthesis. This stress occurs with a load condition corresponding to the normal working condition of the prosthesis (upright position) and could also be affected by the cyclical nature of walking.
Shrink fit
To create a shrink fit of 0.05 mm, modify the previously created cavity. By adding an offset surface towards the inside of the cavity and giving it a thickness it is possible to reduce the cavity while keeping the bone as a multibody part divided into trabecular and cortical (Fig. 5a).
Two configurations were created in the femur file. : default containing the standard cavity and forcing
containing the machining necessary to introduce the desired forcing.
In order to simulate forcing it is necessary to introduce the forcing constraint between the external surfaces of the prosthesis stem and the internal surface of the femoral cavity (fig. 5b ). No loads were added as only the stress state induced by the deformation following the forcing of the prosthesis inside the femur is analyzed. The results are shown in fig. 10 and fig. 11.
Clearly the femur-stem interface is heavily loaded. Trabecular bone is strongly affected by the induced stress but, as already mentioned, this may not be a clinically relevant problem (the bone itself will respond to stress by increasing its density and its resistance where it is loaded most). This is also reflected in the cortical bone which, however, is far from the yield point with the exception of some highly localized areas. The deformation is present at the bone-stem interface with predominance in the trabecular bone areas.
Numerical results
References
- [1] Massimiliano Merola e Saverio Affatato. “Materials for Hip Prostheses: A Review of Wear and Loading Considerations”. In: Materials 12.3 (5 feb. 2019), p. 495. issn: 1996-1944. doi: 10.3390/ma12030495.
- [2] E Isaza, L García e E Salazar. “Determination of Mechanic Resistance of Osseous Element through Finite Element Modeling”. In: (2013), p. 8.
- [3] Ramin Oftadeh et al. “Biomechanics and Mechanobiology of Trabecular Bone: A Review”. In: Journal of Biomechanical Engineering 137.1 (1 gen. 2015), p. 010802. issn: 0148-0731, 1528-8951. doi: 10.1115/1.4029176.
- [4] J. C Lotz. “Mechanical Properties of Trabecular Bone from the Proximal Femur”. In: (1990). doi: 10.1097/00004728-199001000-00020.
- [5] Charles H. Turner et al. “The Elastic Properties of Trabecular and Cortical Bone Tissues Are Similar: Results from Two Microscopic Measurement Techniques”. In: Journal of Biomechanics 32.4 (apr. 1999), pp. 437–441. issn: 00219290. doi: 10.1016/S0021-9290(98)00177-8.
- [6] Donald T. Reilly e Albert H. Burstein. “The Elastic and Ultimate Properties of Compact Bone Tissue”. In: Journal of Biomechanics 8.6 (gen. 1975), pp. 393–405.
- [7] Rod Lakes. “Elastic Anisotropy of Bone”. In: (). url: http: // silver. neep. wisc. edu/ ~lakes/BoneAniso.html.
- [8] John G. Skedros e Richard A. Brand. “Biographical Sketch: Georg Hermann von Meyer (1815-1892)”. In: Clinical Orthopaedics & Related Research 469.11
- [9] Guo Rong She et al. “Total Hip Arthroplasty for Femoral Neck Fracture with Pyoderma Gangrenosum Patient: A Case Report”. In: International Journal of Surgery Case Reports 30 (2017), pp. 134–137.
- [10] European Commission. Joint Research Centre. Institute for Health and Consumer Protection. Total Hip Arthroplasty: State of the Art, Challenges and Prospects. LU: Publications Office, 2012. url:
- [11] MatWeb material property data. Overview of Materials for Nylon 12.
- [12] Antti Alho, Arne Hoiseth e Torstein Husby. “Bone-Mass Distribution in the Femur A Cadaver Study on the Relations of Structure and Strength”. In: Acta Orthopaedica Scandinavica 60.1 (gen. 1989), pp. 101–104. issn: 0001-6470. doi: 10.3109/17453678909150104.
