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Abstract
Upon the arrival of the osteosynthesis, technological advancement has revolutionized the orthopedic surgery, producing increasingly efficient prostheses. Nevertheless, it turns out that over the years of lifetime these orthopedic implants presents complications in vivo. This requires in most cases a reoperation. To improve the total hip replacement lifetime it is imperative to investigate the effects of dynamic loading on the replaced joint. For this reason, we initially studied the mechanical behavior of their different components, according to the nature of hip’s movements, the exerted forces on the femoral head and particularly the muscular forces acting on hip-femur system. Then, we performed numerical simulations of a femur carrying a cemented hip prosthesis type (CMK3), the boundary conditions used in the simulations are identical to those applied in vivo
during the daily activities.
Key words: Total hip prostheses, Surgical cement, Biomechanics, Muscle forces, Dynamic loading, Finite
element analysis
1. Introduction
The durability of a total hip replacement depends on the mechanical behavior of each prosthesis component, especially the surgical cement. Until today the PMMA is the only material used to anchor the femoral implant in to the femoral bone during a cemented orthoplasty. In the cemented hip replacement, the cement is the most fragile material, which has two interfaces; one with the bone and the second with the prosthesis, this cement mantle is the weakest link in the load transfer system (implant – cement – bone).
However, despite the various disadvantages of PMMA, a recent study have shown that a lifetime of cemented hip orthoplasties in patients aged over 50 years is significantly high comparing to a non-cemented prostheses, at least 90% of those cemented prostheses reaches 15 years of lifetime in vivo (BALLARD T. W, et al, 1992).
This study comes within this context and with an objective to analyze the mechanical behavior of surgical cement
under dynamic loading (real body loading). This behavior depends on interactions of the load transfer system (femoral implant - cement - cancellous bone - cortical bone) that are subject to very realistic loading conditions, based on measurement of contact force in vivo and the different EMG signatures of hip joint muscles, for an extended activities to include the major movements of the lower limb in the patient‟s daily life activity.
2. The objective
The hip joint is the strongest joint in the human body and the most mobile of the lower limb, it finds its mobility due to the most powerful muscles of the human body, and it is held in place by a multitude of strong ligaments. This
anatomical specificity has secondary effects on the hip joint, like the irreversible injury, which requires sometimes a replacement of the damaged joint by an artificial articulation, called a total hip replacement or an orthoplasty, this artificial articulation must be strong enough to resist the most important forces in the human body.
The mechanical behavior of total hip prosthesis is, until now, under investigations. This study comes within this context as objective of a three-dimensional analysis of the mechanical behavior of total hip prostheses during the patient‟s daily activities by the finite elements method. This behavior depends on the interaction of four components of the prosthesis exposed to a very realistic loading conditions and boundary conditions, based on measurements of the in vivo hip joint contact forces and different muscular efforts for an extended series of activities including the major movement of the lower limb in daily life of patients.
3. Materials and methods
To determine the mechanical behavior of total hip prostheses under dynamic loading, it is important to know the variation of muscular forces acting on the hip-femur system, and the resultant forces applied on the femoral head, during one cycle of each activity.
As it‟s indicated in figure 5, the cement is supposed to interact with the femoral implant and the spongious bone, however in certain cases the surgeons confirms that they have reached the cortical bone zone when they were preparing the femur for the implantation, which is a new condition to be verified in the bio-competence, because of the cortical bone is much harder and stronger than the cancellous bone as we can realize in the material proprieties description below.
In this work, we will simulate the most unfavorable cases of the total hip orthoplasty, including the case of a direct contact : cement - cortical bone, and even walking with a 22 Kg load which will be simulated as an equally distributed weigh on both hands.
3.1 Muscular forces
The hip muscles are numerous, however, some have a low action on the hip joint articulation, or even negligible
(BESNIER J. P., 1995). In this work, we have determined the efforts of the strongest muscles (such as the gluteus maximus, the gluteus medius, the small gluteus and the iliacus) (Fig. 1.a) (BERGMANN G, et al, 2000).
Boundary conditions
The instrumented THP implant with a telemetric data transmission allows the determination of contact forces generated at the hip, which is essential for the definition of total hip prostheses design (BERGMANN G, et al, 1998) (Fig.2.a). The processing of data that can be transmitted by a modern instrumented total hip prostheses, allows the determination of :
- the nature of exerted forces on the femoral implant (traction, compression, torsion or shear forces ),
- the magnitudes of resulting forces and generated moments around the three axes (BERGMANN G. et al 1993),
- the tridimensional femoral implant deformation,
- the resulting temperature during practiced activities (BERGMANN G, et al, 2000).
After having determined the muscular forces and the applied forces on the femoral implant of each activity, we projected all acquired forces (magnitudes and directions) on the adopted coordinate system (Fig. 3.a): the exerted force on the femoral head is simulated by the decomposition of resulting forces in the three main axes, the muscular forces are also decomposed according to the main axes but their application surface is on the bone and it is similar to their real application sites in vivo, while the knee is considered as a joint with two degrees of freedom, one displacement along the 'Y ' axis and one rotation on the 'X ' axis (Fig 3.b).
Then we proceed to simulate the mechanical behavior of the total hip prosthesis subjected to accurate body forces (dynamic loading). Six "6" essential activities exercised by the patient were selected for this study: normal walking, fast walking, slow walking, walking with an equally distributed load on both hands, ascending and descending stairs.
The analyzed structure
The numerical model of the analyzed total hip prosthesis is illustrated on figure 4. This model is composed of an implant (shaft and implant‟s head) (Fig. 4.a), of a surgical cement (Fig. 4.b) and the femoral bone (cortical bone and spongious bone) (Fig. 4. c & d). The femoral implant and the femoral bone are attached together with the surgical cement as shown in Figure 5. The interactions between these components (implant – cement – bone) determines the lifetime of the cemented hip prostheses (BERRY D. J., et al, 1998).
Results and discussions
In this title we will expose and investigate the behavior of femoral bone and cemented hip prosthesis under accurate in vivo loading and boundary conditions and we will study the intensity and distribution of normal, tangential and Von Mises stresses induced in the three components of the total hip prosthesis (implant – cement – bone) where the 'Z ' axis is the vertical one and it‟s the 3rd axis, the second axis is 'Y ' and it‟s the frontal one and the 'X ' axis is the lateral axis
(normal stress ��zz and the tangential or shear stress ?xy are represented respectively by ��33 and τ12).
4.1 bone’s behavior
The bone‟s response to in vivo dynamic loading is illustrated below; Figure 6 shows that these stresses are distributed inhomogeneously all over the bone. The most significant stresses are oriented according to the 'Z ' axis direction. In fact, the bone is subjected to both tensile and compression stress on the 'Z ' axis direction and this is due to the anatomical specifics of the femoral bone, which induce flexion stresses all over this bone. But the 'Fz' (forces applied according to 'Z ' direction) acting on the femoral head, will generate a compression stress that will be added to
the compression stress induced by the bone flexion and that will increase both : the resulted compression stress ��33 and
the compressed section (inner side of the bone) at the expense of tensile stress and tension section (outer side of the
bone), Fig 6.d shows that the resulted compression stress is 42.73Mpa while the tensile stress magnitude is 39.65Mpa, in consequence the neutral plane is displaced from the inner side to the outer side, which is located in the central plane of the femoral bone in case of pure bending stresses. These compression and tension stresses are distributed on both sides along the bone and divide this element into two parts denoted herein as 'inner side' and 'outer side'. Consequently, the bone is subject to compound stresses:
- A compression stress due to the weight and muscular efforts;
- A bending stress due to the force application surface that is not on the anatomical axis of the femur, and this leads to the formation of a lever arm for the efforts and induces a flexion torque and a bending stresses.
- The normal stresses σ11 and σ22 have comparable intensity magnitudes and are much lower than the third stress level.
2 Implant’s behavior
The simulation results exposed in Figure 8 shows that the most significant normal stresses are σ11 and σ22 and they are located on the neck of the implant. The stress cartography shows that the outer side of this neck is in tension, while the compression is located in the inner side and that σ11 stress about five times more intense than σ22, which is due to the direction of applied forces on the implant makes. On this zone of the implant σ11 tensile stress is almost equal to the compression stress σ33 and it is distributed practically in the same way on either side of the implant neck. The σ33 stresses are concentrated on the lateral sides of the implant (Fig.8.d), according to their nature (a compression in the inner side and tension on the outer side) this stress distribution reveals that this element is under bending stresses, in
fact this flexion loading is transmitted to the cement first then to the femoral bone. The tension and compression stresses are almost equally distributed on either side but the compressive stresses are slightly more intense than tensile stresses.
cement’s behavior
Intended to ensure three essential functions: adhesion, antibiotic transport and load transfer; the surgical cement is the weakest link of the load transfer chain (implant – cement – bone), but also his mechanical behavior determines the reliability, the performance and the durability of cemented total hip prostheses.
The maximum Von Mises stresses are located on the proximal frontal side and the distal lateral zone (fig.10.a), this is mainly due to the absence of the cancellous bone in these areas, which makes a direct contact between cement and cortical bone; while the rest of the surgical cement is under low stress intensity.
The cartography of normal stresses σ11, σ22 and σ33 is illustrated on figures 10.b, c and d respectively. The normal stresses σ11 and σ22 are intensively localized on the proximal and the distal zone and they are generated by a tension forces on the proximal zone and a compression forces on the distal zone; away from these areas, the intensity of normal stresses σ11 and σ22 is negligible.
This ' cement – cortical ' bone direct contact in the two extremities of the surgical cement was created in order to know the mechanical responses of the weakest link of the loads transfer chain if the surgeon reaches the cortical bone zone when preparing the femoral implant housing.
In addition to the proximal frontal region, the distribution of σ33 stress generated in the cement is totally different
from the two other normal stresses (Fig. 10). Indeed, σ33 is the result of the bending force which is transmitted from the femoral implant, and just like the other components it induces in the outer side of the cement tension stresses and in its inner side compressive stresses, and unlike σ11 and σ22, the normal stress σ33 affects softly the distal zone of the cement.
In figures 10.e, f and g are shown the levels and distribution of shear stresses induced in the three planes 'XY ', 'XZ '
and 'YZ ' of the surgical cement, denoted respectively τ12, τ13 and τ23, they are distributed almost in the same way on cement, they are concentrated on the distal zone.
Beyond the distal zone, the shear stresses induced in the surgical cement are relatively low, however, the direct interaction between cortical bone and cement has affected the stresses level in the contact regions but the highest amplitude of shear stresses is much lower than the ultimate shear stresses.
In the outer part of the surgical cement we noticed that the distal zone is under the highest σ33 compressive stresses comparatively to σ11 and σ22 (Fig. 11.c).
The amplitude of shear stresses relating to the planes 'XY ', 'XZ ' and 'YZ ' in the inner side are much lower than those resulting on the outer side (Fig. 11.b & d), while the maximal amplitude is recorded on the extremities of the inner side and only the distal zone of the outer side (Fig.11.b & d). It appears that the cement is exposed to a low intensity share stresses compared to the other components.
Comparative study
We have previously shown that the nature of the activities exerted by the patient determines the level of stresses which are induced all over the total hip prosthesis components. The comparative analysis of the results obtained during the walk activities (slow, normal and fast walking simulation) shows that the Von Mises stresses induced in bone and surgical cement are related to the speed of this activity. Indeed, more this activity is exerted at a slower rate: more the stresses induced in total hip prosthesis components are higher (Fig.12.a).
In comparison between these six activities (slow walking, normal walking, rising and descending stairs, fast walking, walking carrying a load on both hands), the activity that generates the most important tresses in the bone and surgical cement is the last one, indeed walking with an equally distributed load on both hands increase significantly the amplitude of the applied forces on the femoral head (Fig.12.b).
This is explained by the fact that the load is a foreign body that will affect directly the prosthesis through the charge transfer chain (hands to the arms to the spine to the pelvis then to the femur); so in addition to the weight of the load, the hip-joint muscles will exert supplementary force to create an equilibrium moment.
During the practice of the studied activities, each component was differently loaded: the strongest stresses induced
in the surgical cement were located in its extremities (proximal and distal zone), whereas the major stresses generated in the bone were located along its median zone, while the femoral implant most important stresses appeared in the proximal zone, precisely in the implant‟s neck.
. Conclusion
The level of exerted forces on the femoral head depend on the nature of the performed activity, while the generated stresses depends much more on the forces directions than on their levels.
The femoral implant is the most loaded component of the total hip prosthesis and the maximal stress is recorded in the implant‟s neck.
The femoral bone is subjected to bending stress all along its length, and it‟s according to the vertical direction 'Z '
that the most intense σ33 stresses appears, specifically in the median zone. The compressed side is slightly bigger than the one in tension, and inner side is more loaded than that outer side.
The surgical cement is the component the less loaded and during all the simulated activities he verified the bio-competence conditions and requirements even in the presence of non-standard conditions (22 Kg load lifting and direct contact with the cortical bone); the highest stress amplitudes appeared on the proximal and the distal zones, so those regions are the most vulnerable ones, and they are the most exposed zones to the cracks initiations.