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Three-dimensional anatomic finite element modelling of hemi-arthroplasty of human hip joint.

Linear elastic finite element (FE) study was performed to investigate the contact mechanics and stress distribution of hemi-arthroplasty hip resurfacing using a metallic component. Three dimensional anatomic, three and two dimensional axisymmetric FE models were analyzed and compared in this study. The contact mechanics results show a good agreement between three FE models with approximately 0.5% difference between three-dimensional, anatomic and axisymmetric models and approximately 7% difference between three-dimensional, anatomic and two-dimensional, axisymmetric models. Significant differences were found in the maximum predicted von Mises stresses between anatomic and axisymmetric, finite element models. Stress shielding in the bone tissue was found to occur with the hip hemi-resurfacing prosthesis considered in this study. However, the stress shielding was shown to be less than those reported in literature for the MOM hip resurfacings and conventional total hip replacements.

Introduction

Conservative procedures for the treatment of osteonecrosis of the hip have long been advocated because of the typically young age of most patients [1-3] and the poor long-term results of total hip arthroplasty [4,5]. Management of Ficat stage III and IV osteonecrosis of the hip remains difficult, with the average patient aged in the mid 30s [6]. The initial procedure often represents the first step in a life-long treatment plan. Because of the disappointing long-term results of total hip arthroplasty in this young group of patients [7-9], joint and bone preserving procedures such as free vascularized fibular graft [10,11], redirectional osteotomies [12], trap door grafting [13], and hemi-resurfacing hip arthroplasty [14,15] have been used. Hemi-resurfacing arthroplasty has had good to excellent results in Ficat stage III and early IV with an over 80% survivorship at 5 years and 65% at 10 years and 45% at 15 years [14-16]. One must distinguish hemi-resurfacing from full-surface arthroplasty, which had high mid-term failure rates because of large amounts of polyethylene wear debris [17]. In the former, almost no wear debris is produced because the hemi-resurfacing component directly articulates with the acetabular cartilage. Unlike cup arthroplasty, hemi-resurfacing relies on a precision fit of the component to the remaining acetabular cartilage, which is not reamed, and the component is fixed with cement to the reamed femoral head. Hemi-resurfacing preserves proximal femoral bone stock, and conversion does not adversely affect the outcome of THR.

The finite element method has been increasingly adopted in the past few years to study the mechanical behaviour of biological structures. Comparisons between the results obtained from FEA and those obtained from experimental testing reveal a close correlation; hence, this modeling approach has been proven to be viable. If FE models are to be used for pre-clinical testing purposes, they should be used on a comparative basis. Although the bone is a complex biological tissue, the use of FEA is attractive because at the macro-level it exhibits elastic linear behaviour for loads in the normal range of regular daily activities [18]. The proximal femur consists of cortical (compact dense and hard tissue) and trabecular (cellular spongy tissue) regions [19]. The literature reports experimentally derived homogenized mechanical properties of both regions as well as isotropic Young's modulus E and other elastic constants (under the transversely isotropic/orthotropic assumption) of both regions as a function of the bone apparent density [18, 20-25]. Previous FE studies of hip resurfacing have used simplified material parameters, geometry and loading conditions, and do not give evidence of validation [26-29]. FE studies of hip mechanics have modeled the bone as two distinct materials; defining one set of material properties for the cortical bone and one set for the cancellous bone [26,27,29].

The determination of the mechanical stresses that physiological activities induce in human bones is of great importance in both research and clinical practice. Unfortunately, the mechanical stress in bones cannot be measured in living subjects without the use of an invasive surgical procedure [30], which, in general, is not ethically permissible. The only way to estimate bone stresses non-invasively in vivo is ''subject-specific'' finite element modelling. This procedure allows the creation of a numerical model of the bone segment from computed tomography (CT) images of that segment [31]. Computed tomography (CT) represents the method of choice for the generation of the finite element models of bone segments. Taddei et al. (2006) found a closer correlation between experimentally predicted and FE model calculated bone stresses when distributed material parameters were assigned to the elements on the basis of computed tomography (CT) data for bone ash density [32]. Polgar et al. (2003) recommended the use of a physiological load case that simulates the activity of all the major muscles acting on the femur during normal walking [33]. However, the accuracy of the results obtained through FEM depends on the accuracy in the simulation of the finite element model and the optimized mesh generation. Once the finite element mesh has been generated, the analyst should define the material properties relative to each element. If a generic or average bone is modelled, then the mechanical properties of the different bone tissues is usually derived from average values reported in published experimental studies [34-36]. Hence, this type of stress analysis could contribute to the complete understanding of the hip biomechanics before and after different sorts of operation. Also, the result of these investigations should be helpful in estimating the operating methods, commonly used in the treatment of the hip diseases.

Most of studies about hemi-arthroplasty of hip have focused on clinical aspects [37-39], and hemi-arthroplasty has not been studied extensively, particularly from an engineering point of view. The aim of this study was to investigate the contact mechanics and stress distribution of hemi-arthroplasty hip joints by using three dimensional, anatomic FE analysis. This study of stress distribution pattern in pelvic structure, in particular the acetabulum region and contact pressure distribution on acetabular cartilage, would be relevant for a better diagnosis of the low back pain, pelvic pain, and acetabular pain. Hence, this type of stress and contact analysis could contribute to the complete understanding of the hip biomechanics. Also, the result of these investigations should be helpful in estimating the operating methods, commonly used in the treatment of the hip diseases.

Materials and Methods

A three-dimensional anatomic model of hip joint was created from CT scans of a left hip joint. A femoral resurfacing prosthesis was implanted (45[degrees] of abduction and 10[degrees] anteversion) in the original three-dimensional model of femur in IDEAS (Version 11) and the acetabular contact surface was modified based on the assumption that the contact surface between acetabulum and femoral component is spherical and the articulation is concentric [40,41]. The anatomic FE model of hemi-arthroplasty resurfacing of hip joint then meshed in I-DEAS and solved in ABAQUS (Version 6.5).

In hemi-resurfacing arthroplasty of hip joint, the femoral component is usually taken the same size, one size down or two sizes down as the natural femoral head, depending on the fit through trial-and-error during surgery. Therefore, the nominal radial clearance between the femoral component and acetabular cartilage was taken as 0.5 mm (1 size down) in current study. All the interfaces (implant/bone, implant/cement and cement/bone) were assumed to be perfectly bonded. The nominal resultant load was chosen to be 3200 N (approximately four times body weight) representing peak contact hip force during the stance phase of the gait cycle [42-44]. Also muscle and subtrochanteric forces were applied to model and pelvis bone was constrained in all directions as shown in Fig.1.

[FIGURE 1 OMITTED]

Previous studies have used uniform cortical bone thicknesses in the range 1-2 mm [45-48]. Therefore, the finite element model consists of a cancellous region surrounded by a uniform cortical bone layer 1.5 mm thick. The femoral component was fixed to the femur by using non-uniform PMMA cement with thickness of 1.5 mm [46,48]. A stem was used to provide implant alignment and to bridge head-neck junction [49]. All the materials considered in current study were assumed as linear elastic and isotropic. Dalstra et al, [46] concluded that the use of a homogeneous model (constant cortical thickness and constant elastic modulus for trabecular bone) was appropriate for comparative studies. The articular cartilage was considered with nominal thickness of 2 mm [50] and the corresponding material properties in terms of elastic modulus and Poisson's ratio are given in Table 1 [48,51,52]. The finite deformation was included to take account of any large deformation that occurred within the model.

The meshed region of the acetabulum represents an area of potential contact. This surface is congruent with the actual contact region. The contact area was used to decide mesh density in the contact surface. The numbers of contact element were varied from 1000 to 8000 to investigate the effect of mesh density on the predicted contact pressure on articular cartilage of acetabulum. However, there was no obvious effect of the total mesh elements number on results. Therefore, approximately 4000 mesh units were used to represent the possible contact area because it has not large computational time and still represents a smooth surface.

Three-dimensional and two-dimensional axisymmetric finite element models of hemi-arthroplasty resurfacing of hip joint were also created to compare the predicted contact mechanics of the anatomic model as shown in Fig.2. Only the head-neck region of the femur was modelled in axisymmetric models because it was assumed that the region away from the proximal femur was not affected by the presence of an implant [27,53,54]. Because of large computational time of three-dimensional models, two-dimensional axisymmetric model was also created as shown in Fig.2a. Only half a cross-sectional area was required for the axisymmetric, finite element model, due to symmetry and all the nodes along the axis of the symmetry were constrained in the horizontal direction.

After the analysis of anatomic finite element model, the resultant contact force was read from the output file and it was predicted as 554 N in X-direction 717 N in Y-direction and 233 N in Z-direction; hence, only approximate 1/3 of applied load was transferred to pelvis bone due to the muscle and subtrochanteric forces. Therefore, these loading conditions were applied to 3D axisymmetric model and resultant of these forces (approximately 935 N) was applied to 2D axisymmetric model to compare the anatomic and axisymmetric models. Contact elements were used to simulate the contact between the articulating surfaces of both femoral component and articular cartilage. The contact at the bearing surfaces was assumed as frictionless to represent a well-lubricated condition.

[FIGURE 2 OMITTED]

The 3D anatomic finite element model consisted of 3-node shell (S3), 4-node linear tetrahedron (C3D4), 8-node 'brick' (C3D8) and 6-node 'wedge' (C3D6) elements that were used to mesh the bone, articular cartilage and prosthesis component. The 3D axisymmetric, finite element model consisted of 8-node 'brick' (C3D8) and 6-node 'wedge' (C3D6) elements that were used to mesh the bone, articular cartilage and prosthesis component, and 4-node bilinear axisymmetric (CAX4) elements were used to mesh the axisymmetric model. A total of 59338 elements and 66830 nodes were used for the 3D finite element bone model, and 1388 elements and 1974 nodes were used for the axisymmetric model. For the 2D axisymmetric, finite element model, load was applied through the pole of the prosthesis as shown in Figure 2(A).

Results and Discussion

Contact mechanics

Figure 3 shows a comparison of the predicted contact pressure distribution between three-dimensional, anatomic and three-dimensional axisymmetric finite element models for hemi-arthroplasty hip joint. Also the predicted contact pressure distribution from the centre of the contact to edge of acetabulum was compared for three-dimensional, anatomic and two and three dimensional axisymmetric finite element models as shown in Figure 4. The maximum contact pressure was predicted as 2.29 MPa in the three-dimensional, anatomic finite element model. Good overall agreement of the peak predicted contact pressure can be seen between the three models, with approximately 0.5% difference between three-dimensional, anatomic and axisymmetric models and approximately 7% difference between three-dimensional, anatomic and two-dimensional, axisymmetric models. This discrepancy between two and three dimensional finite element models can be mainly attributed to the one dimensional loading condition of two-dimensional model. There were also a good agreement between three models and the contact areas were predicted as 958 [mm.sup.2], 1023 [mm.sup.2] and, 991 [mm.sup.2] for three-dimensional, anatomic, axisymmetric and two-dimensional, axisymmetric finite element models, respectively.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

McGibbon et al has measured the highest peak contact pressures as 4.5-6.5 MPa on acetabular cartilage in their experimental study for an instrumented hemi-arthroplasty [55]. They also noted a significant decrease in the maximum contact pressure magnitudes (approximately 1 MPa / year) in the 32 months after implantation of the instrumented hemi-arthroplasty [55,56]. They concluded that this decrease in hip pressures over time may be linked; that is, neuro-muscular mechanisms may play a role in stress protection of the hip [57]. Therefore, this difference between the current and experimental results may be concerned that normal muscle forces were included in current study.

Stress distribution

In Figure 5, the predicted von Mises distribution on medial and lateral sides of cortical and cancellous regions of femur bone was shown for the hemi-resurfacing arthroplasty of hip joint. The maximum von Mises stress was predicted as 39.24 MPa and located at upper trochanter region. This may be caused by the muscle and subtrochanteric forces attached to this area. In cancellous bone of femur, the peak von Mises stress was also located at upper trochanter region and predicted as 3.35 MPa. Taddei at al was found the maximum von Mises stress in femur as 35.9 MPa for their subject-specific finite element model.

[FIGURE 5 OMITTED]

Medial and lateral views of the von Mises stresses observed in the cortical and cancellous regions of pelvis for the hemi-resurfacing arthroplasty of hip joint was shown in Figure 6. Region of stress concentration was observed at the superior rim of the acetabulum for cortical bone and predicted as 17.68 MPa (Figure 6a). In a number of studies in literature which investigated the stress distribution in pelvis bone, maximum von Mises stresses were between 30-50 MPa [45,58]. This difference in current study may due to use of metallic femoral component leads to stress shielding. However, the stress shielding according to hemi-arthroplasty of hip joint was found to be less than that reported for some metal-on-metal (MOM) hip resurfacing [27,29,59] and conventional total hip replacements (THRs) [51,60]. For the cancellous bone of pelvis, the maximum von Mises stress was predicted as 0.80 MPa and it is interesting to note that stress concentrations were found superior to the acetabulum in the cortical bone, but are found central to the acetabulum in the cancellous bone, in agreement with the results of Dalstra and Huiskes [61]. Majumder et al were also found that the maximum stresses in trabacular bone were between 0.3-1.7 MPa in their study [62]. The stresses found in the cortical bone were about 20 times higher than in the underlying trabecular bone. Hence the pelvic bone acts as a "sandwich construction" [63].

[FIGURE 6 OMITTED]

The stresses observed in the cortical bone of both femur and pelvis were below the reported ultimate strength for cortical bone under compression (approximately 200 MPa) [64] and reportedly below the fatigue strength for cortical bone, quoted as 40-80 MPa @ [10.sup.7] cycles [65] but there are long-term concerns regarding the combined action of cyclic joint forces and the stress shielding effect in the femur.

There are significant differences in the maximum predicted von Mises stresses between anatomic and axisymmetric, finite element models as shown in Table 2. However, it must be noted that the only head-neck region of femur was considered in axisymmetric, finite element models. In anatomic FE model, the peak von Mises stresses in head-neck region were predicted as 6.84 MPa at the bottom of the neck for cortical bone and 1.56 MPa at the end of stem/ cancellous bone interface. Ysibash et al were also found that the maximum von Mises stresses at the bottom of the neck were between 9-10 MPa for the applied load of 1500 N.

Conclusion

The contact mechanics and stress distribution of a hemi-resurfacing arthroplasty hip joint has been analyzed in this study by using three dimensional anatomic, finite element methods. Two and three dimensional axisymmetric finite element models were also developed to compare with the anatomic model. All components of hemi-resurfacing arthroplasty of hip joint were considered as isotropic, homogeneous and linear elastic materials in these FE models. The following are the conclusions:

* There was good agreement between contact mechanics results achieved from anatomic and axisymmetric FE models with approximately 0.5% difference between three-dimensional, anatomic and axisymmetric models and approximately 7% difference between three-dimensional, anatomic and two-dimensional, axisymmetric models. Therefore, it can be concluded that the axisymmetric, FE models can be used for contact mechanics studies because they require less computational time.

* The predicted maximum von Mises stresses were observed in both cortical bone of femur and pelvis. Significant differences were found in the maximum predicted von Mises stresses between anatomic and axisymmetric, finite element models. Therefore, it can be concluded that anatomic FE models give more accurate results for investigation of stress distribution on overall hip joint.

* Stress shielding in the bone tissue was found to occur with the hip hemi-resurfacing prosthesis considered in this study. However, the stress shielding was shown to be less than those reported in literature for the MOM hip resurfacings and conventional total hip replacements.

Acknowledgements

This work was partly supported by The Scientific & Technological Research Council of Turkey (TUBITAK).

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Ahmet C. Cilingira (a) *, Vahdet Ucar (a), Recep Kazan (a)

(a) School of Mechanical Engineering, Esentepe Campus, Sakarya University, 54187, Sakarya, Turkey * cilingir@sakarya.edu.tr (Ahmet C.Cilingir)
Table 1. Mechanical properties of the hemi-arthroplasty
hip-resurfacing materials

 Elastic Modulus,
Material E (MPa) Poisson's ratio (u)

Cortical bone [51] 17000 0.3
Cancellous bone [51] 800 0.2
Articular cartilage [51] 10.35 0.45
Femoral Component (Ti6Al4V) 110000 0.33
Subchondral bone [48] 2000 0.3
PMMA Cement [52] 2270 0.23

Table 2. Predicted maximum von Mises stresses in the components for
cartilage finite element models (BW=3200N and muscle and
subtrochantric forces, c=0. 5 mm)

 Maximum von Mises stresses (MPa)

Component Cortical bone Cancellous bone
 Articular
Model Femur Pelvis Femur Pelvis cartilage

3D Anatomic 39,24 17,68 3,35 2,21 0,58
3D Axisymmetric 29,64 7,75 2,32 2,06 0,57
2D Axisymmetric 6,47 6,87 1,19 1,42 0,51

 Maximum von Mises stresses (MPa)

Component
 PMMA Subchon. Fem.
Model Cement bone Comp.

3D Anatomic 1,24 4,22 17,43
3D Axisymmetric 2,91 2,93 16,53
2D Axisymmetric 0,99 1,97 7,22
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Author:Cilingir, Ahmet C.; Ucar, Vahdet; Kazan, Recep
Publication:Trends in Biomaterials and Artificial Organs
Geographic Code:1USA
Date:Jul 1, 2007
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