Biomed. Eng.-Biomed. Tech. 2015; aop
Hasan Sofuoglu and Mehmet Emin Cetin*
An investigation on mechanical failure of hip joint using finite element method Abstract: The aim of this work was to study how the stress distributions of the hip joint’s components were changed if the activity was switched from walking to stair climbing for three different prostheses types subjected to either concentrated or distributed load. In the scope of the study, three different cemented prostheses, namely, Charnley, Muller, and Hipokrat were used for cemented total hip arthroplasty (THA) reconstruction. The finite element modeling of the hip joint with prosthesis was developed for both hip contact and muscle forces during walking and stair climbing activities. The finite element analyses were then pursued for both concentrated and distributed loading conditions applied statically on these models. Maximum von Mises stresses and strains occurred on the cortical and trabecular layers of bones; prosthesis and cement mantle were determined in order to investigate the mechanical failure of cemented THA reconstruction subjected to the different femoral loading and the activity conditions. This study showed that prosthesis, loading, and activity types had a significant effect on the stresses of components of the hip joint utilized for predicting mechanical failure of the cemented THA reconstruction. Keywords: biomechanics; finite element method; hip joint; prosthesis. DOI 10.1515/bmt-2014-0173 Received November 25, 2014; accepted March 30, 2015
Introduction The hip is the body’s second largest weight-bearing joint after the knee. It is a true ball-and-socket joint at the juncture of the thigh and pelvis surrounded by powerful and well-balanced muscles and ligaments, enabling a wide *Corresponding author: Mehmet Emin Cetin, Research Assistant, Department of Mechanical Engineering, Karadeniz Technical University, Trabzon, Turkey, Phone: +(90-462) 377 4332, Fax: +(90-462) 377 3336, E-mail: [email protected] Hasan Sofuoglu: Department of Mechanical Engineering, Karadeniz Technical University, Trabzon, Turkey
range of motion in several physical planes while also exhibiting remarkable stability. The hip is normally very sturdy because of the fit between the femoral head and acetabulum as well as strong ligaments and muscles at the joints. All of the various components of the hip mechanism assist in the mobility of the joint. A healthy hip can support the body weight and allow it to move without pain. The magnitude and the direction of the resultant hip joint force are different in different body positions during gait, and hence, the contact stress distribution in the hip joint articular surface also changes. The estimation of the hip joint stresses during daily activities is, therefore, helpful in understanding the mechanics of the normal (healthy) hip joint and useful for both preoperative planning and postoperative rehabilitation as well. Any changes in the hip joint from diseases or injuries will significantly affect the body’s gait and create abnormal stress on the hip joint. Damage to any single component can negatively affect the range of motion and the ability to bear weight on the joint. Osteoarthritis (OA) is a kind of joint disease, and it hurts the cartilage of the hip joint. The patient is affected by movement limitations and feels severe pain because of OA. In this situation, total hip arthroplasty (THA) becomes an obligation for the patient. As an increase in hip joint stresses may accelerate degenerative processes in the hip joint [3, 9], it is, therefore, important to study the distribution of the hip joint stresses after certain operative interventions such as THA as well as to design rehabilitation procedures. Although in previous studies, a hip joint contact force was only applied to the prosthetic head, additional muscle forces such as the abductors, the iliotibial tract, vastus lateralis, and the tensor fascia latae were included in the model as the recent studies have shown that the calculated hip contact force was strongly affected by the activity of the muscles that span the hip joint. Hurwitz et al. [6] found an increase in hip contact force of 0.2 times body weight with a 10% increase in antagonistic muscle force. Later on, studies have demonstrated how biomechanical factors and the configuration of muscle models influence hip loading [17] and, consequently, bone remodeling [1]. It has been also shown that the subject-specific anatomy of the hip determines the moment-generating capacity of the surrounding muscles and consequently affects hip joint loading [8].
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2 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint Analysis of joint and muscle loading is fundamental for advancing the science of orthopedic biomechanics. A wide range of research has been done on the subject, and the obtained knowledge has been applied to design the improved joint replacements, the so-called prosthesis. The preclinical tests of hip prosthesis used for THA are crucial in determining optimal process parameters and ideal procedures in providing information for the condition of a disease. Computer simulation techniques are common and ideal procedure to provide such information about a particular condition of a disease. Finite element method (FEM) is one of the widely used method to obtain such output data. The stresses that occur on prosthesis, bones, and cement mantle can be obtained by utilizing FEM, and hence, clinically inferior prosthesis can be determined [16]. The effect of stair climbing on damage accumulation on the cement of a femoral prosthesis, compared with walking, was investigated by Stolk et al. [18], while McNamara et al. [10] used a synthetic femur in both finite element and experimental analyses for investigating the effect of bone-prosthesis on the proximal load transfer. Boyle and Kim [2] analyzed two different prostheses by using three dimensional microlevel bone remodeling algorithm for pre- and post-total hip arthroplasty period. The FEM helped also to design new prosthesis for the hip joint components and to investigate the biomechanical characteristics of the component in resurfacing hip arthroplasty as shown by Watanabe et al. [20]. Joshi et al. [7] designed a new femoral prosthesis with a different proximal fixation to reduce stress shielding by performing finite element analysis (FEA), while Ramos et al. [14] designed a new cemented femoral stem in order to improve load transfer and to reduce cement stress and fatigue failure. Pawlikowski et al. [12] used FEM to design three different prostheses and decide which one was suitable for a particular patient. Senalp et al. [15] performed static, dynamic, and fatigue finite element analyses for stem shapes on which each of them has varying curvatures and compared the results with those of the Charnley prosthesis. The FEM has been successfully used as a convenient simulation method to understand the mechanics of hip joint during daily activities as mentioned in the above studies. However, many researchers used different prostheses by applying different loading types such as concentrated force or distributed load as well as having either stair climbing or walking as daily activity in their analyses. Hence, some variations can be observed in the FEA of the cemented THA reconstruction from one study to another. The purpose of this study was, therefore, to identify the effects of the prosthesis, activity, and loading types on the stresses of the hip joint’s components predicting mechanical failure of the cemented THA reconstruction. In order to address this
purpose, the finite element modeling and analyses were performed for the hip joint with prosthesis (cemented THA reconstruction) and without prosthesis (healthy hip joint) during walking and stair climbing activities for both concentrated and distributed load. A series of finite element modeling and FEA were successfully pursued for three different prostheses. The maximum von Mises stresses and strains, which occurred on cortical and trabecular layers of bone, prosthesis, and cement mantle used to assemble prosthesis into the bone’s intramedullary canal, were determined at the end of the FEA. The output data were then evaluated for identifying the effects of these process parameters on the performances of THA reconstruction’s components, thereby, affecting mechanical failure of the THA reconstruction. Finally, they were compared to the ones produced on the components of a healthy hip joint.
Hip joint models A three-dimensional (3D) third-generation composite femur model was downloaded from “Biomedtown” website (http://www.biomedtown.org) to use in this study. This femur model includes cortical and trabecular layers of bone. Using Solidworks (Dassault Systemes Solidworks Corp., USA) software, 3D realistic models of THA reconstructions, including cortical and trabecular layers of femur bone, prosthesis, and cement mantle, were created. Charnley (Depuy, Johnson & Johnson, Leeds, UK), Muller (JRI Ltd, London, UK), and Hipokrat (Hipokrat A.Ş. Turkey) cemented-type prosthesis were used in the 3D realistic models of THA reconstructions. The 3D model of Charnley prosthesis was also downloaded from “Biomedtown” website (http://www. biomedtown.org) while Muller and Hipokrat prostheses were scanned by using Breuckmann Optotophe (Aicon 3D Systems GmbH, Germany) 3D scanner. Rapidform XOR (3D Systems, USA) and Solidworks (Dassault Systemes Solidworks Corp., USA) softwares were then utilized to obtain 3D models of these two prostheses. All three prostheses types are shown in Figure 1, while their cement mantles are illustrated in Figure 2. It should be noted here that the cement mantle thickness around the prosthesis was designed optimally according to surgical procedure and modeled by using Solidworks software. The cross-section views of THA reconstruction models are also illustrated in Figure 3.
Material properties Mechanical properties of CoCr alloy were used for Charnley, Muller, and Hipokrat prostheses in this study. The
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 3
Figure 1: Types of prostheses used in this study (A) Charnley, (B) Muller, and (C) Hipokrat.
Figure 3: Cross-section views of THA reconstruction models with (A) Charnley, (B) Muller, and (C) Hipokrat prostheses applied.
elastic properties of the materials were taken from Stolk et al. [18], while the trabecular bone, cement, and prostheses were assumed to be isotropic, although cortical bone was taken as an anisotropic material as listed in Table 1.
Finite element models
Figure 2: Cement mantles used in this study along with (A) Charnley, (B) Muller, and (C) Hipokrat prostheses.
The created 3D models were then imported to Ansys Workbench commercial software. It is necessary to choose solid body and contact element types for 3D static FE analysis. Contact surfaces of models were recognized automatically by Ansys Workbench and these surfaces accepted as bonded in this study. The 3D eight-node surface-tosurface contact element was used for the contact surfaces. For a solid body, the 3D 10-node tetrahedral element type shown in Figure 4 (http://www.ansys.com), was selected because it was suitable for complicated geometries such
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4 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint Table 1: Mechanical properties of THA’s components. Components of THA
Material type
Elasticity modulus (GPa)
Poisson’s ratio
Prosthesis Cement mantle Trabecular bone Cortical bone
CoCr alloy PMMA Polyurethane foam Glass fiber-reinforced epoxy
210 2.28 0.4 Ex = Ey = 7.0, Ez = 11.5 Gyz = Gzx = 3.5, Gxy = 2.6
0.3 0.3 0.3 υxy = υyz = υxz = 0.4
Table 2: Number of elements of THA models used in FEA.
L
P Y,v
O I
X,u
Components of THA
R Q K N
M
Z,w
J
Figure 4: The 3D 10-node tetrahedral structural solid element.
as the femur. This element type was used for the finite element mesh of all solid components of the cemented THA reconstructions. Figure 5 shows an example for finite element modeling of the hip joint with prosthesis. The element numbers of each model are tabulated in Table 2.
Loading and boundary conditions In this study, the weight of the human body was assumed to be 750 N. Moreover, both muscle and contact forces that act on the hip joint during walking and stair climbing activities, which are most common in daily life, were chosen for loading. Concentrated force and distributed load were applied on the models as two different loading types. The
Mesh 4/15/2012 4:40 PM Edge/Face connectivity Free Single Double Triple Multiple
0.00
100.00 (mm) 50.00
Figure 5: Finite element modeling of hip joint assembly with Charnley prosthesis.
Number of elements Concentrated load
Prosthesis’s type Charnley Cortical bone Trabecular bone Prosthesis Cement Total Muller Cortical bone Trabecular bone Prosthesis Cement Total Hipokrat Cortical bone Trabecular bone Prosthesis Cement Total No prostheses Cortical bone Trabecular bone Total
34,363 28,532 5121 4996 73,012 22,456 18,113 9936 6222 56,727 28,469 26,001 5168 3274 62,912 21,083 17,209 38,292
Distributed load
45,041 36,860 6637 6292 94,830 22,122 17,652 10,030 6,178 55,982 39,277 36,896 11,432 7106 94,711 49,456 40,200 89,656
loads were applied according to one leg stance position of walking, and the femur was constrained rigidly at the distal end of the femoral diaphysis not to move in both horizontal and vertical directions [11, 15] (Figure 6). Concentrated force configuration taken from Heller et al. [4] was shown, and its magnitudes during walking and stair climbing were tabulated in Tables 3 and 4, respectively. Moreover, distributed force configuration was adapted from Viceconti et al. [19] and was illustrated in Figure 7.
Results and discussion The maximum von Mises stresses of prostheses are given in Table 5. The magnitudes of maximum von Mises
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 5
A B C D E F
Hip contact force: 1783.1 N Abductors: 781.76 N Tensor Fasciae Latae, Proximal: 142.43 N Tensor Fasciae Latae, Distal: 142.65 N Vastus Lateralis: 710.46 N Ridigly Constrained Condyle
0.00
100.00 (mm) 50.00
Figure 6: Boundary conditions for walking under concentrated force.
stresses of prostheses for stair climbing activity were higher than those of walking for both loading types. It can be deduced from these results that stair climbing activity increased the load applied to prostheses creating more stress on them and making stair climbing more dangerous than walking on prostheses. The contour plots of prostheses are given in Figures 8–11. As clearly seen from the figures that the maximum von Mises stress location
of Charnley prosthesis loaded with concentrated and distributed forces was under the neck of the prosthesis for both walking and stair climbing activities. However, the location of the maximum von Mises stresses of Muller prosthesis loaded with concentrated forces was on the stem and close to the tip of the stem for both activities, while the collar’s contact point with bone was found to be that of Muller prosthesis loaded with distributed force for both activities. Similar results were found for the location of the maximum von Mises stresses of the Hipokrat prosthesis. It was obtained at the center of the head where the concentrated hip contact force applied for both walking and stair climbing activities. However, when the distributed load was applied, the location of the maximum von Mises stresses of the Hipokrat prosthesis was shifted to the tip point of the stem for both activities. As a result, the loading type changed the location of the maximum von Mises stress of the Muller and Hipokrat prostheses, while the location of the maximum von Mises stress of the Charnley prosthesis remained in the same position for both the loading and activity types. On the other hand, the maximum von Mises strains of prostheses are tabulated in Table 6. The highest value was 0.0049, and it emerged on the Muller prosthesis when stair climbing forces were applied under the effect of concentrated force.
Table 3: Magnitudes of muscle and contact forces and their acting points on femur during walking. Hip contact force Abductors Tensor fasciae latae, proximal part Tensor fasciae latae, distal part Vastus lateralis
Magnitudes of forces X (N)
Y (N)
Z (N)
-405 435 54 -3.75 -6.75
246 -32.25 -87 5.25 -138.75
1719 -648.75 -99 142.5 696.75
Acts on point
P0 P1 P1 P1 P2
Table 4: Magnitudes of muscles and contact forces and their acting points on femur during stair climbing. Hip contact force Abductors İliotibial tract, proximal part İliotibial tract, distal part Tensor fasciae latae, proximal part Tensor fasciae latae, distal part Vastus lateralis Vastus medialis
Magnitudes of forces X (N)
Y (N)
Z (N)
-444.75 525.75 78.75 -3.75 23.25 -1.5 -16.5 -66
-454.5 216 22.5 -6 36.75 -2.25 168 297
-1772.25 636.75 96 -126 21.75 -48.75 -1013.25 -2003.25
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Acts on point
P0 P1 P1 P1 P1 P1 P2 P3
6 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint
Figure 7: Muscle surfaces on femur for distributed loading [19].
Table 5: The maximum von Mises stresses on prostheses. Prosthesis type Charnley Muller Hipokrat
Loading type
Walking (MPa)
Concentrated force Stair climbing (MPa)
Walking (MPa)
Stair climbing (MPa)
404.81 665.75 335.73
431.01 1029 352.79
298.14 596.05 189.6
315.56 805.48 307.58
In the analysis, the maximum von Mises stresses of the cement mantles were also obtained and are given in Table 7. It can be seen from the table that when the prostheses were loaded by a concentrated force, the lowest stress for walking and the highest stress for stair climbing occurred on the model with the Muller prosthesis applied. However, for distributed load applied models, the highest
Distributed load
value again occurred on the Muller prosthesis for stair climbing, while the lowest stress for walking was obtained on the Hipokrat prosthesis. In addition, the maximum von Mises strains of cement mantles are given in Table 8. It was clear from the table that the highest strains emerged on the Muller prosthesis applied models for both loading and activity types. It can, therefore, be concluded that if
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 7
A
404.81 Max 359.94 315.06 270.18 225.31 180.43 135.55 90.674 45.797
B
665.75 Max 591.88 518.01 444.15 370.28 296.41 222.54 148.68 74.807
Max
0.93978 Min
0.91948 Min
Max 0.00
0.00
100.00 (mm) 50.00
100.00 (mm) 50.00
C
335.73 Max 298.53 261.33 224.13 186.93 149.72 112.52 75.323 38.122
Max
0.92157 Min
0.00
100.00 (mm) 50.00
Figure 8: Stress distributions of (A) Charnley, (B) Muller, and (C) Hipokrat prostheses for walking under concentrated force.
the Muller prosthesis is used for THA reconstruction in the mid to long term, it can cause aseptic loosening and may require revision surgery. This was consistent with the findings of Herberts et al. [5] in which it was mentioned that the Charnley and Muller prostheses had 8% and 13% revision rates after surgery applied in 10 years, respectively. The maximum von Mises stresses of the cortical bone are given in Table 9, while Table 10 tabulated the maximum von Mises strains of the cortical bone. Among the three prostheses, the lowest values emerged on the
Charnley prosthesis-applied model for both loading and activity types. Moreover, the maximum von Mises stresses that occurred on the cortical bones of the Charnley and Hipokrat prostheses were smaller than those of the healthy hip joint, whereas the maximum von Mises stress of Muller prosthesis was higher than that of healthy hip joint. In addition, the same trend was obtained for the maximum von Mises strains of cortical bones, i.e., the smaller values with Charnley and Hipokrat prostheses and the higher values with Muller prosthesis were determined.
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8 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 431.01 Max
A
383.17 335.32 287.48 239.63 191.79 143.94 96.094 48.248
Max
0.40191 Min
1029 Max
B
914.81 800.57 686.33 572.1 457.86 343.62 229.39 115.15
0.91267 Min
Max 0.00
100.00 (mm)
0.00
50.00
100.00 (mm) 50.00
C
352.79 Max 313.66 274.54 235.42 196.3 157.17
Max
118.05 78.928 39.805
0.68283 Min
0.00
100.00 (mm) 50.00
Figure 9: Stress distribution of (A) Charnley, (B) Muller, and (C) Hipokrat prostheses for stair climbing under concentrated force.
The maximum von Mises stresses of the cortical bone of the present study agreed well with those of the study of Ramos and Simoes [13] in which third-generation composite and simplified femur models were employed for comparison purposes. In their study, they used both tetrahedral and hexahedral finite element meshes in the simplified and the realistic femur geometries by taking Stolk et al.’s [16] hip joint and muscle force magnitudes. While performing FES, they used tetrahedral (10-node
tetrahedron) and evaluated the von Mises stress of the cortical bones at the specific point to compare the result with that of the simplified model, which was 24.3 MPa. In our study, on the other hand, we also used the same femur model, the same element type and found a very close magnitude of von Mises stress of cortical bone of 24.76 MPa at the same point (Figure 12). They also compared the proximal femur’s experimental strains with the finite element results of the tetrahedral meshed third-generation
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 9
A
298.14 Max 265.1 232.06 199.02 165.98 132.94 99.897 66.856 33.816
Max
0.77475 Min
B
596.05 Max 529.92 463.78 397.65 331.52 265.39 199.26 133.12 66.993
Max
0.8614 Min
0.00
100.00 (mm)
0.00
100.00 (mm)
50.00
50.00
C
189.6 Max 168.62 147.64 126.66 105.69 84.708 63.73 42.752 21.774
0.7958 Min
Max 0.00
100.00 (mm) 50.00
Figure 10: Stress distribution of (A) Charnley, (B) Muller, and (C) Hipokrat prostheses for walking under distributed force.
composite femur model and mentioned that those results correlated with each other, which also showed a similar trend to the present study. Table 11 listed the maximum von Mises stresses of trabecular bone. The highest value was 17.771 MPa, and it occurred on the Muller prosthesis-applied model for stair climbing activity and concentrated force. On the other
hand, the maximum von Mises strains of trabecular bone are also given in Table 12. When the three prostheses were compared, it was easily seen that the Hipokrat prosthesis caused the lowest strain value on the trabecular bone. It was observed that when compared, the stresses obtained for the cortical and trabecular bones of the hip joint without prosthesis, the maximum von Mises stress
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10 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint
A
315.56 Max 280.64 245.73 210.81 175.9 140.98 106.07 71.151 36.236
B
805.48 Max 716.08 626.68 537.28 447.89 358.49 269.09 179.69 90.293
Max
1.3214 Min
Max
0.89515 Min
0.00
100.00 (mm)
0.00
100.00 (mm)
50.00
50.00
C
307.58 Max 273.53 239.47 205.42 171.36 137.31 103.25 69.194 35.139
1.0833 Min
Max 0.00
100.00 (mm) 50.00
Figure 11: Stress distribution of (A) Charnley, (B) Muller, and (C) Hipokrat prostheses for stair climbing under concentrated force.
occurred on the cortical layer of bone. This was attributed to the fact that in healthy human hip joint, the hip takes care of the loadings caused by the body weight and muscle forces and distributes them to the rest of the hip joint’s components as it acts as a support. However, the stress distributions of the hip joint’s components were
changed after THA reconstruction was applied so that the prosthesis took the most portion of the loading creating the maximum von Mises stress on itself and decreased the stresses of the rest of the components. This is the wellknown phenomena of stress-shielding behavior [7] and is schematically illustrated in Figure 13.
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 11 Table 6: The maximum von Mises strains on prostheses. Prosthesis type
Charnley Muller Hipokrat
Loading type
Walking (mm/mm)
Concentrated force Stair climbing (mm/mm)
Distributed load Walking (mm/mm)
Stair climbing (mm/mm)
0.001928 0.003170 0.001599
0.002052 0.00490 0.00168
0.001420 0.0028383 0.000903
0.001503 0.0038356 0.001465
Table 7: The maximum von Mises stresses on cement mantles. Prosthesis type Charnley Muller Hipokrat
Loading type
Walking (MPa)
Concentrated force Stair climbing (MPa)
Distributed load Walking (MPa)
Stair climbing (MPa)
59.529 50.518 59.747
65.597 79.421 72.037
58.828 56.675 52.254
76.902 82.058 70.026
Table 8: The maximum von Mises strains on cement mantles. Prosthesis type
Charnley Muller Hipokrat
Loading type
Walking (mm/mm)
Concentrated force Stair climbing (mm/mm)
Distributed load Walking (mm/mm)
Stair climbing (mm/mm)
0.026109 0.022157 0.025295
0.028771 0.034834 0.031595
0.025802 0.024857 0.022918
0.033729 0.035991 0.030713
Table 9: The maximum von Mises stresses on cortical bone. Prosthesis type
Charnley Muller Hipokrat No prosthesis
Loading type
Walking (MPa)
Concentrated force Stair climbing (MPa)
Distributed load Walking (MPa)
Stair climbing (MPa)
41.821 96.871 63.275 93.376
87.981 117.5 116.52 99.478
34.547 108.57 37.661 43.676
57.773 141.95 61.011 67.392
Table 10: The maximum von Mises strains on cortical bone. Prosthesis type
Charnley Muller Hipokrat No prosthesis
Loading type
Walking (mm/mm)
Concentrated force Stair climbing (mm/mm)
Distributed load Walking (mm/mm)
Stair climbing (mm/mm)
0.004492 0.01125 0.006572 0.010435
0.009043 0.01369 0.012022 0.01111
0.003423 0.012676 0.003864 0.004481
0.005889 0.016365 0.006230 0.006870
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12 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint
A: Static Structural
Equivalent Stress 2 Type: Equivalent (von-Mises) Stress Unit: MPa Time: 1 18.02.2015 14:41
93.376 Max 83.001 72.626 62.251 51.876 41.501 31.126 20.75 10.375
24.767
0.00030624 Min
0.00
100.00 (mm)
Figure 12: Illustration of the location of the maximum von Mises stress of cortical bone.
Table 11: The maximum von Mises stresses on trabecular bone. Prosthesis type
Charnley Muller Hipokrat No prosthesis
Loading type
Walking (MPa)
Concentrated force Stair climbing (MPa)
Distributed load Walking (MPa)
Stair climbing (MPa)
14.166 13.599 10.157 7.3998
13.628 17.771 12.618 7.8458
13.257 11.442 9.8547 4.030
17.404 16.288 13.456 4.4317
Table 12: The maximum von Mises strains on trabecular bone. Prosthesis type
Charnley Muller Hipokrat No prosthesis
Loading type
Walking (mm/mm)
Concentrated force Stair climbing (mm/mm)
Walking (mm/mm)
Stair climbing (mm/mm)
0.035415 0.33998 0.025393 0.01850
0.034071 0.044429 0.031545 0.019615
0.033142 0.028606 0.024637 0.010075
0.043511 0.04072 0.033640 0.011079
Conclusion Mechanical behavior of the human hip joint with and without prosthesis was investigated by using the FEM.
Distributed load
After pursuing the FEA, the values of the peak stress and strain were determined and then analyzed to explore the effects of each process parameters for predicting the mechanical failure of the cemented THA reconstruction.
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 13
References
Figure 13: Schematic illustration of load transformation (A) before and (B) after THA reconstruction [7].
Under the lights of the above-obtained results, the following conclusions can be drawn. 1. It was clear from the results of the von Mises stress and strain of the cement mantle that stair climbing was more detrimental than walking on predicting mechanical failure of the cement mantle of THA reconstruction. 2. Among the three prostheses types used in the THA reconstruction of this study, the Muller prosthesis caused aseptic loosening and was riskier than the Charnley and Hipokrat prostheses in terms of revision surgery. 3. According to the cortical bone’s maximum von Mises stresses for distributed loading and von Mises strains for both loading conditions, the Muller prosthesis was more destructive in both walking and stair climbing when compared to the Charnley and Hipokrat prostheses. 4. For the loading and activity conditions investigated in this study, the von Mises strains of the trabecular bone on the Hipokrat prosthesis-applied model were closer to those of the healthy trabecular bone. 5. During walking and stair climbing, the Hipokrat prosthesis among the three prostheses investigated in this study had the lowest average stress on the cement mantle for distributed loading. It may then be concluded that the Hipokrat prosthesis can be suggested to patients who have more daily activities.
[1] Bitsakos C, Kerner J, Fisher I, Amis AA. The effect of muscle loading on the simulation of bone remodelling in the proximal femur. J Biol 2005; 38: 133–139. [2] Boyle C, Kim IY. Comparison of different hip prosthesis shapes considering micro-level bone remodeling and stress-shielding criteria using three-dimensional design space topology optimization. J Biol 2011; 44: 1722–1728. [3] Hadley NA, Brown TD, Weinstein SL. The effects of contact pressure elevations and aseptic necrosis on the long-term clinical outcome of congenital hip dislocation. J Orthop Res 1990; 8: 504–513. [4] Heller MO, Bergmann G, Kassi JP, Claes L, Haas NP, Duda GN. Determination of muscle loading at the hip joint for use in pre-clinical testing. J Biol 2005; 38: 1155–1163. [5] Herberts P, Malchau H. Long-term registration has improved the quality of hip replacement: a review of the Swedish THR Register comparing 160000 cases. Acta Orth Scan 2000; 71: 111–121. [6] Hurwitz DE, Foucher KC, Andriacchi TP. A new parametric approach for modeling hip forces during gait. J Biol 2003; 36: 113–119. [7] Joshi MG, Advani SG, Miller F, Santare MH. Analysis of a femoral hip prosthesis designed to reduce stress shielding. J Biol 2000; 33: 1655–1662. [8] Lenaerts G, De Groote F, Demeulenaere B, et al. Subjectspecific hip geometry affects predicted hip joint contact forces during gait. J Biol 2008; 41: 1243–1252. [9] Maxian TA, Brown TD, Weinstein SL. Chronic stress tolerance levels for human articular cartilage: Two nonuniform contact models applied to long term follow-up of CDH. J Biol 1995; 28: 159–166. [10] Mcnamara BP, Cristofolini L, Toni A, Taylor D. Relationship between bone-prosthesis bonding and load transfer in total rip reconstruction. J Biol 1997; 30: 621–630. [11] Okyar AF, Bayoglu R. The effect of loading in mechanical response predictions of bone lengthening. Med Eng Phys 2012; 34: 1362–1367. [12] Pawlikowski M, Skalski K, Haraburda M. Process of hip joint prosthesis design including bone remodeling phenomenon. Comput Struc 2003; 81: 887–893. [13] Ramos A, Simoes JA. Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur. Med Eng Phys 2006; 28: 916–924. [14] Ramos A, Completo A, Relvas C, Simoes JA. Design process of a novel cemented hip femoral stem concept. Mater Des 2012; 33: 313–321. [15] Senalp AZ, Kayabasi O, Kurtaran H. Static, dynamic and fatigue behavior of newly designed stem shapes for hip prosthesis using finite element analysis. Mater Des 2007; 28: 1577–1583. [16] Stolk J, Maher SA, Verdonschot N, Prendergast PJ, Huiskes R. Can finite element models detect clinically inferior cemented hip implants? Clin Orthop Rel Res 2003; 409: 138–150. [17] Stolk J, Verdonschot N, Huiskes R. Hip-joint and abductor- muscle forces adequately represent in vivo loading of a cemented total hip reconstruction. J Biol 2001; 34: 917–926.
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14 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint [18] Stolk J, Verdonschot N, Huiskes R. Stair climbing is more detrimental to the cement in hip replacement than walking. Clin Orthop Rel Res 2002; 405: 294–305. [19] Viceconti M, Ansaloni M, Baleani M, Toni A. The muscle standardized femur: a step forward in the replication of
umerical studies in biomechanics. Proc Inst Mech Eng H n 2003; 217: 105–110. [20] Watanabe Y, Shiba N, Matsuo S, Higuchi F, Tagawa Y, Inoue A. Biomechanical study of the resurfacing hip arthroplasty finite element analysis of the femoral component. J Arthroplasty 2000; 15: 1–7.
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Hasan Sofuoglu and Mehmet Emin Cetin*
An investigation on mechanical failure of hip joint using finite element method Abstract: The aim of this work was to study how the stress distributions of the hip joint’s components were changed if the activity was switched from walking to stair climbing for three different prostheses types subjected to either concentrated or distributed load. In the scope of the study, three different cemented prostheses, namely, Charnley, Muller, and Hipokrat were used for cemented total hip arthroplasty (THA) reconstruction. The finite element modeling of the hip joint with prosthesis was developed for both hip contact and muscle forces during walking and stair climbing activities. The finite element analyses were then pursued for both concentrated and distributed loading conditions applied statically on these models. Maximum von Mises stresses and strains occurred on the cortical and trabecular layers of bones; prosthesis and cement mantle were determined in order to investigate the mechanical failure of cemented THA reconstruction subjected to the different femoral loading and the activity conditions. This study showed that prosthesis, loading, and activity types had a significant effect on the stresses of components of the hip joint utilized for predicting mechanical failure of the cemented THA reconstruction. Keywords: biomechanics; finite element method; hip joint; prosthesis. DOI 10.1515/bmt-2014-0173 Received November 25, 2014; accepted March 30, 2015
Introduction The hip is the body’s second largest weight-bearing joint after the knee. It is a true ball-and-socket joint at the juncture of the thigh and pelvis surrounded by powerful and well-balanced muscles and ligaments, enabling a wide *Corresponding author: Mehmet Emin Cetin, Research Assistant, Department of Mechanical Engineering, Karadeniz Technical University, Trabzon, Turkey, Phone: +(90-462) 377 4332, Fax: +(90-462) 377 3336, E-mail: [email protected] Hasan Sofuoglu: Department of Mechanical Engineering, Karadeniz Technical University, Trabzon, Turkey
range of motion in several physical planes while also exhibiting remarkable stability. The hip is normally very sturdy because of the fit between the femoral head and acetabulum as well as strong ligaments and muscles at the joints. All of the various components of the hip mechanism assist in the mobility of the joint. A healthy hip can support the body weight and allow it to move without pain. The magnitude and the direction of the resultant hip joint force are different in different body positions during gait, and hence, the contact stress distribution in the hip joint articular surface also changes. The estimation of the hip joint stresses during daily activities is, therefore, helpful in understanding the mechanics of the normal (healthy) hip joint and useful for both preoperative planning and postoperative rehabilitation as well. Any changes in the hip joint from diseases or injuries will significantly affect the body’s gait and create abnormal stress on the hip joint. Damage to any single component can negatively affect the range of motion and the ability to bear weight on the joint. Osteoarthritis (OA) is a kind of joint disease, and it hurts the cartilage of the hip joint. The patient is affected by movement limitations and feels severe pain because of OA. In this situation, total hip arthroplasty (THA) becomes an obligation for the patient. As an increase in hip joint stresses may accelerate degenerative processes in the hip joint [3, 9], it is, therefore, important to study the distribution of the hip joint stresses after certain operative interventions such as THA as well as to design rehabilitation procedures. Although in previous studies, a hip joint contact force was only applied to the prosthetic head, additional muscle forces such as the abductors, the iliotibial tract, vastus lateralis, and the tensor fascia latae were included in the model as the recent studies have shown that the calculated hip contact force was strongly affected by the activity of the muscles that span the hip joint. Hurwitz et al. [6] found an increase in hip contact force of 0.2 times body weight with a 10% increase in antagonistic muscle force. Later on, studies have demonstrated how biomechanical factors and the configuration of muscle models influence hip loading [17] and, consequently, bone remodeling [1]. It has been also shown that the subject-specific anatomy of the hip determines the moment-generating capacity of the surrounding muscles and consequently affects hip joint loading [8].
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2 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint Analysis of joint and muscle loading is fundamental for advancing the science of orthopedic biomechanics. A wide range of research has been done on the subject, and the obtained knowledge has been applied to design the improved joint replacements, the so-called prosthesis. The preclinical tests of hip prosthesis used for THA are crucial in determining optimal process parameters and ideal procedures in providing information for the condition of a disease. Computer simulation techniques are common and ideal procedure to provide such information about a particular condition of a disease. Finite element method (FEM) is one of the widely used method to obtain such output data. The stresses that occur on prosthesis, bones, and cement mantle can be obtained by utilizing FEM, and hence, clinically inferior prosthesis can be determined [16]. The effect of stair climbing on damage accumulation on the cement of a femoral prosthesis, compared with walking, was investigated by Stolk et al. [18], while McNamara et al. [10] used a synthetic femur in both finite element and experimental analyses for investigating the effect of bone-prosthesis on the proximal load transfer. Boyle and Kim [2] analyzed two different prostheses by using three dimensional microlevel bone remodeling algorithm for pre- and post-total hip arthroplasty period. The FEM helped also to design new prosthesis for the hip joint components and to investigate the biomechanical characteristics of the component in resurfacing hip arthroplasty as shown by Watanabe et al. [20]. Joshi et al. [7] designed a new femoral prosthesis with a different proximal fixation to reduce stress shielding by performing finite element analysis (FEA), while Ramos et al. [14] designed a new cemented femoral stem in order to improve load transfer and to reduce cement stress and fatigue failure. Pawlikowski et al. [12] used FEM to design three different prostheses and decide which one was suitable for a particular patient. Senalp et al. [15] performed static, dynamic, and fatigue finite element analyses for stem shapes on which each of them has varying curvatures and compared the results with those of the Charnley prosthesis. The FEM has been successfully used as a convenient simulation method to understand the mechanics of hip joint during daily activities as mentioned in the above studies. However, many researchers used different prostheses by applying different loading types such as concentrated force or distributed load as well as having either stair climbing or walking as daily activity in their analyses. Hence, some variations can be observed in the FEA of the cemented THA reconstruction from one study to another. The purpose of this study was, therefore, to identify the effects of the prosthesis, activity, and loading types on the stresses of the hip joint’s components predicting mechanical failure of the cemented THA reconstruction. In order to address this
purpose, the finite element modeling and analyses were performed for the hip joint with prosthesis (cemented THA reconstruction) and without prosthesis (healthy hip joint) during walking and stair climbing activities for both concentrated and distributed load. A series of finite element modeling and FEA were successfully pursued for three different prostheses. The maximum von Mises stresses and strains, which occurred on cortical and trabecular layers of bone, prosthesis, and cement mantle used to assemble prosthesis into the bone’s intramedullary canal, were determined at the end of the FEA. The output data were then evaluated for identifying the effects of these process parameters on the performances of THA reconstruction’s components, thereby, affecting mechanical failure of the THA reconstruction. Finally, they were compared to the ones produced on the components of a healthy hip joint.
Hip joint models A three-dimensional (3D) third-generation composite femur model was downloaded from “Biomedtown” website (http://www.biomedtown.org) to use in this study. This femur model includes cortical and trabecular layers of bone. Using Solidworks (Dassault Systemes Solidworks Corp., USA) software, 3D realistic models of THA reconstructions, including cortical and trabecular layers of femur bone, prosthesis, and cement mantle, were created. Charnley (Depuy, Johnson & Johnson, Leeds, UK), Muller (JRI Ltd, London, UK), and Hipokrat (Hipokrat A.Ş. Turkey) cemented-type prosthesis were used in the 3D realistic models of THA reconstructions. The 3D model of Charnley prosthesis was also downloaded from “Biomedtown” website (http://www. biomedtown.org) while Muller and Hipokrat prostheses were scanned by using Breuckmann Optotophe (Aicon 3D Systems GmbH, Germany) 3D scanner. Rapidform XOR (3D Systems, USA) and Solidworks (Dassault Systemes Solidworks Corp., USA) softwares were then utilized to obtain 3D models of these two prostheses. All three prostheses types are shown in Figure 1, while their cement mantles are illustrated in Figure 2. It should be noted here that the cement mantle thickness around the prosthesis was designed optimally according to surgical procedure and modeled by using Solidworks software. The cross-section views of THA reconstruction models are also illustrated in Figure 3.
Material properties Mechanical properties of CoCr alloy were used for Charnley, Muller, and Hipokrat prostheses in this study. The
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 3
Figure 1: Types of prostheses used in this study (A) Charnley, (B) Muller, and (C) Hipokrat.
Figure 3: Cross-section views of THA reconstruction models with (A) Charnley, (B) Muller, and (C) Hipokrat prostheses applied.
elastic properties of the materials were taken from Stolk et al. [18], while the trabecular bone, cement, and prostheses were assumed to be isotropic, although cortical bone was taken as an anisotropic material as listed in Table 1.
Finite element models
Figure 2: Cement mantles used in this study along with (A) Charnley, (B) Muller, and (C) Hipokrat prostheses.
The created 3D models were then imported to Ansys Workbench commercial software. It is necessary to choose solid body and contact element types for 3D static FE analysis. Contact surfaces of models were recognized automatically by Ansys Workbench and these surfaces accepted as bonded in this study. The 3D eight-node surface-tosurface contact element was used for the contact surfaces. For a solid body, the 3D 10-node tetrahedral element type shown in Figure 4 (http://www.ansys.com), was selected because it was suitable for complicated geometries such
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4 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint Table 1: Mechanical properties of THA’s components. Components of THA
Material type
Elasticity modulus (GPa)
Poisson’s ratio
Prosthesis Cement mantle Trabecular bone Cortical bone
CoCr alloy PMMA Polyurethane foam Glass fiber-reinforced epoxy
210 2.28 0.4 Ex = Ey = 7.0, Ez = 11.5 Gyz = Gzx = 3.5, Gxy = 2.6
0.3 0.3 0.3 υxy = υyz = υxz = 0.4
Table 2: Number of elements of THA models used in FEA.
L
P Y,v
O I
X,u
Components of THA
R Q K N
M
Z,w
J
Figure 4: The 3D 10-node tetrahedral structural solid element.
as the femur. This element type was used for the finite element mesh of all solid components of the cemented THA reconstructions. Figure 5 shows an example for finite element modeling of the hip joint with prosthesis. The element numbers of each model are tabulated in Table 2.
Loading and boundary conditions In this study, the weight of the human body was assumed to be 750 N. Moreover, both muscle and contact forces that act on the hip joint during walking and stair climbing activities, which are most common in daily life, were chosen for loading. Concentrated force and distributed load were applied on the models as two different loading types. The
Mesh 4/15/2012 4:40 PM Edge/Face connectivity Free Single Double Triple Multiple
0.00
100.00 (mm) 50.00
Figure 5: Finite element modeling of hip joint assembly with Charnley prosthesis.
Number of elements Concentrated load
Prosthesis’s type Charnley Cortical bone Trabecular bone Prosthesis Cement Total Muller Cortical bone Trabecular bone Prosthesis Cement Total Hipokrat Cortical bone Trabecular bone Prosthesis Cement Total No prostheses Cortical bone Trabecular bone Total
34,363 28,532 5121 4996 73,012 22,456 18,113 9936 6222 56,727 28,469 26,001 5168 3274 62,912 21,083 17,209 38,292
Distributed load
45,041 36,860 6637 6292 94,830 22,122 17,652 10,030 6,178 55,982 39,277 36,896 11,432 7106 94,711 49,456 40,200 89,656
loads were applied according to one leg stance position of walking, and the femur was constrained rigidly at the distal end of the femoral diaphysis not to move in both horizontal and vertical directions [11, 15] (Figure 6). Concentrated force configuration taken from Heller et al. [4] was shown, and its magnitudes during walking and stair climbing were tabulated in Tables 3 and 4, respectively. Moreover, distributed force configuration was adapted from Viceconti et al. [19] and was illustrated in Figure 7.
Results and discussion The maximum von Mises stresses of prostheses are given in Table 5. The magnitudes of maximum von Mises
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 5
A B C D E F
Hip contact force: 1783.1 N Abductors: 781.76 N Tensor Fasciae Latae, Proximal: 142.43 N Tensor Fasciae Latae, Distal: 142.65 N Vastus Lateralis: 710.46 N Ridigly Constrained Condyle
0.00
100.00 (mm) 50.00
Figure 6: Boundary conditions for walking under concentrated force.
stresses of prostheses for stair climbing activity were higher than those of walking for both loading types. It can be deduced from these results that stair climbing activity increased the load applied to prostheses creating more stress on them and making stair climbing more dangerous than walking on prostheses. The contour plots of prostheses are given in Figures 8–11. As clearly seen from the figures that the maximum von Mises stress location
of Charnley prosthesis loaded with concentrated and distributed forces was under the neck of the prosthesis for both walking and stair climbing activities. However, the location of the maximum von Mises stresses of Muller prosthesis loaded with concentrated forces was on the stem and close to the tip of the stem for both activities, while the collar’s contact point with bone was found to be that of Muller prosthesis loaded with distributed force for both activities. Similar results were found for the location of the maximum von Mises stresses of the Hipokrat prosthesis. It was obtained at the center of the head where the concentrated hip contact force applied for both walking and stair climbing activities. However, when the distributed load was applied, the location of the maximum von Mises stresses of the Hipokrat prosthesis was shifted to the tip point of the stem for both activities. As a result, the loading type changed the location of the maximum von Mises stress of the Muller and Hipokrat prostheses, while the location of the maximum von Mises stress of the Charnley prosthesis remained in the same position for both the loading and activity types. On the other hand, the maximum von Mises strains of prostheses are tabulated in Table 6. The highest value was 0.0049, and it emerged on the Muller prosthesis when stair climbing forces were applied under the effect of concentrated force.
Table 3: Magnitudes of muscle and contact forces and their acting points on femur during walking. Hip contact force Abductors Tensor fasciae latae, proximal part Tensor fasciae latae, distal part Vastus lateralis
Magnitudes of forces X (N)
Y (N)
Z (N)
-405 435 54 -3.75 -6.75
246 -32.25 -87 5.25 -138.75
1719 -648.75 -99 142.5 696.75
Acts on point
P0 P1 P1 P1 P2
Table 4: Magnitudes of muscles and contact forces and their acting points on femur during stair climbing. Hip contact force Abductors İliotibial tract, proximal part İliotibial tract, distal part Tensor fasciae latae, proximal part Tensor fasciae latae, distal part Vastus lateralis Vastus medialis
Magnitudes of forces X (N)
Y (N)
Z (N)
-444.75 525.75 78.75 -3.75 23.25 -1.5 -16.5 -66
-454.5 216 22.5 -6 36.75 -2.25 168 297
-1772.25 636.75 96 -126 21.75 -48.75 -1013.25 -2003.25
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Acts on point
P0 P1 P1 P1 P1 P1 P2 P3
6 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint
Figure 7: Muscle surfaces on femur for distributed loading [19].
Table 5: The maximum von Mises stresses on prostheses. Prosthesis type Charnley Muller Hipokrat
Loading type
Walking (MPa)
Concentrated force Stair climbing (MPa)
Walking (MPa)
Stair climbing (MPa)
404.81 665.75 335.73
431.01 1029 352.79
298.14 596.05 189.6
315.56 805.48 307.58
In the analysis, the maximum von Mises stresses of the cement mantles were also obtained and are given in Table 7. It can be seen from the table that when the prostheses were loaded by a concentrated force, the lowest stress for walking and the highest stress for stair climbing occurred on the model with the Muller prosthesis applied. However, for distributed load applied models, the highest
Distributed load
value again occurred on the Muller prosthesis for stair climbing, while the lowest stress for walking was obtained on the Hipokrat prosthesis. In addition, the maximum von Mises strains of cement mantles are given in Table 8. It was clear from the table that the highest strains emerged on the Muller prosthesis applied models for both loading and activity types. It can, therefore, be concluded that if
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 7
A
404.81 Max 359.94 315.06 270.18 225.31 180.43 135.55 90.674 45.797
B
665.75 Max 591.88 518.01 444.15 370.28 296.41 222.54 148.68 74.807
Max
0.93978 Min
0.91948 Min
Max 0.00
0.00
100.00 (mm) 50.00
100.00 (mm) 50.00
C
335.73 Max 298.53 261.33 224.13 186.93 149.72 112.52 75.323 38.122
Max
0.92157 Min
0.00
100.00 (mm) 50.00
Figure 8: Stress distributions of (A) Charnley, (B) Muller, and (C) Hipokrat prostheses for walking under concentrated force.
the Muller prosthesis is used for THA reconstruction in the mid to long term, it can cause aseptic loosening and may require revision surgery. This was consistent with the findings of Herberts et al. [5] in which it was mentioned that the Charnley and Muller prostheses had 8% and 13% revision rates after surgery applied in 10 years, respectively. The maximum von Mises stresses of the cortical bone are given in Table 9, while Table 10 tabulated the maximum von Mises strains of the cortical bone. Among the three prostheses, the lowest values emerged on the
Charnley prosthesis-applied model for both loading and activity types. Moreover, the maximum von Mises stresses that occurred on the cortical bones of the Charnley and Hipokrat prostheses were smaller than those of the healthy hip joint, whereas the maximum von Mises stress of Muller prosthesis was higher than that of healthy hip joint. In addition, the same trend was obtained for the maximum von Mises strains of cortical bones, i.e., the smaller values with Charnley and Hipokrat prostheses and the higher values with Muller prosthesis were determined.
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8 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 431.01 Max
A
383.17 335.32 287.48 239.63 191.79 143.94 96.094 48.248
Max
0.40191 Min
1029 Max
B
914.81 800.57 686.33 572.1 457.86 343.62 229.39 115.15
0.91267 Min
Max 0.00
100.00 (mm)
0.00
50.00
100.00 (mm) 50.00
C
352.79 Max 313.66 274.54 235.42 196.3 157.17
Max
118.05 78.928 39.805
0.68283 Min
0.00
100.00 (mm) 50.00
Figure 9: Stress distribution of (A) Charnley, (B) Muller, and (C) Hipokrat prostheses for stair climbing under concentrated force.
The maximum von Mises stresses of the cortical bone of the present study agreed well with those of the study of Ramos and Simoes [13] in which third-generation composite and simplified femur models were employed for comparison purposes. In their study, they used both tetrahedral and hexahedral finite element meshes in the simplified and the realistic femur geometries by taking Stolk et al.’s [16] hip joint and muscle force magnitudes. While performing FES, they used tetrahedral (10-node
tetrahedron) and evaluated the von Mises stress of the cortical bones at the specific point to compare the result with that of the simplified model, which was 24.3 MPa. In our study, on the other hand, we also used the same femur model, the same element type and found a very close magnitude of von Mises stress of cortical bone of 24.76 MPa at the same point (Figure 12). They also compared the proximal femur’s experimental strains with the finite element results of the tetrahedral meshed third-generation
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 9
A
298.14 Max 265.1 232.06 199.02 165.98 132.94 99.897 66.856 33.816
Max
0.77475 Min
B
596.05 Max 529.92 463.78 397.65 331.52 265.39 199.26 133.12 66.993
Max
0.8614 Min
0.00
100.00 (mm)
0.00
100.00 (mm)
50.00
50.00
C
189.6 Max 168.62 147.64 126.66 105.69 84.708 63.73 42.752 21.774
0.7958 Min
Max 0.00
100.00 (mm) 50.00
Figure 10: Stress distribution of (A) Charnley, (B) Muller, and (C) Hipokrat prostheses for walking under distributed force.
composite femur model and mentioned that those results correlated with each other, which also showed a similar trend to the present study. Table 11 listed the maximum von Mises stresses of trabecular bone. The highest value was 17.771 MPa, and it occurred on the Muller prosthesis-applied model for stair climbing activity and concentrated force. On the other
hand, the maximum von Mises strains of trabecular bone are also given in Table 12. When the three prostheses were compared, it was easily seen that the Hipokrat prosthesis caused the lowest strain value on the trabecular bone. It was observed that when compared, the stresses obtained for the cortical and trabecular bones of the hip joint without prosthesis, the maximum von Mises stress
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10 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint
A
315.56 Max 280.64 245.73 210.81 175.9 140.98 106.07 71.151 36.236
B
805.48 Max 716.08 626.68 537.28 447.89 358.49 269.09 179.69 90.293
Max
1.3214 Min
Max
0.89515 Min
0.00
100.00 (mm)
0.00
100.00 (mm)
50.00
50.00
C
307.58 Max 273.53 239.47 205.42 171.36 137.31 103.25 69.194 35.139
1.0833 Min
Max 0.00
100.00 (mm) 50.00
Figure 11: Stress distribution of (A) Charnley, (B) Muller, and (C) Hipokrat prostheses for stair climbing under concentrated force.
occurred on the cortical layer of bone. This was attributed to the fact that in healthy human hip joint, the hip takes care of the loadings caused by the body weight and muscle forces and distributes them to the rest of the hip joint’s components as it acts as a support. However, the stress distributions of the hip joint’s components were
changed after THA reconstruction was applied so that the prosthesis took the most portion of the loading creating the maximum von Mises stress on itself and decreased the stresses of the rest of the components. This is the wellknown phenomena of stress-shielding behavior [7] and is schematically illustrated in Figure 13.
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 11 Table 6: The maximum von Mises strains on prostheses. Prosthesis type
Charnley Muller Hipokrat
Loading type
Walking (mm/mm)
Concentrated force Stair climbing (mm/mm)
Distributed load Walking (mm/mm)
Stair climbing (mm/mm)
0.001928 0.003170 0.001599
0.002052 0.00490 0.00168
0.001420 0.0028383 0.000903
0.001503 0.0038356 0.001465
Table 7: The maximum von Mises stresses on cement mantles. Prosthesis type Charnley Muller Hipokrat
Loading type
Walking (MPa)
Concentrated force Stair climbing (MPa)
Distributed load Walking (MPa)
Stair climbing (MPa)
59.529 50.518 59.747
65.597 79.421 72.037
58.828 56.675 52.254
76.902 82.058 70.026
Table 8: The maximum von Mises strains on cement mantles. Prosthesis type
Charnley Muller Hipokrat
Loading type
Walking (mm/mm)
Concentrated force Stair climbing (mm/mm)
Distributed load Walking (mm/mm)
Stair climbing (mm/mm)
0.026109 0.022157 0.025295
0.028771 0.034834 0.031595
0.025802 0.024857 0.022918
0.033729 0.035991 0.030713
Table 9: The maximum von Mises stresses on cortical bone. Prosthesis type
Charnley Muller Hipokrat No prosthesis
Loading type
Walking (MPa)
Concentrated force Stair climbing (MPa)
Distributed load Walking (MPa)
Stair climbing (MPa)
41.821 96.871 63.275 93.376
87.981 117.5 116.52 99.478
34.547 108.57 37.661 43.676
57.773 141.95 61.011 67.392
Table 10: The maximum von Mises strains on cortical bone. Prosthesis type
Charnley Muller Hipokrat No prosthesis
Loading type
Walking (mm/mm)
Concentrated force Stair climbing (mm/mm)
Distributed load Walking (mm/mm)
Stair climbing (mm/mm)
0.004492 0.01125 0.006572 0.010435
0.009043 0.01369 0.012022 0.01111
0.003423 0.012676 0.003864 0.004481
0.005889 0.016365 0.006230 0.006870
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12 H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint
A: Static Structural
Equivalent Stress 2 Type: Equivalent (von-Mises) Stress Unit: MPa Time: 1 18.02.2015 14:41
93.376 Max 83.001 72.626 62.251 51.876 41.501 31.126 20.75 10.375
24.767
0.00030624 Min
0.00
100.00 (mm)
Figure 12: Illustration of the location of the maximum von Mises stress of cortical bone.
Table 11: The maximum von Mises stresses on trabecular bone. Prosthesis type
Charnley Muller Hipokrat No prosthesis
Loading type
Walking (MPa)
Concentrated force Stair climbing (MPa)
Distributed load Walking (MPa)
Stair climbing (MPa)
14.166 13.599 10.157 7.3998
13.628 17.771 12.618 7.8458
13.257 11.442 9.8547 4.030
17.404 16.288 13.456 4.4317
Table 12: The maximum von Mises strains on trabecular bone. Prosthesis type
Charnley Muller Hipokrat No prosthesis
Loading type
Walking (mm/mm)
Concentrated force Stair climbing (mm/mm)
Walking (mm/mm)
Stair climbing (mm/mm)
0.035415 0.33998 0.025393 0.01850
0.034071 0.044429 0.031545 0.019615
0.033142 0.028606 0.024637 0.010075
0.043511 0.04072 0.033640 0.011079
Conclusion Mechanical behavior of the human hip joint with and without prosthesis was investigated by using the FEM.
Distributed load
After pursuing the FEA, the values of the peak stress and strain were determined and then analyzed to explore the effects of each process parameters for predicting the mechanical failure of the cemented THA reconstruction.
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H. Sofuoglu and M.E. Cetin: Mechanical failure of hip joint 13
References
Figure 13: Schematic illustration of load transformation (A) before and (B) after THA reconstruction [7].
Under the lights of the above-obtained results, the following conclusions can be drawn. 1. It was clear from the results of the von Mises stress and strain of the cement mantle that stair climbing was more detrimental than walking on predicting mechanical failure of the cement mantle of THA reconstruction. 2. Among the three prostheses types used in the THA reconstruction of this study, the Muller prosthesis caused aseptic loosening and was riskier than the Charnley and Hipokrat prostheses in terms of revision surgery. 3. According to the cortical bone’s maximum von Mises stresses for distributed loading and von Mises strains for both loading conditions, the Muller prosthesis was more destructive in both walking and stair climbing when compared to the Charnley and Hipokrat prostheses. 4. For the loading and activity conditions investigated in this study, the von Mises strains of the trabecular bone on the Hipokrat prosthesis-applied model were closer to those of the healthy trabecular bone. 5. During walking and stair climbing, the Hipokrat prosthesis among the three prostheses investigated in this study had the lowest average stress on the cement mantle for distributed loading. It may then be concluded that the Hipokrat prosthesis can be suggested to patients who have more daily activities.
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