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The effect of cup inclination and wear on the contact mechanics and cement fixation for ultra high molecular weight polyethylene total hip replacements
Medical Engineering & Physics 34 (2012) 318–325
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Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
The effect of cup inclination and wear on the contact mechanics and cement fixation for ultra high molecular weight polyethylene total hip replacements Xijin Hua a , B. Michael Wroblewski b , Zhongmin Jin a,c , Ling Wang a,∗ a b c
Institute of Medical and Biological Engineering, School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom Wrightington Hospital, Wigan WN6 9EP, United Kingdom School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China
a r t i c l e
i n f o
Article history: Received 9 February 2011 Received in revised form 14 June 2011 Accepted 24 July 2011 Keywords: Wear Cement fixation Contact mechanics Cup orientation Charnley hip
a b s t r a c t The present study aimed to investigate individual and combined influences of the cup inclination and wear on the contact mechanics and fixation of a Charnley hip replacement using finite element method. The effects of cup inclination and penetration on the contact mechanics of articulating bearings as well as the stress within the cement and at the bone–cement interface were examined. The maximum contact pressure and the von Mises stress on the cup were reduced by ∼30% and ∼20% respectively when even a small penetration occurred. However, no large differences were found between different cup penetration depths with regards to either the contact pressure or the von Mises stress. The von Mises stress at the bone–cement interface was predicted almost unaltered with an increased cup inclination angle to 55◦ for a cup penetration to 4 mm. These predictions suggest that the contact mechanics and the cement stress are insensitive to the cup inclination and wear under these normal conditions investigated, therefore explaining the robustness of the Charnley hip implant. An increase in the cup inclination angle to 65◦ , coupled with a maximum penetration of 4 mm, resulted in a large increase in the maximum von Mises stress at the bone–cement interface. © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction The long-term clinical performance of artificial hip joints depends on both the tribology of the bearing surfaces and the fixation of prosthetic components. The fixation of total hip joint replacement (THR) is an important procedure during hip surgeries, as it critically affects the long-term stability of THRs. One of the major types of fixation techniques is using bone cement, particularly for the acetabular cups. Although the cemented THR is reported to have a good long-term survival rate of minimum 70% at 35 years [1], the aseptic loosening is considered as a major indication for revision. The twenty-year follow up study of the cemented Charnley THRs reported that the aseptic loosening rate of the acetabular cups is two to four times that of the femoral components [1,2]. The reasons behind the failure of the THRs are multi-factorial, however, it is generally accepted that wear of the polyethylene cups is mainly responsible for the loosening failure of the cups. However, there are two different views as how this occurs; biological or mechanical.
∗ Corresponding author. Tel.: +44 1133437472. E-mail address: [email protected] (L. Wang).
From the biological point of view, the osteolytic bone resorption to the wear particles could cause the aseptic loosening and long-term failure of THRs [3]. From the mechanical perspective, high stresses in the bone cement might be sufficient in promoting the crack growth and debonding of the cement mantle, which ultimately may lead to failure of THRs [4–6]. The 17 years in vivo studies showed eight-folds revision rate of the high cup wear group compared to that of the low cup wear group [7]; while there was no statistical difference between the two groups with respect to the femoral component. This indicates the elevated stresses in the bone cement, induced by the high wear and reduction in cup thickness, as well as the increased likelihood of potential impingement, may be responsible for the mechanical loosening of the cups. Furthermore, polyethylene cup penetration is reported to be associated with aseptic loosening [7,8] and bone–cement debonding [9]. Wroblewski et al. [8] compared the incidence of aseptic loosening of Charnley THRs with different penetration depths. They concluded that there was an increased incidence of aseptic loosening associated with the increased penetration depth on the acetabular cup, which attributed to the additional impingement between the neck and the cup [10]. The same conclusion was also drawn by Coultrup et al. [11], who examined the effect of polyethylene wear rate, cement mantle thickness and porosity on the failure of the acetabular cement mantle and indicated the increase in the cement mantle
1350-4533/$ – see front matter © 2011 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2011.07.026
X. Hua et al. / Medical Engineering & Physics 34 (2012) 318–325
Fig. 1. A schematic diagram (cross-section) of the femoral head and the UHMWPE cup with penetration indicated.
Fig. 2. The geometry (left) and boundary conditions (right) of the full anatomic hip model (the direction of the load was 10◦ medially) [25]. 35 30
True stress [MPa]
stress with the cup penetration, and consequently the decrease in the cement mantle fatigue life. Therefore, both the fixation of the cups and the tribology (wear) at the articulating surfaces become important considerations for the long-term clinical success of THRs. Both the fixation and the wear are closely related to the contact mechanics between the acetabular cup and the femoral head, such as how the load is transferred through the interface between the cement and the bone, and how the contact pressure is distributed on the bearing surfaces. In addition, cup angle is also a major consideration in the hip implantation surgery, which can affect both the contact mechanics and potentially the polyethylene wear. Patil et al. [12] investigated the contact stress using the finite element analysis considering different acetabular component orientations, and concluded peak contact stresses were increased with the increasing abduction angle and the predicted linear wear followed the same trend. The computational predictions were compared to hip wear simulator measurements, and both results were further validated by clinical studies. Other modelling studies and laboratory tests [13–15] also highlighted the importance of optimizing the surgical position of acetabular component in order to reduce the contact stresses between the contact bearing surfaces as well as to minimize the wear. All these studies have shown that an increased cup angle led to elevated contact stress between the articulating bearings and wear of the acetabular components. A steep cup angle may cause contact between the femoral head and the superolateral rim of the acetabular cup (edge contact) and can sharply increase the contact stress and associated wear between the bearing surfaces. Although the effects of cup angles on the contact mechanics of the metal-on-polyethylene hip joint have been extensively investigated, to the authors’ knowledge, the study of the contribution of cup angles to the cup fixation, with respect to the cement mantle, is still lacking. Contact mechanics at the articulating surfaces and the fixation of the polyethylene cups are closely linked, and are dependent on the wear of polyethylene cups and cup angles. This is particularly true when the cup penetration is increased. However, the majority of studies reported in the literature have addressed these two problems separately as reviewed above. Furthermore, the cup inclination angle on the contact mechanics and fixation of a metal-on-polyethylene hip implant has not been investigated comprehensively in the literature. Majority of the studies have been conducted under a normal cup angle, as to how the penetration depth affects the cement mantle stress under different cup angles has not been investigated yet. The purpose of the present study was thus to investigate the individual and combined influence of the cup inclination and wear on the contact mechanics and cement fixation of a metal-on-polyethylene hip replacement.
319
25 20 15 10 5 0 0.00
0.02
0.04
0.06
0.08
0.10
0.12
Strain Fig. 3. The plastic stress–strain relation for UHMWPE [16,26].
2. Materials and methods A typical hemi-spherical Charnley hip system was modelled [11], consisting of an ultra high molecular weight polyethylene (UHMWPE) cup with an inner diameter of 22.59 mm and an outer diameter of 40 mm and a stainless steel femoral head with a diameter of 22.225 mm, giving a radial clearance of 0.1825 mm and a cup thickness of approximately 8.7 mm. The thickness of bone cement was selected as 2 mm [11]. Geometrical characterization of the wear on the UHMWPE cups was performed by intersecting the cup using the femoral head in the direction of the resultant loading, as illustrated in Fig. 1. Different linear penetrations were considered; 1, 2, and 4 mm. The maximum penetration of 4 mm was considered as the limit beyond which the impingement between the neck and cup would occur [8]. For a linear penetration rate of 0.1–0.2 mm/year [2], this would represent a maximum service life of 20–40 years.
Three dimensional finite element models were created to simulate the positions of both the head and the cup implanted in a hemi-pelvic hip joint bone model (Fig. 2) [25,27]. The hemi-pelvic FE bone model consisted of a cancellous bone region surrounded by a uniform cortical shell of 1.5 mm thickness. The acetabular cup was fixed into the acetabulum using the bone cement. In order to examine the effect of cup inclination and polyethylene penetration depth simultaneously, the inclination angles of the acetabular cups with different penetration depths of 0, 1, 2 and 4 mm were simulated for different cup orientation at 45◦ to 65◦ respectively. All the materials were modelled as homogeneous, isotropic and linear elastic, except the UHMWPE which was modelled as nonlinear elastic–plastic based on the plastic stress–strain constitutive relationship presented in Fig. 3. The plastic stress–strain data were taken from Liu [16] for a similar polyethylene material. The other material properties used in this study are given in Table 1. The femoral head was assumed to be rigid as the elastic modulus of
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Table 1 Material properties used in the present study [25,27]. Component
Materials
Young’s modulus (GPa)
Poisson’s ratio
UHMWPE insert Bone cement Cortical shell Cancellous bone
UHMWPE PMMA Cortical bone Cancellous bone
0.85 2.5 17 0.8
0.4 0.254 0.3 0.2
the material of the metallic femoral head is at least two orders of magnitude greater than that of UHMWPE. A fixed resultant hip joint contact force of 2500 N with the direction of 10◦ medially, corresponding to about 3–4 times body weight for an average weight of 70 kg, was applied on the models through the centre of the femoral head simulating the mid-to-terminal stance loading of the gait cycle (Fig. 2) [17]. Nodes at the sacro-iliac joint and about the pubic symphysis in the hemi-pelvic FE bone model were fully constrained (Fig. 2). The FE model consisted of a total of approximately 10,000 nodes and 12,000 elements, including ‘brick’ and ‘wedge’ for the cancellous bone, bone cement and prosthetic components, and ‘thin-shell’ elements for the cortical bone. The solid models were meshed in I-DEAS (Version 11, EDS, USA) and solved using ABAQUS (Version 6.9, Abaqus Inc.). Mesh sensitivity studies were performed to check the accuracy of the predictions to ensure that the difference of maximum contact pressures in the acetabular cups and von Mises stress in the cement mantle was within 3% by doubling the number of the elements in the FE models. The contact at the bearing surfaces between the cup and femoral head was modelled by frictionless surface-based elements, as coefficients of friction less than 0.1 should not have appreciable effects on the predicted contact mechanics [18]. The contact interfaces in the FE model between the bone cement and the cup as well as between the bone and the cement were assumed to be firmly bonded for this study to simulate a fully bone cement interlock and perfect fixation.
Cement stress was used as an indication to potential failure rather than the fatigue and crack based approach [11]. The main reason for such a simplified approach was that contact stresses are directly related to fatigue and also the present study focused on the medium to long-term period rather than the long-term period when bone cement crack ultimately develops. The bone–cement interface was examined in detail, since the cement failure is likely to be initiated at this interface [5,19].
3. Results The predicted contact pressure at the cup surface and the von Mises stresses in the cup, in the cement mantle and at the bone–cement interface for a 1 mm penetration depth and 45◦ angle are presented in Fig. 4. The predicted contact pressure distributions at the acetabular inner bearing surface at different cup orientation angles for different cup penetration models are plotted in Fig. 5. Corresponding to this figure, the predicted maximum contact pressure and von Mises stress are presented as a function of the cup angle for different depths of penetration in Fig. 6a and b respectively. Generally, for all the cup penetration depths, the predicted area of contact pressure was located about the superior region of the cup in the loading direction. Contact area was shifted towards the edge of the cup as the inclination angle was increased. Both the maximum contact pressure and the von Mises stress were markedly reduced by ∼30% and ∼20% respectively when even a small penetration depth of 1 mm occurred. However, there was no large difference between the different cup penetration depth with regards to either contact pressure or von Mises stress. Furthermore, the increase in the cup angle only resulted in a modest increase in the maximum contact pressure and the maximum von Mises stress (less than 10%). These values were predicted corresponding to the mid-to-terminal stance portion of the gait cycles, and might not be
Fig. 4. The predicted stresses (MPa) of the full anatomic THR model at 45◦ of cup angle and 1 mm of penetration depth: (a) contact pressures of the UHMWPE cup, (b) Von Mises stress in the UHMWPE cup, (c) Von Mises stress in the cement mantle (cross-section), (d) Von Mises stress at the bone–cement interface.
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Fig. 5. The predicted contact pressures (MPa) distributions and contact areas as a function of cup angle for the UHMWPE cup with different penetration depth.
the same when considering other instants of the walking cycle or other activities such as sitting, standing and stair climbing. The predicted von Mises stress distributions of the cement mantle at the bone–cement interface corresponding to the FE models are plotted in Fig. 7 for different cup angles and different cup
penetration depths. Corresponding to this figure, the predicted maximum von Mises stress is presented as a function of the cup inclination for different depth of penetration in Fig. 8. With increased cup inclination, the distribution of von Mises stresses on the bone–cement interface was shifted towards the
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Max contact pressures (MPa)
a
20 18 16 14 12 10 8
No penetraon
6
Penetraon 1mm
4
Penetraon 2mm
2
Penetraon 4mm
0 45
55
65
Cup angles (°)
b
14
Max Von Mises (MPa)
12 10 8 6
No penetraon Penetraon 1mm
4
Penetraon 2mm
2
Penetraon 4mm
0 45
55
65
Cup angles (°) Fig. 6. (a) The predicted maximum contact pressures (MPa), (b) the predicted maximum Von Mises stresses (MPa) of UHMWPE cup with different cup angles and penetration depths.
edge of the cement as well, and the stresses were elevated slightly with increased cup angle for all the cup penetration depth. When wear of 1 and 2 mm on the acetabular component occurred, the stress was reduced by about 15–20%. There were small differences of the predicted maximum von Mises stress between different penetration depths. The effect of the cup angle on the predicted maximum von Mises was also small up to 55◦ . However, a combination of a maximum penetration depth of 4 mm and a cup inclination angle of 65◦ resulted in a large increase in the predicted von Mises stress by more than 40%, slightly above the unworn cup. 4. Discussion The main purpose of the present study was to investigate the effect of the inclination cup angles and wear rate on the combined contact mechanics of the articulating surfaces and fixation stresses in the cement mantle, with respect to a typical metal-on-UHMWPE Chanrley THR. The major parameters examined included the contact pressure and contact area at the articulating surfaces as well as the stresses within the cup and more importantly within the cement mantle and at the bone–cement interface. The validation of the present prediction was partially carried out by comparing the predicted maximum contact pressure and contact radius with the finite element prediction and experimental measurement by Jin et al. [20] under the same condition. An excellent agreement was obtained, with relative differences of less than 5%. Under the typical conditions considered, the maximum contact pressure and von Mises stress of the acetabular component were
predicted to be ∼18 MPa and ∼13 MPa respectively in the present simulations. Under these conditions, the wear of the polyethylene surface should take the form of the surface wear rather than the low-cycle fatigue [21]. It is also interesting to note that the maximum von Mises stress within the cement mantle occurred at the cup/cement interface. However, the bone–cement interface is usually where the debonding occurred [5] and therefore the maximum von Mises stress at the bone–cement interface was considered further in the following parametric studies. An increase in the cup inclination from 45◦ to 65◦ resulted in a noticeable shift of the contact area from the centre of the acetabular cup towards the edge. However, the increase in the maximum contact pressure and the maximum von Mises stress within the polyethylene cup was rather modest, less than 10%, which is consistent with the previous simulation studies [12,13]. Also no edge contact occurred and no sharp increase in the contact stress was observed, as opposed to the hard-on-hard bearings [22]. This may explain to a certain extent the robustness of the soft-on-hard Charnley hip system, as compared with the hard-on-hard articulations. An increase of the penetration resulted in a large reduction in both the maximum von Mises and contact pressure of the acetabular cup, more than 20–30%. This is largely due to the increased conformity between the acetabular cup and femoral head as a result of wear. However, the difference was almost negligible between different penetration depths, and between different cup angles. A similar conclusion was drawn by Coultrup et al. [11] that an increased cup penetration was associated with increased cement mantle stresses, resulting in a reduction of the cement mantle fatigue life of 9–11% for a high cup penetration depth. Once again this highlights the rather in-sensitivity of wear on the polyethylene cup to both the wear rate and cup angles, as compared with the running-in wear of hard-on-hard articulations of metal-on-metal and ceramic-on-ceramic. The maximum von Mises stress at the bone–cement interface occurred within the cement central region, rather than towards the edge, even when the cup inclination was increased to 65◦ . It is interesting to note that a modest penetration depth actually resulted in a reduction in the predicted maximum von Mises stress. There are two competing factors in this process. The cement stress depended on both the contact pressure at the articulating surfaces and also how the contact stresses were transferred to the bone cement interface. Although an increase in the penetration depth resulted in a potential increase in the cement stress due to the reduction in the cup thickness, the improved conformity and the corresponding reduction in the contact pressure actually resulted in a reduction in the cement stress. This once again explains the robustness of the Charnley metal-on-polyethylene hip system. However, this observation is only limited to small penetration depths. When the penetration depth was increased to 4 mm, the effect of the cup thickness reduction became more dominant and consequently, the maximum cement stress was increased consequently. This is particularly evident, when combined with a steep cup inclination angle of 65◦ , that the maximum von Mises stresses was increased above that of the un-worn cup. For the conditions considered in the present study which represented the successful Charnley cups, neither the cup inclination nor the penetration affected the contact mechanics and the fixation markedly. This suggests that the Charnley system is quite robust; insensitive to the cup inclination and wear, as compared with the hard-on-hard articulations. These observations are consistent with the clinical observations reported in the literature. However, beyond these conditions when the penetration or the inclination angle is increased further, a marked increase in the maximum von Mises on the cement mantle would be predicted from the trend observed in Fig. 8. These may cause the rim crack and
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Fig. 7. The predicted Von Mises stresses (MPa) distributions of the cement mantle at the bone–cement interface as a function of cup angle for the UHMWPE cup with different penetration depth.
the rapid failure of the cement mantle. Furthermore, it should be pointed out that although the results in the present study reinforced the robustness of the Charnley total hip replacement, every effort should still be made to select the correct patient and to position the prosthesis correctly. There are a number of limitations of the present study, particularly regarding validation. In the present study, an indirect validation was performed by comparing with the previous study [20]. Besides, in the present simulation, the cup was assumed to be
bonded to the bone cement using a tied contact formulation rather than modelling the macro-features on the cup external surface explicitly. Although this geometric simplification was reasonable in the computational simulation of the contact mechanics at the bearing surfaces [4,5,11], it would inevitably affect the stress in the cement mantle. The maximum penetration depth of 4 mm was simulated in the present study. Only the maximum von Mises stress within the bone–cement interface was focused on, rather than the fatigue based approach [11]. Nevertheless, the small increase
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Max Von Mises (MPa)
12
conformity due to wear. The predictions from the present computational modelling study provide further support to the robustness of the Charnley hip system.
10 8
Acknowledgements
6
No penetraon Penentraon 1mm Penentraon 2mm Penetraon 4mm
4 2 0 45
55
65
Cup angles(°) Fig. 8. The predicted maximum Von Mises stresses (MPa) of the cement mantle at the bone–cement interface with different cup angles and penetration depths.
in the maximum von Mises stress as the penetration increased was consistent with the previous study [10]. Furthermore, a clinic follow-up study of the Charnley total hip replacement [8] showed an increased incidence of aseptic loosening associated with increasing cup penetration. This differs from the present prediction since the effect of the penetration depth was predicted to be quite small, unlikely to cause the observed clinical difference. There are a number of potential reasons for this discrepancy. The present study only focused on the potential mechanical loosening based on the static contact stress, rather than the bone cement fatigue and the wear debris induced biological mechanism. One of the most important concepts in the Charnley hip system is the low frictional torque. This was not simulated in the present finite element modelling. A typical coefficient of friction for a metal-on-polyethylene combination is 0.08. Assuming a uniform shear stress at the bone–cement interface, the additional shear stress induced as a result of the frictional torque was estimated to be approximately 0.04 MPa. Therefore, considering the effect of friction is unlikely to affect the major conclusions from the present study. The penetration of the acetabular cup was simulated towards the direction of the resultant load in the present study, which was 10◦ medially. However, it is interesting to note in retrieval studies where the direction of wear was generally observed to be lateral [23]. This may be due to the complex motion occurring during the different daily activities. The specific direction of the wear needs to be further studied. Furthermore, a simple worn geometry with a zero clearance to the head was considered and this may affect how the contact pressure distributes at the articulating surfaces and potentially the stress in the cement mantle. It was shown in a retrieval study [20] that there were clearly clearances between the worn area of the cup and the femoral head. More adverse conditions such as large penetration and potential impingement and higher cup inclination angles as well as anteversion angles should also be simulated. Other cup designs, particularly a thicker polyethylene cup or different cement thicknesses should also be investigated as well to further understand the clinical observations [24]. 5. Conclusions A general methodology combining contact mechanics between the articulating surfaces and fixation of the cement mantle was developed for a metal-on-polyethylene hip system under different cup angles and the penetration depths. A typical Charnley system was modelled. Neither the inclination angle up to 55◦ nor the penetration depth up to 4 mm was predicted to affect the contact mechanics and the fixation stress markedly. This is particularly true for the stress at the bone–cement interface, due to the competing effects between reduction in the cup thickness and the improved
Xijin Hua is funded by a Full International Research Scholarship of University of Leeds. This work was supported by the NIHR as part of collaboration with the LMBRU. This work was partially funded through WELMEC, a Centre of Excellence in Medical Engineering, funded by the Wellcome Trust and EPSRC (grant number WT 088908/Z/09/Z).
Conflict of interest There is no conflict of interests for the work of this manuscript.
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X. Hua et al. / Medical Engineering & Physics 34 (2012) 318–325 [21] Bartel DL, Bicknell VL, Wright TM. The effect of conformity: thickness, and material on stresses in ultra-high molecular weight components for total joint replacement. J Bone Joint Surg Am Vol 1986;68(7):1041–51. [22] Liu F, Jin ZM, Rieker C, Hirt F, Roberts P, Grigoris P. Comparison of contact mechanics between a total hip replacement and a hip resurfacing with a metalon-metal articulation. J Bone Joint Surg Br 2006;88-B(Suppl. III):383-a. [23] Wroblewski BM. Direction and rate of socket wear in Charnley low-friction arthroplasty. J Bone Joint Surg Br 1985;67-B(5):757–61. [24] Wroblewski BM, Siney PD, Fleming PA. Charnley low-friction arthroplasty: survival patterns to 38 years. J Bone Joint Surg Br 2007;89-B(8):1015–8.
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Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
The effect of cup inclination and wear on the contact mechanics and cement fixation for ultra high molecular weight polyethylene total hip replacements Xijin Hua a , B. Michael Wroblewski b , Zhongmin Jin a,c , Ling Wang a,∗ a b c
Institute of Medical and Biological Engineering, School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom Wrightington Hospital, Wigan WN6 9EP, United Kingdom School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China
a r t i c l e
i n f o
Article history: Received 9 February 2011 Received in revised form 14 June 2011 Accepted 24 July 2011 Keywords: Wear Cement fixation Contact mechanics Cup orientation Charnley hip
a b s t r a c t The present study aimed to investigate individual and combined influences of the cup inclination and wear on the contact mechanics and fixation of a Charnley hip replacement using finite element method. The effects of cup inclination and penetration on the contact mechanics of articulating bearings as well as the stress within the cement and at the bone–cement interface were examined. The maximum contact pressure and the von Mises stress on the cup were reduced by ∼30% and ∼20% respectively when even a small penetration occurred. However, no large differences were found between different cup penetration depths with regards to either the contact pressure or the von Mises stress. The von Mises stress at the bone–cement interface was predicted almost unaltered with an increased cup inclination angle to 55◦ for a cup penetration to 4 mm. These predictions suggest that the contact mechanics and the cement stress are insensitive to the cup inclination and wear under these normal conditions investigated, therefore explaining the robustness of the Charnley hip implant. An increase in the cup inclination angle to 65◦ , coupled with a maximum penetration of 4 mm, resulted in a large increase in the maximum von Mises stress at the bone–cement interface. © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction The long-term clinical performance of artificial hip joints depends on both the tribology of the bearing surfaces and the fixation of prosthetic components. The fixation of total hip joint replacement (THR) is an important procedure during hip surgeries, as it critically affects the long-term stability of THRs. One of the major types of fixation techniques is using bone cement, particularly for the acetabular cups. Although the cemented THR is reported to have a good long-term survival rate of minimum 70% at 35 years [1], the aseptic loosening is considered as a major indication for revision. The twenty-year follow up study of the cemented Charnley THRs reported that the aseptic loosening rate of the acetabular cups is two to four times that of the femoral components [1,2]. The reasons behind the failure of the THRs are multi-factorial, however, it is generally accepted that wear of the polyethylene cups is mainly responsible for the loosening failure of the cups. However, there are two different views as how this occurs; biological or mechanical.
∗ Corresponding author. Tel.: +44 1133437472. E-mail address: [email protected] (L. Wang).
From the biological point of view, the osteolytic bone resorption to the wear particles could cause the aseptic loosening and long-term failure of THRs [3]. From the mechanical perspective, high stresses in the bone cement might be sufficient in promoting the crack growth and debonding of the cement mantle, which ultimately may lead to failure of THRs [4–6]. The 17 years in vivo studies showed eight-folds revision rate of the high cup wear group compared to that of the low cup wear group [7]; while there was no statistical difference between the two groups with respect to the femoral component. This indicates the elevated stresses in the bone cement, induced by the high wear and reduction in cup thickness, as well as the increased likelihood of potential impingement, may be responsible for the mechanical loosening of the cups. Furthermore, polyethylene cup penetration is reported to be associated with aseptic loosening [7,8] and bone–cement debonding [9]. Wroblewski et al. [8] compared the incidence of aseptic loosening of Charnley THRs with different penetration depths. They concluded that there was an increased incidence of aseptic loosening associated with the increased penetration depth on the acetabular cup, which attributed to the additional impingement between the neck and the cup [10]. The same conclusion was also drawn by Coultrup et al. [11], who examined the effect of polyethylene wear rate, cement mantle thickness and porosity on the failure of the acetabular cement mantle and indicated the increase in the cement mantle
1350-4533/$ – see front matter © 2011 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2011.07.026
X. Hua et al. / Medical Engineering & Physics 34 (2012) 318–325
Fig. 1. A schematic diagram (cross-section) of the femoral head and the UHMWPE cup with penetration indicated.
Fig. 2. The geometry (left) and boundary conditions (right) of the full anatomic hip model (the direction of the load was 10◦ medially) [25]. 35 30
True stress [MPa]
stress with the cup penetration, and consequently the decrease in the cement mantle fatigue life. Therefore, both the fixation of the cups and the tribology (wear) at the articulating surfaces become important considerations for the long-term clinical success of THRs. Both the fixation and the wear are closely related to the contact mechanics between the acetabular cup and the femoral head, such as how the load is transferred through the interface between the cement and the bone, and how the contact pressure is distributed on the bearing surfaces. In addition, cup angle is also a major consideration in the hip implantation surgery, which can affect both the contact mechanics and potentially the polyethylene wear. Patil et al. [12] investigated the contact stress using the finite element analysis considering different acetabular component orientations, and concluded peak contact stresses were increased with the increasing abduction angle and the predicted linear wear followed the same trend. The computational predictions were compared to hip wear simulator measurements, and both results were further validated by clinical studies. Other modelling studies and laboratory tests [13–15] also highlighted the importance of optimizing the surgical position of acetabular component in order to reduce the contact stresses between the contact bearing surfaces as well as to minimize the wear. All these studies have shown that an increased cup angle led to elevated contact stress between the articulating bearings and wear of the acetabular components. A steep cup angle may cause contact between the femoral head and the superolateral rim of the acetabular cup (edge contact) and can sharply increase the contact stress and associated wear between the bearing surfaces. Although the effects of cup angles on the contact mechanics of the metal-on-polyethylene hip joint have been extensively investigated, to the authors’ knowledge, the study of the contribution of cup angles to the cup fixation, with respect to the cement mantle, is still lacking. Contact mechanics at the articulating surfaces and the fixation of the polyethylene cups are closely linked, and are dependent on the wear of polyethylene cups and cup angles. This is particularly true when the cup penetration is increased. However, the majority of studies reported in the literature have addressed these two problems separately as reviewed above. Furthermore, the cup inclination angle on the contact mechanics and fixation of a metal-on-polyethylene hip implant has not been investigated comprehensively in the literature. Majority of the studies have been conducted under a normal cup angle, as to how the penetration depth affects the cement mantle stress under different cup angles has not been investigated yet. The purpose of the present study was thus to investigate the individual and combined influence of the cup inclination and wear on the contact mechanics and cement fixation of a metal-on-polyethylene hip replacement.
319
25 20 15 10 5 0 0.00
0.02
0.04
0.06
0.08
0.10
0.12
Strain Fig. 3. The plastic stress–strain relation for UHMWPE [16,26].
2. Materials and methods A typical hemi-spherical Charnley hip system was modelled [11], consisting of an ultra high molecular weight polyethylene (UHMWPE) cup with an inner diameter of 22.59 mm and an outer diameter of 40 mm and a stainless steel femoral head with a diameter of 22.225 mm, giving a radial clearance of 0.1825 mm and a cup thickness of approximately 8.7 mm. The thickness of bone cement was selected as 2 mm [11]. Geometrical characterization of the wear on the UHMWPE cups was performed by intersecting the cup using the femoral head in the direction of the resultant loading, as illustrated in Fig. 1. Different linear penetrations were considered; 1, 2, and 4 mm. The maximum penetration of 4 mm was considered as the limit beyond which the impingement between the neck and cup would occur [8]. For a linear penetration rate of 0.1–0.2 mm/year [2], this would represent a maximum service life of 20–40 years.
Three dimensional finite element models were created to simulate the positions of both the head and the cup implanted in a hemi-pelvic hip joint bone model (Fig. 2) [25,27]. The hemi-pelvic FE bone model consisted of a cancellous bone region surrounded by a uniform cortical shell of 1.5 mm thickness. The acetabular cup was fixed into the acetabulum using the bone cement. In order to examine the effect of cup inclination and polyethylene penetration depth simultaneously, the inclination angles of the acetabular cups with different penetration depths of 0, 1, 2 and 4 mm were simulated for different cup orientation at 45◦ to 65◦ respectively. All the materials were modelled as homogeneous, isotropic and linear elastic, except the UHMWPE which was modelled as nonlinear elastic–plastic based on the plastic stress–strain constitutive relationship presented in Fig. 3. The plastic stress–strain data were taken from Liu [16] for a similar polyethylene material. The other material properties used in this study are given in Table 1. The femoral head was assumed to be rigid as the elastic modulus of
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Table 1 Material properties used in the present study [25,27]. Component
Materials
Young’s modulus (GPa)
Poisson’s ratio
UHMWPE insert Bone cement Cortical shell Cancellous bone
UHMWPE PMMA Cortical bone Cancellous bone
0.85 2.5 17 0.8
0.4 0.254 0.3 0.2
the material of the metallic femoral head is at least two orders of magnitude greater than that of UHMWPE. A fixed resultant hip joint contact force of 2500 N with the direction of 10◦ medially, corresponding to about 3–4 times body weight for an average weight of 70 kg, was applied on the models through the centre of the femoral head simulating the mid-to-terminal stance loading of the gait cycle (Fig. 2) [17]. Nodes at the sacro-iliac joint and about the pubic symphysis in the hemi-pelvic FE bone model were fully constrained (Fig. 2). The FE model consisted of a total of approximately 10,000 nodes and 12,000 elements, including ‘brick’ and ‘wedge’ for the cancellous bone, bone cement and prosthetic components, and ‘thin-shell’ elements for the cortical bone. The solid models were meshed in I-DEAS (Version 11, EDS, USA) and solved using ABAQUS (Version 6.9, Abaqus Inc.). Mesh sensitivity studies were performed to check the accuracy of the predictions to ensure that the difference of maximum contact pressures in the acetabular cups and von Mises stress in the cement mantle was within 3% by doubling the number of the elements in the FE models. The contact at the bearing surfaces between the cup and femoral head was modelled by frictionless surface-based elements, as coefficients of friction less than 0.1 should not have appreciable effects on the predicted contact mechanics [18]. The contact interfaces in the FE model between the bone cement and the cup as well as between the bone and the cement were assumed to be firmly bonded for this study to simulate a fully bone cement interlock and perfect fixation.
Cement stress was used as an indication to potential failure rather than the fatigue and crack based approach [11]. The main reason for such a simplified approach was that contact stresses are directly related to fatigue and also the present study focused on the medium to long-term period rather than the long-term period when bone cement crack ultimately develops. The bone–cement interface was examined in detail, since the cement failure is likely to be initiated at this interface [5,19].
3. Results The predicted contact pressure at the cup surface and the von Mises stresses in the cup, in the cement mantle and at the bone–cement interface for a 1 mm penetration depth and 45◦ angle are presented in Fig. 4. The predicted contact pressure distributions at the acetabular inner bearing surface at different cup orientation angles for different cup penetration models are plotted in Fig. 5. Corresponding to this figure, the predicted maximum contact pressure and von Mises stress are presented as a function of the cup angle for different depths of penetration in Fig. 6a and b respectively. Generally, for all the cup penetration depths, the predicted area of contact pressure was located about the superior region of the cup in the loading direction. Contact area was shifted towards the edge of the cup as the inclination angle was increased. Both the maximum contact pressure and the von Mises stress were markedly reduced by ∼30% and ∼20% respectively when even a small penetration depth of 1 mm occurred. However, there was no large difference between the different cup penetration depth with regards to either contact pressure or von Mises stress. Furthermore, the increase in the cup angle only resulted in a modest increase in the maximum contact pressure and the maximum von Mises stress (less than 10%). These values were predicted corresponding to the mid-to-terminal stance portion of the gait cycles, and might not be
Fig. 4. The predicted stresses (MPa) of the full anatomic THR model at 45◦ of cup angle and 1 mm of penetration depth: (a) contact pressures of the UHMWPE cup, (b) Von Mises stress in the UHMWPE cup, (c) Von Mises stress in the cement mantle (cross-section), (d) Von Mises stress at the bone–cement interface.
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Fig. 5. The predicted contact pressures (MPa) distributions and contact areas as a function of cup angle for the UHMWPE cup with different penetration depth.
the same when considering other instants of the walking cycle or other activities such as sitting, standing and stair climbing. The predicted von Mises stress distributions of the cement mantle at the bone–cement interface corresponding to the FE models are plotted in Fig. 7 for different cup angles and different cup
penetration depths. Corresponding to this figure, the predicted maximum von Mises stress is presented as a function of the cup inclination for different depth of penetration in Fig. 8. With increased cup inclination, the distribution of von Mises stresses on the bone–cement interface was shifted towards the
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Max contact pressures (MPa)
a
20 18 16 14 12 10 8
No penetraon
6
Penetraon 1mm
4
Penetraon 2mm
2
Penetraon 4mm
0 45
55
65
Cup angles (°)
b
14
Max Von Mises (MPa)
12 10 8 6
No penetraon Penetraon 1mm
4
Penetraon 2mm
2
Penetraon 4mm
0 45
55
65
Cup angles (°) Fig. 6. (a) The predicted maximum contact pressures (MPa), (b) the predicted maximum Von Mises stresses (MPa) of UHMWPE cup with different cup angles and penetration depths.
edge of the cement as well, and the stresses were elevated slightly with increased cup angle for all the cup penetration depth. When wear of 1 and 2 mm on the acetabular component occurred, the stress was reduced by about 15–20%. There were small differences of the predicted maximum von Mises stress between different penetration depths. The effect of the cup angle on the predicted maximum von Mises was also small up to 55◦ . However, a combination of a maximum penetration depth of 4 mm and a cup inclination angle of 65◦ resulted in a large increase in the predicted von Mises stress by more than 40%, slightly above the unworn cup. 4. Discussion The main purpose of the present study was to investigate the effect of the inclination cup angles and wear rate on the combined contact mechanics of the articulating surfaces and fixation stresses in the cement mantle, with respect to a typical metal-on-UHMWPE Chanrley THR. The major parameters examined included the contact pressure and contact area at the articulating surfaces as well as the stresses within the cup and more importantly within the cement mantle and at the bone–cement interface. The validation of the present prediction was partially carried out by comparing the predicted maximum contact pressure and contact radius with the finite element prediction and experimental measurement by Jin et al. [20] under the same condition. An excellent agreement was obtained, with relative differences of less than 5%. Under the typical conditions considered, the maximum contact pressure and von Mises stress of the acetabular component were
predicted to be ∼18 MPa and ∼13 MPa respectively in the present simulations. Under these conditions, the wear of the polyethylene surface should take the form of the surface wear rather than the low-cycle fatigue [21]. It is also interesting to note that the maximum von Mises stress within the cement mantle occurred at the cup/cement interface. However, the bone–cement interface is usually where the debonding occurred [5] and therefore the maximum von Mises stress at the bone–cement interface was considered further in the following parametric studies. An increase in the cup inclination from 45◦ to 65◦ resulted in a noticeable shift of the contact area from the centre of the acetabular cup towards the edge. However, the increase in the maximum contact pressure and the maximum von Mises stress within the polyethylene cup was rather modest, less than 10%, which is consistent with the previous simulation studies [12,13]. Also no edge contact occurred and no sharp increase in the contact stress was observed, as opposed to the hard-on-hard bearings [22]. This may explain to a certain extent the robustness of the soft-on-hard Charnley hip system, as compared with the hard-on-hard articulations. An increase of the penetration resulted in a large reduction in both the maximum von Mises and contact pressure of the acetabular cup, more than 20–30%. This is largely due to the increased conformity between the acetabular cup and femoral head as a result of wear. However, the difference was almost negligible between different penetration depths, and between different cup angles. A similar conclusion was drawn by Coultrup et al. [11] that an increased cup penetration was associated with increased cement mantle stresses, resulting in a reduction of the cement mantle fatigue life of 9–11% for a high cup penetration depth. Once again this highlights the rather in-sensitivity of wear on the polyethylene cup to both the wear rate and cup angles, as compared with the running-in wear of hard-on-hard articulations of metal-on-metal and ceramic-on-ceramic. The maximum von Mises stress at the bone–cement interface occurred within the cement central region, rather than towards the edge, even when the cup inclination was increased to 65◦ . It is interesting to note that a modest penetration depth actually resulted in a reduction in the predicted maximum von Mises stress. There are two competing factors in this process. The cement stress depended on both the contact pressure at the articulating surfaces and also how the contact stresses were transferred to the bone cement interface. Although an increase in the penetration depth resulted in a potential increase in the cement stress due to the reduction in the cup thickness, the improved conformity and the corresponding reduction in the contact pressure actually resulted in a reduction in the cement stress. This once again explains the robustness of the Charnley metal-on-polyethylene hip system. However, this observation is only limited to small penetration depths. When the penetration depth was increased to 4 mm, the effect of the cup thickness reduction became more dominant and consequently, the maximum cement stress was increased consequently. This is particularly evident, when combined with a steep cup inclination angle of 65◦ , that the maximum von Mises stresses was increased above that of the un-worn cup. For the conditions considered in the present study which represented the successful Charnley cups, neither the cup inclination nor the penetration affected the contact mechanics and the fixation markedly. This suggests that the Charnley system is quite robust; insensitive to the cup inclination and wear, as compared with the hard-on-hard articulations. These observations are consistent with the clinical observations reported in the literature. However, beyond these conditions when the penetration or the inclination angle is increased further, a marked increase in the maximum von Mises on the cement mantle would be predicted from the trend observed in Fig. 8. These may cause the rim crack and
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Fig. 7. The predicted Von Mises stresses (MPa) distributions of the cement mantle at the bone–cement interface as a function of cup angle for the UHMWPE cup with different penetration depth.
the rapid failure of the cement mantle. Furthermore, it should be pointed out that although the results in the present study reinforced the robustness of the Charnley total hip replacement, every effort should still be made to select the correct patient and to position the prosthesis correctly. There are a number of limitations of the present study, particularly regarding validation. In the present study, an indirect validation was performed by comparing with the previous study [20]. Besides, in the present simulation, the cup was assumed to be
bonded to the bone cement using a tied contact formulation rather than modelling the macro-features on the cup external surface explicitly. Although this geometric simplification was reasonable in the computational simulation of the contact mechanics at the bearing surfaces [4,5,11], it would inevitably affect the stress in the cement mantle. The maximum penetration depth of 4 mm was simulated in the present study. Only the maximum von Mises stress within the bone–cement interface was focused on, rather than the fatigue based approach [11]. Nevertheless, the small increase
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Max Von Mises (MPa)
12
conformity due to wear. The predictions from the present computational modelling study provide further support to the robustness of the Charnley hip system.
10 8
Acknowledgements
6
No penetraon Penentraon 1mm Penentraon 2mm Penetraon 4mm
4 2 0 45
55
65
Cup angles(°) Fig. 8. The predicted maximum Von Mises stresses (MPa) of the cement mantle at the bone–cement interface with different cup angles and penetration depths.
in the maximum von Mises stress as the penetration increased was consistent with the previous study [10]. Furthermore, a clinic follow-up study of the Charnley total hip replacement [8] showed an increased incidence of aseptic loosening associated with increasing cup penetration. This differs from the present prediction since the effect of the penetration depth was predicted to be quite small, unlikely to cause the observed clinical difference. There are a number of potential reasons for this discrepancy. The present study only focused on the potential mechanical loosening based on the static contact stress, rather than the bone cement fatigue and the wear debris induced biological mechanism. One of the most important concepts in the Charnley hip system is the low frictional torque. This was not simulated in the present finite element modelling. A typical coefficient of friction for a metal-on-polyethylene combination is 0.08. Assuming a uniform shear stress at the bone–cement interface, the additional shear stress induced as a result of the frictional torque was estimated to be approximately 0.04 MPa. Therefore, considering the effect of friction is unlikely to affect the major conclusions from the present study. The penetration of the acetabular cup was simulated towards the direction of the resultant load in the present study, which was 10◦ medially. However, it is interesting to note in retrieval studies where the direction of wear was generally observed to be lateral [23]. This may be due to the complex motion occurring during the different daily activities. The specific direction of the wear needs to be further studied. Furthermore, a simple worn geometry with a zero clearance to the head was considered and this may affect how the contact pressure distributes at the articulating surfaces and potentially the stress in the cement mantle. It was shown in a retrieval study [20] that there were clearly clearances between the worn area of the cup and the femoral head. More adverse conditions such as large penetration and potential impingement and higher cup inclination angles as well as anteversion angles should also be simulated. Other cup designs, particularly a thicker polyethylene cup or different cement thicknesses should also be investigated as well to further understand the clinical observations [24]. 5. Conclusions A general methodology combining contact mechanics between the articulating surfaces and fixation of the cement mantle was developed for a metal-on-polyethylene hip system under different cup angles and the penetration depths. A typical Charnley system was modelled. Neither the inclination angle up to 55◦ nor the penetration depth up to 4 mm was predicted to affect the contact mechanics and the fixation stress markedly. This is particularly true for the stress at the bone–cement interface, due to the competing effects between reduction in the cup thickness and the improved
Xijin Hua is funded by a Full International Research Scholarship of University of Leeds. This work was supported by the NIHR as part of collaboration with the LMBRU. This work was partially funded through WELMEC, a Centre of Excellence in Medical Engineering, funded by the Wellcome Trust and EPSRC (grant number WT 088908/Z/09/Z).
Conflict of interest There is no conflict of interests for the work of this manuscript.
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