- Email: [email protected]
Influence of press-fit parameters on the primary stability of uncemented femoral resurfacing implants
Available online at www.sciencedirect.com
Medical Engineering & Physics 31 (2009) 160–164
Technical note
Influence of press-fit parameters on the primary stability of uncemented femoral resurfacing implants A. Gebert ∗ , J. Peters, N.E. Bishop, F. Westphal, M.M. Morlock Biomechanics Section, TUHH Hamburg University of Technology, Hamburg, Denickestrasse 15, D-21073 Hamburg, Germany Received 4 August 2007; received in revised form 15 April 2008; accepted 16 April 2008
Abstract Primary stability is essential to the success of uncemented prostheses. It is strongly influenced by implantation technique, implant design and bone quality. The goal of this study was to investigate the effect of press-fit parameters on the primary stability of uncemented femoral head resurfacing prostheses. An in vitro study with human specimens and prototype implants (nominal radial interference 170 and 420 m) was used to investigate the effect of interference on primary stability. A finite element model was used to assess the influence of interference, friction between implant and bone, and bone quality. Primary stability was represented by the torque capacity of the implant. The model predicted increasing stability with actual interference, bone quality and friction coefficient; plastic deformation of the bone began at interferences of less than 100 m. Experimentally, however, stability was not related to interference. This may be due to abrasion or the collapse of trabecular bone structures at higher interferences, which could not be captured by the model. High nominal interferences as tested experimentally appear unlikely to result in improved stability clinically. An implantation force of about 2500 N was estimated to be sufficient to achieve a torque capacity of about 30 N m with a small interference (70 m). © 2008 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Resurfacing; Press-fit; Finite element model; Total hip arthroplasty
1. Introduction Resurfacing hip arthroplasty has had its resurgence over the last decade due to improved manufacturing techniques. Early clinical results for uncemented femoral resurfacing are promising [1,2]. However, long-term results are not yet available. Potential problems include femoral neck fractures, implant loosening and avascular necrosis [3–5]. Primary stability is a prerequisite for press-fitted prostheses, since osseointegration is only possible with low interface motion [6,7]. This is achieved by the radial interference between bone and implant. Press-fit design, implantation precision and bone quality could affect the mechanical stability, which must be achieved simultaneously with suitable seating of the implant, and under limited implantation forces. Numerical models in the literature refer only to cemented fixation, and have mainly been used to investigate stress distributions
in the head and femoral neck [8–10]. The relation between stability, implantation force and bone damage in uncemented resurfacing has not been addressed. The objective of this study was to determine the influence of bone quality and press-fit design parameters on the primary stability of an uncemented hip resurfacing prosthesis.
2. Materials and methods The effect of interference on primary stability was determined experimentally using a torque test. A finite element model based on one of the tested specimens was then used to investigate the effects of bone quality and friction on primary stability. 2.1. Experiment
∗
Corresponding author. Tel.: +49 40 42878 3253; fax: +49 40 42878 2996. E-mail address: [email protected] (A. Gebert). URL: http://www.tu-harburg.de/bim/ (A. Gebert).
Femoral heads were separated from 7 fresh frozen human femura at the neck-shaft junction (mean age 51, range
1350-4533/$ – see front matter © 2008 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2008.04.007
A. Gebert et al. / Medical Engineering & Physics 31 (2009) 160–164
161
Fig. 1. (A) The prototype uncemented hip resurfacing prosthesis, (B) detail view of the porous coating at the edge of the head, (C) cross section of an implanted resurfacing prosthesis (implantation height of 18 mm, lower inner diameter 37.65 mm).
47–57 years; mean trabecular apparent density for each head >250 mg/cm3 ). Several screws were implanted into the neck prior to embedding in a metal pot using acrylic resin. The embedded head was reamed using standard instruments mounted in a pillar drill. Prototype uncemented resurfacing heads (outside diameter 45 mm, inside taper angle 3.5◦ , DePuy International, UK) were implanted with nominal radial interferences of 170 and 420 m, determined according to the difference between reamer and implant diameters, given by the manufacture (Fig. 1). Interference was achieved by ‘under-reaming’ of the bone in comparison to the prosthesis geometry. Implantation was performed under axial displacement control at 1 mm/s using a materials testing machine (Bionix 858.2, MTS, Eden Prairie, MN) until complete seating; axial forces were recorded. Due to reaming variations and manufacturing tolerances of the porous coating, the corrected nominal interference was calculated for each of the 7 implantations from the tangent of the taper angle and the distance displaced onto the bone. This distance was determined from the position of initial contact (at 50 N) and the seated position with the system unloaded. Torsional rotation was applied to the implant immediately after implantation via an equatorial clamp at 0.5 N m/s with an axial pre-load of 1000 N until 15◦ of rotation were achieved (Fig. 2A). Slipping between clamp and implant, or
bone and embedding material, was checked by the change in distance between pen marks. If slipping occurred the sample was excluded. The torque capacity was taken as measure for the primary stability. It was defined as the peak value of the torque-rotation curve. Linear regression between radial interference and implantation forces and torque capacity was performed with a Type I error probability of α = 0.05 (SPSS V.13). 2.2. Finite element model A conical FE model of the reamed cancellous bone was created based on the CT-scan of one of the tested specimens. Surface-to-surface contact analysis was used to model the interface between head and bone (Fig. 2B). The bone was rigidly fixed close to the end of the reamed zone. Calculations were performed using linear tetrahedral elements C3D4 (ABAQUS 6.5, 18,421 d.o.f.). The implant (Young’s modulus = 210 GPa, ν = 0.3) was pushed onto the bone to its seated position by displacement of the polar node along the direction of the axis of the reaming. The interference for the calculations was varied in a broad range (0, 85, 170, 420 m) by changing the internal diameter of the implant. For the bone a homogenous elastic-plastic, isotropic hardening material model was used. A Young’s
Fig. 2. (A) Setup for the experimental torque test with pre-load F and torque T; (B) the FE model with interference r.
162
A. Gebert et al. / Medical Engineering & Physics 31 (2009) 160–164
modulus of 354 MPa was assigned to the bone based on the mean apparent density measured from the calibrated CT dataset of the respective specimen [11]. The influence of bone quality was investigated by variation of Young’s modulus: 150 (poor), 500 MPa (good). Post-yield modulus was set to 5% of the elastic modulus [12]. A compressive yield strain of 0.0085 was used for the cancellous bone [13]. Poisson’s ratio was set to ν = 0.3. Contact was simulated using coulomb friction with a friction coefficient of μ = 0.4 to represent the experimental porous coat interface and also 0.6 and 0.8 to simulate different implant interfaces [14]. During implantation the reaction force at the polar node in the z-direction was calculated and elements exceeding the yield strength were identified for every 0.3 mm of implantation displacement. After implantation torsion with an axial pre-load of 1000 N at the pole of the implant was applied to the outer surface at the equator by means of coupling elements (DCOUP3D). The torque capacity was defined when all nodes at the interface were sliding. Numerical convergence was confirmed.
Fig. 3. Experimentally determined and calculated implantation forces (for the 3 bone qualities, μ = 0.4) in relation to the corrected nominal (for the experiment) and the actual interference (for the model). The circled experimental data point refers to the specimen, which was used for the FE model.
3. Results 3.1. Experiment Two specimens were excluded due to slipping between clamp and implant. For the nominal interference of 170 m (re. 420 m) corrected nominal interferences of 176 and 451 m (re. 516, 576 and 581 m) were determined. Larger interferences tended to require higher implantation forces for seating (R2 = 0.319, p = 0.19, Fig. 3), whereas torque capacity decreased very slightly with interference (R2 = 0.084, p = 0.33, respectively, Fig. 4). Neither result was significant. The mean torque capacity for all interferences was 26.5 ± 4.1 N m.
Fig. 4. Experimentally determined and calculated torque capacity T (for the 3 bone qualities, μ = 0.4) in relation to the corrected nominal (for the experiment) and the actual interference (for the model). The circled experimental data point refers to the specimen, which was used for the FE model.
Fig. 5. Elements which exceed the yield strain during implantation for the medium quality bone (von Mises plastic strain is shown in the color bar; Young’s modulus: 354 MPa; friction coefficient μ = 0.4).
A. Gebert et al. / Medical Engineering & Physics 31 (2009) 160–164
163
Table 1 Calculated implantation forces and torque capacities for the different interferences, bone qualities, friction coefficients (μ), and the ratio of “torque capacity” to “implantation force” (normalised to model 2). Model
Bone quality (MPa)
μ
Radial interference (m)
Implantation force (N)
Torque capacity (N m)
Torque capacity/implantation force
1 2 3 4 5 6 7
354 354 354 354 354 150 500
0.4 0.4 0.4 0.6 0.8 0.4 0.4
32 85 170 85 85 85 85
1000 3011 5011 4558 6255 1516 4195
16 35 38 41 47 14 50
1.38 1.00 0.65 0.77 0.65 0.79 1.03
Model 1 with a nominal interference of 0 m results in an actual interference of 32 m due to the pre-load of 1000 N.
3.2. FE model Better bone quality and higher interferences required higher implantation forces (Fig. 3). The slope of the force-interference relation decreased at the onset of plastic deformation. Onset occurred at lower interferences with increasing friction coefficient (μ = 0.4: 57 m, Fig. 5; μ = 0.6: 28 m; μ = 0.8: 16 m). At an interference of 170 m the whole head had plastified for all friction coefficients and bone qualities. After plastification of the whole head, calculation of the implantation force was not evaluated further. Torque capacity increased with bone quality and showed a bi-linear dependency on the interference. Only little increase after 85 m interference was achieved for all bone qualities (Fig. 4). A torque capacity of 30 N m was estimated for an interference of 70 m, which required an implantation force of 2400 N (medium quality bone, μ = 0.4). Higher friction coefficients were associated with higher implantation forces and higher torque capacities (models 2, 4, 5 in Table 1). Lower bone stiffness led to lower torque capacity and lower implantation forces (models 2, 6, 7 in Table 1). The ratio of “torque capacity” to “implantation force” represents the ratio of “primary stability” to “loading of the bone during implantation”. This ratio was higher for smaller interferences (models 1–3 in Table 1). Increasing the friction coefficient as well as decreasing the bone quality reduced this ratio (models 2, 4, 5 re. 2, 6, 7 in Table 1).
4. Discussion Greater interferences might be expected to increase the torque capacity. However, the experimentally measured torque capacities were found to be rather independent of interference, although higher interferences tended to require higher implantation forces. The discrepancy could be due to abrasion or plastic deformation of the bone during implantation. Assuming that primary stability is provided only by the elastic deformation component of the bone, no further improvement would be achieved after full plastic deformation of the bone (71 m for fully developed circumferential plasticity and 172 m for the entire bone, Fig. 5). The small but steady increase in post-yield torque capacity predicted
by the FE model was not observed in the experimental data (Fig. 4). This could be due to abrasion occurring in the experiment, which is not represented by the plastic material law used in the model. “Rough” prosthesis and bone surfaces may provide only local traction until bone asperities have been deformed or abraded and full surface contact has been attained. Marked differences were found between nominal and corrected nominal interferences which were probably due to low reaming accuracy. This problem would lead to difficulties in achieving consistent seating of the prosthesis on the bone with reasonable forces in clinical practice, especially since manual reaming would introduce even more variability. The ratio of “torque capacity” to “implantation force” decreased with increasing friction coefficient indicating that a higher implantation force will be needed for higher friction coefficients to achieve similar stability. The torque-to-force ratio also decreases with poor bone quality, indicating that stability could be reduced in soft bone, as plastic deformation starts earlier. Joint friction moments of large diameter metal-on-metal resurfacing implants of up to 7.9 N m have been measured [15]. The torque capacities observed in this study even at low interferences are clearly higher. This suggests that only small interferences are necessary to obtain primary implant stability and that only small implantation forces in the range of joint loads during every day activities are required. Furthermore, it can be concluded, that high interferences will cause excessive bone damage. No viscoelastic effects were explicitly taken into account. This has to be viewed as a limitation as a reduction in pressfit could potentially occur due to relaxation over time [16]. However, mean equilibrium stress for cancellous bone is stated to be about 80% of the peak applied stress [17]. This is much less than the (up to) 700% greater torque capacity that would be predicted by extrapolating the elastic part of the torque-interference curve (Fig. 4) than that actually measured. Most of this loss of press-fit is, therefore, attributed to plastic failure, rather than to viscoelasticity. The findings of this study indicate that an implantation force of about 2400 N is sufficient to achieve a torque capacity of about 30 N m (with an actual interference of ∼70 m). Such a scenario should provide sufficient primary stability and limit the possibility of bone damage and neck fracture
164
A. Gebert et al. / Medical Engineering & Physics 31 (2009) 160–164
[4]. The problem of how to achieve implantation conditions as accurately as has been shown to be required remains a challenge to be solved in the future. Acknowledgment We would like to thank DePuy International for providing the implants and implantation tools. Conflict of interest The study was supported by DePuy International in respect of provision of the prostheses. There was no other financial and personal relationships with other people or organizations. References [1] Schmalzried TP, Fowble VA, Ure KJ, Amstutz HC. Metal on metal surface replacement of the hip. Technique, fixation, and early results. Clin Orthop Relat Res 1996:106–14. [2] Lilikakis AK, Vowler SL, Villar RN. Hydroxyapatite-coated femoral implant in metal-on-metal resurfacing hip arthroplasty: minimum of two years follow-up. Orthop Clin North Am 2005;36:215–22. [3] Amstutz HC, Campbell PA, Le Duff MJ. Fracture of the neck of the femur after surface arthroplasty of the hip. J Bone Joint Surg Am 2004;86-A:1874–7. [4] Morlock MM, Bishop NE, R¨uther W, Delling W, Hahn M. Biomechanical, morphological and histological analysis of early failures in hip resurfacing arthroplasty. J Eng Med 2006;220:333–44. [5] Ritter MA, Lutgring JD, Berend ME, Pierson JL. Failure mechanisms of total hip resurfacing: implications for the present. Clin Orthop Relat Res 2006;453:110–4.
[6] Jasty M, Bragdon C, Burke D, O’Connor D, Lowenstein J, Harris WH. In vivo skeletal responses to porous-surfaced implants subjected to small induced motions. J Bone Joint Surg Am 1997;79:707–14. [7] Pilliar RM, Lee JM, Maniatopoulos C. Observations on the effect of movement on bone ingrowth into porous-surfaced implants. Clin Orthop Relat Res 1986:108–13. [8] Huiskes R, Strens PH, van HJ, Slooff TJ. Interface stresses in the resurfaced hip. Finite element analysis of load transmission in the femoral head. Acta Orthop Scand 1985;56:474–8. [9] Shybut GT, Askew MJ, Hori RY, Stulberg SD. Computational stress analysis of cup replacement hip arthroplasty. Trans Am Soc Artif Intern Organs 1979;25:24–6. [10] 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: 505–11. [11] Wirtz DC, Schiffers N, Pandorf T, Radermacher K, Weichert D, Forst R. Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. J Biomech 2000;33:1325–30. [12] Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech 2004;37:27–35. [13] Morgan EF, Keaveny TM. Dependence of yield strain of human trabecular bone on anatomic site. J Biomech 2001;34:569–77. [14] Grant JA, Bishop NE, G¨otzen N, Sprecher C, Honl M, Morlock MM. Artificial composite bone as a model of human trabecular bone: The implant-bone interface. J Biomech 2007;40:1158–64. [15] Bishop NE, Waldow F, Morlock MM. Friction moment of large metalon-metal hip joint bearings and other modern designs. Med Eng Phys, 2008 Feb 19, in press [Epub ahead of print]. [16] Norman TL, Ackerman ES, Smith TS, Gruen TA, Yates AJ, Blaha JD, et al. Cortical bone viscoelasticity and fixation strength of pressfit femoral stems: an in-vitro model. J Biomech Eng 2006;128: 13–7. [17] Bredbenner TL, Davy DT. The effect of damage on the viscoelastic behavior of human vertebral trabecular bone. J Biomech Eng 2006;128:473–80.
Medical Engineering & Physics 31 (2009) 160–164
Technical note
Influence of press-fit parameters on the primary stability of uncemented femoral resurfacing implants A. Gebert ∗ , J. Peters, N.E. Bishop, F. Westphal, M.M. Morlock Biomechanics Section, TUHH Hamburg University of Technology, Hamburg, Denickestrasse 15, D-21073 Hamburg, Germany Received 4 August 2007; received in revised form 15 April 2008; accepted 16 April 2008
Abstract Primary stability is essential to the success of uncemented prostheses. It is strongly influenced by implantation technique, implant design and bone quality. The goal of this study was to investigate the effect of press-fit parameters on the primary stability of uncemented femoral head resurfacing prostheses. An in vitro study with human specimens and prototype implants (nominal radial interference 170 and 420 m) was used to investigate the effect of interference on primary stability. A finite element model was used to assess the influence of interference, friction between implant and bone, and bone quality. Primary stability was represented by the torque capacity of the implant. The model predicted increasing stability with actual interference, bone quality and friction coefficient; plastic deformation of the bone began at interferences of less than 100 m. Experimentally, however, stability was not related to interference. This may be due to abrasion or the collapse of trabecular bone structures at higher interferences, which could not be captured by the model. High nominal interferences as tested experimentally appear unlikely to result in improved stability clinically. An implantation force of about 2500 N was estimated to be sufficient to achieve a torque capacity of about 30 N m with a small interference (70 m). © 2008 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Resurfacing; Press-fit; Finite element model; Total hip arthroplasty
1. Introduction Resurfacing hip arthroplasty has had its resurgence over the last decade due to improved manufacturing techniques. Early clinical results for uncemented femoral resurfacing are promising [1,2]. However, long-term results are not yet available. Potential problems include femoral neck fractures, implant loosening and avascular necrosis [3–5]. Primary stability is a prerequisite for press-fitted prostheses, since osseointegration is only possible with low interface motion [6,7]. This is achieved by the radial interference between bone and implant. Press-fit design, implantation precision and bone quality could affect the mechanical stability, which must be achieved simultaneously with suitable seating of the implant, and under limited implantation forces. Numerical models in the literature refer only to cemented fixation, and have mainly been used to investigate stress distributions
in the head and femoral neck [8–10]. The relation between stability, implantation force and bone damage in uncemented resurfacing has not been addressed. The objective of this study was to determine the influence of bone quality and press-fit design parameters on the primary stability of an uncemented hip resurfacing prosthesis.
2. Materials and methods The effect of interference on primary stability was determined experimentally using a torque test. A finite element model based on one of the tested specimens was then used to investigate the effects of bone quality and friction on primary stability. 2.1. Experiment
∗
Corresponding author. Tel.: +49 40 42878 3253; fax: +49 40 42878 2996. E-mail address: [email protected] (A. Gebert). URL: http://www.tu-harburg.de/bim/ (A. Gebert).
Femoral heads were separated from 7 fresh frozen human femura at the neck-shaft junction (mean age 51, range
1350-4533/$ – see front matter © 2008 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2008.04.007
A. Gebert et al. / Medical Engineering & Physics 31 (2009) 160–164
161
Fig. 1. (A) The prototype uncemented hip resurfacing prosthesis, (B) detail view of the porous coating at the edge of the head, (C) cross section of an implanted resurfacing prosthesis (implantation height of 18 mm, lower inner diameter 37.65 mm).
47–57 years; mean trabecular apparent density for each head >250 mg/cm3 ). Several screws were implanted into the neck prior to embedding in a metal pot using acrylic resin. The embedded head was reamed using standard instruments mounted in a pillar drill. Prototype uncemented resurfacing heads (outside diameter 45 mm, inside taper angle 3.5◦ , DePuy International, UK) were implanted with nominal radial interferences of 170 and 420 m, determined according to the difference between reamer and implant diameters, given by the manufacture (Fig. 1). Interference was achieved by ‘under-reaming’ of the bone in comparison to the prosthesis geometry. Implantation was performed under axial displacement control at 1 mm/s using a materials testing machine (Bionix 858.2, MTS, Eden Prairie, MN) until complete seating; axial forces were recorded. Due to reaming variations and manufacturing tolerances of the porous coating, the corrected nominal interference was calculated for each of the 7 implantations from the tangent of the taper angle and the distance displaced onto the bone. This distance was determined from the position of initial contact (at 50 N) and the seated position with the system unloaded. Torsional rotation was applied to the implant immediately after implantation via an equatorial clamp at 0.5 N m/s with an axial pre-load of 1000 N until 15◦ of rotation were achieved (Fig. 2A). Slipping between clamp and implant, or
bone and embedding material, was checked by the change in distance between pen marks. If slipping occurred the sample was excluded. The torque capacity was taken as measure for the primary stability. It was defined as the peak value of the torque-rotation curve. Linear regression between radial interference and implantation forces and torque capacity was performed with a Type I error probability of α = 0.05 (SPSS V.13). 2.2. Finite element model A conical FE model of the reamed cancellous bone was created based on the CT-scan of one of the tested specimens. Surface-to-surface contact analysis was used to model the interface between head and bone (Fig. 2B). The bone was rigidly fixed close to the end of the reamed zone. Calculations were performed using linear tetrahedral elements C3D4 (ABAQUS 6.5, 18,421 d.o.f.). The implant (Young’s modulus = 210 GPa, ν = 0.3) was pushed onto the bone to its seated position by displacement of the polar node along the direction of the axis of the reaming. The interference for the calculations was varied in a broad range (0, 85, 170, 420 m) by changing the internal diameter of the implant. For the bone a homogenous elastic-plastic, isotropic hardening material model was used. A Young’s
Fig. 2. (A) Setup for the experimental torque test with pre-load F and torque T; (B) the FE model with interference r.
162
A. Gebert et al. / Medical Engineering & Physics 31 (2009) 160–164
modulus of 354 MPa was assigned to the bone based on the mean apparent density measured from the calibrated CT dataset of the respective specimen [11]. The influence of bone quality was investigated by variation of Young’s modulus: 150 (poor), 500 MPa (good). Post-yield modulus was set to 5% of the elastic modulus [12]. A compressive yield strain of 0.0085 was used for the cancellous bone [13]. Poisson’s ratio was set to ν = 0.3. Contact was simulated using coulomb friction with a friction coefficient of μ = 0.4 to represent the experimental porous coat interface and also 0.6 and 0.8 to simulate different implant interfaces [14]. During implantation the reaction force at the polar node in the z-direction was calculated and elements exceeding the yield strength were identified for every 0.3 mm of implantation displacement. After implantation torsion with an axial pre-load of 1000 N at the pole of the implant was applied to the outer surface at the equator by means of coupling elements (DCOUP3D). The torque capacity was defined when all nodes at the interface were sliding. Numerical convergence was confirmed.
Fig. 3. Experimentally determined and calculated implantation forces (for the 3 bone qualities, μ = 0.4) in relation to the corrected nominal (for the experiment) and the actual interference (for the model). The circled experimental data point refers to the specimen, which was used for the FE model.
3. Results 3.1. Experiment Two specimens were excluded due to slipping between clamp and implant. For the nominal interference of 170 m (re. 420 m) corrected nominal interferences of 176 and 451 m (re. 516, 576 and 581 m) were determined. Larger interferences tended to require higher implantation forces for seating (R2 = 0.319, p = 0.19, Fig. 3), whereas torque capacity decreased very slightly with interference (R2 = 0.084, p = 0.33, respectively, Fig. 4). Neither result was significant. The mean torque capacity for all interferences was 26.5 ± 4.1 N m.
Fig. 4. Experimentally determined and calculated torque capacity T (for the 3 bone qualities, μ = 0.4) in relation to the corrected nominal (for the experiment) and the actual interference (for the model). The circled experimental data point refers to the specimen, which was used for the FE model.
Fig. 5. Elements which exceed the yield strain during implantation for the medium quality bone (von Mises plastic strain is shown in the color bar; Young’s modulus: 354 MPa; friction coefficient μ = 0.4).
A. Gebert et al. / Medical Engineering & Physics 31 (2009) 160–164
163
Table 1 Calculated implantation forces and torque capacities for the different interferences, bone qualities, friction coefficients (μ), and the ratio of “torque capacity” to “implantation force” (normalised to model 2). Model
Bone quality (MPa)
μ
Radial interference (m)
Implantation force (N)
Torque capacity (N m)
Torque capacity/implantation force
1 2 3 4 5 6 7
354 354 354 354 354 150 500
0.4 0.4 0.4 0.6 0.8 0.4 0.4
32 85 170 85 85 85 85
1000 3011 5011 4558 6255 1516 4195
16 35 38 41 47 14 50
1.38 1.00 0.65 0.77 0.65 0.79 1.03
Model 1 with a nominal interference of 0 m results in an actual interference of 32 m due to the pre-load of 1000 N.
3.2. FE model Better bone quality and higher interferences required higher implantation forces (Fig. 3). The slope of the force-interference relation decreased at the onset of plastic deformation. Onset occurred at lower interferences with increasing friction coefficient (μ = 0.4: 57 m, Fig. 5; μ = 0.6: 28 m; μ = 0.8: 16 m). At an interference of 170 m the whole head had plastified for all friction coefficients and bone qualities. After plastification of the whole head, calculation of the implantation force was not evaluated further. Torque capacity increased with bone quality and showed a bi-linear dependency on the interference. Only little increase after 85 m interference was achieved for all bone qualities (Fig. 4). A torque capacity of 30 N m was estimated for an interference of 70 m, which required an implantation force of 2400 N (medium quality bone, μ = 0.4). Higher friction coefficients were associated with higher implantation forces and higher torque capacities (models 2, 4, 5 in Table 1). Lower bone stiffness led to lower torque capacity and lower implantation forces (models 2, 6, 7 in Table 1). The ratio of “torque capacity” to “implantation force” represents the ratio of “primary stability” to “loading of the bone during implantation”. This ratio was higher for smaller interferences (models 1–3 in Table 1). Increasing the friction coefficient as well as decreasing the bone quality reduced this ratio (models 2, 4, 5 re. 2, 6, 7 in Table 1).
4. Discussion Greater interferences might be expected to increase the torque capacity. However, the experimentally measured torque capacities were found to be rather independent of interference, although higher interferences tended to require higher implantation forces. The discrepancy could be due to abrasion or plastic deformation of the bone during implantation. Assuming that primary stability is provided only by the elastic deformation component of the bone, no further improvement would be achieved after full plastic deformation of the bone (71 m for fully developed circumferential plasticity and 172 m for the entire bone, Fig. 5). The small but steady increase in post-yield torque capacity predicted
by the FE model was not observed in the experimental data (Fig. 4). This could be due to abrasion occurring in the experiment, which is not represented by the plastic material law used in the model. “Rough” prosthesis and bone surfaces may provide only local traction until bone asperities have been deformed or abraded and full surface contact has been attained. Marked differences were found between nominal and corrected nominal interferences which were probably due to low reaming accuracy. This problem would lead to difficulties in achieving consistent seating of the prosthesis on the bone with reasonable forces in clinical practice, especially since manual reaming would introduce even more variability. The ratio of “torque capacity” to “implantation force” decreased with increasing friction coefficient indicating that a higher implantation force will be needed for higher friction coefficients to achieve similar stability. The torque-to-force ratio also decreases with poor bone quality, indicating that stability could be reduced in soft bone, as plastic deformation starts earlier. Joint friction moments of large diameter metal-on-metal resurfacing implants of up to 7.9 N m have been measured [15]. The torque capacities observed in this study even at low interferences are clearly higher. This suggests that only small interferences are necessary to obtain primary implant stability and that only small implantation forces in the range of joint loads during every day activities are required. Furthermore, it can be concluded, that high interferences will cause excessive bone damage. No viscoelastic effects were explicitly taken into account. This has to be viewed as a limitation as a reduction in pressfit could potentially occur due to relaxation over time [16]. However, mean equilibrium stress for cancellous bone is stated to be about 80% of the peak applied stress [17]. This is much less than the (up to) 700% greater torque capacity that would be predicted by extrapolating the elastic part of the torque-interference curve (Fig. 4) than that actually measured. Most of this loss of press-fit is, therefore, attributed to plastic failure, rather than to viscoelasticity. The findings of this study indicate that an implantation force of about 2400 N is sufficient to achieve a torque capacity of about 30 N m (with an actual interference of ∼70 m). Such a scenario should provide sufficient primary stability and limit the possibility of bone damage and neck fracture
164
A. Gebert et al. / Medical Engineering & Physics 31 (2009) 160–164
[4]. The problem of how to achieve implantation conditions as accurately as has been shown to be required remains a challenge to be solved in the future. Acknowledgment We would like to thank DePuy International for providing the implants and implantation tools. Conflict of interest The study was supported by DePuy International in respect of provision of the prostheses. There was no other financial and personal relationships with other people or organizations. References [1] Schmalzried TP, Fowble VA, Ure KJ, Amstutz HC. Metal on metal surface replacement of the hip. Technique, fixation, and early results. Clin Orthop Relat Res 1996:106–14. [2] Lilikakis AK, Vowler SL, Villar RN. Hydroxyapatite-coated femoral implant in metal-on-metal resurfacing hip arthroplasty: minimum of two years follow-up. Orthop Clin North Am 2005;36:215–22. [3] Amstutz HC, Campbell PA, Le Duff MJ. Fracture of the neck of the femur after surface arthroplasty of the hip. J Bone Joint Surg Am 2004;86-A:1874–7. [4] Morlock MM, Bishop NE, R¨uther W, Delling W, Hahn M. Biomechanical, morphological and histological analysis of early failures in hip resurfacing arthroplasty. J Eng Med 2006;220:333–44. [5] Ritter MA, Lutgring JD, Berend ME, Pierson JL. Failure mechanisms of total hip resurfacing: implications for the present. Clin Orthop Relat Res 2006;453:110–4.
[6] Jasty M, Bragdon C, Burke D, O’Connor D, Lowenstein J, Harris WH. In vivo skeletal responses to porous-surfaced implants subjected to small induced motions. J Bone Joint Surg Am 1997;79:707–14. [7] Pilliar RM, Lee JM, Maniatopoulos C. Observations on the effect of movement on bone ingrowth into porous-surfaced implants. Clin Orthop Relat Res 1986:108–13. [8] Huiskes R, Strens PH, van HJ, Slooff TJ. Interface stresses in the resurfaced hip. Finite element analysis of load transmission in the femoral head. Acta Orthop Scand 1985;56:474–8. [9] Shybut GT, Askew MJ, Hori RY, Stulberg SD. Computational stress analysis of cup replacement hip arthroplasty. Trans Am Soc Artif Intern Organs 1979;25:24–6. [10] 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: 505–11. [11] Wirtz DC, Schiffers N, Pandorf T, Radermacher K, Weichert D, Forst R. Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. J Biomech 2000;33:1325–30. [12] Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech 2004;37:27–35. [13] Morgan EF, Keaveny TM. Dependence of yield strain of human trabecular bone on anatomic site. J Biomech 2001;34:569–77. [14] Grant JA, Bishop NE, G¨otzen N, Sprecher C, Honl M, Morlock MM. Artificial composite bone as a model of human trabecular bone: The implant-bone interface. J Biomech 2007;40:1158–64. [15] Bishop NE, Waldow F, Morlock MM. Friction moment of large metalon-metal hip joint bearings and other modern designs. Med Eng Phys, 2008 Feb 19, in press [Epub ahead of print]. [16] Norman TL, Ackerman ES, Smith TS, Gruen TA, Yates AJ, Blaha JD, et al. Cortical bone viscoelasticity and fixation strength of pressfit femoral stems: an in-vitro model. J Biomech Eng 2006;128: 13–7. [17] Bredbenner TL, Davy DT. The effect of damage on the viscoelastic behavior of human vertebral trabecular bone. J Biomech Eng 2006;128:473–80.