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Effect of Hip Stem Taper on Cement Stresses

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Abstract

The aim of this study was to use finite element models to investigate the effect of the design of the taper of polished, collarless, total hip replacement femoral components on stresses in the cement mantle surrounding the component. A single-taper prosthesis, double-taper prosthesis, and triple-taper prosthesis were compared. Peak stresses and stress distributions in the cement mantle were found to be a function of taper design, although the differences between designs were minor. Using a probability of failure technique based on the initial cement stress distribution, a triple-taper prosthesis was predicted to cause less cement mantle damage (0.15% of the volume of the cement mantle failing after 20 million loading cycles) than a double-taper prosthesis (0.74%) or a single-taper prosthesis (1.50%). Further research is required to confirm this finding.

Cemented total hip arthroplasty remains the standard treatment for patients with disabling hip disorders. When all patient groups are considered, the cumulative frequency of revision of cemented hip prostheses is <3% in 10 years.¹ However, the challenge of aseptic loosening of prostheses remains, particularly in young and active patients because they place heavy mechanical demands on their reconstructed joints. The design of the prosthesis is also an important factor in aseptic loosening. Although the precise etiology of aseptic loosening remains unclear, several authors have proposed that accumulation of damage in the cement mantle is significant.^1,2

The design philosophy underpinning all polished, collarless, tapered total hip replacement femoral components is the minimization and accommodation of cement damage. In principle, a polished taper and the absence of a collar and distal support allow a prosthesis to subside within the cement mantle and accommodate cumulative permanent deformations of the cement while maintaining a compressive load transfer between prosthesis and cement and cement and bone. This concept was first demonstrated in the Exeter prosthesis (Stryker Orthopaedics, Limerick, Ireland). Although Roentgen stereophotogrammetric analysis has shown that all prostheses subside, evidence suggests that most of the subsidence of the Exeter prosthesis occurs between stem and cement rather than between cement and bone or within bone.³ It is unclear if this subsidence is due to creep of the cement mantle or to the gradual breaking of the cement mantle as a result of accumulated fatigue fractures. However, the evidence suggests that cement cannot creep enough to account for the amount of subsidence of the stems seen clinically and experimentally, and that subsidence is caused by cement cracking.⁴

Regardless of the exact mechanism of subsidence, efforts to design stems that minimize cement stresses continue. The aim of this study was to use a finite element model of the implanted proximal femur to examine how stresses in the cement mantle surrounding polished, collarless, tapered, total hip replacement femoral prostheses result from the type of taper used in the prosthesis design.

Materials and Methods

Prosthesis Designs
Commercially available, polished, collarless, tapered, total hip replacement femoral prostheses designs can be classified into three categories, single-taper prostheses, double-taper prostheses, and triple-taper prostheses. Single-taper prostheses (Figure 1A) feature a reduction in medial-lateral dimension (taper) in the frontal plane, but have a constant anteroposterior dimension when moving distally along the stem. Double-taper prostheses (Figure 1B) feature tapers in the frontal plane and sagittal plane. Triple-taper prostheses (Figure 1C) include a reduction in anteroposterior dimension through the cross section of the prosthesis when moving in the lateral to medial direction (the third taper), in addition to tapers in the frontal plane and sagittal plane. The third taper increases the area of prosthesis-cement contact and reduces cement stresses. It also limits relative movement between prosthesis and cement and improves proximal loading of the femur. In this study, the polished Charnley flatback prosthesis (DePuy International Ltd., a Johnson and Johnson Company, Leeds, UK) was used as an example of a typical single-taper prosthesis; the Exeter prosthesis (Stryker UK Ltd., Newbury, UK) was used as an example of a typical double-taper prosthesis, and the C-stem prosthesis (DePuy International Ltd., a Johnson and Johnson Company, Leeds, UK) was used as an example of a typical triple-taper prosthesis.

Finite Element Model Geometry
The finite element model of the femur was based on a computer-aided design (CAD) model of the Sawbones (Sawbones Europe, Malmo, Sweden) third-generation composite femur biomechanical model.^5,6 The CAD models of the prostheses were supplied by DePuy International Ltd. The prostheses were implanted in a neutral position central to the canal using the centerline of the medullary canal and the center of the femoral head as guides. Small adjustments to the prosthesis position (translations of up to 2 mm and rotations of up to 2°) were made to prevent geometrical complications such as interference of the prosthesis and the cortical bone.

In the proximal region of the femur, where cemented prostheses are typically supported in cancellous bone, a 2-mm layer of cement was generated around the prosthesis. To prepare for the proximal femur to receive the double taper prosthesis and the triple taper prosthesis, the femur is broached using a tool introduced at the piriformis fossa and directed along the long axis of the femur. The presence of the broaching tool along the long axis of the femur causes the removal of some cancellous bone proximal to the final position of the prosthesis. This removal results in a cavity, which is filled with cement when prosthesis cementation is completed. However, this cement was not added to any of the models. Instead, it was assumed that the cancellous bone would remain. This assumption, which simplified the modelling, was reasonable because of the nature of the load transfer in the proximal femur and the small difference in the relevant materials and properties of cement and cancellous bone. It was assumed that the cement would fill the canal in the distal region.

To avoid end bearing, no cement distal to the tip of the prosthesis was modelled. (Both C-stem prostheses and Exeter prostheses are packaged with distal centralizers designed to avoid end bearing of the tip of the prosthesis.) When the cement mantle had been defined, the gap between the external surface of the cement mantle and the cortex in the proximal femur was filled to model the cancellous bone.

The CAD operations helped to position the prosthesis and define the additional geometry required for the representation of the cement and cancellous bone. After the CAD operations had been completed, the solid regions of the model were meshed with second-order tetrahedral structural elements to allow straightforward meshing of the complex geometries involved. The prostheses were meshed with elements with a maximum edge length of 2.4 mm to ensure that sufficient elements were generated to capture the curvature of the external surface of the prosthesis, resulting in a smooth transfer of load from prosthesis to cement. The maximum element edge length was increased to 2.75 mm in the cement mantle, 5 mm in the cancellous bone, and 7 mm in the cortex to reduce computational costs. Finally, a Coulomb friction model using face-to-face contact elements was used to form an interface between the prosthesis and cement (Table). Cross-sectional views of the resulting meshes are shown in Figure 2.

Material Properties
Material properties for the regions of the model corresponding to cortical and cancellous bone were assigned using data supplied by the manufacturer of the model bone. For the purposes of analysis, it was assumed prostheses were manufactured from a generic “high stiffness alloy.” (In practice, the types of prostheses discussed here would be made of stainless steel or cobalt-chromium alloy.) It was assumed that all materials were homogeneous, isotropic, and linear-elastic. Other materials and properties required for the specification of the model are shown in the Table.

Loading and Boundary Conditions
A joint reaction force of 1630 N was applied as a point load to the center of the femoral head or the center of the end plane of the taper in prostheses without femoral heads. The force was applied in an inferior-posterior-lateral direction at an angle of 10° in the frontal plane and 10° in the sagittal plane to the midline of the femur as specified in ISO7206-4.⁷ To simulate the action of the abductor muscles, a superiorly directed distributed force totalling 720 N was applied to nodes on the proximal lateral aspect of the greater trochanter (Figure 2). All nodes at the base of the distal femoral osteotomy were built-in to prevent rigid body motion of the model.

Table

Materials and Other Properties Specified for the Finite Element Model Material Young's modulus (MPa) Poisson's ratio Coefficient of friction Contact Stiffness (N/mm) Cortical bone 19x103 0.3 - - Cancellous bone 250 0.3 - - Prosthesis 220x103 0.3 - - Cement 2.5x103 0.3 - - Prosthesis-cement interface - - 0.22* 2x103† * Data for polished cobalt chromium alloy against acrylic cement.8 † Parameter used in contact element formulation, determined by trial-and-error.

Presentation of Results
Results are presented as plots of tensile stress (first principal stress) in the cement because tensile stresses are the most damaging stresses. Plots of the fraction of the volume of the cement mantle with a particular level of tensile stress (stressed volume plots) are also presented. In turn, Lennon’s and Prendergast’s⁸ method and Murphy’s and Prendergast’s⁹ data allowed the use of tensile stresses in the cement to predict the fraction of the total volume of cement failing after 20 million loading cycles, assuming that hand-mixed cement presented a worst-case scenario. The probability of failure (P_f) of each element with stress between 3 MPa and 10 MPa was calculated by substituting the stresses in each element () into the experimentally derived regression equation:

P_f=0.0018³-0.0391²+0.3595-0.5252

Elements with stresses below 3 MPa were assigned a probability of failure of 0, and elements with stresses above 10 MPa were assigned a probability of failure of 1. The percentage by volume of the cement mantle with a probability of failure greater than 0.5 was then plotted so that the three prosthesis designs could be compared.

Results

Figure 3 shows contour plots of the contact pressure between prosthesis and cement on the anterior half of the prosthesis-cement interface for the three prostheses. For all prostheses, contact pressures were greatest on the medial aspect of the prosthesis close to the osteotomy level. Secondary peaks occurred along the length of the prostheses in regions of high curvature (small radii) and at the tip of the prostheses.

Figure 4 shows plots of tensile stress in the cement at the cement-prosthesis interface at 3 levels in each model — at the proximal osteotomy level (A), on a plane perpendicular to the diaphysial axis of the femur distal to the lesser trochanter (midsection) (B), and at the distal tip of the prosthesis (C). Stresses are plotted as a function of angle from the most medial point on the border of the prosthesis-cement interface, with positive angles representing anterior locations.

For the triple-taper prosthesis, peak cement stresses at the level of the proximal osteotomy occurred in the vicinity of the medial border, with a secondary peak of almost equal magnitude in the posterior lateral region (approximately -135°). Both peaks were associated with regions with a small radius of curvature around the circumference of the prosthesis. At the level of the midsection, the stress peak at the -135° location became dominant.

The double-taper prosthesis showed a different pattern of cement stress at the level of the proximal osteotomy, with two stress peaks 70° to 80° anterior and posterior to the medial aspect of the femur. To a lesser extent, these stress peaks were a feature of the cement stress distribution for the single taper prosthesis and may be a result of the more rectangular cross-sections and decreasing corner radii of the single taper prosthesis and double taper prosthesis. Although the stress peaks occurred at different locations, the magnitudes of the stress peaks of the double taper prosthesis and the triple taper prosthesis were comparable. Both double taper prosthesis and triple taper prosthesis had peak stress magnitudes lower than the single taper prosthesis.

At the level of the midsection, two medial stress peaks for the double-taper prosthesis and single-taper prosthesis remained present. In both cases, the medial stresses were higher than they were in the triple-taper prosthesis. The single-taper prosthesis generated higher stresses than the double-taper prosthesis. Laterally, the triple-taper prosthesis generated higher stresses than both the double-taper prosthesis and the single-taper prosthesis.

Distally, the double-taper prosthesis generated higher stresses than the single-taper prosthesis and the triple-taper prosthesis. This higher stress level may be related to the relative sizes of the tips of the three prostheses.

Figure 5 shows plots of the fraction of the volume of the cement mantle at each level of tensile stress for each prosthesis. Figure 6 shows a prediction of the volume of the cement failure after 20 million cycles for each prosthesis using Lennon’s and Prendergast’s⁸ probability of failure model. The stressed volume plots show that a large fraction of the cement mantles in all three prostheses have low stress. The predicted volume of cement failure after 20 million cycles was greatest for the single taper prosthesis and lowest for the triple-taper prosthesis, despite the fact that the double-taper prosthesis and the triple-taper prosthesis were the only prostheses with cement mantle stresses exceeding 8 MPa (Figure 6). The greater volume of cement in the 5 - 5.99, 6 - 6.99, and 7 - 7.99 MPa bands explains this finding. Similarly, the double-taper prosthesis showed larger volumes of cement in all the bands >3 MPa than the triple-taper prosthesis, explaining why a greater volume of cement was predicted to fail after 20 million cycles in the double taper prosthesis than in the triple-taper prosthesis.

Figure 5: Stressed volume plots showing the percentage volume of cement at a given stress level for the 3 prostheses. Graph A shows the stress bands below 5 MPa and graph B shows the stress bands above 5 MPa. Note the 2 orders of magnitude difference in the y-axis scale for the 2 plots.

Discussion

The results of the finite element analyses show stresses in the cement mantle to be a function of the design of the taper of polished, collarless total hip replacement femoral components. Although peak stresses at the proximal osteotomy level were similar for all prostheses, the shape of the stress distribution as a function of angular position around the prosthesis was influenced by the taper design. The triple-taper prosthesis showed a single stress peak medially, whereas the single-taper prosthesis generated two medial stress peaks, one anterior and one posterior to the most medial aspect. With the double taper prosthesis, two medial stress peaks were discerned, but the anterior peak was more anterior than the anterior peak in the single-taper prosthesis, and the posterior peak was reduced. The remaining stress peak in the posterolateral region occurred at a similar position and was of a similar magnitude for all the prostheses. Conversely, the shapes of the stress distributions were more similar at the midsection than in other areas, but differences in the peak stresses of the midsection were more marked. Peak stresses were greater in the single-taper prosthesis than in the double-taper prosthesis, and stresses in the double-taper prosthesis were greater than stresses in the triple-taper prosthesis. At the distal level, the double-taper prosthesis generated higher stresses than the single-taper prosthesis or the triple-taper prosthesis.

Although taper design influenced the values of the peak stresses and the stress distribution in the cement mantles, predicting the lifetime of the cement mantle for each prosthesis or ranking the performance of each prosthesis on the basis of the present results is challenging. Lennon’s and Prendergast’s probability of failure model has been used to predict cement mantle lifetimes from the initial stress distribution in the cement mantle.⁸ When this model is used, the cement mantle surrounding the triple taper prosthesis is expected to have accumulated less damage after 20 million cycles than the other prostheses. According to the theory that cement mantle failure precedes aseptic loosening, the triple-taper prosthesis has the longest survivorship of the three prostheses.² However, failure of the cement mantle is a non-linear process, and the probability of failure based on the initial stress conditions using the present model may not be reliable in all situations, particularly when variations exist between prosthesis designs. For example, although high focal peak stresses in the cement mantle during the first few loading cycles may result in local cracking, these cracks may stop growing due to changes in the stress distribution caused by the cracks themselves. Cracks that stop growing will tend to remain isolated and not coalesce and result in bulk fracture of the cement mantle. More sophisticated finite element-based techniques able to withstand changes in stress distribution are currently being applied in our unit to help predict cement mantle lifetimes as a function of taper design.

Conclusions

Peak stresses and stress distributions in the cement mantle are a function of prosthesis design for polished, collarless, total hip replacement femoral prostheses despite the minor differences among prosthesis designs. Using a probability of failure technique based on the initial cement stress distribution, the triple taper prosthesis was predicted to delay cement mantle failure longer than the single taper prosthesis or the double taper prosthesis. Further research is required to confirm this finding.

References

1. Malchau H, Herberts P, Garellick G, Söderman P, Eisler T. Prognosis of Total Hip Replacement: Update of Results and Risk-Ratio Analysis for Revision and Re-revision from the Swedish National Hip Arthroplasty Register 1979-2000. Scientific exhibition at the 69th Annual Meeting of the American Academy of Orthopaedic Surgeons. 2002, Dallas.
2. Jasty M, Maloney WJ, Bragdon CR, O’Connor DO, Haire T, Harris WH. The initiation of failure in cemented femoral components of hip arthroplasties. J Bone Joint Surg Br. 1991; 73:551-558.
3. Alfaro-Adrian J, Gill HS, Murray DW. Cement migration after THR. A comparison of charnley elite and exeter femoral stems using RSA. J Bone Joint Surg Br. 1999; 81:130-134.
4. Verdonschot, N. Biomechanical failure scenarios for cemented total hip replacement. Ph.D. Thesis - Catholic University of Nijmegen, 1995; 85-101.
5. Papini M, Zalzal P. Third generation composite femur, Biomechanics European Laboratory: The BEL Repository. http://www.tecno.ior.it/VRLAB/researchers/repository/BEL_repository.html#3rdGenFemur.
6. Viceconti M. The standardized femur solid model, Biomechanics European Laboratory: The BEL Repository. http://www.tecno.ior.it/VRLAB/researchers/repository/BEL_repository.html#3rdGenFemur.
7. International Organization for Standardization. ISO 7206-4 Implants for surgery - Partial and total hip joint prostheses - Part 4: Determination of endurance properties of stemmed femoral components with application of torsion: 1989.
8. Lennon AB, Prendergast PJ. Evaluation of cement stresses in finite element analyses of cemented orthopaedic implants. J Biomech Eng. 2001; 123:623-628.
9. Murphy BP, Prendergast PJ. On the magnitude and variability of the fatigue strength of acrylic bone cement. International Journal of Fatigue. 2000; 22:855-864.

Authors

From *Bioengineering Science Research Group, School of Engineering Sciences, University of Southampton, Southampton, and †The John Charnley Research Institute, Wrightington Hospital for Joint Disease, Hall Lane, Appley Bridge, Wigan, United Kingdom.