- Email: [email protected]
Stress analysis of the proximo-medial femur after total hip replacement
Stress analysis of the proximo-medial total hip replacement
femur after
P.J. Prendergast and D. Taylor Biomaterials Research Centre, Department of Mechanical Engineering, Trinity College, Dublin, Ireland Received November
1989, accepted December 1989
Abstract S&es+induced bone loss in theproximo-mediafur has been ia!sntz$ed as a factor hading to ioosening in th artijicial hip joint. In an e$ort to develop a quantitative understanding of the stress dtitribution that causes bone loss, axial and hoop stresses in the medial calcar of thefimur have been a!&rmined a+ total hip replacement, usingfinite element stress analysti. Stress distributions fir a high and a low Young’s modulus prosthesis material are compared for both collared and uncollured prosthks a!signs.i% use of a low-modulus material, and of a collar, are predicted to be advantageous, giving rise to proximo-medial stress patterns similar to those of the normal, intact femur.
Keywords: Bone loss, calcar femur stress, prosthesis design
INTRODUCTION Bone loss in the proximal segment of the medial side of the femur after hip replacement has been reported in many follow-up studies. For example, Beckenbaugh and Ilstrup’ in a review of 333 cases, reported resorption was approximately 2 mm in most cases, and occasionally much higher. The importance of the bone loss phenomenon is that it is one initiation mechanism for loosening of the prosthesis within the medullary canal. Hence, to maximize joint lifetimes, particular attention must be given to the effect of prosthesis design on the stress distribution in this segment of the femur; not only on the stress immediately after insertion but also on how the stress changes as bone loss develops after insertion2. One of the suggested causes of bone loss is ‘stress shielding’, whereby stresses are reduced because the prosthesis takes the stress that would normal1 be transferred to the proximo-medial femur. J tress analyses reported in the literature support this idea. For example, Cook et aL3, Lewis et al? and Fagan and Lee5 have investi ted femur stress after total hip replacement. Cooy et aL3, in a two-dimensional model, varied prosthesis Young’s modulus and found that low Young’s modulus prostheses generated higher axial stresses. Lewis et aL4, in a three-dimensional model with about 5000 de ess of freedom, found that Young’s modulus had a e same effect on axial stress, and furthermore that a prosthesis without a collar was ineffective in transmitting axial stress no matter how low the prosthesis Young’s modulus. The hoyp;tress distributiyn was not reported by Lewis et . . agan and Lee , in a three-dimensional finite element model with over 6000 degrees of freedom, Correspondence
to: Dr David Taylor
analysed both axial and hoop stresses. They found that the presence of a collar increased the axial compressive stress and reduced the tensile hoop stress. To reduce the extent of ‘stress shielding’, some work has been done to develop polymer composite prostheses of low stiffness (for example, Christel et aL6 and Henn et uZ.~).Such low stiffness prostheses, according to the stress analysis results, would transfer more stress to the proximo-medial femur and therefore reduce the stimulus for bone loss. The work presented here is a further examination of the effect of prosthesis Young’s modulus and of the collar on that part of the femur where bone loss is observed atier total hip replacement. Such results as these are a starting point for further study into mechanistic methods to simulate bone remodelling.
METHODS A three-dimensional finite element model of the artificial hip joint was used as shown in Figure 1. The model, which was constructed using the PAFEC finite element code, has 12416 degrees of freedom, making it one of the largest models available for this isoparametric brick a plication. Twenty-noded ePements and 15noded isoparametric wedge elements were used throughout. A 3 kN load was a plied at an angle of 20” to the femur shaft. An aIZductor load of 1.25 kN was applied at an angle of 20” over the roximal third of the greater trochanter. An illio-tibi s tract load of 250 N was a plied in a distal direction parallel to the shaft of the Pemur. Two values of prosthesis Young’s modulus were analysed; 200 GPa, representing a Cr/Co material, and 25 GPa, representing a particulate composite material under development in our laboratory7. Cement Young’s modulus was 2.3 GPa and the cortical and cancellous
0 1990 Butterworth-Heinernann for BES 0141-5425/90/050379-04
J. Biomed. Eng. 1990, Vol. 12, September
379
Stress analysis
in th
femur: PJ Prendmgast and D. Taylor such sliding is to be expected since no adhesive bond is formed between the cement and the collar or the bone and the collar. Further details of the model, and stress data, are presented elsewhere’, where it is shown that results from the model compare favourably with those from previous workers.
RESULTS Stresses on the cement-femur interface are resented for the region extending 23 mm disJ to the femur neck. Axial stresses are plotted in Figure 2 stresses in Figure 3. A cross-section and hoo throu h tKe three-dimensional mesh is shown alongside tRese figures to indicate exact1 where the stress has been computed. To allow fuJ er assessment of the finite element, a closer view of a cross-section of the relevant portion of the mesh is shown in F&p-e 4, where the element properties are also indicated. DISCUSSION The above results should be compared with reported values for stresses in the same region of the intact femur. Considering the axial stress, strain-gauging experiments by Oh and Harris9 and by Engelhardt and Saha (personal communication) gave stress values (when adjusted to the 3 kN applied load and assuming E= 17.6GPa for bone) of 49.7 MPa and 47.9 MPa, respectively, for the most proximal gauge
Figure femur
1
Finite element mesh of the prosthesis implanted in the
bone moduli were 17.6 GPa and 300 MPa, respectively. Collar-femur interface nodes were uncoupled, and the direction of their de ees of freedom was changed to the angle of the co1?rar to allow frictionless sliding of the collar on the femur neck. In reality,
380
J. Biomed. Eng. 1990, Vol. 12, September
I
40
30
20
10
I
10
20
Figure 2 Axial stresses in a region extending 23 mm below the femur neck. 0 collared prosthesis, E = 25 GPa; A collared prosthesis, E = 200 GPa; L collared prosthesis, E = 200 GPa (collar-on-femur slip prevented); 0 uncollared prosthesis, E = 25 GPa; A uncollared prosthesis, E = 200 GPa. Numbers on the vertical axis correspond to numbered positions on the model, as shown
Stress analysis in thejmur:PJ
Prenhgast
and D. Taylor
given in Figure 3 where a small tensile hoop stress is observed. It is our view (and also the view of Fagan and Lee5) that the value and sign of the hoop stress may be more critical than its small magnitude would suggest. One could postulate that bone damage is more easily induced in the hoop direction than in the axial direction due to the fact that osteons are aligned axially. The concept of reduced ‘stress shielding’, used to argue the case for the use of low stiffness prostheses, is not entirely ade uate. As one theory suggestslo, bone will remode 7 to a change in any component of the stress state. Hence, the fact that the tensile hoop stress is increased in uncollared low stiffness rostheses compared with the hoop stress in uncol Pared higher stiffness prostheses cannot be overlooked when selecting prosthesis material. Further work to examine the importance of each component of the stress state is required before confident predictions of a reduction in bone loss with low stiffness prostheses can be made. CONCLUSIONS
I
5
I
,
I
10
Figure 3 Hoop stresses in a region extending 23 mm below the femur neck (for key see Figure 2)
on the medial side. Finite element results for the intact femur by Fagan and Lee5 give approximately 40 MPa axial compressive stress in the calcar region. Comparing these values with those in Figure2 for the femur after total hip replacement shows that a collared, low stiffness prosthesis can achieve this axial stress level, but without a collar, a low stiffness prosthesis can only achieve this stress level much further down the femoral neck. A higher stiffness prosthesis confers lower axial stress throughout the bone region under study. Figure 2 also shows that allowing for collar-on-femur sli profoundly affects the proximomedial stress distri1 ution predicted in the bone. Considering hoop stresses, Fagan and Lee5 reported compressive stress in the intact femur of maximum magnitude 3 MPa. However, Figure 3 shows that uncollared prostheses create tensile hoop stresses. This is attributable to the wedging effect of the tapered prosthesis stem. For collared prosthesis, and particularly for the Sheehan prosthesis of the present study, which has a large stiff medial collar, this wedging effect does not operate and the result is a compressive hoop stress. This contrasts with the tensile hoop stress results reported by Fagan and Lee5 for a collared Exeter prosthesis. Part of the reason is that our finite element model allows collar-on-femur sliding and hence no shear stress is directly transferred to the medial femur neck and the corresponding radial displacement does not occur. Therefore, it would seem that if the slip is modelled, the model simulates similar deformation in the calcar segment to that which would occur if that segment were still part of an intact femur. Hence, the stress state is the same, i.e. compression. In support of this reasoning, results of a simulation where sliding was not allowed are
Collared prostheses create higher compressive axial stresses and higher compressive hoop stresses. Since this stress state seems to approximate more closely to the intact femur stress state, then a collar should reduce the driving force for bone loss. This can only be the case if collar-on-femur support is permanent. A low stiffness rosthesis causes higher axial stresses, whether co Plared or uncollared. Therefore,
Figure 4 Close-up view of a cross-section of the finite element mesh at the interface between the collar and the femur and cement (P = prosthesis, C = cement, B = bone)
J. Biomed. Eng. 1990, Vol. 12, September
381
Stressanalysisin thefour: PJ. Pnnabgast and D. Taylor
the use of a low stiffness material such as a polymer corn osite should be advantageous. A Pow stiffnessprosthesis causes higher tensile hoop stresses if uncollared and higher compressive hoop stresses if collared. Thus in terms of reproducin the intact femur stress state, the use of a low stii! ness material, with a collar that has long-term effectiveness, is an optimal rosthesis design. To assess proper Py the effect of a collar using the finite element method, it is necessary to decouple the nodes on the collar-femur interface to allow sliding.
ACKNOWLEDGJMENTS The authors acknowledge financial assistance from EOLAS (The Irish Science and Technology A ency) and thank Mr Thilaksri Gunawardhana, !4enior Scientific Officer with EOLAS, for his advice on finite element modelling.
RETERENCES 1. Beckenbaugh RD, Il.&up DM. Total hip arthroplasty - a review of three hundred and thirty-three cases with long follow up. JBoru Joint Surg; 1978; 60A: 306-13.
382
J. Biomed. Eng. 1990, Vol. 12, September
2. Huiskes R. Stress patterns, failure modes and bone remodelling. In: Fitzgerald, R ed. Non-Cemented Total Hip Ati~roprCrr~,New York: Raven Press, 1988. 3. Cook SD, Klawitter J, Weinstein AM. The influence of design parameters on calcar stresses following femoral head arthroplasty. JBiomed Mat Z&s 1980; 14: 133-44. 4. Lewis& Askew MJ, Wixon RL, Kramer GM, Tarr RR. The influence of prosthetic stem stiffness and of a calcar collar on the stresses in the proximal end of the femur with a cemented femoral component. J BoneJoint Surg 1984; 66A: 280-6. 5. Fagan MJ, Lee AJC. Role of the collar on the femoral stem of cemented total hip replacements. JBiomed Eng 1986; 8:
295-304. 6. Christel P, Meunier A, Leclercq S, Bouquet Ph, Buttazzoni B. Development
of a carbon-carbon
hip prosthesis.
JBiomed Mat Bes 1987; 21: 191-218. 7. Henn G, Prendergast PJ, Taylor D. An assessment of a particulate composite material for use in hip joint prostheses. In: Taylor D, Taplin DMR, eds. In hceedings ofth 6th ZriskMaterials Forum, Dublin: Trinity College, 1989. 8. Prendergast PJ, Monaghan J, Taylor D. Materials selection in the artificial hip joint using the finite element stress analysis. Clinical Materials 1989; 4: 361-76. 9. Oh I, Harris WH. Proximal strain distribution in the loaded femur. JBoruJoint Surg 1978; 6OA: 75-85. 10. Cowin S C. Bone remodelling of diaphyseal surfaces by torsional loads: theoretical predictions. JBiomeck 1987; 20: 1111-20.
femur after
P.J. Prendergast and D. Taylor Biomaterials Research Centre, Department of Mechanical Engineering, Trinity College, Dublin, Ireland Received November
1989, accepted December 1989
Abstract S&es+induced bone loss in theproximo-mediafur has been ia!sntz$ed as a factor hading to ioosening in th artijicial hip joint. In an e$ort to develop a quantitative understanding of the stress dtitribution that causes bone loss, axial and hoop stresses in the medial calcar of thefimur have been a!&rmined a+ total hip replacement, usingfinite element stress analysti. Stress distributions fir a high and a low Young’s modulus prosthesis material are compared for both collared and uncollured prosthks a!signs.i% use of a low-modulus material, and of a collar, are predicted to be advantageous, giving rise to proximo-medial stress patterns similar to those of the normal, intact femur.
Keywords: Bone loss, calcar femur stress, prosthesis design
INTRODUCTION Bone loss in the proximal segment of the medial side of the femur after hip replacement has been reported in many follow-up studies. For example, Beckenbaugh and Ilstrup’ in a review of 333 cases, reported resorption was approximately 2 mm in most cases, and occasionally much higher. The importance of the bone loss phenomenon is that it is one initiation mechanism for loosening of the prosthesis within the medullary canal. Hence, to maximize joint lifetimes, particular attention must be given to the effect of prosthesis design on the stress distribution in this segment of the femur; not only on the stress immediately after insertion but also on how the stress changes as bone loss develops after insertion2. One of the suggested causes of bone loss is ‘stress shielding’, whereby stresses are reduced because the prosthesis takes the stress that would normal1 be transferred to the proximo-medial femur. J tress analyses reported in the literature support this idea. For example, Cook et aL3, Lewis et al? and Fagan and Lee5 have investi ted femur stress after total hip replacement. Cooy et aL3, in a two-dimensional model, varied prosthesis Young’s modulus and found that low Young’s modulus prostheses generated higher axial stresses. Lewis et aL4, in a three-dimensional model with about 5000 de ess of freedom, found that Young’s modulus had a e same effect on axial stress, and furthermore that a prosthesis without a collar was ineffective in transmitting axial stress no matter how low the prosthesis Young’s modulus. The hoyp;tress distributiyn was not reported by Lewis et . . agan and Lee , in a three-dimensional finite element model with over 6000 degrees of freedom, Correspondence
to: Dr David Taylor
analysed both axial and hoop stresses. They found that the presence of a collar increased the axial compressive stress and reduced the tensile hoop stress. To reduce the extent of ‘stress shielding’, some work has been done to develop polymer composite prostheses of low stiffness (for example, Christel et aL6 and Henn et uZ.~).Such low stiffness prostheses, according to the stress analysis results, would transfer more stress to the proximo-medial femur and therefore reduce the stimulus for bone loss. The work presented here is a further examination of the effect of prosthesis Young’s modulus and of the collar on that part of the femur where bone loss is observed atier total hip replacement. Such results as these are a starting point for further study into mechanistic methods to simulate bone remodelling.
METHODS A three-dimensional finite element model of the artificial hip joint was used as shown in Figure 1. The model, which was constructed using the PAFEC finite element code, has 12416 degrees of freedom, making it one of the largest models available for this isoparametric brick a plication. Twenty-noded ePements and 15noded isoparametric wedge elements were used throughout. A 3 kN load was a plied at an angle of 20” to the femur shaft. An aIZductor load of 1.25 kN was applied at an angle of 20” over the roximal third of the greater trochanter. An illio-tibi s tract load of 250 N was a plied in a distal direction parallel to the shaft of the Pemur. Two values of prosthesis Young’s modulus were analysed; 200 GPa, representing a Cr/Co material, and 25 GPa, representing a particulate composite material under development in our laboratory7. Cement Young’s modulus was 2.3 GPa and the cortical and cancellous
0 1990 Butterworth-Heinernann for BES 0141-5425/90/050379-04
J. Biomed. Eng. 1990, Vol. 12, September
379
Stress analysis
in th
femur: PJ Prendmgast and D. Taylor such sliding is to be expected since no adhesive bond is formed between the cement and the collar or the bone and the collar. Further details of the model, and stress data, are presented elsewhere’, where it is shown that results from the model compare favourably with those from previous workers.
RESULTS Stresses on the cement-femur interface are resented for the region extending 23 mm disJ to the femur neck. Axial stresses are plotted in Figure 2 stresses in Figure 3. A cross-section and hoo throu h tKe three-dimensional mesh is shown alongside tRese figures to indicate exact1 where the stress has been computed. To allow fuJ er assessment of the finite element, a closer view of a cross-section of the relevant portion of the mesh is shown in F&p-e 4, where the element properties are also indicated. DISCUSSION The above results should be compared with reported values for stresses in the same region of the intact femur. Considering the axial stress, strain-gauging experiments by Oh and Harris9 and by Engelhardt and Saha (personal communication) gave stress values (when adjusted to the 3 kN applied load and assuming E= 17.6GPa for bone) of 49.7 MPa and 47.9 MPa, respectively, for the most proximal gauge
Figure femur
1
Finite element mesh of the prosthesis implanted in the
bone moduli were 17.6 GPa and 300 MPa, respectively. Collar-femur interface nodes were uncoupled, and the direction of their de ees of freedom was changed to the angle of the co1?rar to allow frictionless sliding of the collar on the femur neck. In reality,
380
J. Biomed. Eng. 1990, Vol. 12, September
I
40
30
20
10
I
10
20
Figure 2 Axial stresses in a region extending 23 mm below the femur neck. 0 collared prosthesis, E = 25 GPa; A collared prosthesis, E = 200 GPa; L collared prosthesis, E = 200 GPa (collar-on-femur slip prevented); 0 uncollared prosthesis, E = 25 GPa; A uncollared prosthesis, E = 200 GPa. Numbers on the vertical axis correspond to numbered positions on the model, as shown
Stress analysis in thejmur:PJ
Prenhgast
and D. Taylor
given in Figure 3 where a small tensile hoop stress is observed. It is our view (and also the view of Fagan and Lee5) that the value and sign of the hoop stress may be more critical than its small magnitude would suggest. One could postulate that bone damage is more easily induced in the hoop direction than in the axial direction due to the fact that osteons are aligned axially. The concept of reduced ‘stress shielding’, used to argue the case for the use of low stiffness prostheses, is not entirely ade uate. As one theory suggestslo, bone will remode 7 to a change in any component of the stress state. Hence, the fact that the tensile hoop stress is increased in uncollared low stiffness rostheses compared with the hoop stress in uncol Pared higher stiffness prostheses cannot be overlooked when selecting prosthesis material. Further work to examine the importance of each component of the stress state is required before confident predictions of a reduction in bone loss with low stiffness prostheses can be made. CONCLUSIONS
I
5
I
,
I
10
Figure 3 Hoop stresses in a region extending 23 mm below the femur neck (for key see Figure 2)
on the medial side. Finite element results for the intact femur by Fagan and Lee5 give approximately 40 MPa axial compressive stress in the calcar region. Comparing these values with those in Figure2 for the femur after total hip replacement shows that a collared, low stiffness prosthesis can achieve this axial stress level, but without a collar, a low stiffness prosthesis can only achieve this stress level much further down the femoral neck. A higher stiffness prosthesis confers lower axial stress throughout the bone region under study. Figure 2 also shows that allowing for collar-on-femur sli profoundly affects the proximomedial stress distri1 ution predicted in the bone. Considering hoop stresses, Fagan and Lee5 reported compressive stress in the intact femur of maximum magnitude 3 MPa. However, Figure 3 shows that uncollared prostheses create tensile hoop stresses. This is attributable to the wedging effect of the tapered prosthesis stem. For collared prosthesis, and particularly for the Sheehan prosthesis of the present study, which has a large stiff medial collar, this wedging effect does not operate and the result is a compressive hoop stress. This contrasts with the tensile hoop stress results reported by Fagan and Lee5 for a collared Exeter prosthesis. Part of the reason is that our finite element model allows collar-on-femur sliding and hence no shear stress is directly transferred to the medial femur neck and the corresponding radial displacement does not occur. Therefore, it would seem that if the slip is modelled, the model simulates similar deformation in the calcar segment to that which would occur if that segment were still part of an intact femur. Hence, the stress state is the same, i.e. compression. In support of this reasoning, results of a simulation where sliding was not allowed are
Collared prostheses create higher compressive axial stresses and higher compressive hoop stresses. Since this stress state seems to approximate more closely to the intact femur stress state, then a collar should reduce the driving force for bone loss. This can only be the case if collar-on-femur support is permanent. A low stiffness rosthesis causes higher axial stresses, whether co Plared or uncollared. Therefore,
Figure 4 Close-up view of a cross-section of the finite element mesh at the interface between the collar and the femur and cement (P = prosthesis, C = cement, B = bone)
J. Biomed. Eng. 1990, Vol. 12, September
381
Stressanalysisin thefour: PJ. Pnnabgast and D. Taylor
the use of a low stiffness material such as a polymer corn osite should be advantageous. A Pow stiffnessprosthesis causes higher tensile hoop stresses if uncollared and higher compressive hoop stresses if collared. Thus in terms of reproducin the intact femur stress state, the use of a low stii! ness material, with a collar that has long-term effectiveness, is an optimal rosthesis design. To assess proper Py the effect of a collar using the finite element method, it is necessary to decouple the nodes on the collar-femur interface to allow sliding.
ACKNOWLEDGJMENTS The authors acknowledge financial assistance from EOLAS (The Irish Science and Technology A ency) and thank Mr Thilaksri Gunawardhana, !4enior Scientific Officer with EOLAS, for his advice on finite element modelling.
RETERENCES 1. Beckenbaugh RD, Il.&up DM. Total hip arthroplasty - a review of three hundred and thirty-three cases with long follow up. JBoru Joint Surg; 1978; 60A: 306-13.
382
J. Biomed. Eng. 1990, Vol. 12, September
2. Huiskes R. Stress patterns, failure modes and bone remodelling. In: Fitzgerald, R ed. Non-Cemented Total Hip Ati~roprCrr~,New York: Raven Press, 1988. 3. Cook SD, Klawitter J, Weinstein AM. The influence of design parameters on calcar stresses following femoral head arthroplasty. JBiomed Mat Z&s 1980; 14: 133-44. 4. Lewis& Askew MJ, Wixon RL, Kramer GM, Tarr RR. The influence of prosthetic stem stiffness and of a calcar collar on the stresses in the proximal end of the femur with a cemented femoral component. J BoneJoint Surg 1984; 66A: 280-6. 5. Fagan MJ, Lee AJC. Role of the collar on the femoral stem of cemented total hip replacements. JBiomed Eng 1986; 8:
295-304. 6. Christel P, Meunier A, Leclercq S, Bouquet Ph, Buttazzoni B. Development
of a carbon-carbon
hip prosthesis.
JBiomed Mat Bes 1987; 21: 191-218. 7. Henn G, Prendergast PJ, Taylor D. An assessment of a particulate composite material for use in hip joint prostheses. In: Taylor D, Taplin DMR, eds. In hceedings ofth 6th ZriskMaterials Forum, Dublin: Trinity College, 1989. 8. Prendergast PJ, Monaghan J, Taylor D. Materials selection in the artificial hip joint using the finite element stress analysis. Clinical Materials 1989; 4: 361-76. 9. Oh I, Harris WH. Proximal strain distribution in the loaded femur. JBoruJoint Surg 1978; 6OA: 75-85. 10. Cowin S C. Bone remodelling of diaphyseal surfaces by torsional loads: theoretical predictions. JBiomeck 1987; 20: 1111-20.