Tibial knee implant: Comparative Study of Stresses In the Bone of an Implanted Tibia with those in an Intact tibia.

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Garey Taylor
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1 African Biographical Centre Afr J Med Phy, Biomed Eng & Sc, 2010, 2, Tibial knee implant: Comparative Study of Stresses In the Bone of an Implanted Tibia with those in an Intact tibia. *A. Mekonnen Biomedical Engineering Group, University of Sussex, United Kingdom (Received September 16, 2010; Revised October 11, 2010; Accepted October 15, 2010) The stresses in the bone of an implanted tibia are calculated at points around the bone-implant interface and are compared with the stresses at the same points of an identical intact tibia. A graphical method is used to identify those regions around the implant where the change in stress is greatest. The regions where there is a large increase in stress could lead to local micro-cracking of the bone and the regions where there is a large decrease could lead to atrophy and remodelling of the bone. Both effects might be expected to contribute to loosening of the implant. 1. Introduction As with other implants, one of the most common causes of failure in knee implants is the loss of component fixation to the bone. [1, 2] This progressive loosening is generally most prevalent in the tibial component and, with cemented implants, usually occurs at the interface between the cement and the bone whereas, for non-cemented implants, it is caused by remodelling of the cancellous bone that is in direct contact with the implant. [3-11] One of the reasons postulated for loosening is that there is significant remodelling of the bone over time caused by artificially low stresses at certain points around the implant arising from stress shielding due to the high stiffness of the implant as well as artificially high stresses at other points due to the geometry of the implant. In their 1985 paper, Cheal et al wrote that both low stresses and excessively high stresses in regions of the tibia around an implant are thought to result in abnormal bone response and eventual loosening. Finite-element models have been used widely in biomechanics to investigate the stresses within bone in an attempt to improve the performance of implants. In particular, there have been various studies of knee implants [12-17] but none in which the stress distribution in an implanted tibia has been compared directly with that in a corre- sponding intact tibia. The purpose of this study is to consider an implanted non-cemented tibia and to compare the stresses in the bone at points along the interface around the implant with stresses at the self-same points of an equivalent intact tibia. This can be done most easily using stress contour plots. However, contour plots can give, at best, only a qualitative overview in comparing different stress distributions. In the present work, therefore, stresses have been calculated along different paths around the implant and these have been compared with stresses calculated at the same points of the corresponding model of the intact tibia. 2. Materials and method An image data set of a male skeleton was acquired from the National Health Library of America and the data relating to the tissues in and around the tibial bone were exported into a Mimics image-processing software package (Materialise, N.V.). This package is able to isolate tissues of interest based on density threshold and three-dimensional segmentation using a region-growing technique. In this case, the hard tissues of the tibia (cortical and cancellous bone) were identified and Mimics was then able to generate a line-model of the bone. Using another Materialise package, MedCad, *Corresponding author aamekonnen@fc.ul.pt a b c * * ABC Publishers Inc Directories of African Biog rp hy

78 A. Mekonnen this model was modified so that it could be exported into a CAD environment and, after this, was imported into Rhino (Robert McNeel and Associates) where surfaces were fitted to the

) prior to exporting it into the finiteelement package Ansys (Ansys Inc.). A finite-element model was now set up consisting of two volumes one representing the outer cortical bone and the other the interior cancellous bone.

2 78 A. Mekonnen this model was modified so that it could be exported into a CAD environment and, after this, was imported into Rhino (Robert McNeel and Associates) where surfaces were fitted to the lines. Any discontinuities or degradation of the model were repaired at this stage within CadFix (International Techne- Group Inc.) prior to exporting it into the finiteelement package Ansys (Ansys Inc.). A finite-element model was now set up consisting of two volumes one representing the outer cortical bone and the other the interior cancellous bone. A second finite-element model was also set up using the same tibia but with the top resurfaced and with a knee implant (the tibial component of a Johnson & Johnson PFC Sigma knee implant) incorporated into the model. In both cases, the lower part of the tibia was rigidly constrained and the top was subjected to a force of 2.2kN corresponding to approximately three times average body weight. dial and lateral condyles of the intact tibia i.e. The same point loads as were used with the implanted tibia; the second loading condition considered was uniformly-distributed pressure acting over the whole area of the articulating surface. Of the two loading conditions evaluated, the uniformly-distributed pressure load was used for the present quantitative comparison of the intact and implanted tibia stresses. See figure 1(b). This is because the actual loading is distributed (albeit with peak pressures at the condyles) and the point-load model gives artificially high stresses in the vicinity of the loading. In both models, the cortical and cancellous bone was assumed to be isotropic, homogeneous and linearly elastic as was the implant. All the components were assumed to have a Poisson s ratio of 0.33 whilst Young s modulus of cortical bone was taken to be 17kN/mm 2 and that of cancellous bone to be (a) Implanted tibia For the implanted tibia, the 2.2kN load was split in the ratio 3:2 with 60% of the load acting on the medial side and 40% on the lateral as shown in figure 1(a). [13, 18] For the intact tibia, two different loading conditions were evaluated each of which the same resultant load of 2.2kN. The first condition considered was: two point loads acting directly on the me- (b) Intact tibia Figure 1: Finite element model of the intact and implanted tibia. 0.3kN/mm 2. The metal (titanium) of the implant was assumed to have a Young s modulus of 110kN/ mm 2 whereas, for the plastic insert (polyethelene), it was 0.5kN/mm 2. All the material properties except for the cortical bone are taken from the paper by Taylor et al.; [13] for both diaphyseal and metaphyseal cortical bone, a modulus of elasticity 17kN/mm 2 is assumed.

Afr J Med Phy, Biomed Eng & Sc, 2010, 2, 77-84 79 [19] Each model was meshed with quadratic tetrahedral elements as shown in Fig. 1.

3 Afr J Med Phy, Biomed Eng & Sc, 2010, 2, [19] Each model was meshed with quadratic tetrahedral elements as shown in Fig. 1. In addition, for the implanted tibia, the press-fit between the bone and the implant was modelled with surface-tosurface contact elements with a friction coefficient of [13] 3. Results The effect of an implant on the stress distribution within the knee is investigated. In order to calculate the stresses, two finite element models of the tibia are used: implanted and intact. The stress contour plots from both the finite element models are shown Figure 2: Anterior view of (equivalent) stress contours acting over the surface of the two tibia models Intact Tibia Implanted Tibia Figure 3a: Graphs of equivalent stress against distance around selected pathway (identical to bone-implant boundary) for the cross-section at 0 0 (anterior view). Figure 3b: Graphs of equivalent stress against distance around selected pathway (identical to bone-implant boundary) for the cross-section at 0 0 (anterior view).

80 A. Mekonnen Artificial boundary identical to boundary between implant and bone Plastic insert Implant Cancellous bone Cancellous bone Cortical bone Cortical bone Intact tibia Implanted tibia Fig.

However, contour plots can give only a qualitative overview in comparing the stress distributions of the two models.

4 80 A. Mekonnen Artificial boundary identical to boundary between implant and bone Plastic insert Implant Cancellous bone Cancellous bone Cortical bone Cortical bone Intact tibia Implanted tibia Fig. 4 Anterior cross-sectional view of the intact and implanted models of the tibia. in figure 2. However, contour plots can give only a qualitative overview in comparing the stress distributions of the two models. In the present work, a Figure 5: Anterior view of (equivalent) stress contours acting over the cross section passing through the vertical axis of the implant stem graphical method is devised in which graphs are plotted of equivalent stress in the bone of the implanted tibia around the bone-implant interface and these are then compared with graphs of stress calculated at identical points in the intact tibia. See Fig. 3a and 3b. Identifying the same points in the intact tibia as those chosen in the implanted model is straightforward because, as described earlier, the two models are meshed in such a way that nodes are in identical positions at or below the level of the boneimplant interface. The simplest way of plotting the graphs for the implanted tibia is to consider various crosssections in the vertical plane all of which passed through the axis of the implant stem. For each cross -section, stresses in the bone are obtained at equidistant points around the path defining the boundary of the implant and are plotted against distance around the boundary. Likewise, for the intact tibia, the same crosssections and the same pathways within each crosssection are used to plot analogous graphs of stress against distance along the path. For example, in the anterior cross-sectional view shown in figure 4, stresses at points around the dotted line are plotted.

Afr J Med Phy, Biomed Eng & Sc, 2010, 2, 77-84 81 A C B Figure.

5 Afr J Med Phy, Biomed Eng & Sc, 2010, 2, A C B Figure. 6: Difference in equivalent stress between the implanted tibia and the intact tibia around selected pathway (identical to bone-implant boundary) for the cross-section at 0 o. In order to adequately cover the area of bone that is in contact with the implant, it is found necessary to consider eighteen cross-sections and hence eighteen different In order to adequately cover the area of bone that is in contact with the implant, it is found necessary to consider eighteen cross-sections and hence eighteen different pathways. The cross-sections are at 10 o intervals around the axis of the implant stem; the cross-section relating to the anterior view of the tibia (figures 4 and 5) is taken to be 0 o and the eighteenth cross-section is 170 o around from this. The graphs of equivalent stress for all eighteen pathways are similar to those shown in figure 3a and 3b for the 0 o cross-section. It can be seen that the largest increase in stress occurs almost 80 mm along the pathway. However, the largest decrease in stress cannot easily be identified without subtracting one curve from the other. When the graph of the intact tibia is subtracted from that of the implanted tibia, the graph is as shown in figure 6. Note that A and C in figure 6 correspond to points where the decrease in stress is a maximum and B is the point where the increase in stress is greatest. Note also where A, B and C occur on the path around the implant. Because of stress shielding at points such as A and C, there is the possibility that there might be some long-term atrophy of the bone in these regions whereas; close to point B, there could be micro-cracking of the bone. Both conditions could lead ultimately to loosening of the implant. By considering points such as A, B and C on all eighteen cross-sections, a profile of the largest stress changes around the implant can be determined. In particular, the largest increase in stress occurs in a region which includes point B on the 0 o cross-section together with equivalent points on other cross-sections over an arc of 90 o from -80 o to +10 o (angles measured anticlockwise when viewed from above). In this region, the stress is between five and ten times larger than the stress in the intact tibia; five times larger at 10 o and -80 o rising to a tenfold increase at -50 o. The largest decrease in stress occurs at the top of the implant stem corresponding to point A on the 0 o cross-section. Again, the largest decreases are over an arc from -80 o to +10 o and in this region the stresses are typically one fifth of those in the intact tibia. 4. Discussion Stress distribution in the bone of an implanted tibia

6 82 A. Mekonnen and intact tibia is quantitatively compared using finite element models. In order that stresses in the bone of the implanted tibia calculated at the boneimplant interface could be compared with stresses at exactly the same points of the intact tibia, the finiteelement mesh of the bone in the implanted tibia has to be reproduced exactly in the corresponding region of the intact tibia. In particular, the nodes in that region of the tibia where the bone is in immediate contact with the implant should be replicated in the finite-element model of the intact tibia. This is achieved by dividing the model of the intact tibia into two separate parts. This is depicted in Fig. 4 where the dotted line follows the same path as the bone-implant interface of the implanted tibia. Since the lower part is now identical to that of the implanted model, this region can be meshed with exactly the same elements and nodes as those that form the mesh in the bone of the implanted tibia. The same resultant load of 2.2kN was applied to the top of each model although the distribution of the load was different: For the implanted tibia, because of the way in which the two parts of the knee joint interact, this force was split into two point loads acting on the top surface of the polyethylene insert which is itself supported by the metal tray of the implant. [20] Although the femoral component of the implant makes contact with the polyethylene insert over two areas each of which is finite, these areas are small. Also the forces are acting on the top surface of the insert so that the pressure distribution under the metal tray is effectively unchanged by the assumption of point loads. For the intact tibia, the pressure distribution over the top surface has been studied by numerous researchers [23-26] In which; they all showed that the pressure distribution is complex and, from the first two of these four papers, it can be concluded that the pressure acts over the complete area of the articulating surfaces of the femur and tibia when the resultant load is 2.2kN and the knee is straight (i.e. no flexion). In the present study, two different loading conditions were evaluated each of which the same resultant load of 2.2kN. Although both loading con- figurations considered are a crude approximation to the actual loading, the forces provided by the constraints at the distal end of the tibia were found to be virtually independent of the load being applied. This indicates that the two loading systems are statically equivalent and would imply also that the different distribution of loading has only a localized effect in the immediate region of the loading itself. As long ago as 1982, Lewis et al wrote that bone atrophy due to abnormally low stresses and micro-cracking as a result of high localized stresses contribute to loosening of implants. [20] From the present study we can confirm that stress concentration is prevalent in the implanted tibia. Moreover, the region susceptible to high stress concentration is identified as the tip of the implant stem. In agreement with these findings, a large increase of the stresses in the region around the bottom of the stem has been observed in other clinical studies. For example, Barrack et al (1999) conducted clinical and radiographic assessment of patients who had revision surgery. [21] Their results showed that patients fitted with long stemmed implants experienced pain in the diaphyseal region of the tibia. They attributed the pain to stress concentration at, or stress transfer to, the tip of the stem. It is also shown that large decrease of the stresses in the region beneath the tibial tray close to the stem is present in the implanted tibia. A clinical radiographic study by Regner et al (2000) has also reported on similar observations. In their paper they stated that radiolucent zones under the tibial tray around the stem were seen frequently. [22] 5. Conclusion Finite element models of an intact tibia and an implanted tibia are used to calculate the stress distribution within the bone. Stresses from the two finiteelement models are compared. This can most easily be done using contour plots of the equivalent or von Mises stress. Clearly the contour plots are much more informative and enable stresses around the implant to be compared directly. Even so, comparing stresses in this way using contour plots is effectively a qualitative exercise and no precise information can

7 Afr J Med Phy, Biomed Eng & Sc, 2010, 2, be obtained as to which points in the bone around the bone-implant interface show the largest changes of stress compared with the same points in the intact tibia. The graphical analysis of results is a useful tool to quantitatively compare stresses in the intact tibia with that of the implanted hence study the effect of implants on the stress distribution within the bone. References [1] Cheal, E.J., Hayes, W.C., Lee, C.H., Snyder, B.D., Miller, J., Stress analysis of a condylar tibial component: influence of metaphyseal shell properties and cement injection depth. Journal of Orthopaedic Research 3, [2] Hashemi, A., Shirazi-Adl, A., Finite element analysis of tibial implants-effect of fixation design and friction model. Computer Methods in Biomechanics and Biomedical Engineering 3, [3] Walker, P.S., Green, D., Reilly D., Thatcher, J., Ben-Dov, M., Ewald, F.C., Fixation of tibial components of knee prostheses. Journal of Bone and Joint Surgery 63A, [4] Jaycox, D.P., Lewis, J.L., Hanmer, R.S., A three dimensional finite element system using interactive graphics. Rehabilitation Engineering program report, Northwestern University, Chicago, Illinois. [5] Albrektsson, B.E., Carlsson, L.V., Freeman, M.A., Herberts, P., Ryd L., Proximally cemented versus uncemeneted Freeman- Samuelson knee arthroplasty. A prospective randomised study. Journal of Bone and Joint Surgery 74B, [6] Garg, A., Walker, P.S., The effect of the interface on the bone stresses beneath tibial components. Journal of Biomechanics 19, [7] Insall, J., Tria, A.J., Scott, W.N., The total condylar knee prosthesis: the first 5 years. Clinical Orthopaedics 145, [8] Kaufer, H., Mattews, L.S., Spherocentric arthroplasty of the knee: clinical experience with an average four year follow up. Journal of Bone and Joint Surgery 63A, [9] Kettlekamp, D.B., Knee implants: review of current states. In: total joint replacements. Proceedings of a workshop at Northwestern University, ed by CL Compere, J.L. Lewis, Chicago, Illinois, Rehabilitation Engineering Report, Northwestern University, [10]Bartel, D.L., Burstein, A.H., Santavicca, E.A., Insall, J.N., Performance of the total tibial component in total knee replacement. Journal of Bone and Joint Surgery 64A, [11]Hori, R.Y., Lewis, J.L., Wixson, R.L., Kramer, G.M., An analysis of 130 total hips and knees. In: Proceedings of the conference of implant retrieval, material and biological analysis, Gaithersburg, MD, National Bureau of Standards, [12]Tissakht, M., Eskandari, H., Ahmed, A.M., Micromotion analysis of the fixation of total knee tibial component. Computers and Structures 56, [13]Taylor, M., Tanner, K.E., Freeman, M.A.R., Finite element analysis of the implanted proximal tibia: a relationship between the initial cancellous bone stresses and implant migration. Journal of Biomechanics 31, [14]Miyoshi, S., Takahashi, T., Ohtani, M., Yamamoto, H., Kameyama, K., Analysis of the shape of the tibial tray in total knee arthroplasty using a three dimension finite element model. Clinical Biomechanics 17, [15]Shirazi-Adl, A., Patenaude, O., Dammak, M., Zukor, D., Experimental and finite element comparison of various fixation designs in combined loads. Journal of Biomechanical Engineering 123, [16]Rakotomanana, R.L., Leyvraz, P.F., Curnier, A., Heegaard, J.H., Rubin, P.J., A finite element model for evaluation of tibial prosthesisbone interface in total knee replacement. Journal of Biomechanics 25, [17]Mursae, K., Crowninshield, R.D., Pederson, D.R., Chang, T.S., An analysis of tibial component design in total knee arthroplasty. Journal of Biomechanics 16, [18]Morrison, J.B., The mechanics of the knee joint in relation to normal walking. Journal of

8 84 A. Mekonnen Biomechanics 3, [19]Little, R.B., Wevers, H.W., Siu, D., Cooke, T.D.V., A three-dimensional finite element analysis of the upper tibia. Journal of Biomechanical Engineering 108, [20]Lewis, J.L., Askew, M.J., Jaycox, D.P., A comparative evaluation of tibial component designs of total knee prostheses. Journal of Bone and Joint Surgery 64A, [21]Barrack R.L., Rorabeck C., Burt M., Sawhney J., Pain at the end of the stem after revision total knee arthroplasty. Clin Orthop Relat Res. 367: [22]Regnér L., Carlsson L., Kärrholm J., Herberts P., Tibial component fixation in porousand hydroxyapatite-coated total knee arthroplasty: a radiostereo metric evaluation of migration and inducible displacement after 5 years. J Arthroplasty.15(6): [23]Fukubayashi, T. and Kurosawa, H., The contact area and pressure distribution pattern of the knee. A study of normal and osteoarthrotic knee joints. Acta Orthop Scand. 51(6): [24]Ahmed, A.M. and Burke, D.L., 1983, In-vitro measurement of static pressure distribution in synovial joints--part I: Tibial surface of the knee. J Biomech Eng. 105(3): [25]Perie, D. and Hobatho, M.C., 1998, In vivo determination of contact areas and pressure of the femorotibial joint using non-linear finite element analysis. Clin Biomech (Bristol, Avon). 13 (6): [26]Donahue T.L., Hull M.L., Rashid M.M., Jacobs C.R., 2002, A finite element model of the human knee joint for the study of tibio-femoral contact. J Biomech Eng. 124(3):

Topology optimisation of hip prosthesis to reduce stress shielding

Computer Aided Optimum Design in Engineering IX 257 Topology optimisation of hip prosthesis to reduce stress shielding S. Shuib 1, M. I. Z. Ridzwan 1, A. Y. Hassan 1 & M. N. M. Ibrahim 2 1 School of Mechanical