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Finite Element Analysis of Resurfacing Depth and Obliquity on Patella Stress and Stability in TKA
The Journal of Arthroplasty 28 (2013) 978–984
Contents lists available at SciVerse ScienceDirect
The Journal of Arthroplasty journal homepage: www.arthroplastyjournal.org
Finite Element Analysis of Resurfacing Depth and Obliquity on Patella Stress and Stability in TKA Farid Amirouche PhD a, Kwang Won Choi MS a, Wayne M. Goldstein MD a, b, Mark H. Gonzalez MD a, Stefanie Broviak a a b
Department of Orthopeadics, University of Illinois at Chicago, Chicago, Illinois Illinois Bone and Joint Institute, Morton Grove, Illinois
a r t i c l e
i n f o
Article history: Received 2 April 2012 Accepted 5 February 2013 Keywords: total knee arthroplasty patella resurfacing finite element analysis bone stress
a b s t r a c t Patella resurfacing in total knee arthroplasty (TKA) reduces postoperative complications and revisions; however, the optimal cutting depth and angle that minimize patellar strain and fracture remain unclear. We performed three-dimensional finite element analysis (FEA) of resurfacing cutting depth and obliquity to assess the stresses in each component of the knee joint, and fatigue testing to determine cyclic loading conditions over the expected life span of the implant. Maximum stress on the patella increased as cutting depth increased up to 8 mm; peak stresses on the idealized button further increased at 10-mm depth. Medial superior obliquities below 3° showed the lowest stress on the patella and button and the highest fatigue life. An oblique cut of 3° with respect to the inferior end increased patellar stress and reduced fatigue life, making this the least successful approach. Taken together, our FEA supports the use of minimal cutting depths at − 3° with respect to the superior end for patellar resurfacing in TKA in order to minimize stresses in the structure and improve TKA durability. Future studies will assess the effect of patella button placement to account for real-world practice variations. © 2013 Elsevier Inc. All rights reserved.
Total knee arthroplasty(TKA) is a common orthopedic procedure, and most TKAs involve resurfacing of the patella. Failure to resurface the patella in TKA results in reoperation rates of approximately 5% [1– 4], and studies have shown that post-TKA anterior knee pain is 5.3% with resurfacing compared with 25.1% without resurfacing [5]. Patellar cutting depth and obliquity of the cut can affect the placement and orientation of the patella in relation to the patellofemoral groove of the femur; however, the optimal cutting depth and angle in patella resurfacing remain unclear [6–11]. There are wide variations in these parameters due to differences in both interpatient patellar anatomy and individual surgeon practices [1]. The degree of subluxation following resurfacing affects the amount of force acting on the patella and the likelihood of fractures [12–17]. Post-TKA fractures can have long-term consequences on anterior knee joint pain, extensor muscle lag, weakness, stiffness, and disability [2,18,19]. For this reason, it is important to determine the optimal cutting depth and angle for each patient prior to patellar button placement to reduce the likelihood of post-TKA stress fractures and associated complications. We performed three-dimensional finite element analysis (FEA) of resurfacing cutting depth and obliquity to assess the stresses in each The Conflict of Interest statement associated with this article can be found at http:// dx.doi.org/10.1016/j.arth.2013.02.002. Reprint requests: Farid Amirouche, PhD, 835 S. Wolcott Ave., Room E270, Chicago, IL 60607. 0883-5403/2806-0020$36.00/0 – see front matter © 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.arth.2013.02.002
component of the knee joint, particularly the patella. Similar studies have been conducted using the 2D parametric modeling approach [20]. Our 3D model provides a more accurate assessment of the effect of patella resurfacing parameters on the bone and the likelihood of fracture, and may be useful for determining optimal patella resurfacing cutting depth and obliquity in TKA for individual patients. We hypothesized that deeper cuts made during patella resurfacing result in higher peak stresses in the bone, and that changing the obliquity of the cut when depth is held constant affects bone stress values. Methods Three-Dimensional Patella Modeling A 3D parametric model of the patella bone was generated using a discrete set of parameters—measured via CT imaging—including width, height, thickness, and surface slopes. The CT scanned images of cadaveric knees were saved into a Digital Imaging and Communications in Medicine (DICOM) format (Fig. 1). The acquired data were further refined in Pro-Engineer 4.0 (PTC Inc., Needham, MA). The patellar image was first divided into 10 sections to create 2D drawings (Fig. 1) consisting of several arcs to represent the surface curvature between points on the patella (Fig. 2). We projected each section onto a 2D plane, and identified and measured both the origin
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Fig. 1. (A) CT scanned DICOM image of the knee joint. (B) Sections for reconstruction in ISO view. The patella image generated from the CT scan was divided into sections from 0 to 10.
and the radii of the corresponding arc circles. The 3D model was then reconstructed using the Surface Sweeping Method as outlined in the Pro/E software (PTC Inc., Needham, MA). We used Gaussian integration points in ANSYS as the method of contact modeling to simulate applied force to the patella bone. In this method, models are built between the femoral–tibial joint surface and the patella–femoral joint interface, where the bone acts as the target surface and the applied force as the contact segment. We set the friction coefficients in both synovial joints to 0.01. The forces applied to the femur are then shown in terms of their components in the x and y directions. The five muscles of the quadriceps bound to the superior end of the patella can be subdivided by location in the coronal view of the
anterior surface. These muscles are ordered from lateral to medial as follows: vastus lateralis (VL), vastus intermedius (VI), rectus femoris (RF), vastus medialis longus (VML), and vastus medialis obliquus (VMO). For our modeling, we applied a load of 1127.76 N (115 kg) of total quadriceps muscle force, which represents the resultant force at full knee extension with 0° flexion. A reaction force of similar magnitude was also applied to the patellar tendon. In order to formulate the muscle force exactly, the total quadriceps force was subdivided among the five distinctive quadriceps muscles based on each contributing muscle's cross-sectional area. The individual force contributed by the quadriceps muscles, patellar tendon, and muscular insertion point and angles for each of these tissues upon the surface of the patella was calculated (Table 1).
Fig. 2. Creation of a three-dimensional patella model. (A) Measurement of section 0 (highlighted in red). For each section, the circle origin and radius were determined to generate position and shape parameters—including width, height, and thickness—to represent the curvature of the patella. (B) Reconstructed model of section 0 on a 2D plane. (C) Sections for reconstruction. Each section in the 2D plane was stacked to create a 3D model. (D) Section sweeping for reconstruction in ISO view. The 10 sections in the 2D plane were reconstructed to create a 3D model of the patella bone.
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Table 1 Distribution of Forces in the Five Quadriceps Muscles. Percentage of Cross Section Distributed Forcea
Muscles Vastus lateralis (VL) Vastus intermedius (VI) Rectus femoris (RF) Vastus medialis longus (VML) Vastus medialis obliquus (VMO) a
40% 20% 15% 15% 10%
451.10 225.55 169.16 169.16 112.77
N N N N N
the patella model retained the material property of human cortical bone. Although the patella button implanted in TKA is not physically identical to that of the removed portion of the patella, for the purposes of this study it was assumed that the patella button was an idealized replacement, identical to the removed portion in terms of material properties and dimensions. Modeling the Patella Cutting Angle
The total force among muscles was used as the total applied force.
It is known that when the resultant force is calculated along the coronal plane, it can be found as nearly parallel to the femoral axis [21]. Through simulation of the applied forces, actual physiological consequences were modeled on the patellar components. The applied load was set to mimic that of a 70-kg individual in a simple leg stand. To apply the tensile forces and simulate the actual physiological response to a load placed on the patella bone, surrounding components such as the femur and tibia were geometrically attached to the patella model using Pro-Engineer software and data taken from CT images (Fig. 3). Tibia movement was fixed in all planes, while the femur was fixed in the x and y directions with free movement in the z direction. The patella bone had free movement in the y direction and fixed movement in the x and z directions. We accounted for femoral internal/external rotation through these constraints and simulated a normal knee flexion–extension for the various patella cutting depths and obliquities. Modeling Patella Cutting Depth After the knee joint was geometrically assembled, the model was modified to account for patella resurfacing and different cutting depths in order to analyze and determine the optimal cut for TKA (Fig. 4). Coronal (X–Z) planar cuts were used to assess depths of approximately 10.6% (6-mm cut), 19.2% (8-mm cut), and 30.9% (10mm cut) of the total anterior-to-posterior thickness. ANSYS was used to change the material properties of the model between the cutting plane and the remaining distance to the posterior surface of the model to the properties of UHMWPE. The density of the UHWMPE section was converted to 970 kg/m 3 and a Poisson's ratio of 0.4 was applied. The residual patella bone section of
In order to study the effect of cutting angle, the model was modified to account for differences in cutting obliquity about the ends of the patella. Each cut was geometrically compared to the ideal plane, with a standard cutting depth of 8 mm from the posterior end of the patella. In total, nine different obliquities in patellar cuts were compared to determine which cut allowed for optimal strength and stability of the joint. In addition to a single standard cut of 0 mm off the standard plane, cuts were made at 3° and −3° from the medial, lateral, superior, and inferior end points (Fig. 5). Fatigue Testing For human structural implants, devices must be capable of withstanding a maximum cyclic stress that does not lead to fatigue failure in 5 × 10 7 cycles, which approximates 25 years of normal use. We performed virtual fatigue testing using ANSYS and the S–N curves of cortical and cancellous bone and polyethylene implants to assess the modes of failure that result from repeated stress, at magnitudes lower than those achieved in daily use. We used selected points from the S–N curves to reflect life cycle numbers and investigated the corresponding FE stresses after patella resurfacing at various depths and obliquities. The objective of these tests was to determine how cyclic loading conditions over the expected life span of the combined implant (polyethylene and bone) fall under the S–N curve. Results Optimal Cutting Depth for the Patella To evaluate the amount of static stress on the patellar components resulting from cutting depth variation, the Von Misses stress yield was
Fig. 3. Knee joint mesh assembly. (A) Patella bone with idealized patellar button attached. (B) FEM model of the knee joint. Medial view is shown.
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Fig. 4. Patella model and patellar cutting depths. Patella FEM with no cutting, 6-mm cut, 8-mm cut, and 10-mm cut. All cuts were made beginning on the posterior part of the patella and are shown from the superior view point.
measured (Fig. 6). The stresses on the patella bone and the idealized UHMWPE patella button were measured for cuts of different depths along the coronal plane of the patella (Fig. 6A). The bone showed an
increase in stress up to cutting depths of 8 mm. More specifically, as the linear cutting depth increased from no cut to a 6-mm cut from the posterior, stress on the bone increased 17.88%. As the cutting depth
Fig. 5. Comparison of 8-mm linear and oblique cuts. (A–D) Superior view. (A) 0° of obliquity of patella cutting (8-mm standard cut). (B) −3° of obliquity of patella cutting about medial end point. (C) 3° of obliquity of patella cutting about medial end point. (D) 3° of obliquity of patella cutting about lateral end point. (E–H) Lateral sagittal view. (E) −3° of obliquity of patella cutting about inferior end point. (F) 3° of obliquity of patella cutting about inferior end point. (G) 3° of obliquity of patella cutting about superior end point. (H) −3° of obliquity of patella cutting about superior end point.
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Fig. 6. Comparison of Von Misses Stress vs. Cutting Depth. (A) Stress on the patella bone and the UHMWPE patella button for 6-, 8-, and 10-mm non-oblique cutting depths. (B) Von Misses stresses (Pa) in the patella bone in posterior view. Scale bar = Von Misses stress (Pa).
increased to 8 mm, the stress on the bone rose dramatically, by 53.87%. Conversely, the patella button showed an initial increase in peak stresses with the 6-mm cut, which then decreased 57.32% as the cutting depth increased from 6 to 8 mm. It is interesting to note that, with a 10-mm cut, the peak stress on the patella was 117.92 MPa, which was 53.58% higher than the stress at no cut, but only 0.53% lower than the 8-mm cut. By contrast, the stress on the button with a 10-mm cut increased by approximately 260% compared with the peak stress with an 8-mm cut. These findings indicate that below and up to a cutting depth of 8 mm, the patella bone is under a higher relative stress than the polyethylene patella button, but as cutting depth increases, the idealized button begins to experience higher peak stresses. Durability of the patella and patella implant was measured in cycles of fatigue life for each normal cutting depth (Table 2). A decrease of 46.05% in fatigue life was noted between cutting depths of 8 to 10 mm, which is a fraction of the overall decrease in fatigue life of 96.3% when the cut depth was increased to 10 mm. Optimal Cutting Angle for the Idealized Patella Button To study the effect of cutting angle on peak stresses in the patella and idealized polyethylene button, peak stresses and fatigue life Table 2 Fatigue Life of the Patella with Variation in Cutting Depth. Cutting depth None 6 mm 8 mm 10 mm a
Fatigue Life (Cycles)a N/A 6034.4 410.6 221.5
Fatigue life was measured by the magnitude of life cycles until failure.
were measured for oblique cuts at a cutting depth of 8 mm from the anterior (Fig. 7). For a non-oblique cut (0°) of 8-mm depth, peak stresses of 117.92 and 31.57 MPa were noted on the whole patella and the button, respectively. A maximum peak stress of 257.77 MPa was seen in the patella with an oblique cut of − 3° with respect to the medial end, a 118.60% greater stress than that seen with the nonoblique cut. High stresses were also seen on the patella bone when the cut was 3° from the lateral end and 3° from the inferior end, which were 80.01% and 70.16% higher than the non-oblique cut, respectively. It is interesting to note that at these same three cut angles, the idealized patella button showed lower peak stresses compared with the non-oblique cut. In the idealized button, a cut of 3° with respect to the lateral end produced the lowest peak stress, which was 87.23% lower than a non-oblique cut. In contrast, a cut of − 3° from the lateral end produced a stress 253.12% higher than with a non-oblique cut. Compared with the non-oblique cut, lower peak stresses on the patella were noted at − 3° with respect to the superior end (88.37% lower) and − 3° with respect to the inferior end (38.63% lower). A similarly low stress was seen in both the patella and the polyethylene button at − 3°with respect to the superior end; stress in the button was 56.57% lower than for a non-oblique cut. Finally, we assessed the effect of the cut obliquity on durability of the patella bone in fatigue life testing (Table 3). Patella durability was significantly higher compared with the non-oblique cut for the cuts made at 3° with respect to the medial end and 3° with respect to the superior end. The lifetime with these cuts was increased by 640.49%– 2333.36%. In contrast, cuts of 3° from the lateral end and 3° from the inferior end resulted in lifetimes approximately 99.6% less than that experienced by the bone with 0° obliquity. These results suggest that medial superior obliquities below 3° are preferred for patella resurfacing and are able to sustain stress over the life span of the TKA. Due to the loss of static stress or exposure to stress, fatigue life
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Fig. 7. Comparison of Von Misses stresses vs. cutting obliquity. (A) Stress on the patella bone and UHMWPE patella button for various cutting obliquities. Posterior view of representative Von Misses stresses (Pa) with (B) −3° of obliquity of patella cutting about the superior end point and with (C) −3° of obliquity of patella cutting about the inferior end point. Von Misses stress scale bar is shown in Fig. 6.
testing of the patella resurfacing at − 3°obliquity was not conducted with respect to the superior end.
Discussion In this paper, we performed finite element analysis of the patella to generate a 3D model of the knee, then applied this model to determine the changes in stress on the patella bone and patella button with varying cutting depths and obliquities of resurfacing in TKA. Cutting depth had a significant effect on the stresses in the knee joint and on the durability of the patella. The fully intact patella, with no resurfacing, experienced minimal stress at the inferior end of patella connection to the tibia. When we plotted the relationship
Table 3 Fatigue Life (cycles) of the Patella with Variation in Obliquity of Patellar Cutting. Oblique Angle (All 8-mm Depth) 0° 3° WRT medial −3° WRT medial −3° WRT lateral 3° WRT lateral −3° WRT superior 3° WRT superior 3° WRT inferior −3° WRT inferior a
Fatigue Life (Cycles)a 221.5 5389.9 76.5 43.3 1.0 N/A 1640.2 0.8 6474.6
Fatigue life was measured by the magnitude of life cycles until failure.
between cutting depth and maximum stress, maximum stress on the patella increased as cutting depth increased, up to 8 mm. At a 10-mm cutting depth, there was no further increase in stress on the patella; by contrast, stress on the UHMWPE patella button implant increased by 259.57%. Thus, as the stresses on the patella plateau after 8-mm depth, the amount of stress on the button continues to increase. We found that as the cutting depth increased, peak stresses occurred at the inferior end of patella, which is connected to the patella tendon. We also found that the button fatigue life decreased as cutting depth increased, such that larger cutting depths shortened the life time of the structure. In total knee replacement surgery with resurfacing, 10 mm from the articular surface of the patella is cut and replaced with a patella button. The cutting angle lies parallel to coronal plane of patella, but a perfectly linear cut is often difficult, if not impossible, to achieve clinically. In our FEA, we found that when the angle of cutting is parallel to the coronal plane, there was a peak stress of 117.92 MPa, which decreased 88% when the cut was made at a − 3° oblique angle with respect to superior end. By comparison, an oblique cut of − 3° with respect to the medial end experienced a stress 54.2% higher and a fatigue life 65.5% lower than the default (0°) cut. An oblique cut of 3° with respect to the inferior end experienced an initial stress 41.3% higher and fatigue life 99.6% higher than when no oblique cut was present, making this the least successful approach to patella resurfacing for TKA. Taken together, our FEA supports the use of minimal cutting depths and an obliquity of − 3° with respect to the superior end in patellar resurfacing for TKA in order to minimize the stresses in the structure and improve TKA durability.
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Finite element modeling has been applied to various biomechanical research topics, including the prediction of a reduction in patellofemoral lateral shear forces based on external rotation of femoral components [22]. Previous studies have also used 3D FEA to study the patellofemoral interface [23,24] and the distribution of contact stresses in polyethylene components in prosthetic knee joints [25]. In a previous cadaveric study by Wulff and Incavo [26], the authors evaluated the anterior strain on the patella after resurfacing as a measure of the potential for patellar fracture and implant failure after TKA. Our results are consistent with their observation that anterior strain on the patella increases with progressively greater cutting depth, thereby weakening the bone and increasing the risk of postoperative fracture. The biomechanical modeling data derived in this study further expand our understanding of the postoperative strain caused by the obliquity of patella resurfacing, and the optimal obliquity of the cut that will minimize strain and the risk of patellar fracture. Several limitations exist in the current study. Both simulations represent the ideal linear cut where the removed portion is replaced with an identical match. However, in orthopedic surgical practice, the articular surface of the patella that is removed during resurfacing is not uniform in shape and varies among patients. Furthermore, the patella button implant is uniformly circular in shape. While the button covers a large section of the removed portion, it does not fully cover the surface and does not perfectly replace the shape of the bone removed. Future studies would need to include testing with the addition of the patella button to account for real-world variations that occur in practice. Current work is being undertaken to investigate the effect of button placement and to further validate these studies using cadaveric specimens. Acknowledgments The authors thank Stacey C. Tobin, PhD, for editorial assistance. References 1. Greenfield MA, Insall JN, Case GC, et al. Instrumentation of the patellar osteotomy in total knee arthroplasty. The relationship of patellar thickness and lateral retinacular release. Am J Knee Surg 1996;9:129. 2. Scott RD, Turoff N, Ewald FC. Stress fracture of the patella following duopatellar total knee arthroplasty with patellar resurfacing. Clin Orthop Relat Res 1982: 147.
3. Scott WN, Rubinstein M, Scuderi G. Results after knee replacement with a posterior cruciate-substituting prosthesis. J Bone Joint Surg Am 1988;70:1163. 4. Scott WN, Rozbrunch JD, Otis JE, et al. Clinical and biomechanical evaluation of patella replacement in total knee arthoplasty. Orthop Trans 1978;2:203. 5. Waters TS, Bentley G. Patellar resurfacing in total knee arthroplasty. A prospective, randomized study. J Bone Joint Surg Am 2003;85-A:212. 6. Barrack RL. Orthopaedic crossfire—all patellae should be resurfaced during primary total knee arthroplasty: in opposition. J Arthroplasty 2003;18:35. 7. Barrack RL, Bertot AJ, Wolfe MW, et al. Patellar resurfacing in total knee arthroplasty. A prospective, randomized, double-blind study with five to seven years of follow-up. J Bone Joint Surg Am 2001;83-A:1376. 8. Barrack RL, Wolfe MW. Patellar resurfacing in total knee arthroplasty. J Am Acad Orthop Surg 2000;8:75. 9. Bourne RB, Rorabeck CH, Vaz M, et al. Resurfacing versus not resurfacing the patella during total knee replacement. Clin Orthop Relat Res 1995:156. 10. Feller JA, Bartlett RJ, Lang DM. Patellar resurfacing versus retention in total knee arthroplasty. J Bone Joint Surg Br 1996;78:226. 11. Keblish PA, Varma AK, Greenwald AS. Patellar resurfacing or retention in total knee arthroplasty. A prospective study of patients with bilateral replacements. J Bone Joint Surg Br 1994;76:930. 12. Bindelglass DF, Vince KG. Patellar tilt and subluxation following subvastus and parapatellar approach in total knee arthroplasty. Implication for surgical technique. J Arthroplasty 1996;11:507. 13. Chan KC, Gill GS. Postoperative patellar tilt in total knee arthroplasty. J Arthroplasty 1999;14:300. 14. Chew JT, Stewart NJ, Hanssen AD, et al. Differences in patellar tracking and knee kinematics among three different total knee designs. Clin Orthop Relat Res 1997:87. 15. Grelsamer RP, Bazos AN, Proctor CS. Radiographic analysis of patellar tilt. J Bone Joint Surg Br 1993;75:822. 16. Laughlin RT, Werries BA, Verhulst SJ, et al. Patellar tilt in total knee arthroplasty. Am J Orthop (Belle Mead NJ) 1996;25:300. 17. Windsor RE, Scuderi GR, Insall JN. Patellar fractures in total knee arthroplasty. J Arthroplasty 1989(4 Suppl):S63. 18. Le AX, Cameron HU, Otsuka NY, et al. Fracture of the patella following total knee arthroplasty. Orthopedics 1999;22:395. 19. Tria Jr AJ, Harwood DA, Alicea JA, et al. Patellar fractures in posterior stabilized knee arthroplasties. Clin Orthop Relat Res 1994:131. 20. Nabhani F, Sotudeh R, Hart AN, et al. 2D stress analysis of the human patella using the finite element approach. In: Middleton J, Jones ML, Pande GN, editors. Computer methods in biomechanics and biomedical engineering. Amsterdam, The Netherlands: Gordon and Breach Science Publishers SA; 1996. p. 197. 21. Amis AA. Current concepts on anatomy and biomechanics of patellar stability. Sports Med Arthrosc 2007;15:48. 22. D'Lima DD, Chen PC, Kester MA, et al. Impact of patellofemoral design on patellofemoral forces and polyethylene stresses. J Bone Joint Surg Am 2003;85A(Suppl 4):85. 23. Chien WL, Lo CC, Wang CS, et al. Evaluation and analysis of the onlay patellar component in total knee arthroplasty. Adv Materials Res 2010;97–101:3773. 24. Fernandez JW, Hunter PJ. An anatomically based patient-specific finite element model of patella articulation: towards a diagnostic tool. Biomech Model Mechanobiol 2005;4:20. 25. Shashishekar C, Ramesh CS. Finite element analysis of prosthetic knee joint using ANSYS. Biomed Health 2007;12:65. 26. Wulff W, Incavo SJ. The effect of patella preparation for total knee arthroplasty on patellar strain: a comparison of resurfacing versus inset implants. J Arthroplasty 2000;15:778.
Contents lists available at SciVerse ScienceDirect
The Journal of Arthroplasty journal homepage: www.arthroplastyjournal.org
Finite Element Analysis of Resurfacing Depth and Obliquity on Patella Stress and Stability in TKA Farid Amirouche PhD a, Kwang Won Choi MS a, Wayne M. Goldstein MD a, b, Mark H. Gonzalez MD a, Stefanie Broviak a a b
Department of Orthopeadics, University of Illinois at Chicago, Chicago, Illinois Illinois Bone and Joint Institute, Morton Grove, Illinois
a r t i c l e
i n f o
Article history: Received 2 April 2012 Accepted 5 February 2013 Keywords: total knee arthroplasty patella resurfacing finite element analysis bone stress
a b s t r a c t Patella resurfacing in total knee arthroplasty (TKA) reduces postoperative complications and revisions; however, the optimal cutting depth and angle that minimize patellar strain and fracture remain unclear. We performed three-dimensional finite element analysis (FEA) of resurfacing cutting depth and obliquity to assess the stresses in each component of the knee joint, and fatigue testing to determine cyclic loading conditions over the expected life span of the implant. Maximum stress on the patella increased as cutting depth increased up to 8 mm; peak stresses on the idealized button further increased at 10-mm depth. Medial superior obliquities below 3° showed the lowest stress on the patella and button and the highest fatigue life. An oblique cut of 3° with respect to the inferior end increased patellar stress and reduced fatigue life, making this the least successful approach. Taken together, our FEA supports the use of minimal cutting depths at − 3° with respect to the superior end for patellar resurfacing in TKA in order to minimize stresses in the structure and improve TKA durability. Future studies will assess the effect of patella button placement to account for real-world practice variations. © 2013 Elsevier Inc. All rights reserved.
Total knee arthroplasty(TKA) is a common orthopedic procedure, and most TKAs involve resurfacing of the patella. Failure to resurface the patella in TKA results in reoperation rates of approximately 5% [1– 4], and studies have shown that post-TKA anterior knee pain is 5.3% with resurfacing compared with 25.1% without resurfacing [5]. Patellar cutting depth and obliquity of the cut can affect the placement and orientation of the patella in relation to the patellofemoral groove of the femur; however, the optimal cutting depth and angle in patella resurfacing remain unclear [6–11]. There are wide variations in these parameters due to differences in both interpatient patellar anatomy and individual surgeon practices [1]. The degree of subluxation following resurfacing affects the amount of force acting on the patella and the likelihood of fractures [12–17]. Post-TKA fractures can have long-term consequences on anterior knee joint pain, extensor muscle lag, weakness, stiffness, and disability [2,18,19]. For this reason, it is important to determine the optimal cutting depth and angle for each patient prior to patellar button placement to reduce the likelihood of post-TKA stress fractures and associated complications. We performed three-dimensional finite element analysis (FEA) of resurfacing cutting depth and obliquity to assess the stresses in each The Conflict of Interest statement associated with this article can be found at http:// dx.doi.org/10.1016/j.arth.2013.02.002. Reprint requests: Farid Amirouche, PhD, 835 S. Wolcott Ave., Room E270, Chicago, IL 60607. 0883-5403/2806-0020$36.00/0 – see front matter © 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.arth.2013.02.002
component of the knee joint, particularly the patella. Similar studies have been conducted using the 2D parametric modeling approach [20]. Our 3D model provides a more accurate assessment of the effect of patella resurfacing parameters on the bone and the likelihood of fracture, and may be useful for determining optimal patella resurfacing cutting depth and obliquity in TKA for individual patients. We hypothesized that deeper cuts made during patella resurfacing result in higher peak stresses in the bone, and that changing the obliquity of the cut when depth is held constant affects bone stress values. Methods Three-Dimensional Patella Modeling A 3D parametric model of the patella bone was generated using a discrete set of parameters—measured via CT imaging—including width, height, thickness, and surface slopes. The CT scanned images of cadaveric knees were saved into a Digital Imaging and Communications in Medicine (DICOM) format (Fig. 1). The acquired data were further refined in Pro-Engineer 4.0 (PTC Inc., Needham, MA). The patellar image was first divided into 10 sections to create 2D drawings (Fig. 1) consisting of several arcs to represent the surface curvature between points on the patella (Fig. 2). We projected each section onto a 2D plane, and identified and measured both the origin
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Fig. 1. (A) CT scanned DICOM image of the knee joint. (B) Sections for reconstruction in ISO view. The patella image generated from the CT scan was divided into sections from 0 to 10.
and the radii of the corresponding arc circles. The 3D model was then reconstructed using the Surface Sweeping Method as outlined in the Pro/E software (PTC Inc., Needham, MA). We used Gaussian integration points in ANSYS as the method of contact modeling to simulate applied force to the patella bone. In this method, models are built between the femoral–tibial joint surface and the patella–femoral joint interface, where the bone acts as the target surface and the applied force as the contact segment. We set the friction coefficients in both synovial joints to 0.01. The forces applied to the femur are then shown in terms of their components in the x and y directions. The five muscles of the quadriceps bound to the superior end of the patella can be subdivided by location in the coronal view of the
anterior surface. These muscles are ordered from lateral to medial as follows: vastus lateralis (VL), vastus intermedius (VI), rectus femoris (RF), vastus medialis longus (VML), and vastus medialis obliquus (VMO). For our modeling, we applied a load of 1127.76 N (115 kg) of total quadriceps muscle force, which represents the resultant force at full knee extension with 0° flexion. A reaction force of similar magnitude was also applied to the patellar tendon. In order to formulate the muscle force exactly, the total quadriceps force was subdivided among the five distinctive quadriceps muscles based on each contributing muscle's cross-sectional area. The individual force contributed by the quadriceps muscles, patellar tendon, and muscular insertion point and angles for each of these tissues upon the surface of the patella was calculated (Table 1).
Fig. 2. Creation of a three-dimensional patella model. (A) Measurement of section 0 (highlighted in red). For each section, the circle origin and radius were determined to generate position and shape parameters—including width, height, and thickness—to represent the curvature of the patella. (B) Reconstructed model of section 0 on a 2D plane. (C) Sections for reconstruction. Each section in the 2D plane was stacked to create a 3D model. (D) Section sweeping for reconstruction in ISO view. The 10 sections in the 2D plane were reconstructed to create a 3D model of the patella bone.
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Table 1 Distribution of Forces in the Five Quadriceps Muscles. Percentage of Cross Section Distributed Forcea
Muscles Vastus lateralis (VL) Vastus intermedius (VI) Rectus femoris (RF) Vastus medialis longus (VML) Vastus medialis obliquus (VMO) a
40% 20% 15% 15% 10%
451.10 225.55 169.16 169.16 112.77
N N N N N
the patella model retained the material property of human cortical bone. Although the patella button implanted in TKA is not physically identical to that of the removed portion of the patella, for the purposes of this study it was assumed that the patella button was an idealized replacement, identical to the removed portion in terms of material properties and dimensions. Modeling the Patella Cutting Angle
The total force among muscles was used as the total applied force.
It is known that when the resultant force is calculated along the coronal plane, it can be found as nearly parallel to the femoral axis [21]. Through simulation of the applied forces, actual physiological consequences were modeled on the patellar components. The applied load was set to mimic that of a 70-kg individual in a simple leg stand. To apply the tensile forces and simulate the actual physiological response to a load placed on the patella bone, surrounding components such as the femur and tibia were geometrically attached to the patella model using Pro-Engineer software and data taken from CT images (Fig. 3). Tibia movement was fixed in all planes, while the femur was fixed in the x and y directions with free movement in the z direction. The patella bone had free movement in the y direction and fixed movement in the x and z directions. We accounted for femoral internal/external rotation through these constraints and simulated a normal knee flexion–extension for the various patella cutting depths and obliquities. Modeling Patella Cutting Depth After the knee joint was geometrically assembled, the model was modified to account for patella resurfacing and different cutting depths in order to analyze and determine the optimal cut for TKA (Fig. 4). Coronal (X–Z) planar cuts were used to assess depths of approximately 10.6% (6-mm cut), 19.2% (8-mm cut), and 30.9% (10mm cut) of the total anterior-to-posterior thickness. ANSYS was used to change the material properties of the model between the cutting plane and the remaining distance to the posterior surface of the model to the properties of UHMWPE. The density of the UHWMPE section was converted to 970 kg/m 3 and a Poisson's ratio of 0.4 was applied. The residual patella bone section of
In order to study the effect of cutting angle, the model was modified to account for differences in cutting obliquity about the ends of the patella. Each cut was geometrically compared to the ideal plane, with a standard cutting depth of 8 mm from the posterior end of the patella. In total, nine different obliquities in patellar cuts were compared to determine which cut allowed for optimal strength and stability of the joint. In addition to a single standard cut of 0 mm off the standard plane, cuts were made at 3° and −3° from the medial, lateral, superior, and inferior end points (Fig. 5). Fatigue Testing For human structural implants, devices must be capable of withstanding a maximum cyclic stress that does not lead to fatigue failure in 5 × 10 7 cycles, which approximates 25 years of normal use. We performed virtual fatigue testing using ANSYS and the S–N curves of cortical and cancellous bone and polyethylene implants to assess the modes of failure that result from repeated stress, at magnitudes lower than those achieved in daily use. We used selected points from the S–N curves to reflect life cycle numbers and investigated the corresponding FE stresses after patella resurfacing at various depths and obliquities. The objective of these tests was to determine how cyclic loading conditions over the expected life span of the combined implant (polyethylene and bone) fall under the S–N curve. Results Optimal Cutting Depth for the Patella To evaluate the amount of static stress on the patellar components resulting from cutting depth variation, the Von Misses stress yield was
Fig. 3. Knee joint mesh assembly. (A) Patella bone with idealized patellar button attached. (B) FEM model of the knee joint. Medial view is shown.
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Fig. 4. Patella model and patellar cutting depths. Patella FEM with no cutting, 6-mm cut, 8-mm cut, and 10-mm cut. All cuts were made beginning on the posterior part of the patella and are shown from the superior view point.
measured (Fig. 6). The stresses on the patella bone and the idealized UHMWPE patella button were measured for cuts of different depths along the coronal plane of the patella (Fig. 6A). The bone showed an
increase in stress up to cutting depths of 8 mm. More specifically, as the linear cutting depth increased from no cut to a 6-mm cut from the posterior, stress on the bone increased 17.88%. As the cutting depth
Fig. 5. Comparison of 8-mm linear and oblique cuts. (A–D) Superior view. (A) 0° of obliquity of patella cutting (8-mm standard cut). (B) −3° of obliquity of patella cutting about medial end point. (C) 3° of obliquity of patella cutting about medial end point. (D) 3° of obliquity of patella cutting about lateral end point. (E–H) Lateral sagittal view. (E) −3° of obliquity of patella cutting about inferior end point. (F) 3° of obliquity of patella cutting about inferior end point. (G) 3° of obliquity of patella cutting about superior end point. (H) −3° of obliquity of patella cutting about superior end point.
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Fig. 6. Comparison of Von Misses Stress vs. Cutting Depth. (A) Stress on the patella bone and the UHMWPE patella button for 6-, 8-, and 10-mm non-oblique cutting depths. (B) Von Misses stresses (Pa) in the patella bone in posterior view. Scale bar = Von Misses stress (Pa).
increased to 8 mm, the stress on the bone rose dramatically, by 53.87%. Conversely, the patella button showed an initial increase in peak stresses with the 6-mm cut, which then decreased 57.32% as the cutting depth increased from 6 to 8 mm. It is interesting to note that, with a 10-mm cut, the peak stress on the patella was 117.92 MPa, which was 53.58% higher than the stress at no cut, but only 0.53% lower than the 8-mm cut. By contrast, the stress on the button with a 10-mm cut increased by approximately 260% compared with the peak stress with an 8-mm cut. These findings indicate that below and up to a cutting depth of 8 mm, the patella bone is under a higher relative stress than the polyethylene patella button, but as cutting depth increases, the idealized button begins to experience higher peak stresses. Durability of the patella and patella implant was measured in cycles of fatigue life for each normal cutting depth (Table 2). A decrease of 46.05% in fatigue life was noted between cutting depths of 8 to 10 mm, which is a fraction of the overall decrease in fatigue life of 96.3% when the cut depth was increased to 10 mm. Optimal Cutting Angle for the Idealized Patella Button To study the effect of cutting angle on peak stresses in the patella and idealized polyethylene button, peak stresses and fatigue life Table 2 Fatigue Life of the Patella with Variation in Cutting Depth. Cutting depth None 6 mm 8 mm 10 mm a
Fatigue Life (Cycles)a N/A 6034.4 410.6 221.5
Fatigue life was measured by the magnitude of life cycles until failure.
were measured for oblique cuts at a cutting depth of 8 mm from the anterior (Fig. 7). For a non-oblique cut (0°) of 8-mm depth, peak stresses of 117.92 and 31.57 MPa were noted on the whole patella and the button, respectively. A maximum peak stress of 257.77 MPa was seen in the patella with an oblique cut of − 3° with respect to the medial end, a 118.60% greater stress than that seen with the nonoblique cut. High stresses were also seen on the patella bone when the cut was 3° from the lateral end and 3° from the inferior end, which were 80.01% and 70.16% higher than the non-oblique cut, respectively. It is interesting to note that at these same three cut angles, the idealized patella button showed lower peak stresses compared with the non-oblique cut. In the idealized button, a cut of 3° with respect to the lateral end produced the lowest peak stress, which was 87.23% lower than a non-oblique cut. In contrast, a cut of − 3° from the lateral end produced a stress 253.12% higher than with a non-oblique cut. Compared with the non-oblique cut, lower peak stresses on the patella were noted at − 3° with respect to the superior end (88.37% lower) and − 3° with respect to the inferior end (38.63% lower). A similarly low stress was seen in both the patella and the polyethylene button at − 3°with respect to the superior end; stress in the button was 56.57% lower than for a non-oblique cut. Finally, we assessed the effect of the cut obliquity on durability of the patella bone in fatigue life testing (Table 3). Patella durability was significantly higher compared with the non-oblique cut for the cuts made at 3° with respect to the medial end and 3° with respect to the superior end. The lifetime with these cuts was increased by 640.49%– 2333.36%. In contrast, cuts of 3° from the lateral end and 3° from the inferior end resulted in lifetimes approximately 99.6% less than that experienced by the bone with 0° obliquity. These results suggest that medial superior obliquities below 3° are preferred for patella resurfacing and are able to sustain stress over the life span of the TKA. Due to the loss of static stress or exposure to stress, fatigue life
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Fig. 7. Comparison of Von Misses stresses vs. cutting obliquity. (A) Stress on the patella bone and UHMWPE patella button for various cutting obliquities. Posterior view of representative Von Misses stresses (Pa) with (B) −3° of obliquity of patella cutting about the superior end point and with (C) −3° of obliquity of patella cutting about the inferior end point. Von Misses stress scale bar is shown in Fig. 6.
testing of the patella resurfacing at − 3°obliquity was not conducted with respect to the superior end.
Discussion In this paper, we performed finite element analysis of the patella to generate a 3D model of the knee, then applied this model to determine the changes in stress on the patella bone and patella button with varying cutting depths and obliquities of resurfacing in TKA. Cutting depth had a significant effect on the stresses in the knee joint and on the durability of the patella. The fully intact patella, with no resurfacing, experienced minimal stress at the inferior end of patella connection to the tibia. When we plotted the relationship
Table 3 Fatigue Life (cycles) of the Patella with Variation in Obliquity of Patellar Cutting. Oblique Angle (All 8-mm Depth) 0° 3° WRT medial −3° WRT medial −3° WRT lateral 3° WRT lateral −3° WRT superior 3° WRT superior 3° WRT inferior −3° WRT inferior a
Fatigue Life (Cycles)a 221.5 5389.9 76.5 43.3 1.0 N/A 1640.2 0.8 6474.6
Fatigue life was measured by the magnitude of life cycles until failure.
between cutting depth and maximum stress, maximum stress on the patella increased as cutting depth increased, up to 8 mm. At a 10-mm cutting depth, there was no further increase in stress on the patella; by contrast, stress on the UHMWPE patella button implant increased by 259.57%. Thus, as the stresses on the patella plateau after 8-mm depth, the amount of stress on the button continues to increase. We found that as the cutting depth increased, peak stresses occurred at the inferior end of patella, which is connected to the patella tendon. We also found that the button fatigue life decreased as cutting depth increased, such that larger cutting depths shortened the life time of the structure. In total knee replacement surgery with resurfacing, 10 mm from the articular surface of the patella is cut and replaced with a patella button. The cutting angle lies parallel to coronal plane of patella, but a perfectly linear cut is often difficult, if not impossible, to achieve clinically. In our FEA, we found that when the angle of cutting is parallel to the coronal plane, there was a peak stress of 117.92 MPa, which decreased 88% when the cut was made at a − 3° oblique angle with respect to superior end. By comparison, an oblique cut of − 3° with respect to the medial end experienced a stress 54.2% higher and a fatigue life 65.5% lower than the default (0°) cut. An oblique cut of 3° with respect to the inferior end experienced an initial stress 41.3% higher and fatigue life 99.6% higher than when no oblique cut was present, making this the least successful approach to patella resurfacing for TKA. Taken together, our FEA supports the use of minimal cutting depths and an obliquity of − 3° with respect to the superior end in patellar resurfacing for TKA in order to minimize the stresses in the structure and improve TKA durability.
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Finite element modeling has been applied to various biomechanical research topics, including the prediction of a reduction in patellofemoral lateral shear forces based on external rotation of femoral components [22]. Previous studies have also used 3D FEA to study the patellofemoral interface [23,24] and the distribution of contact stresses in polyethylene components in prosthetic knee joints [25]. In a previous cadaveric study by Wulff and Incavo [26], the authors evaluated the anterior strain on the patella after resurfacing as a measure of the potential for patellar fracture and implant failure after TKA. Our results are consistent with their observation that anterior strain on the patella increases with progressively greater cutting depth, thereby weakening the bone and increasing the risk of postoperative fracture. The biomechanical modeling data derived in this study further expand our understanding of the postoperative strain caused by the obliquity of patella resurfacing, and the optimal obliquity of the cut that will minimize strain and the risk of patellar fracture. Several limitations exist in the current study. Both simulations represent the ideal linear cut where the removed portion is replaced with an identical match. However, in orthopedic surgical practice, the articular surface of the patella that is removed during resurfacing is not uniform in shape and varies among patients. Furthermore, the patella button implant is uniformly circular in shape. While the button covers a large section of the removed portion, it does not fully cover the surface and does not perfectly replace the shape of the bone removed. Future studies would need to include testing with the addition of the patella button to account for real-world variations that occur in practice. Current work is being undertaken to investigate the effect of button placement and to further validate these studies using cadaveric specimens. Acknowledgments The authors thank Stacey C. Tobin, PhD, for editorial assistance. References 1. Greenfield MA, Insall JN, Case GC, et al. Instrumentation of the patellar osteotomy in total knee arthroplasty. The relationship of patellar thickness and lateral retinacular release. Am J Knee Surg 1996;9:129. 2. Scott RD, Turoff N, Ewald FC. Stress fracture of the patella following duopatellar total knee arthroplasty with patellar resurfacing. Clin Orthop Relat Res 1982: 147.
3. Scott WN, Rubinstein M, Scuderi G. Results after knee replacement with a posterior cruciate-substituting prosthesis. J Bone Joint Surg Am 1988;70:1163. 4. Scott WN, Rozbrunch JD, Otis JE, et al. Clinical and biomechanical evaluation of patella replacement in total knee arthoplasty. Orthop Trans 1978;2:203. 5. Waters TS, Bentley G. Patellar resurfacing in total knee arthroplasty. A prospective, randomized study. J Bone Joint Surg Am 2003;85-A:212. 6. Barrack RL. Orthopaedic crossfire—all patellae should be resurfaced during primary total knee arthroplasty: in opposition. J Arthroplasty 2003;18:35. 7. Barrack RL, Bertot AJ, Wolfe MW, et al. Patellar resurfacing in total knee arthroplasty. A prospective, randomized, double-blind study with five to seven years of follow-up. J Bone Joint Surg Am 2001;83-A:1376. 8. Barrack RL, Wolfe MW. Patellar resurfacing in total knee arthroplasty. J Am Acad Orthop Surg 2000;8:75. 9. Bourne RB, Rorabeck CH, Vaz M, et al. Resurfacing versus not resurfacing the patella during total knee replacement. Clin Orthop Relat Res 1995:156. 10. Feller JA, Bartlett RJ, Lang DM. Patellar resurfacing versus retention in total knee arthroplasty. J Bone Joint Surg Br 1996;78:226. 11. Keblish PA, Varma AK, Greenwald AS. Patellar resurfacing or retention in total knee arthroplasty. A prospective study of patients with bilateral replacements. J Bone Joint Surg Br 1994;76:930. 12. Bindelglass DF, Vince KG. Patellar tilt and subluxation following subvastus and parapatellar approach in total knee arthroplasty. Implication for surgical technique. J Arthroplasty 1996;11:507. 13. Chan KC, Gill GS. Postoperative patellar tilt in total knee arthroplasty. J Arthroplasty 1999;14:300. 14. Chew JT, Stewart NJ, Hanssen AD, et al. Differences in patellar tracking and knee kinematics among three different total knee designs. Clin Orthop Relat Res 1997:87. 15. Grelsamer RP, Bazos AN, Proctor CS. Radiographic analysis of patellar tilt. J Bone Joint Surg Br 1993;75:822. 16. Laughlin RT, Werries BA, Verhulst SJ, et al. Patellar tilt in total knee arthroplasty. Am J Orthop (Belle Mead NJ) 1996;25:300. 17. Windsor RE, Scuderi GR, Insall JN. Patellar fractures in total knee arthroplasty. J Arthroplasty 1989(4 Suppl):S63. 18. Le AX, Cameron HU, Otsuka NY, et al. Fracture of the patella following total knee arthroplasty. Orthopedics 1999;22:395. 19. Tria Jr AJ, Harwood DA, Alicea JA, et al. Patellar fractures in posterior stabilized knee arthroplasties. Clin Orthop Relat Res 1994:131. 20. Nabhani F, Sotudeh R, Hart AN, et al. 2D stress analysis of the human patella using the finite element approach. In: Middleton J, Jones ML, Pande GN, editors. Computer methods in biomechanics and biomedical engineering. Amsterdam, The Netherlands: Gordon and Breach Science Publishers SA; 1996. p. 197. 21. Amis AA. Current concepts on anatomy and biomechanics of patellar stability. Sports Med Arthrosc 2007;15:48. 22. D'Lima DD, Chen PC, Kester MA, et al. Impact of patellofemoral design on patellofemoral forces and polyethylene stresses. J Bone Joint Surg Am 2003;85A(Suppl 4):85. 23. Chien WL, Lo CC, Wang CS, et al. Evaluation and analysis of the onlay patellar component in total knee arthroplasty. Adv Materials Res 2010;97–101:3773. 24. Fernandez JW, Hunter PJ. An anatomically based patient-specific finite element model of patella articulation: towards a diagnostic tool. Biomech Model Mechanobiol 2005;4:20. 25. Shashishekar C, Ramesh CS. Finite element analysis of prosthetic knee joint using ANSYS. Biomed Health 2007;12:65. 26. Wulff W, Incavo SJ. The effect of patella preparation for total knee arthroplasty on patellar strain: a comparison of resurfacing versus inset implants. J Arthroplasty 2000;15:778.