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SECTION II: ORIGINAL ARTICLES: Knee

Influence of Post-cam Design on Stresses on Posterior-stabilized Tibial Posts

Huang, Chang-Hung*; Liau, Jiann-Jong; Huang, Chun-Hsiung*,‡; Cheng, Cheng-Kung*

Author Information
Clinical Orthopaedics and Related Research: September 2006 - Volume 450 - Issue - p 150-156
doi: 10.1097/01.blo.0000218739.76871.28

Abstract

Posterior-stabilized total knee arthroplasties (TKA) have satisfactory long-term survival rates8,12,31 and good functional performance.2,16 The post-cam mechanism in posterior-stabilized knee prostheses can prevent posterior subluxation of the tibia in flexion11 and restore femoral rollback.23 However, retrieval studies on posterior-stabilized knee prostheses showed that tibial post wear contributes to an increased risk of osteolysis and loosening.14,22,26

Fatigue failure of the polyethylene component is one of the dominant failure modes with contributions from compressive, tensile, and deviatoric stress components.3 Nakayama et al,25 in a study measuring contact pressure at the post-cam mechanism in different knee prosthesis designs, suggested there were high contact pressures on different tibial post designs although mobile-bearing posterior-stabilized prostheses had reduced stress concentration on the tibial post. However, placement of the sensor used in that study could affect the stress fields, and use of a pressure sensor can only measure the contact pressure of the articular surface. The maximum principal stress (tensile stress) on the polyethylene tibial insert and the von Mises stress, a measurement of material distortion often used to predict subsurface delamination wear,3 cannot be measured by pressure sensors, but can be calculated by finite element analysis.

The post-cam of posterior-stabilized knee prostheses can be categorized into flat-on-flat or curve-on-curve contact surfaces. In neutral contact, the flat-on-flat design has a broad area for support and therefore would be expected to have low contact stress. However, with small tibial rotations (10o),16 there is potential for much smaller contact areas with the design.

We hypothesized that the curve-on-curve design of post-cam feature would provide lower stresses at the tibial post compared with the flat-on-flat design, especially during axial tibiofemoral rotation.

MATERIALS AND METHODS

We constructed two finite element models of posterior-stabilized tibiofemoral components and compared the post-cam mechanism in flat-on-flat and curve-on-curve models (Fig 1). The two models had the same conformity in tibiofemoral articular surfaces. The geometric data for the flat-on-flat model were from Uknee system (United Orthopedic Co, Taipei, Taiwan). The contact surfaces of the tibial post and femoral cam on the transverse plane were flat-on-flat. There were two fillets with a radius of 2.5 mm at the corners of the post. The post-cam geometric data for the curve-on-curve model were modified from the post-cam mechanism of the flat-on-flat model. The radius (transverse plane) of the tibial post of the curve-on-curve model was 9.5 mm and the femoral cam was 10 mm. The width of the tibial post was 19 mm and the femoral cam was 20 mm in both models. To avoid geometric discontinuity of the femoral cam on the sagittal plane, the change of curvature at the femoral cam of the flat-on- flat and curve-on-curve models maintained smooth outlines at 60°-150° engagement. The sagittal radius of the femoral cam in the flat-on-flat model was larger than that of the curve-on-curve model (Fig 2). We used Hypermesh 7.0 (Altair HyperWorks, Altair Engineering Inc, Troy, MI) for modeling and meshing, and ABAQUS 6.3-1 (Hibbit, Karlsson & Sorensen, Inc, Pawtucket, RI) for finite element analysis.

Fig 1A
Fig 1A:
B. Two finite element knee models show (A) flat-on-flat and (B) curve-on-curve contact of post-cam mechanisms. The flat-on-flat design has a broad area for support in neutral contact and would be expected to have low contact stress. However, with small tibial rotations, stress concentration might occur with the design. We hypothesized that the curve-on-curve design would provide lower stresses at the tibial post compared with the flat-on-flat design, especially during axial tibial rotation.
Fig 2A
Fig 2A:
B. The outline of the femoral cam on the sagittal plane is shown in the (A) flat-on-flat and (B) curve-on-curve models. The curvature at the femoral cam of both models maintained smooth outlines from 60°-150° knee flexion.

The femoral component was assumed to be a rigid body because the elastic modulus of metal is substantially larger than that of polyethylene. Solid block elements were used to mesh the tibial component. Convergence testing was performed to verify that the solution did not change appreciably with mesh refinement (Fig 3). The final tibial insert in the curve-on-curve and flat-on-flat models consisted of 20,485 and 19,801 elements, respectively. The femoral component in the curve-on-curve model contained 1287 quadrilateral and 3326 triangular elements, and the femoral component in the flat-on-flat model contained 1240 quadrilateral elements and 3331 triangular elements. We used quadrilateral elements at the femoral cam for smoothing the contact surface. We used geometric and material nonlinearities for analysis. The material property of the polyethylene insert was set as an elastoplastic behavior of fourth-order polynomial relationship27 with a Poisson's ratio of 0.45.13 We determined the stress/strain curve (Fig 4) as its relationship can predict elastoplastic behavior up to 35 MPa.27 The curve segment after 35 MPa appeared to be straight, therefore a constant modulus was assumed after the end of the curve. We used finite sliding with hard contact in the ABAQUS program to define the contact between the master and the slave surfaces. The friction coefficient was assumed as zero.

Fig 3
Fig 3:
A graph shows the typical results of the convergence test. The contact area decreases with element refinement, and contact and von Mises stresses increase with element refinement. Only element refinement at the tibial post was considered when performing the convergence test.
Fig 4
Fig 4:
A graph shows the true stress/strain curve of the elastoplastic material model.

To validate this finite element model, we compared the peak contact pressure and contact area on the upper tibial insert of the model with contact pressure and area in a previous experimental study,4 in which pressure-sensitive film (Fuji Film Co, Tokyo, Japan) was used to estimate contact pressures and areas when the knee was at full extension and sustained a compressive load of 3000 N. The finite element model has the same conformity in the tibiofemoral articular surfaces as the test specimen (United Orthopedic Co), and the testing procedure was identical to that used in the experimental study.

We simulated two contact situations. Neutral contact was defined as no axial tibiofemoral rotation, and axial tibial rotation contact was defined as the tibial insert with 10° internal rotation relative to the femoral component.16,17 An anteroposterior (AP) shear force of 500 N24,25 was applied to the femoral component in 60°, 90°, 120°, and 150° flexion. The center of the posterior condylar radius (on the sagittal plane) of the femoral component was set as the rotation center for simulating different knee flexions.5 The bottom of the tibial insert was fixed in all degrees of freedom. The femoral component was constrained to move along the AP direction only.

We calculated the von Mises stress, peak contact stress, and maximum principal stress on the tibial post in the curve-on-curve and flat-on-flat models. We also compared the stresses in axial tibial rotation with stresses in neutral contact.

RESULTS

The validation test showed the calculated contact area and peak contact stress from finite element analysis were 228.2 mm2 and 24.1 MPa, respectively, and from the measurement of sensitive film, they were 197.2 mm2 and 23.6 MPa, respectively. The maximum difference in contact area and stress on the tibial articular surface between finite element calculation and sensitive film measurement were 16 % and 2.6 %, respectively. It revealed good agreement between finite element analysis and experimental measured data in predicting contact stress.

In neutral contact (Fig 5; Fig 6A), the flat-on-flat model had greater von Mises stress than the curve-on-curve model at deep flexion angles. The von Mises stress and peak contact stress in the flat-on-flat model increased with increasing knee flexion angles. The maximum von Mises stress was 27.6 MPa and peak contact stress was 31.2 MPa at 150° knee flexion (Table 1). The von Mises stress and peak contact stress in the curve-on-curve model did not obviously increase with increasing knee flexion angles. The maximum von Mises stress was 21.6 MPa and peak contact stress was 36.6 MPa at 150° knee flexion (Table 1). The maximum principal stress was 18.8 MPa in the flat-on-flat model and 16.8 MPa in the curve-on-curve model.

TABLE 1
TABLE 1:
Maximum Stresses in Flat-on-Flat and Curve-on-Curve Models in Neutral Contact and Axial Tibial Rotation
Fig 5A
Fig 5A:
B. A graph shows the (A) maximum von Mises stress and (B) peak contact stress for the flat-on-flat and curve-on- curve models in neutral and axial tibial rotation at different knee flexions. The von Mises stress and peak contact stress in the flat-on-flat model increased with increasing angles of knee flexion and axial tibial rotation, but less change was seen in curve-on-curve model.
Fig 6A
Fig 6A:
B. The contour of von Mises stress in the flat-on-flat model is shown in the (A) neutral contact and (B) axial tibial rotation. There was stress concentration at the corner of the tibial post in the flat-on-flat model under axial tibial rotation. The contour scales of stresses were set the same in both models to clearly present differences in stress distribution.

In the flat-on-flat model, there was increased stress concentration at the posterior corner during axial tibial rotation (Fig 6B). The von Mises stress and peak contact stress increased with increasing knee flexion angles (Fig 5). The maximum von Mises stress was 48.2 MPa and peak contact stress was 59 MPa at 150° knee flexion. In the curve- on-curve model, the von Mises stress and peak contact stress did not obviously change with increasing axial tibial rotation. There was no stress concentration at the tibial post. The maximum principal stress was 34.5 MPa in the flat-on-flat model and 17.7 MPa in the curve-on-curve model.

To compare stresses on the tibial post at axial tibial rotation with stresses in neutral contact, the flat-on-flat design had larger stress increments than curve-on-curve design. The greatest increments of von Mises stress, peak contact stress, and maximum principal stress in the flat- on-flat model were 126.3%, 151%, and 103%, respectively (at 120° knee flexion). The increments of von Mises stress (10.7 %), maximum principal stress (18.6%), and peak contact stress (7.2 %) were much smaller in the curve-on- curve model.

DISCUSSION

The beneficial effects of increasing femoral posterior translation and restoring normal knee kinematics in posterior-stabilized prostheses have been shown in various in vivo1,2 and in vitro15,16 studies. However, investigators of clinical studies reported that the deleterious effects of tibial post wear14,22,29 and post fractures6,7,20,21 were attributable to load-bearing when the tibial post engages with the femoral cam. We hypothesized that a curve-on- curve post-cam design would reduce stress concentration on the tibial post during deep knee flexion in axial tibial rotation.

Our study has several limitations. First, polyethylene wear is a dynamic process affected by sliding distance, frictional behavior, and cyclic load. Static simulation and frictionless post-cam contact cannot fully simulate the reality of polyethylene wear. Second, compressive tibiofem- oral loading, soft tissues, and posterior inclinations of the tibial component were not considered but could affect stress distribution on the tibial post. Third, the position of the post on the polyethylene insert may affect the engaged angle of the post-cam mechanism. The tibial insert was in the same position for both models. We assumed that the tibial post and femoral cam start to engage from 60° flexion.

Numerous researchers have performed kinematics10,15-17 and kinetics24 studies of tibiofemoral joints at high flexion angles. High AP shear force24 and tibial rotation16 existing on the knee were seen at deep knee flexion angles. Investigators of kinematics studies16,17 reported that internal tibial rotation increased with knee flexion to a maximum of 11.1° for intact knees17 and 10° for TKAs16 at 150° knee flexion. However, in a kinetics study, Nagura et al24 indicated that deep knee flexion activities could generate high net AP shear forces (58.3-67.8% body weight) to the knee. We think high AP shear force and tibial rotation at high knee flexion could damage the tibial post of posterior-stabilized prostheses. Therefore, we evaluated stress distribution on the tibial post.

The post-cam mechanism is a complex articulation that plays an important role in biomechanical performance.15 Polyethylene wear at the tibial post is influenced by multiple factors such as post location, post height, alignment of the tibiofemoral joint, and post-cam shapes.29 The post- cam designs of posterior-stabilized knee prostheses generally include either flat-on-flat or curve-on-curve contact surfaces. The design that more effectively avoids excessive wear or tibial post fracture should be evaluated by biomechanical studies and verified by retrieval studies.

In a retrieval study, Puloski et al29 performed wear score analysis on the tibial post in four brands of posterior- stabilized prostheses (Kinemax/kinematic, Howmedica, Rutherford, NJ; Genesis I/II, Smith and Nephew Richard, Memphis, TN; AMK/Coordinate, DePuy, Warsaw, IN; and IB I/II, Zimmer, Warsaw, IN). All of the retrieval post-cam designs had flat-on-flat contact surfaces, and polyethylene wear and damage were observed on all tibial posts. Wear primarily was observed on the posterior side of the post, but wear also was seen on the anterior, medial, and lateral surfaces. Severe wear as delamination and involving gross loss of polyethylene was apparent on 30% of all tibial posts. In another retrieval study,30 the retrieved implant (Scorpio PS knee, Stryker, Allendale, NJ) had a round post on the tibial insert. The data suggest delami- nation represented only 0.1% of the total surface damage and there was no evidence of severe peripheral damage of polyethylene caused by edge loading. Our biomechanical data are consistent with data from these retrieval studies and suggest curve-on-curve of post-cam designs provide the advantage of reducing edge loading, therefore resulting in lower stresses than the flat-on-flat design.

There are few studies related to stress analysis at the post-cam mechanism. Only one experimental study25 has measured the contact pressure and contact area at the post- cam mechanism in different posterior-stabilized TKAs. With a compressive posterior load of 500 N applied to the tibial component against the femoral component, Nakayama et al showed that high contact pressures occurred at the tibial post.25 The contact pressure increased when tibial rotation was simulated. Their tested specimens of Kirschner (Kirschner Medical Corporation, Timonium, MD) and Scorpio prostheses were designed as flat-on-flat and curve-on-curve contact of post-cam mechanisms, respectively.25 At 120° knee flexion, the peak contact pressure of the Kirschner prosthesis was 33.9 MPa in neutral contact and 56.9 MPa in tibial rotation. For the Scorpio prosthesis, the stresses were 32.4 MPa in neutral contact and 37.7 MPa in tibial rotation.25 In our study, the contact stress in the flat-on-flat model was 22.2 MPa in neutral contact and 55.7 MPa in tibial rotation. The contact stress in the curve-on-curve model was 33 MPa in neutral contact and 35.4 MPa in tibial rotation. Our flat-on-flat model had less contact stress in the neutral contact than the Kirschner knee prosthesis, possibly because of dimensional difference in the post and cam widths, which were 19 mm and 20 mm, respectively, in our flat-on-flat model and 17.8 mm and 18.7 mm, respectively, for the Kirschner design (ie, the Kirschner prosthesis had a smaller area for contact and therefore had a greater contact stress). However, during tibial rotation the difference in the contact stress between our flat-on-flat model and the Kirschner prosthesis was small because the stress concentration at the post corner was more influenced by the corner curvature than the dimensions of the prosthetic components. The peak contact stress in the curve-on-curve model was similar to that of the Scorpio prosthesis at 120° flexion. Our results suggest curve-on-curve contact surfaces of the tibial post and the femoral cam are advantageous during tibial rotation contact.

The cyclic compressive and tensile stresses at the polyethylene component cause fatigue failure, and are dominant modes of tibial insert failure.3 The maximum principal stress was near the posterior end of the post (Fig 7) because the tibial post is like a cantilever beam that sustains a bending moment when an AP shear force is applied to the post. Comparing axial tibial rotation with neutral contact, the greatest increment was 103% in the flat-on- flat model, and 18.6% in the curve-on-curve model. The larger tensile stress in the flat-on-flat model can be interpreted as axial tibial rotation causing the tibial post to endure bending and torsion simultaneously. Torsion was less in the curve-on-curve model because of less edge loading.

Fig 7A
Fig 7A:
B. The contour of the maximum principal stress is shown in axial tibial rotation for the (A) flat-on-flat and (B) curve-on- curve models. The maximum principal stress occurred near the posterior end of the tibial post in both models.

Stresses on the upper articular surface of the tibial insert have been reported in several finite element studies3,9,19 intended to predict polyethylene wear, but these studies provided little information regarding the tibial post. The peak stresses on the articular surface can range from 40 MPa in compression to 17 MPa in tensile, which vary between different conformities of contact surfaces.3,9,19 In these studies, the peak compressive stress on the articular surface was larger than the reported yielding stress of approximately 20-25 MPa of ultrahigh weight molecular polyethylene,18,28 suggesting greater wear rates for low- conformity designs. The maximum tensile stress of the upper articular surface which appeared near the edge of contact region3 was less than the yielding tensile strength of 24 MPa.28 However, the maximum tensile stress on the end of the tibial post was greater than the yielding tensile strength. This may be because the tibial post had more complex loadings including compressive loading and bending moment, therefore increasing the tensile stress on its end. The post experienced greater compressive stress and greater tensile stress than in the upper articular surface of the tibial insert. We think tibial posts have a greater risk of catastrophic failure than the upper articular surface of prostheses in TKAs. The post-cam mechanism does not afford entirely innocuous articulation at all contacting surfaces, and stress concentration at the post should be avoided. Tibial post failure can occur during deep knee bending, squatting, and kneeling. The curve-on-curve design offers the advantage of mitigating the edge loading and impingement of the post-cam mechanism.

The curve-on-curve contact of the post-cam mechanism had lower contact stress and tensile stress than the flat-on- flat design, especially in axial tibial rotation. The curve- on-curve design reduced edge loading at the post-cam mechanism compared with the flat-on-flat design and allowed more axial tibiofemoral rotation.

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