Total knee arthroplasty (TKA) typically involves replacing diseased bone and cartilage in the knee with metal and polyethylene components. Component malalignment after TKA can cause several complications including soft-tissue imbalance, increased polyethylene wear, and tibial tray subsidence, all leading to revision surgery.1–5 Tibial tray alignment perpendicular to the tibial shaft is generally accepted as optimal. To assist in accurate component alignment, surgical instrumentation (intramedullary and extramedullary), and surgical navigation systems have been developed.6–8 Tibial tray malalignment, especially in varus, has been implicated in greater subsidence with 60% increase in revision rate.1 However, at least one clinical follow-up study has failed to correlate tibial varus with poorer outcomes.9
The biomechanical axis of the lower limb passes from the center of the femoral head to the center of the ankle. Varus malalignment of the tibial tray results in a greater proportion of the knee joint contact load being transmitted through the medial compartment (Fig. 1). This problem is compounded further during walking because of the normal tendency for an adduction moment across the knee. In addition, varus alignment of the tray increases the shear component of force at the implant–bone interface, which can increase the risk for interface failure. The increase in local compartmental forces combined with the increase in the shear leads to excessive stresses at the implant–bone interface resulting in increased micromotion, bone collapse, and subsidence of the tibial component.2 While these theoretical formulations are plausible, quantitative biomechanical evidence to directly support this mechanism is incomplete.
Finite element analysis has been used to study the stresses and strains in the proximal tibia after TKA. Early reports used axisymmetric10 and two-dimensional models11 or simpler three-dimensional geometry.12 Later reports have used CT scans to generate more realistic geometries of the proximal tibia.13, 14 The material properties of the corticocancellous region of the proximal tibia are complex. Finite element models have used material parameters based on the properties of polyurethane foam for cancellous bone,15, 16 published elastic properties from indentation testing,10, 12 and CT density-based calculations for spatially varying elastic properties.14 While finite element models can simulate complex biomechanical conditions, few have been validated experimentally.14, 16
We recently completed a series of cadaver tests to demonstrate that the change in mediolateral distribution of loads increased the risk for early bone failure in fatigue.17 In that study, we found an increase in subsidence in tibial specimens that were subjected to a mediolateral load distribution of 75:25 compared to a more balanced load distribution. The objective of the present study was to construct a finite element model of knee arthroplasty validated with in vitro cadaver testing to determine the alteration in bone stresses and strains in the proximal tibia and to test the hypothesis that varus malalignment of the tibial tray increases the risk of tray subsidence by increasing proximal tibial strains over the threshold for fatigue damage.
MATERIALS AND METHODS
The results of experimental testing including surrogate bone models and cadaver testing have been submitted elsewhere for publication.17 Details relevant to the present study are provided. The proximal tibiae were harvested from unpaired fresh-frozen human knees (N = 4) and implanted with a current-generation knee arthroplasty cruciate-retaining tibial tray. A surgical navigation system (Stryker Navigation, Stryker Instruments, Kalamazoo, MI) was used to register the tibial plateau and the mechanical axis of the tibia, which were recorded by digitizing the intercondylar eminence and the medial and lateral malleoli. The tibial plateau was cut at 0° posterior slope and perpendicular to the mechanical axis of the tibia. The tibial tray was cemented using surgical bone cement (Simplex P, Stryker Orthopedics, Mahwah, NJ). The implanted tibial specimens were mounted on a multiaxial testing rig (Force 5, AMTI, Watertown, MA) and subjected to loading (ISO-recommended knee wear simulation conditions) for up to 100,000 cycles in phosphate buffered saline supplemented with protease inhibitors. Flexion, anteroposterior translation, and axial rotation were displacement controlled. Axial load was force controlled. The tibial tray was free to translate in the mediolateral direction and free to rotate about the anteroposterior axis (in varus–valgus). Displacement sensors were mounted on the tray and the underlying bone to measure displacement in the vertical direction at the anterior, medial, and lateral aspects of the tray, and anteroposterior displacement at the medial and lateral aspects of the tray (Fig. 2). Five displacement sensors (MG-DVRT-3 Microstrain, Williston, VT) with a resolution of 1.5 µm and an accuracy of 3 µm were rigidly attached to the tibial tray using custom aluminum holders. Malleable craniomaxillofacial plates (Leibinger Orthognathic Maxillofacial Kit, Stryker Instruments) were fixed to the tibia using 1.7 mm self-tapping screws to serve as reference positions on the bone for the displacement sensors. Three sensors were oriented vertically to measure superoinferior displacement in lateral, anterior, and medial positions of the tibial tray. Two more sensors were oriented horizontally to measure anteroposterior displacement in lateral and medial positions on the tibial tray.
Knee Arthroplasty Implants
CAD models of the Stryker Triathlon cruciate-retaining design (Stryker Orthopaedics) were used. The tibial plateau was cut at 0° posterior slope and 90° to the mechanical axis of the tibia using extramedullary alignment. Appropriately sized 10 mm cruciate-retaining Triathlon polyethylene components were inserted into the sizes 4 and 5 tibial trays and were tested against size 4 Triathlon cruciate-retaining femoral components.
Finite Element Model
Before testing, the human cadaver knees (N = 4) were subjected to qCT scans at 0.65 mm slice intervals. A K2HPO4 calibration phantom (Image Analysis, Inc., Columbia, KY) was used to compute local bone density. The qCT scans of the tested cadaver knees were segmented using MIMICS (Materialise, Leuven, Belgium) and solid meshed using Hypermesh (Altair Engineering, Troy, MI). Material properties of bone were spatially assigned based on qCT bone density using previously reported conversion of bone density to elastic modulus.18, 19 The tibial geometry was resected with a plane placed at the level of the tibial cut. The geometry of the tray and stem was subtracted using Boolean operations between the tibial geometry and implant geometry (Fig. 3). A cement layer was generated between the under surface of the tray and the tibial bone cut, but not around the stem (reflecting the cementing technique in our institution). A finite element model was constructed using Abaqus 6.8 (Simulia, Dassault Systèmes, Providence, RI). The tray was assigned material properties of cobalt chrome alloy (E = 210 GPa, Poisson ratio = 0.3). The cement layer was assigned material properties of polymethylmethacrylate (E = 2,839 MPa, Poisson ratio = 0.3). The interface between the cement and bone and between the cement and tray was constrained to prevent any relative motion. Contact with friction (coefficient = 0.4) was simulated between the stem and the cancellous bone. Boundary conditions (constraining the displacement of the surface nodes of the tibial mesh corresponding to the portion cemented into the holding fixture) were applied to simulate experimental mounting conditions. The tray was subjected to a single load cycle representing that applied during cadaver testing (ISO-recommended input waveforms for displacement controlled wear simulation20). The axial load was offset medially to generate either 55:45 or 75:25 medial to lateral distribution on the tibial tray. For validation of the finite element model, the computed superoinferior displacement of the tibial tray relative to bone on the medial side was compared to that measured experimentally in four specimens. Principal stresses and strains and von Mises stresses were computed. To compute the volume of bone at risk, we selected a damage threshold of 0.4% compressive strain for cortical bone21 and 0.3% compressive strain for cancellous bone22 and calculated the volume of bone elements that were above this threshold.
Four unpaired tibial specimens were modeled. In two of the specimens, the application of vertical load was shifted medially to generate a load distribution ratio of 55:45 (medial/lateral) to represent a tibial tray in neutral varus–valgus alignment. In the remaining two specimens, a load distribution ratio of 75:25 was generated to represent a tibial tray in 5° varus alignment. The load distribution for the neutral alignment was obtained from in vivo measured tibial force distribution during walking.23 The load distribution for the varus alignment was obtained from previously published reports in which the varus–valgus angulation of the tibial tray was related to the mediolateral shift in the mechanical axis of the knee relative to the center of the tray.24, 25 In the paired analysis, we subjected each of the four models to both mediolateral force distributions (55:45 and 75:25) to control for differences in geometry and bone density.
The effect of varus malalignment of the tray was simulated by adjusting the mediolateral distribution of forces due to the offset in the mechanical axis of the knee relative to the center. Varus malalignment of the tray results in genu varum if the femoral component is aligned to the mechanical axis of the femur (Fig. 1). Therefore, in addition to the change in mediolateral distribution of axial forces, we added a small shear component. To determine whether this angulation changed the shear forces, the finite element analysis was repeated for the 75:25 mediolateral distribution with the implanted tibia placed in 5° varus.
Paired t-tests were used to detect significant differences in cortical and cancellous volume of bone above the threshold for fatigue damage. A p-value of <0.05 was considered significant.
The computed superoinferior displacement of the tibial tray relative to bone on the medial side was comparable to that measured experimentally in four specimens (Fig. 4) and served to validate the models. The variation in average bone density and calculated elastic modulus at the tibial cut among specimens is provided in Table 1. Overall, peak stresses were mainly seen in the proximal tibial cortex. The 75:25 distribution of load generated substantially higher peak von Mises stresses, compressive stresses, and strain in the medial aspect of the proximal tibia (Fig. 5). In addition, the magnitudes of compressive stresses and strains were greater in the medial compartment. On the other hand, differences in mediolateral shear stresses on the tibial cut were small (<5%).
Table 1. Average Bone Density and Calculated Elastic Modulus at the Surface of the Tibial Cut
Average Bone Density (mg/cm3)
Average Elastic Modulus (MPa)
The critical fatigue damage threshold in cyclic compression for cortical bone is 0.4% strain.21 We therefore computed the volume of cortical bone above this damage threshold, which reflected the variation among the specimens (Fig. 6A).
Stresses in cancellous bone varied by region and by local density and were below 4 MPa. We computed the volume of cancellous bone at or above a fatigue damage threshold of 0.3% compressive strain. This value represented the strain threshold for fatigue damage initiation within 100,000 cycles and was computed from lifetime curves reported for cyclic testing of human cancellous bone.22 The relative volume of cancellous bone above the threshold was increased on the medial side for the specimens subjected to 75:25 ML loading (Fig. 7); the total volume was also greater (Fig. 6B). Since each load-distribution group contained only two specimens the results were not statistically significant.
The distribution of stresses in the cement changed with the mediolateral distribution of forces (Fig. 8). However, the peak stresses were below 6 MPa, which is below the fatigue strength of polymethylmethacrylate.26, 27
We observed a large variation among specimens presumably due to differences in bone anatomy, bone density, and cortical thickness. We therefore subjected each model to both mediolateral force distributions for a paired comparison. There was a consistent increase (average 15%, p = 0.02) in the cancellous bone volume at risk (>0.3% compressive strain) under a mediolateral load distribution of 75:25. The increase for cortical bone volume at risk was even higher (Fig. 9, p = 0.025).
To determine the effect of varus angulation on shear forces, the finite element analysis was repeated for the 75:25 mediolateral distribution with the implanted tibia placed in 5° varus. However, the simulation of 5° varus angulation generated minimal differences in von Mises stresses, compressive stresses, shear stresses, compressive strains, and shear strains.
Component malalignment is thought to lead to implant failure.1–5 However, not all clinical outcomes have supported this link.9 We previously reported on increased subsidence in tibial trays loaded under malalignment conditions.17 However, we found a high variation among specimens that might explain the conflicting clinical outcomes. We therefore constructed subject-specific finite element models of proximal tibial loading after knee arthroplasty and validated the predictions against experimental data. We then explored the relevance of biomechanical factors contributing to potential aseptic loosening.
The displacement of the tray in the superoinferior direction, computed under conditions of normal walking, directly correlated with subsidence and failure in cadaver testing. Quantitatively, a significantly greater volume of proximal tibial cancellous bone was compressed to a strain greater than the threshold of 3,000 microstrain in the varus alignment group, indicating an increased risk for fatigue damage. Alteration in the mediolateral distribution of vertical load led to an increase in local strains in the proximal tibia, which can be directly linked to tibial subsidence and failure.
Although varus malalignment can also increase shear at the implant–cement–bone interface, no significant increase in shear stresses was noted. Orienting the tibia in varus, in addition to altering the mediolateral distribution of forces, also did little to increase shear stresses at the implant–cement–bone interface. These results indicate that interface shear is not a major factor in malalignment-induced aseptic loosening. Stresses in the cement mantle were redistributed reflecting the change in mediolateral force distribution but remained below 6 MPa, which is lower than the fatigue threshold reported for polymethylmethacrylate.26, 27
Since bone strength is related to the initial stiffness, the variations in bone density among specimens can affect the potential for damage. This result is reflected in the individual differences in stresses and strains. One approach to address this issue is to use matched pairs. However, even right- and left-sided knees from the same donor have some differences in bone geometry, alignment, and density.28 We therefore chose to simulate each of the four finite element models to both loading conditions, which controlled for all three of the above variables. The modeling of individual donors validated and supported the subject-specific approach. The simulated paired analysis permitted controlled comparison of the effects of altered loading. A significant increase in bone volume at risk was found. In this paired analysis, the cortical bone volume at risk was consistently and substantially higher for the 75:25 mediolateral distribution group despite the original variability among specimens.
Subject-specific finite element models have been used to study the effect of tray stem design on stresses and strain in the proximal tibia.28 These models were validated experimentally using similar outcomes measures as the present study. The finite element approach has also been used to study tray malalignment. One study reported increased compressive and shear stresses with varus malalignment.29 Those results were based on a single tibial geometry and the material properties of the cancellous bone were divided into two zones comprising a central low-density region and a more peripheral, high-density region. No direct validation with experimental results was provided. Another study analyzed the effect of tray alignment in varus and valgus and reported increased stresses in the cancellous bone with varus malalignment.30 However, in that study, a single load of 2,200YN centered on the medial compartment was applied for all alignment conditions. This load is comparable to a 100:0 medial to lateral distribution in our model setup. Again, no direct comparison to experimental results was reported.
One well-designed patient-specific finite element analysis used CT-based bone geometry and material properties similar to our modeling approach.14 The authors used the ratio of von Mises stresses to the ultimate compressive strength to define predictors that estimated the risk for tray migration. Despite assumptions made in loading magnitude and distribution, the patients with the highest predicted risk for failure migrated more on radiostereometric analysis. In our study, instead of computing ultimate strength based on CT density, we used strain as threshold for failure since this has been well-documented experimentally.21, 22
The early postoperative biomechanical response can play a major role in determining long-term outcomes such as aseptic loosening.2, 14 The initial events leading to late aseptic loosening most likely occur very early in the postoperative period, since early migration is often a marker for increased risk of aseptic loosening. Clinical studies of tibial tray micromotion by radiostereometry report an initially high rate of tibial tray migration, which in most patients stabilizes by 2 years postoperatively.2, 31–33 Those patients in whom migration continued beyond 2 years were at increased risk for late aseptic loosening.2 Tibial trays were more likely to exhibit continuous migration in patients with varus alignment. A finite element model of early migration and subsidence would therefore be of high relevance in predicting longer term failure. Newer techniques are emerging in which the placement of the component is customized to the patients natural prearthritic alignment, which in many cases is different from the traditional 0° alignment.34 A method that determines the risk of bone damage in a patient-specific manner can provide the surgeon with a safe range for component alignment and might even be applicable in preoperative planning.
Several factors can contribute to bone damage and implant subsidence. Bone damage is strain dependent.21, 35 Therefore, the subject's bodyweight, activity level, and local bone density all contribute to the risk for failure. Our results show that tibial tray varus malalignment can increase the peak strains in the medial tibial compartment and can increase the volume of bone that is at risk for damage. However, in subjects with healthier bone, lower bodyweight, or reduced activity level the increase in volume of bone at risk may not be sufficient to induce clinical subsidence or implant loosening. In our study, the magnitude of stresses increased medially under a varus tray. However, the computed volume of cortical bone (using strain as a marker for damage) at risk did not increase with malalignment reflecting this variability among specimens. On the other hand, when the effect of tray alignment was compared in the same specimen in a paired manner (controlling all other variables such as bone size, shape, density, and corticocancellous morphology) there was a consistent increase in the cortical volume at risk. This suggests that additional factors can confound the link between varus alignment and tray subsidence and may explain some of the variability in clinical reports.
The major weakness of our study was that we tested subsidence in nonviable bone. Bone remodeling and healing is likely to reduce the cumulative damage that typically occurs in cadaveric testing. We only tested one activity: walking. Nevertheless we noted a distinct difference in the peak strains of the finite element models, which correlated with experimental subsidence and damage. In the experimental study, the loads were applied through the femoral component throughout the gait cycle that included flexion, axial rotation, and anteroposterior translation. In the finite element model we only simulated the mediolateral distribution of axial loads in a static condition on the tray and did not simulate the effects of axial rotation or anteroposterior translation. Despite these limitations, the there was close agreement between the measured and computed displacement in the superoinferior direction at the medial aspect of the tray.
In summary, we generated subject-specific finite element models of implanted proximal tibiae and validated the computed results against experimental measures. The models predicted increased risk for bone damage in the medial cancellous and cortical bone of the proximal tibia but not at the implant–bone interface or the cement layer. The results also indicate differences among subjects to potential failure in part due to variations in bone density. These variations among patients might explain the conflicting reports of clinical studies regarding the statistical link between tray alignment and outcomes. This type of subject-specific modeling can be extremely valuable in studying the effect of surgical alignment, loading, and activity on damage to proximal bone and in predicting damage and outcomes in individual patients.
Funds in partial support of this study were provided by NIH R21 AR057561 awarded to Darryl D. D'Lima and research funds from Stryker Orthopaedics to Scripps Health.