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Keywords:

  • knee;
  • total knee arthroplasty;
  • component rotation;
  • computer simulation

Abstract

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. REFERENCES
  8. Supporting Information

Modern total knee arthroplasty (TKA) is an effective procedure to treat pain and disability due to osteoarthritis, but some patients experience quadriceps weakness after surgery and have difficulty performing important activities of daily living. The success of TKA depends on many factors, but malalignment of the prosthetic components is a major cause of postoperative complications. Significant variability is associated with femoral and tibial component rotational alignment, but how this variability translates into functional outcome remains unknown. We used a forward-dynamic computer model of a simulated squatting motion to perform a parametric study of the effects of variations in component rotational alignment in TKA. A cruciate-retaining and posterior-stabilized version of the same TKA implant were compared. We found that femoral rotation had a greater effect on quadriceps forces, collateral ligament forces, and varus/valgus kinematics, while tibial rotation had a greater effect on anteroposterior translations. Our findings support the tendency for orthopedic surgeons to bias the femoral component into external rotation and avoid malrotation of the tibial component. © 2011 Orthopaedic Research Society Published by Wiley Periodicals, Inc. J Orthop Res 29: 969–975, 2011

Modern total knee arthroplasty (TKA) is generally considered to be a safe and cost-effective operation to alleviate pain and restore function in patients who suffer from osteoarthritis (OA).1, 2 Despite clinical success, some patients have difficulty performing important activities of daily living3 and experience quadriceps weakness after surgery.4, 5 Postoperative decreases in quadriceps strength can be as high as 60%,5 some patients have stiffness, limited motion, and instability due to improperly managed collateral ligaments.6, 7

The success of TKA depends on many factors, including prosthesis design, the preoperative condition of the joint, surgical technique, and postoperative rehabilitation. Error in surgical technique has been considered the most common cause for revision TKA.8 Incorrect implant positioning or orientation can lead to accelerated wear and loosening and suboptimal functional performance.8 Despite this importance, there is significant variability associated with femoral component rotational alignment.9–11 Siston et al.11 found rotational alignment errors ranging from 13° internal rotation to 16° external rotation. Errors can often occur in tibial component rotational alignment in the transverse plane,12–14 ranging from 44° internal rotation to 46° external rotation.14 The large variability may be due to the fact that small linear errors in identifying anatomic landmarks translate into large rotational errors.15

Variability in femoral and tibial component rotational alignment can lead to improper joint kinematics and pain. Poor alignment is a major cause of patellofemoral complications,16, 17 with a strong correlation between combined femoral and tibial component internal rotation and the severity of patellofemoral complications.18 Rotation of the femoral component of 5° from the transepicondylar axis alters tibiofemoral kinematics and patellar tracking.19 Malrotation of the tibial component will lead to impingement of the polyethylene, which could lead to loss of motion and wear.20 A study of patients with anterior knee pain found that the average tibial component alignment was 6.2° internal rotation, compared with 0.4° external rotation for patients without pain.21 Despite reports of internal component rotation being associated with more severe complications than external rotation,18, 21, 22 the biomechanical reasons for these complications remain largely unknown.

How variability in rotational alignment may impact TKA patients' ability to perform activities that they deem important remains unknown. Therefore, our purpose was to determine how this variability affects knee joint mechanics. We created a forward-dynamic simulation of an Oxford Rig that simulates knee flexion under quadriceps control. This rig mimics knee kinematics when rising from a chair, or climbing stairs, or riding a bicycle.23 Forward-dynamic simulations enable cause–effect relationships to be identified and are well-suited for performing “what if?” studies,24 wherein the rotation of a prosthetic component can be changed over a range of values while holding all other parameters constant. Establishing ranges of “acceptable” and “unacceptable” rotational alignment may provide orthopedic surgeons with guidelines to ensure more successful postoperative functional outcomes.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. REFERENCES
  8. Supporting Information

The Oxford Rig uses a ball joint to represent the ankle, a universal joint to represent the hip, and permits the pelvis to translate vertically with respect to the ankle. This model topology provides 6 degrees of freedom to the tibiofemoral and patellofemoral joints. A 7-segment model was created using the SIMM/Dynamics Pipeline (MusculoGraphics, Inc., Santa Rosa, CA) and SD/FAST (Parametric Technologies, Inc., Needham, MA) software packages. Segment lengths and inertial characteristics of the femur and tibia were computed for a male subject 180 cm tall with body mass of 75 kg and used relationships for predicting anthropometric values published by Winter.25 Approximate masses and moments of inertia for the implants were estimated from component dimensions and material properties (Table 1).

Table 1. Inertial Properties of Simulated Oxford Rig
SegmentSimulated Cadaver
Mass (kg)Moments of Inertia (kg m−2)
Pelvis30.00Ixx,yy,zz = 0.001
Femur6.93Ixx,zz = 0.1134
Iyy = 0.001
Femoral component0.20Ixx,yy,zz = 0.001
Patella0.025Ixx,yy,zz = 0.001
Patellar component0.025Ixx,yy,zz = 0.001
Tibia3.22Ixx,zz = 0.0543
Iyy = 0.001
Tibial component0.20Ixx,yy,zz = 0.001

Internal forces that influenced kinematics were created by 1 simplified quadriceps muscle (vastus intermedius), and 4 ligaments [patellar, lateral collateral (LCL), medial collateral (MCL), and, when present, posterior cruciate]. Force-generating muscle properties were based on the model of Delp et al.26 The PCL was modeled using 10 fibers, characterized by unique attachment points and slack lengths as described by Makino et al.27 Ligaments were modeled as springs with quadratic force–deformation relationships.28 Other muscles (semitendinosus, semimembranosus, short and long heads of biceps femoris, and medial and lateral gastrocnemius) were included, but remained passive, generating forces of <5 N. Wrapping surfaces were used to prevent muscles and ligaments from passing through bony surfaces.

Contact forces between articulating surfaces were computed using a custom written implementation of a rigid-body-spring-model29 in which forces depended on the interpenetration of contacting implant surfaces. Surface geometries were derived from CAD representations of size 5 Scorpio (Stryker, Mahwah, NJ) cruciate-retaining (CR) and posterior-stabilized (PS) implants.

A proportional-derivative feedback controller was used in conjunction with a simplified planar model of the Oxford Rig to determine the quadriceps force required to lower the pelvis in a controlled manner. We chose proportional-derivative control because we believe it is more easily extendable to complex models with multiple muscles requiring static optimization in future studies. The simplified 2D sagittal plane model was necessary so that estimations of the required knee extension moment could be made without needing to consider the accelerations produced by articular contact forces in a 3D contact-based model. For both the 2D and 3D models, the initial pelvis height corresponded to 20° of knee flexion. A rate of descent of the pelvis of 7.8 cm s−1 was chosen so that the final pose of the 2D model bent the knee to 120° of flexion in 5 s. A slow rate of descent was chosen to reduce inertial effects and maintain stability during the motion. Within the feedback loop, position and velocity errors of the 3D model in relation to the 2D model were multiplied by gains of 60 s−2 and 2 s−1 (arrived at by trial-and-error). The resulting acceleration terms were then added to the expected acceleration (0 ms−2) to find the corrected 3D pelvis acceleration that was used to track the descent of the 2D pelvis. The corrected acceleration and closed-form equations of motion for the simplified 2D model were used to compute the desired knee extensor moment for the 3D model. By assuming a quadriceps moment arm that linearly decreased from 4 to 2 cm as knee flexion changed from 20° to 120°,30 the required force to be applied along the line of action of vastus intermedius was determined.

The default positions of the TKA assembly were established according to the manufacturer's surgical guidelines, relative to bony landmarks. Identical default positions with a 0° cut on the tibial plateau were used for CR and PS designs. Based on our previous studies,11, 14 femoral rotational alignment was varied between 15° external rotation and 15° internal rotation in 5° increments, and tibial rotational alignment for the CR implant was varied between 20° external rotation and 20° internal rotation in 5° increments. Due to its more highly constrained design, the simulation failed for the PS implant at the more extreme tibial rotational alignments. Therefore, tibial rotational alignment of the PS implant was varied between 15° external rotation and 15° internal rotation in 5° increments. Combinations of these rotations provided 63 simulations for the CR implant design and 49 simulations for the PS implant design. We analyzed the effects of these rotations on quadriceps muscle force, collateral ligament forces, and varus/valgus knee angle using the Grood and Suntay convention31 with bone-embedded coordinate systems. We also analyzed tibiofemoral anteroposterior translation as defined by the centers of pressure for the two designs using implant-embedded coordinate systems.

RESULTS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. REFERENCES
  8. Supporting Information

Femoral component alignment had a greater effect on most variables than tibial component alignment or implant design. Internal rotation of the femoral component yielded more undesirable results than external rotation of the femoral component.

Quadriceps Muscle Force

Internally rotated femoral components required the highest forces of the lumped quadriceps in deep flexion. The combination of internally rotated CR femoral components and internally rotated tibial components caused increases to a maximum force of 5,470 N (Fig. 1). The combination of externally rotated femoral components with any rotation of tibial components produced nominal changes in quadriceps force, with a minimum value of 4,770 N. In all cases, the quadriceps forces were the same until ∼80° of flexion.

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Figure 1. Effect of femoral and tibial component rotational alignment on quadriceps force at 120° knee flexion for the CR implant design. The quadriceps demand was greatest for internal femoral and tibial component rotations.

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Collateral Ligament Force

Force in the MCL was only generated for internal femoral component rotations of ≥10°, while force in the LCL was only generated for external femoral component rotations of ≥10°. This was true for both implant designs, regardless of tibial component rotation. When the femoral component rotation was varied with the tibial component held fixed at 0°, the maximum MCL forces were ∼475 N at 90° of flexion for the CR implant and ∼700 N at 120° of flexion for the PS implant (Fig. 2). The maximum LCL force occurred at 20° flexion for both implants, with values of ∼75 N for the CR implant and ∼100 N for the PS implant (Fig. 3). When both the tibial and femoral component rotations were varied in the CR implant, internally rotating the tibial component increased the MCL force, but only when the femoral component was at 15° internal rotation.

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Figure 2. Effect of femoral component rotation on MCL force for the CR and PS implant designs. The MCL force is higher for the PS design than for the CR design and is 0 for the neutrally aligned condition.

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Figure 3. Effect of femoral component rotation on LCL force for the CR and PS implant designs. The LCL force is higher for the PS design than for the CR design and is 0 for the neutrally aligned condition.

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Varus/Valgus Knee Angle

The varus/valgus knee angle for both CR and PS designs was similarly affected by variations in femoral and tibial rotational alignment and was more sensitive to variations in femoral than to variations in tibial component rotation. Externally rotated femoral components induced a varus alignment throughout flexion, with a maximum value of 15° varus, while internally rotated femoral components induced a valgus alignment, with a maximum value of 15° valgus (Fig. 4). Variations in tibial component rotation induced varus/valgus angles of ≤1°.

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Figure 4. Effect of femoral component rotation on varus/valgus knee angle for the CR implant design. Externally rotated femoral components induced a varus alignment throughout flexion, while internally rotated femoral components induced a valgus alignment throughout flexion.

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Tibiofemoral Anterior/Posterior Translation

Based on the motion of the center of pressure of the tibiofemoral joint, anteroposterior translations for both the CR and PS designs were more sensitive to variations in tibial than to variations in femoral alignment. An externally rotated tibial component permitted greater anterior translation than an internally rotated tibial component (Figs. 5 and 6). For the CR implant, the medial condyle consistently exhibited anterior translation, while the lateral contact point exhibited a posterior translation only when the tibial component was internally rotated (Fig. 5). For the PS implant, all combinations of component rotation exhibited posterior translation. Posterior translations of the medial condyle appeared to be lessened in the cases of external tibial component rotation (Fig. 6). Overall, the PS implant exhibited more posterior translation than the CR implant, which was relatively stationary throughout flexion.

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Figure 5. Effect of femoral and tibial component rotation on center of pressure locations on the medial and lateral tibial condyles between 20° and 120° knee flexion for the CR implant design. The anterior translation was greatest for external tibial component rotation. A superior view of a right tibial component is shown.

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Figure 6. Effect of femoral and tibial component rotation on center of pressure locations on the medial and lateral tibial condyles between 20° and 120° knee flexion for the PS implant design. The anterior translation was greatest for external tibial component rotation. A superior view of a right tibial component is shown. Tibial component rotations between 15° external rotation and 15° internal rotation are shown due to complications with simulating tibial malrotations of greater than 15°.

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We also analyzed the effects of component alignment variability on patellar tracking and the screw-home motion. These data can be found as Supplementary Material online, along with video clips of some of the Oxford Rig simulations.

DISCUSSION

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. REFERENCES
  8. Supporting Information

Despite the reported high variability in rotational alignment of the femoral and tibial components in TKA, the biomechanical effects of this variability on functional tasks remained unknown. A previous study investigated the joint contact forces due to varying tibial component orientation during a simulated squat.32 However, to our knowledge, no study systematically investigated the effects of varying both the femoral and tibial components together, and no study investigated the effects of component alignment on muscle force or ligament forces during a simulated functional task. Interestingly, our variables of interest were affected differently by femoral rotation and tibial rotation. Femoral rotation had a greater effect on quadriceps forces, collateral ligament forces, and varus/valgus kinematics, while tibial rotation had a greater effect on anteroposterior translations.

The advantage of a computational simulation of a single subject is that we could determine the effects of component alignment within the same “person” and exclude effects of variables such as weight, height, bony geometry, ligament properties, and component size. By holding these other variables constant and using a small number of implant designs, a common approach for computer simulation studies of TKA,28, 33 we could perform the large number of required simulations and elucidate the effects of variability in component alignment and design. However, despite these advantages, implant designs with different tibiofemoral articular conformity, mobile-bearing designs, and designs with a medial or lateral pivot would likely influence knee joint forces and kinematics, especially anteroposterior translation, and could lead to results different from ours. In particular, the Scorpio implant has femoral condyles that have a single ML radius of curvature, unlike many other CR implant designs that have separate centers of curvature for the medial and lateral condyles in the coronal plane. Future work should determine the sensitivity of our results to subject characteristics and implant geometry.

There are some potential limitations of the Oxford Rig computer model. The Oxford Rig simulates a perfect up-down movement with the hip directly above the ankle and does not simulate trunk flexion. This configuration places a much higher demand on the quadriceps muscle and ligaments than what would be seen in a true squat. The pelvis is only permitted to translate vertically, the foot is permitted to plantarflex a large amount during knee flexion, and the only muscle in the model that carries any force is the lumped quadriceps muscle. Also, we assumed material properties and attachment points for the ligaments in the model based on literature values, though there is considerable variability in reported values. However, our objective was not to determine the actual values for muscle and ligament forces, but instead to determine the effect of variability in component alignment on our variables of interest. The Oxford Rig is an established clinical model and is a commonly used biomechanical testing device.23, 34 Combining its proven capabilities with the advantages of forward-dynamic computer simulations was an effective means to perform our parametric investigation of the effects of component alignment variability.

The quadriceps force required to perform the squatting motion was greater for the internally rotated femoral components than for the externally rotated femoral components by as much as 500 N for knee flexion angles >80°. Increased quadriceps strength leads to improved functional performance.35, 36 Since OA patients and TKA patients experience significant quadriceps weakness,4, 5 component rotation that increases the required quadriceps force could make it more difficult for patients to kneel, squat, or rise from a chair.

Large amounts of internal femoral component rotation may be detrimental to the MCL. Errors in femoral rotational alignment contribute to an imbalanced soft tissue envelope and lead to instability and a limited range of motion.37–39 For both CR and PS knees, we found internal femoral component rotation of 15° created forces within the MCL that are above the published yield point of 453 N.40 Regardless of whether the MCL would rupture, the larger MCL forces associated with internal femoral component rotation would likely be perceived as stiffness by TKA patients, which may inhibit postoperative function. The increase in LCL force induced by external rotation of the femoral component may be due not only to external rotation of the tibia with respect to the femur, but also a combination of rotation and translation. In the model, when the femoral component was externally rotated, the femur was positioned more medially on the tibia in early flexion, and then translated laterally with flexion, which may explain why LCL force is greatest in extension and decreases with flexion.

Our results show a strong correlation between component alignment and tibiofemoral kinematics and are consistent with previous studies. Internally rotated femoral components induce dynamic valgus in the knee (greater valgus orientation with knee flexion).19, 37 We found that an externally rotated tibial component biases the position of the medial condyle posteriorly, which could explain the paradoxical anterior femoral translation that has been observed following TKA.14, 41, 42 Also, we found more posterior femoral rollback for the PS implant than for the CR implant, consistent with a previous in vivo study of knee bend activities.43 Our results for patellofemoral kinematics also agree with those of previous studies,19, 22, 37 which found that internally rotated femoral components tilt and displace the patella more medially compared with neutrally aligned components. Details are in the Supplementary Material.

To test the accuracy of the motions predicted using the simulated Oxford Rig, we performed two validation studies. First, measurements were made using a physical Oxford Rig and compared to simulations that were tailored to match its characteristics (Table S1). The physical model held a mechanical linkage fitted with a TKA rather than a cadaver specimen. After correcting for minor errors in registration of the components in the physical model, simulated collateral ligament lengths and knee angles (abduction/adduction and internal/external rotation) were found to agree with measured values with average RMS errors between simulation and experiment of 1.29 mm and 0.90°. Second, since we used ligament properties from the literature, we performed a sensitivity analysis of the effect of variations in our ligament parameters. Increasing the stiffness of the MCL, LCL, and PCL or decreasing the slack length of the MCL led to an increase in ligament forces, but had no effect on varus/valgus knee angle or the required quadriceps force. Decreasing the slack length of the PCL led to an increase in ligament force and a decrease in quadriceps force, but had no effect on varus/valgus knee angle. Although ligament forces increased with increased stiffness or decreased slack length, the forces increased in a predictable manner and exhibited the same trends as the ligament parameters chosen for our simulations. These validation studies give us confidence in our simulation results. Full details of these tests are provided in the Supplementary Material.

Our findings may support the tendency for orthopedic surgeons to bias the femoral component into external rotation11 and avoid malrotation of the tibial component. Internal femoral component rotations of >10° place a greater demand on the quadriceps and induce higher MCL forces, which may translate into joint stiffness, while external alignment appears to have some advantages, such as less quadriceps demand. External tibial component rotations permit more anterior femoral translation. These results suggest that the combination of internally rotated femoral components and externally rotated tibial components may inhibit function in TKA patients following surgery. Future studies may capitalize on the predictive capabilities for forward-dynamic simulations and may help us understand the relationship between surgical parameters and the ability to perform important functional activities. Such investigations may be key steps towards ensuring patient satisfaction and improving postoperative performance.

Acknowledgements

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. REFERENCES
  8. Supporting Information

Funding for this research was provided by the NSF Graduate Research Fellowship program to Julie Thompson. The authors thank Stryker Orthopaedics for supplying the implant geometry and Ajit Chaudhari for his assistance.

REFERENCES

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. REFERENCES
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. Acknowledgements
  7. REFERENCES
  8. Supporting Information

Additional Supporting Information may be found in the online version of this article.

FilenameFormatSizeDescription
jor_21344_sm_SuppData.doc21KSupplementary Data
jor_21344_sm_SuppMov1.mpeg1212KSupplementary Movie 1
jor_21344_sm_SuppMov2.mpeg1190KSupplementary Movie 2
jor_21344_sm_SuppMov3.mpeg1258KSupplementary Movie 3
jor_21344_sm_SuppMov4.mpeg1200KSupplementary Movie 4
jor_21344_sm_SuppMov5.mpeg1206KSupplementary Movie 5
jor_21344_sm_SuppMov6.mpeg1204KSupplementary Movie 6
jor_21344_sm_SuppMov7.mpeg1204KSupplementary Movie 7
jor_21344_sm_SuppMov8.mpeg1200KSupplementary Movie 8
jor_21344_sm_SuppMov9.mpeg1222KSupplementary Movie 9
jor_21344_sm_SuppMov10.mpeg1214KSupplementary Movie 10

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