Sagittal curvature of total knee replacements predicts in vivo kinematics

1. Introduction 

The description of in vivo kinematics after performing total knee arthroplasty (TKA) is one of the challenging topics of modern orthopedics. By evaluating kinematics of the knee joint, it is possible to quantify the displacement of the tibia relative to the femur under different loading conditions pre-, intra- and postoperatively. In the case of performing an analysis after TKA, the motion reflects the restoration of the knee function, and provides one indicator of the surgical outcome. The precise description of in vivo kinematics requires four-dimensional (space and time) tracking of the tibia and the femur and thereafter a meaningful representation of the measured spatial position data.

Current noninvasive methods to investigate the knee kinematics after TKA use, e.g., goniometric (Chao, 1980), electromagnetical (Bull and Amis, 1998), optoelectronic (Duck et al., 2004), or ultrasonical (Cappozzo et al., 2005, Marin et al., 2006) technologies. Typically, for all techniques external markers or devices are attached to the shank and the thigh. One major limitation of these approaches are soft tissue artifacts, which could blur the assessment of the bony tibial and femoral localizations (Stagni et al., 2005). In contrast Roentgen stereophotogrammetry analysis (RSA) based on X-ray imaging enables accurate three-dimensional localization of the tibia and the femur (Kärrholm, 1989). Video fluoroscopy generates a two-dimensional X-ray sequence by providing a continuous sequence of X-ray images at video-rates. Banks et al. improved the fluoroscopy method by a shape recognition technique (Banks and Hodge, 1996), which allowed the three-dimensional localization of the bone during real-life load-bearing activities (e.g., squat, gait).

A mathematical description of the knee motion requires clinical interpretation in terms of flexion–extension, adduction–abduction, internal–external rotation and anterior–posterior drawer. It decomposes the position of the tibia with regard to the femur into three sequential rotations along three predefined axes (Grood and Suntay, 1983). These axes are defined by palpated anatomical landmarks (Cappozzo et al., 1995). Flexion–extension corresponds to a rotation around the transepicondylar axis of the femur, internal–external axial rotation as a rotation around the long axis of the tibia, and abduction–adduction around a floating axis which is orthogonal to the previous two. However, the palpation of anatomical knee landmarks is unreliable and consequently induces a cross-talk effect, which can confuse the interpretation of joint kinematics (Hollister et al., 1993, Piazza and Cavanagh, 2000).

An alternative description of the knee motion, which does not depend on subjectively assessed anatomical landmarks, is the determination of instantaneous helical axes (IHA) (Woltring, 1994) or finite helical axis (FHA) based on the screw theory (Ball, 1998, Chasles, 1880). The screw theory is based on the idea that any rigid body displacement can be described by a rotation about and a translation along a unique axis, which is called the helical axis (HA). Consequently the localization, orientation, and rotation of the HA reflects 6 degrees of freedom (DoF) of motion. In general, a total knee replacement and a normal knee joint do not have a unique or single axis of rotation in the sagittal plane. This means during flexion motion one unique helical axis from each recorded position to the next one can be calculated. This results in multiple axes along the whole flexion motion. Only in the special case of a hinge joint all calculated axes are the same, which is of course not the case for a normal knee joint or a TKA. The FHA algorithm is increasingly used for the quantification of joint kinematics and joint instability (Duck et al., 2003, Gal et al., 2004, Mannel et al., 2004a, Mansour et al., 2004). Nevertheless the FHA method has not been widely accepted by orthopedic surgeons because of its abstract nature (Bull and Amis, 1998).

This study addressed two specific aims. First, we sought to compare in vivo motions of two groups of knees having different implant designs. We hypothesized that different femoral and tibial component designs would influence in vivo kinematics, and that the single-radius TKA design would show a more consistent FHA pattern. The second aim of this study was to illustrate how the screw theory can be integrated into the classical clinical description of in vivo kinematics after TKA.

2. Methods 

Thirteen patients were analyzed after total knee arthroplasty. Seven patients received a dual radius design (Series 7000 Cruciate Retaining, Stryker, Mahwah, MA, USA) and 6 patients received a single radius total knee prosthesis (Scorpio Cruciate Retaining, Stryker, Mahwah, MA, USA). Two surgeons participated, with each surgeon implanting all prostheses of a single design. For both implant designs, identical operative techniques were used. Performing the classic method of bone resection, the femoral component rotation was referenced along the transepicondylar axis (Berger et al., 1993). All patients in this series had a minimum follow-up of 12 months, were active, had no pain, and were rated clinically successful according to a good or excellent functional score (>85 Hospital for Special Surgery rating (Ranawat and Shine, 1973)). The Scorpio CR prosthesis has a sagittal single radius design from −10° to 75° while the 7000 CR has a dual radius design in the sagittal plane (Fig. 1a, Fig. 1b). All patients were tested with the same experimental set-up, a 20cm stair climbing exercise. All subjects were approved by the Institutional Review Board and gave written informed consent. Individual fluoroscopic frames with a 10Hz sampling rate of the step climbing were stored on videotape and then digitized. The position of femoral and tibial components was determined using a three-dimensional fitting technique described by Banks (Banks and Hodge, 1996). The computer aided design solid models were overlaid on the two-dimensional radiographic images. Measurement errors averaged approximately <0.5mm for in-plane translation and 1.0° for all rotations (Banks and Hodge, 1996). The orientations and positions of the tibial tray relative to the femoral component were determined from the three-dimensional models to infer the kinematics of tibia and femur. This transformation allowed us to compute the FHAs for each prosthesis design. Two parameters were computed to describe knee kinematics during the range of knee flexion. First, the angular deviation of the FHA α, describing the angle between the FHA and the medio-lateral axis of the femoral component of the prosthesis was calculated. Second, the localization deviation of the FHA δ was calculated representing the distance between each FHA and the geometric center of the femoral component of the prosthesis.

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Fig. 1a. Femoral component in the sagittal plane for the single radius (Scorpio) design.

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Fig. 1b. Femoral component in the sagittal plane for the dual radius (Series 7000) design.

3. Statistical analysis 

Two statistical parameters were computed: the median and the interquartile range (IQR) of α and δ. The IQR is a robust estimate of the spread of the data, since changes in the upper and lower 25% of the data do not affect it. Therefore, IQR is more representative than calculating the standard deviation (SD) in case of outliers in the data. The statistical differences between the two designs were evaluated by the non-parametric Wilcoxon test with median and IQR values.

4. Results 

The FHAs for one patient with a single-radius TKA and one patient with a dual-radius TKA design are exemplarily illustrated in Fig. 2, Fig. 3. It was found that the kinematics of the single radius design matched closely the kinematics of a hinge-like joint. The angular deviations α for the single radius TKA design ranged among all subjects from 2.6° to 6.5° and the distance δ was 0.06–0.62cm (Fig. 4). The comparative values for the dual radius design were 5.0°–12.4° and 1.4–2.1cm, respectively (Fig. 4). The difference in median angle deviation was not statistical significant (P=0.051), while the difference in median localization deviation was highly statistical different (P=0.001). The IQR values for localization and angle deviation was significantly different between groups (P=0.0083/0.0082), with lower values for the single radius design (Table 1, Fig. 5).

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Fig. 2. Representation of the FHA for the single radius design. The black line indicates the medio-lateral axis of the component.

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Fig. 3. Representation of the FHA for the dual radius design. The black line indicates the medio-lateral axis of the component.

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Fig. 4. Graphs of the median of the angular deviation versus median of the localization deviation for both designs.

Table 1. Wilcoxon test of the difference between the Scorpio design and the 7000 CR design

		P value	Significant difference
	Median angle deviation	0.0513	No
	Median localization deviation	0.0012	Yes
	IQR angle deviation	0.0082	Yes
	IQR localization deviation	0.0083	Yes

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Fig. 5. Graphs of the median IQR of the angular deviation versus median IQR of the localization deviation for both designs.

5. Discussion 

The major finding of the current study was that different TKA designs result in different in vivo kinematics. Since the spread of the helical axes is less pronounced for the single radius design compared to the dual radius TKA, we conclude that for the stair climbing motion the single radius design provides a more uniform movement.

Furthermore, it proved the concept of the TKA design, that for midflexion motion the single radius design is more stable than the dual radius one in terms of varus–valgus laxity. This is shown by the markedly less tilt of the helical axes in the transverse plane for the single radius model.

This study also showed that knee joint kinematics after TKA can be meaningfully described by the concept of finite helical axes.

The fact that two different surgeons performed the surgery of the two groups could be rated as a limitation of the study. Nozaki et al. showed that two surgeons attempting the same surgical technique with the same prosthesis could obtain different results (Nozaki et al., 2002). However, the results of the current study are rather consistent within the two groups indicating the consistency of each surgeons technique. Two surgeons with varying technique would lead to more overlap of the resulting joint kinematics. We therefore believe that the kinematical differences between the two groups due to surgical inconsistency can be estimated as low. However, the results would have been even more reliable if both groups had been operated by the same surgeon.

An important issue of modern TKA is the lift-off phenomena due to internal rotation of the femoral component or unfavorable TKA designs, which can lead to a midflexion instability. This has been described previously by different authors (Insall et al., 2002, Stiehl et al., 1999). In the worst case this can cause revision surgery (Romero et al., 2003). However, the small angular and localization deviations of the FHAs for the single radius design found in the current study indicate a more uniform motion especially in midflexion. This demonstrates that the shape of the femoral component of a total knee arthroplasty may influence the in vivo motion behavior to a considerable and positive degree.

The results of this study indicate that knee kinematics is dominated by the design of the femoral component. Churchill et al. reported that a single flexion axis approximated by the transepicondylar axis can be used to describe the kinematic behavior of the knee after TKA (Churchill et al., 1998). The findings of our study are in agreement with his conclusions only for the Scorpio TKA, which has a single axis design. For the patients who received a Scorpio TKA the FHAs approximated a unique single axis close to the medio-lateral axis passing through the geometrical center in the sagittal plane. On the contrary the dual radius design (Series 7000) has two rotational axes in the sagittal plane, and the FHA is floating between these two axes. Using video fluoroscopy alone, these differences in the kinematic behavior could not be described. Banks et al. calculated the position of the tibial rotation axis in a transverse plane by connecting femoro-tibial contact points of the medial and lateral condyle in different flexion–extension positions (Banks and Hodge, 2004). The current study adds information on the complex three-dimensional characteristics of the instantaneous flexion–extension axes, which reveals variations also in the saggital plane.

Another potential advantage of FHAs for the description of joint kinematics is observer independency (Mannel et al., 2004b). Since there is no need for localizing anatomical landmarks, which can vary considerably among different investigators, the use of FHA has potential clinical application and benefit. The mathematical algorithm is not limited to the analysis of video fluoroscopy data. In addition an improved intraoperative use might be applicable. The current surgical technique for TKA procedures does not implement any technical evaluation of knee kinematics. The majority of surgeons rely on their experience. By incorporating the described algorithm into a navigation system, useful kinematic data might be obtained. The surgeon would gain intraoperative information about joint stability, both before performing the final bony cuts with trial components in place, and after the final positioning of the implants. Especially for computer assisted TKA procedures the use of FHAs could be beneficial because of their independency on anatomically based coordinate systems. Even more interesting, these data could be compared with the post operative data received either from video fluoroscopy or gait analysis. This could allow for a direct comparison of intraoperative kinematical variations due to different surgical techniques and the post operative outcome, which would lead to a better global understanding of TKA procedures.

The following explanations intend to contribute to a better understanding of the screw axes in a clinical context. The position of the FHA relative to the joint structures gives information about the roll–glide behavior of the TKA. To elucidate the relationship between the FHA position and the roll–glide characteristics, six examples are illustrated (Fig. 6). In case 1 the FHA is equivalent with the medio-lateral axis of the femoral component of the TKA. This represents pure gliding of the tibial component along the femoral curvature. The tibial component moves hinge like around the geometrical center of the femoral component without any anterior or posterior translation. In case 2 the FHA runs through the contact points between the femoral and tibial component. This case represents pure rolling. The femoral component rolls back or forth without any gliding or slippage. In the case of an FHA intermediate to the contact point plane and the geometrical center of the femoral component, both rolling and gliding take place simultaneously (case 3). Case 4 is a special case representing a pure translation between the components. Here the FHA is located at an infinite distance because the components are sliding back or forth without any rotation. Case 5 and 6 show the FHA with coupled rotations. In case 5 the FHA is tilted in the frontal plane so that it points through the contact point on the lateral side and the medio-lateral axis of the femoral component on the medial side. This situation is created by a flexion which is accompanied by an additional tibial axial rotation. This leads to rolling on the lateral and gliding on the medial side. Case 6 shows an FHA, that is, tilted in the transverse plane. In this case gliding on both sides takes place but the axis of rotation is not parallel to the medio-lateral axis.

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Fig. 6. Illustration of different cases of localization of the FHA, which reflects different kinematical mechanisms.

Screw axis analysis of in vivo fluoroscopic motion data has been carried out before to analyze knee joint kinematics (Dennis et al., 2005). However, to our knowledge no paper has been published using in vivo video fluoroscopic kinematic data after TKA to calculate screw axes. The coupling of joint rotations as flexion–extension and tibial axial rotation could be detected and parameterized by the angle between the medio-lateral axis and the finite helical axis as was shown before for normal and ACL deficient knee joint (Marin et al., 2003). Additionally the glide–roll mechanisms were parameterized by the distance between the FHA and the medio-lateral axis of the femoral component. The same approach to describe the roll–glide behavior has been used previously in a cadaveric study on human knee joints (Blaha et al., 2003). In an open kinematic chain experiment, the authors assessed the flexion range over which rolling, gliding or both occurred on the medial and lateral side of the knee joint by calculating and evaluating the FHAs.

6. Conclusion 

We propose that the functional approach of FHA analysis could be used as a general and useful tool to analyze kinematical differences for varying femoral component designs. It also proves the suitability of the described method to obtain objective information on TKA kinematics under in vivo conditions. Since the kinematical description using screw axes is observer independent, it might be a future approach to analyze intraoperative knee kinematics by using an optical navigation system. In addition the knowledge of in vivo kinematics of TKA provides important information for designers of TKAs. Since the roll–glide behavior is closely related to abrasive processes, the information obtained from FHA analyses could be used beside other methods (Fregly et al., 2005) to optimize the design for wear reduction.