Summary
Important information on knee kinematics can be ob- tained using in vitro methods. Specifically, mounting a cadaver lower extremity on an “Oxford” knee jig allows loading of the knee joint and makes it possible to observe physiological motion. This approach can provide a de- tailed description of the displacements and rotations of the patella, femur, and tibia, and direct measurement of load at both the patellofemoral and tibiofemoral articu- lations.Using this approach,the “two-axis”description of tibiofemoral kinematics has been advanced.Another ap- plication of this method describes lower patellofemoral contact forces when a more posterior femorotibial con- tact point is present after total knee arthroplasty. This kinematic information is useful when considering new designs in knee arthroplasty.
Introduction
Although it is clear that the forces and moments trans- mitted across the patellofemoral and tibiofemoral joints affect metabolism of articular cartilage in the normal knee, and wear of joint replacements, very little is known about the magnitude and direction of these forces in vivo.
In part, this is because the tools that are currently avail- able permit only accurate measurement of displacements and rotations in vivo; they do not permit quantification of the forces and moments. Indeed, a great deal is known about the displacement biomechanics of normal and es- pecially prosthetic joints in vivo,while very little is known about the forces and moments transmitted across these joints. In an effort to gain insight into the loads and mo- ments transmitted across the knee, many in vitro studies have used a knee-loading fixture, commonly referred to as an “Oxford” knee jig. These loading fixtures have been developed to recreate common activities such as squat- ting by attempting to simulate muscle contraction and weight bearing. The quadriceps are the most common muscle group that has been simulated, because contrac- tion of these muscles is important during daily activity, and because the orientation of the quadriceps, patella,
and patellar tendon makes it readily accessible to pro- duce a realistic muscle action simply by pulling on the quadriceps tendon. Two approaches have been used to apply body weight to the knee. Either the ankle joint is held stationary and the hip is allowed to translate in a vertical direction, or the hip joint remains stationary and the ankle joint translates in a vertical direction. Both approaches permit 6° of freedom at the knee, such that flexion-extension movement of the knee is constrained by articular contact and the soft tissues that span this joint, and not the loading fixture. With these techniques, the knee is loaded such that a flexion moment is created, and stability is obtained by applying a tensile load to the quadriceps tendon through a load sensor. Compressive loads can be applied about the hip to simulate body weight, and using this feature, activities such as stair- climbing or squatting are simulated.
A tensile load applied to the quadriceps results in a compressive load at the knee joint. Ideally, an additional load is applied to the hamstrings and gastrocnemius muscles. Because the loading jig allows completely unre- strained knee joint motion,very accurate kinematic mea- surements can be made during physiological knee mo- tion. While kinematic measurements can be made using different techniques, we have utilized electromagnetic position sensors rigidly fixed to the femur, tibia, and patella.Additionally,load sensors can be used to measure joint forces during physiological knee motion (⊡ Fig.
23-1). Thus, this in vitro approach allows detailed de- scription of the displacements and rotations of the patel- la,femur,and tibia,and direct measurement of load at the patellofemoral and tibiofemoral interfaces.
There are, however, several limitations associated with using cadaver models to simulate the in vivo condi- tion.First,the actual magnitude of muscle contraction in- volved during squatting is unknown, and thus it can only be estimated, through analytic prediction.An alternative approach is to recreate the load of body weight and then apply a force to the extensor mechanism such that equi- librium is established or flexion-extension motion is cre- ated. Second, when using a cadaver model to simulate squatting, body-weight loads are typically applied through the center of the hip and ankle joints throughout
23 In Vitro Kinematics of the Replaced Knee
S. Incavo, B. Beynnon, K. Coughlin
the entire flexion-extension motion of the knee. In con- trast, when squatting in vivo, the force produced by body weight acts through the center of gravity of the trunk, which is located anterior to the hip, while the force pro- duced by the ground reaction acts through the forefoot, which is located anterior to the ankle joint. Thus, the extension moment arm may be smaller in vivo than in vitro, and the corresponding muscle forces required to extend the leg or maintain a fixed flexion angle would be much less.For these reasons,the quadriceps force applied to flex and extend a cadaver lower extremity with a fixed body-weight load may be greater than the quadriceps forces that occur in vivo.A third concern associated with the use of a cadaver model to recreate knee biomechan- ics is that few studies have simulated contraction of the extensor and flexor muscle groups, specifically the com- bined contraction of the hamstring and gastrocnemius muscles. Clearly, contraction of these muscles has an effect on the biomechanical behavior of the knee, and studies including these combined contractions should be more meaningful than earlier studies.
Another in vitro approach utilizes a robotic system [15]. The robotic testing system serves as both a position- control device and a force-moment sensor. When a knee specimen is mounted and moved through a range of motion, the specimen’s motion pattern is “learned” and then repeated after the specimen has been modified.
Even with these limitations, in vitro studies have pro- vided important insights into several areas of knee kine- matics and biomechanics. Specifically, the kinematic be- havior of the normal knee is not universally agreed upon,
and recent studies challenge conventional understanding of the instantaneous center of rotation model. Several controversial aspects of knee arthroplasty are addressed by in vitro study, such as the role of the PCL and the kine- matic behavior of various knee designs. Another area in which in vitro studies have provided new information in- volves patellar forces associated with knee arthroplasty.
These topics will be discussed separately.
Kinematics of The Normal Knee
It is somewhat surprising that the kinematic behavior of the normal human knee has been variously described in apparently contradictory ways. These descriptions include the instantaneous center of rotation model, the helical-axis model, and the two-axis model. A brief description of the first two is included, and is followed by a more detailed description of the two-axis theory, which is supported by more recent in vitro studies.
Instantaneous Center of Rotation
The motion of the knee in the sagittal plane has tradition- ally been modeled as a four-bar linkage [9].One of the bars represents the ACL,one represents the PCL,and the two re- maining bars connect the tibial ACL and PCL attachments and the femoral ACL and PCL attachments.At a given knee flexion angle the intersection of the ACL and PCL is termed the “instantaneous center of rotation”. At different knee flexion angles, the intersection between the ACL and the PCL changes. Moving from extension to flexion, the in- stantaneous center of rotation follows a semicircular pathway (referred to as the “J” curve), which produces a changing roll-glide ratio with the tibia relative to the femur.
That is, the femur does not roll posteriorly off the tibia, but also slides on the tibia during increasing flexion.
The model has been used to explain the posterior translation of the femur relative to the tibia during flexion, and it has been used to explain resistance to pos- terior drawer motion.The model is useful in showing that the center of rotation of the knee is not rigidly fixed to the femur or the tibia.
The four bar linkage model has proven to be useful in enhancing our understanding of the motions of the knee, although the model assumptions have limitations. The cruciate ligaments are modeled as rigid bars, when, in re- ality, the ligaments elongate during knee motion. In ad- dition, the knee is modeled in two dimensions (flexion- extension in the sagittal plane) only, and the model is not applicable if rotation of 15° or more exists in the other planes [17]. In fact, out-of-plane rotation will lead to errors of up to 20 mm, which is too large to accurately describe knee kinematics [3].
Chapter 23 · In Vitro Kinematics of the Replaced Knee – S. Incavo, B. Beynnon, K. Coughlin
⊡ Fig. 23-1.Oxford loading jig. Hip and ankle joints provide all rotational degrees of freedom. Tibiofemoral kinematics are measured by electro- magnetic position sensors. Constant body-weight and hamstring loads are applied, while flexion cycles are activated by varying the quadriceps load
It is well known that motions of the knee are coupled.
Thus,the functional axis of rotation of the knee is not par- allel to the frontal or the coronal planes. Modeling knee motions using the helical axis of rotation accounts for the oblique angle of the functional axis relative to comm- only referenced anatomical axes. The helical-axis model describes rotations about, and translations along, a fixed axis. Blankevoort showed that patterns of the helical axes are reproducible and consistent when care is taken to ensure that the motion pathways are consistent [2]. The helical-axis technique has been used in vivo combined with roentgen stereophotogrammetric analysis [13,14,18]
and in vitro [1].
The helical axis is not dependent on the choice of the anatomical coordinate system. When the instantaneous helical-axis model is used, the center of rotation is not necessarily the intersection of the ACL and the PCL, sug- gesting that the colateral ligaments and the articular geometry of the knee are also responsible for the location of the helical axis.
Although the helical-axis theory models the knee in three dimensions, there are several drawbacks. The data from the helical-axis model are not unique; they are dependent on the particular motion pathway. Obtaining the model data requires accurate measurement tech- niques. Position and direction parameters of the helical axes are highly susceptible to measurement errors when the rotations are small [19].Finally,it is difficult to discuss the helical axis in clinically meaningful terms and anatomical planes.
Two-Axis Model
As mentioned above, descriptions of knee kinematics based on the instantaneous center of rotation method or helical-axis method have been called into question. Be- cause of this, investigators began to look for a more straightforward approach to describing knee kinematics.
This was based, in part, on the recognition that the pos- terior femoral condyles can be described as circular.
Prior to this recognition, the femur – when viewed from that anatomical lateral – view was thought to be elliptical in the posterior aspect. Based on this circular profile, a single fixed knee flexion axis passing through the condy- lar centers has been postulated [8]. Building on this con- cept, Hollister et al. described knee kinematics based on motions about two fixed axes: a flexion axis located in the femur and a rotational axis in the tibia [10].
To more fully evaluate knee kinematics and expand on these findings, a mathematical modeling technique was applied to cadavers in an Oxford-loaded knee rig by Churchill et al. [3]. The modeling technique identifies
both the optimal knee flexion axis and the longitudinal rotational axis.Once the flexion axis is identified,it can be compared to the femoral epicondylar axis and the longi- tudinal rotational axis can be compared to the tibial axis.
Two significant findings of this work were noted.
First, optimal flexion and longitudinal rotation axes were accurately identified for each specimen from 5° to 90° of flexion. Second, the location of the axes was identified.
The flexion axis very closely aligned with the femoral epi- condylar axis (± 3 mm, 3°), and the longitudinal rotation- al axis was found to intersect the tibial plateau in the re- gion of the medial tibial plateau sulcus. This verifies ear- lier studies which showed that the knee has two bony-fixed primary axes. This model has been described as a “compound hinge model” but is better termed the
“two-axis theory” of knee kinematics (⊡ Fig. 23-2).
At both extremes of the flexion cycle, the two-axis theory does not necessarily apply, however. Noncircular portions of the femoral condyles come into contact with the tibia and menisci in terminal extension (screw-home mechanism) and in flexion beyond 90° (roll-back mech- anism). Nonetheless, this theory represents a subtle, but important distinction in the understanding of knee kine- matics, especially throughout the most functional range of knee motion.
Upon first inspection, the two-axis theory appears to contradict the accepted phenomenon of femoral roll- back. However, this is explained by the fact that the lon- gitudinal rotational axis is located in the medial tibial
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⊡ Fig. 23-2. The “two-axis” theory of knee kinematics, with the femoral epicondylar axis as the flexion axis and the tibial axis as the internal- external rotational axis
FE axis
tibial axis
flexion- extension rotation
internal- extension rotation
plateau. With tibial rotation, more lateral tibial plateau motion occurs than medial plateau motion. Because of this,even though the longitudinal rotational axis does not move posteriorly with respect to the femoral epicondylar axis (roll-back), the femur appears to roll back with knee flexion.This phenomenon can be referred to as “apparent roll-back.” Churchill et al. reported that no true femoral roll-back occurs during much of the flexion cycle (0°- 75°).However,true roll-back does occur for flexion angles generally greater than 75°. Stated differently, “apparent roll-back”occurs from 0° to 75°,and true roll-back occurs over 75° [3].
Once the femoral epicondylar axis is considered to be the flexion axis of the knee,it is logical to examine the tib- ial and patellar axes in relation to the femoral epicondy- lar axis.A follow-up in vitro study supports this logic [5].
When the femoral epicondylar axis was used to reference the tibial axis, the tibial shaft axis was found to be per- pendicular to the femoral epicondylar axis (average 90.5°
from 5° to 90° of knee flexion(⊡ Fig. 23-3).
Tibial rotation was observed to be 5°-15° throughout the flexion cycle. However, nearly all rotation occurred near terminal extension.With flexion greater than 10°-15°, virtually no tibial rotation occurs.
The two-axis theory of knee kinematics has favorable implications for knee arthroplasty. When using a “classi- cal” (perpendicular) tibial cut, rotationally aligning the femoral component along the femoral epicondylar axis should result in a rectangular flexion gap because of the perpendicular relationship of the epicondylar and tibial axes. Furthermore, a femoral component with a circular sagittal profile can yield constant colateral ligament ten- sioning throughout the functional knee motion. Con-
cerning tibial rotations, several aspects of arthroplasty component design should be noted. If the terminal tibial external rotation is excluded (as likely happens after to- tal knee arthroplasty), then the neutral tibial rotational position is more externally rotated than traditionally con- sidered. This externally rotated tibial base-plate position is also supported by a recent MRI study [12].If the femoral epicondylar axis is selected for femoral component rota- tion, the mid portion (rather than the medial one third) of the tibial tubercle may be a preferable rotational land- mark for the tibial base plate.
It is important to mention that while the two-axis model is an excellent description of femoral and tibial motions, it represents a simplification of knee kinemat- ics. For example, the tibial axis is not always perpendicu- lar to the epicondylar axis, but ranges from 85° to 94°
throughout the flexion cycle.Nonetheless,one angle must be selected for placement of the tibial component in TKA, and the average experimentally observed angle of 90° to the tibial shaft axis (a classical tibial cut) reflects both biomechanical and clinical logic.
The two-axis theory is directly applicable to a rotat- ing-platform (mobile-bearing) TKA design. For a rotat- ing tibial design, the rotational center can be located ei- ther centrally or off-center,but most rotating-bearing de- signs utilize a central rotation point.
In vitro studies are particularly suitable to examine options for a given prosthetic design: for example,PCL re- tention vs. substitution and fixed vs. mobile-bearing ar- ticulations. Multiple in vitro studies have examined the role of the PCL in knee arthroplasty [4,11].Agreement ex- ists that in a PCL-retaining design,anterior positioning of the femur on the tibia (paradoxical roll-back) occurs and is worsened if the PCL is deficient.For knee kinematics to be restored even partially, either an intact PCL or a cam- spine mechanism is necessary.
Several in vitro studies have compared fixed-bearing and mobile-bearing design options for the same knee arthroplasty system [7,16].In general,little tibial insert ro- tation occurs, and increasing conformity or rotational constraint in mobile-bearing designs does not adversely affect knee kinematics.
Three-Axis Model
To extend the two-axis model to include the patellofemoral joint we have examined patellar tracking in vitro and referenced this to the femoral epicondylar axis. In a plane perpendicular to the epicondylar axis the patellar axis can be described as a circle with the center approximately 10 mm anterior and 10 mm proximal to the epicondylar axis (⊡ Fig. 23-4). Minimal medial-lateral movement (4 mm) is observed along the epicondylar axis (⊡ Fig. 23-5). This biomechanical finding supports the Chapter 23 · In Vitro Kinematics of the Replaced Knee – S. Incavo, B. Beynnon, K. Coughlin
⊡ Fig. 23-3.Average tibial varus-valgus angulation throughout the knee flexion cycle. The tibial shaft axis was found to be perpendicular to the femoral epicondylar axis (average 90.5° (1.9°) from 5° to 90° of knee flexion. (From [5])
clinical observation that external rotation of the femoral component aids patellar tracking in TKA.
Patellar Component Forces
Patellar tracking and patellar component failure are im- portant aspects of total knee arthroplasty. While fluoro- scopic in vivo studies provide data regarding tibiofemoral kinematics, they do not show the effect of tibiofemoral kinematics on the patellofemoral articulation. In vitro studies can provide helpful information on patellar kine- matics and patellar loading by including a patellar force transducer while measuring kinematics. In one study, the anterior-posterior position of the femur on the tibia was examined and direct comparisons were made based on the status of the PCL [4].The specific conditions that were
studied included the intact PCL, the loose PCL, and a PCL-substituting design. Additionally, the post position was varied from 2 mm more anterior to 4 mm more pos- terior. These implant conditions were shown to directly affect the anterior-posterior position of the femur on the tibia (⊡ Fig. 23-6a). Simultaneous measurement of patellofemoral contact forces demonstrated about 20%
lower forces for the most posterior femoral position (⊡ Fig. 23-6b).
Another in vitro study by D’Lima et al. also supports these findings that a more posterior femoral position (roll-back) significantly decreases patellar compressive forces [6]. This occurs in a normal knee with an intact PCL or with a posterior-stabilized implant but is less like- ly in a PCL-retaining design, especially when the PCL is loose or deficient.
In vitro setups have also been used to study patellar preparation in TKA [20].Comparisons were made for dif- ferent patellar prosthesis designs (resurfacing vs. inset).
When measuring anterior patellar bone strain,it was con- cluded that a patellar resurfacing design is superior (less alteration to strain) to an inset design and that the os- teotomy for patellar resurfacing is more tolerant to error by excess cutting than is the reaming technique required for an inset design.Another finding of the study was that if the ideal depth of the cut or reaming is surpassed (mak- ing the patella too thin), attempts to recreate the original patellar thickness by using a thicker prosthesis are me- chanically detrimental.
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⊡ Fig. 23-4.Schematic of a distal femur (dark line) and the path of the patellar tracking from full extension to 90° flexion (right). The center of the arc describing the patellar path is located at a distance (approximately 10 mm anteriorly and 10 mm proximally) from the FE axis [3]. R Radius of the epicondylar circle, r radius of the arc describing the patellar tracking
⊡ Fig. 23-5. The average patella shift in the frontal plane along the FE axis is 4.3 mm. Open circles represent the patellar position at flexion angles between 0° and 15°; solid circles represent the patellar position at flexion angles between 20° and 90°. (From [5])
FE axis
Conclusions
Knee kinematics and TKA design have been successfully studied using in vitro methods and represent useful com- plements to in vivo studies. In particular, in vivo studies can examine individual cases, while in vitro studies are most useful to study the same specimen with a variety of different treatment options.
References
1. Blaha JD et al (2003) Kinematics of the human knee using an open chain cadaver model. Clin Orthop 410:25-34
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3. Churchill DL et al (1998) The transepicondylar axis approximates the optimal flexion axis of the knee. Clin Orthop 356:111-118
4. Churchill DL et al (2001) The influence of femoral roll-back on patellofemoral contact loads in total knee arthroplasty. J Arthroplasty 16:909-918
5. Coughlin KM et al (2003) Tibial axis and patellar position relative to the femoral epicondylar axis during squatting. J Arthroplasty 18:1048- 1055
Chapter 23 · In Vitro Kinematics of the Replaced Knee – S. Incavo, B. Beynnon, K. Coughlin
Posterior
FR (mm)
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-4
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PCL substituting TKA, post positioned posteriorly
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PCL substituting TKA, standard post position PCL subsituting TKA, post positioned anteriorly PCL retaining TKA, with PCL intact
PCL sacrificing TKA, with PCL resected
800
600
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0 20 40 60 80 100
Flexion Angle (degrees)
PCL sacrificing TKA, PCL resected PCL retaining TKA, PCL intact
PCL substituting TKA, post positioned posteriorly PCL substituting TKA, standard post position PCL substituting TKA, post positioned anteriorly
⊡ Fig. 23-6a, b. a Average difference in the femoral roll-back (■■FR) versus flexion. ■■ FR is the difference in femoral roll-back between the treatment of interest and the reference (standard post position) treatment. b Average patellofemoral contact load (PL) versus flexion. (From [4])
a
b
7. D’Lima DD et al (2000) Comparison between the kinematics of fixed and rotating bearing knee prostheses. Clin Orthop 380:151-157
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