The Use of Functional Analysis in Evaluating Knee Kinematics : Clinical Orthopaedics and Related Research®

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SECTION I SYMPOSIUM: Symposium: Knee Kinematics and Total Knee Replacement Design

The Use of Functional Analysis in Evaluating Knee Kinematics

Andriacchi, Thomas P. PhD*; Dyrby, Chris O. MS*; Johnson, Todd S. PhD**

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Clinical Orthopaedics and Related Research 410():p 44-53, May 2003. | DOI: 10.1097/01.blo.0000062383.79828.f5
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Many of the past improvements in the design of knee replacement have been based on information derived from in vivo functional biomechanical measurements obtained during activities of daily living. For example, one of the major problems limiting the use of total knee replacement in the 1970s and early 1980s was tibial component loosening. 8,15 The problem of tibial component loosening could be related to an imbalance between the load acting on medial and lateral surface of the tibia during walking. Identifying the asymmetry in the load distribution between the medial and lateral compartments of the knee during gait 2,34,40 also provided a strong rationale for correcting a varus deformity of the knee to normal alignment or slight valgus alignment after total knee arthroplasty. Once the information on the asymmetry of the loading across the knee was taken into account, tibial component loosening was reduced substantially through the use of metal-backed tibial components, improved axial alignment, and sophisticated ligament balancing. 8,15

In vivo functional measurements also can provide an objective evaluation of specific design characteristics. Although subjective clinical evaluations 13 or kinematic measures 43 have not shown differences among some types of designs, differences in patient function associated with retention or sacrifice of the posterior cruciate ligament have been associated with specific kinetic measures during stair climbing. Patients with designs that retain the posterior cruciate ligament have more normal quadriceps function while ascending stairs than patients with knee replacements where the cruciate ligament is removed. 4,13,14,29,43 One of the key features of the functional abnormality while ascending stairs was a reduction in the moment sustained by the net quadriceps contraction. 5 Patients with cruciate-sacrificing knee replacements had a tendency to reduce this moment by leaning forward during the portion of the support phase of ascending stairs when the quadriceps moment would reach a peak value. This finding also was consistent with a study where electromyographic activity was measured during stair climbing. 13 In that study, maximum quadriceps activity was found in patients with posterior cruciate ligament-sparing and sacrificing designs. However, patients with posterior cruciate ligament-sacrificing designs required increased use of the soleus muscle while stair climbing. The increased soleus activity suggested a forward lean was occurring to accommodate weak quadriceps in the posterior cruciate ligament-sacrificing designs.

The ability to generate a normal quadriceps moment during stair climbing in patients with cruciate-retaining designs was explained 4 by differences in femoral roll back during flexion between patients with cruciate-retaining and sacrificing designs. Roll back will increase the lever arm of the extensor mechanism providing increased mechanical advantage for the quadriceps during stair climbing. The reports of several studies 4,13,43 are consistent with the interpretation that patients in whom roll back does not occur have a pattern of locomotion develop (forward lean as described above) that reflects an apparent quadriceps weakness during stair climbing.

Passive femoral roll back with flexion has been described in studies done on cadavers. 14,22 Typically, the lateral condyle moves posterior with flexion, which reflects a coupled rotation 22 with flexion. The net effect of roll back 14 or rotation 22 as described in the studies done on cadavers is to increase the lever arm of the quadriceps with flexion. The measurement of roll back during in vivo studies 7,28,41,42 has been more variable then reported from studies done on cadavers. Clearly, during in vivo testing the external forces (including muscle contraction) during a specific activity will influence the kinematics of the knee. Therefore, the characteristics of femoral roll back are activitydependent and differences between passive femoral roll back and in vivo measurements of roll back during activities such as squatting should not be considered paradoxic. 41,42 Several studies have used imaging techniques (fluoroscopic, magnetic resonance imaging, radiographic) to quantify femoral roll back during squatting with one knee in front of the other knee, assisted stepping up during support phase, or the stance phase of walking on a treadmill. 6,7,21,35,41,42 Although these studies have provided useful insights on knee kinematics, the limited field of view of these imaging methods does not permit tests to be done under conditions that reflect the patient’s natural patterns of locomotion. In particular, knee kinematics during walking and stair climbing are a function of a preprogrammed pattern of muscle firing. Conditions such as walking on a treadmill or constraining movement to a small field of view can interfere with the normal patterns of limb movement and will produce knee kinematics that do not reflect patterns of locomotion that occur during activities of daily living. Therefore, there is a need for methods to acquire knee kinematics without constraining or interfering with natural patterns of locomotion.

Although in vivo functional biomechanical measurements have provided useful design information for total knee replacement requirements, future improvement will require a better understanding of the in vivo kinematics of the knee during activities of daily living. The solutions to reducing surface wear, 32,44,45 maintaining ligament function 5 and providing knee function in deep flexion 12,17,20,30,33 will be based on kinematic principles.

The lack of appropriate kinematic information during in vivo activities is caused by the difficulty in obtaining meaningful six-degrees-of-freedom motion of the knee during unencumbered movement. Markers placed on the skin will move relative to the underlying bone and limit the resolution of detailed joint movement. 38 In most cases, only large motions such as flexion and extension have acceptable error limits with skin-based marker systems. Skeletal movement has been measured using alternative approaches to a skin-based marker system. These approaches include stereoradiography, 27,28 bone pins, 31,38 external fixation devices, 3 or single plane fluoroscopic techniques. 6,7,40,41 All of these methods are invasive or expose the test subject to radiation. Therefore, the widespread applicability of these methods is limited.

A previously developed method described as a point cluster technique permits direct in vivo measurement of the anteroposterior (AP) motion and the complete six-degrees-of-freedom motion of the femur on the tibia while doing activities of daily living. 3 The purpose of the current study was to describe some fundamental principles associated with describing the six-degrees-of-freedom motion of the joint. These kinematic principles were used to analyze the influence of the posterior cruciate ligament on AP motion of the knee during stair climbing, the relationship between knee kinematics and wear, and knee kinematics in deep flexion.


All of the studies described by the current authors used the point cluster technique, which permits direct in vivo measurement of the complete six-degrees-of-freedom motion of the femur on the tibia while doing activities of daily living. The technique uses a cluster of points placed on the thigh and shank to measure the motion of the knee. The method minimizes the error associated with skin movement and permits in vivo measurement kinematics measurements of the knee with sufficient resolution to analyze the complete six-degrees-of-freedom motion of the joint. A complete description of the method and error analysis was published previously. 1,3

Reference Frame and Motion Definition

The appropriate interpretation of in vivo kinematic measurements requires a precise and physically meaningful definition of anatomic references. 10,11,19,31,36 For these studies, the motion of the femur was described relative to the tibia. The origin of the femoral coordinate system was located at the midpoint of the transepicondylar line of the distal femur (Fig 1). The origin of the tibial coordinate system was set at the midpoint of a line connecting the medial and lateral points of the tibial plateau.

Fig 1.:
The anatomic coordinate systems used to describe the motion of the femur with respect to the tibia are shown. Flexion and extension (FE), abduction and adduction (AA), and internal and external rotation (IE) were defined by the projection of the anatomic femoral or the axes onto planes fixed in the tibial coordinate system.

Translations were expressed as the displacement of the origin of the femoral coordinate system relative to the tibial system. Anteroposterior motion is the femoral displacement projected on the AP axis of the tibia. Similarly, mediolateral and inferosuperior motion are determined from the projection on the corresponding tibial axis. Locating the position of the femoral reference along the transepicondylar axis minimizes the amount of translation caused by pure rotation, because this axis is close to the instantaneous axis of motion.

Rotation was expressed as projection angles of the femoral axis projected onto planes defined by the axis of the tibia. Internal and external rotations were measured by projecting the mediolateral femoral axis onto a plane created by two reference axes in the tibia, the AP and the mediolateral axes. Abduction and adduction angles also were calculated by projecting the mediolateral femoral axis onto a plane created by the mediolateral and superoinferior tibial axes. Anteroposterior translation was determined by calculating the distance between the origins of the femoral and tibial coordinate systems in the sagittal plane. These rotational definitions clearly reflect the functional aspect of each component rotation. For example, consider internal rotation of the femur with respect to the tibia with the knee at full extension. Internal rotation of the femur will stress the anterior portion of the lateral meniscus and the posterior portion of the medial. Using the projection angle definition similar stress is applied to the menisci during internal rotation with the knee flexion at 90°. This approach particularly is important when studying rotation of the knee in deep flexion because this definition of rotational motion remains anatomically consistent independent of the angle of flexion.

Kinematic Changes Associated With Total Knee Replacement Designs

As described previously, the functional differences between the posterior cruciate ligament-retaining and sacrificing designs suggest patients without a functional posterior cruciate ligament adapt an abnormal pattern of motion during stair climbing by leaning forward to reduce the moment sustained by the quadriceps muscles. This finding has been explained by the differences in tibiofemoral roll back between different designs. Roll back with flexion will cause the lever arm (distance between tibiofemoral contact and patellar ligament) of the quadriceps increases. 4 If roll back does not occur, the quadriceps muscles will have a reduced lever arm. Abnormal roll back was one explanation for the reduced quadriceps moment associated with cruciate sacrificing, because reduced roll back would shorten the lever arm of the quadriceps muscle. The purpose of the current study was to test the hypothesis that femoral roll back occurs during stair climbing and that the characteristics of the AP movement of the femur are dependent on the function of the posterior cruciate ligament.


Fifteen patients were tested after total knee replacement. All patients had implants from the NexGen™ system (Zimmer, Warsaw, IN) and were selected on the basis of a good or excellent clinical result (> 85 Hospital for Special Surgery rating). 37 The patients were tested after a minimum of 9 months after surgery. Ten knee replacements were cruciate-retaining and seven replacements were posterior-stabilized. The implants had nearly identical tibiofemoral and patellofemoral geometry. In addition, seven healthy subjects were tested. All patients were tested during level walking and climbing a 20-cm step. All subjects were approved by the Institutional Review Board and received informed consent.

Anteroposterior Movement During Stair Climbing

The temporal pattern of AP movement of the femur relative to the tibia during the stair climbing cycle had several features that were common to all healthy subjects and patients after total knee replacement. The stair climbing cycle began with elevating the limb (swing phase). Through the early swing phase, the femur moves forward relative to the tibia with flexion (Fig 2). This reverse roll back does not contradict what usually is described as femoral roll back, because roll back is a passive movement with flexion and the forward movement of the femur with flexion during the early swing phase of stair climbing was produced by hamstring contraction that pulls the tibia posterior. As the swing phase continues to approximately 45°, the femur reaches a maximum anterior position and reverses direction. An offset (defined as the maximum difference between the AP position of the femur at identical flexion angles) was observed for the movement of the femur during walking and stair climbing (Fig 2). For example, there was an offset between the swing phase position of the femur and the stance phase position at identical angles of knee flexion. The offset (at maximum AP translation) between the swing and stance phase position provides a quantitative measure to compare AP movement of the knee. The average offset in AP translation for the healthy population (1.9 cm ± 0.6 cm) occurred at a flexion angle of 45°.

Fig 2.:
This graph shows the averaged normal phase plot of femoral translation versus knee flexion during stair climbing. During the early swing phase, the femoral reference point (midpoint of transepicondylar axes) translates anterior with flexion. During the late swing phase, femoral reference point translates posterior with flexion. During the support phase, there is minimal translation of the femoral reference point.

This value was significantly less than for either group of patients after total knee replacement. The cruciate-retaining group was 2.9 cm ± 0.6 cm whereas the posterior-stabilized group was 3.3 cm ± 0.8 cm. The posterior-stabilized group had the greatest anterior position at 66° ± 7° knee flexion. The cruciate-retaining group had a maximum anterior position at 54° ± 8° knee flexion whereas the healthy group reached a maximum anterior position at 45° ± 5° knee flexion (Fig 3).

Fig 3.:
A graph shows a comparison of the averaged phase plots of femoral translation versus knee flexion during stair climbing for healthy subjects, patients with a cruciate-retaining design (CR), and patients with a cruciate-sacrificing (PS) design. The patients with a cruciate-sacrificing design maintained an anterior location of contact until approximately 70° flexion where the cam usually engages. The patients with a cruciate-retaining design also had more anterior translation than the healthy group. The swing phase AP motion before stair climbing seems to be dependent on the function of the posterior cruciate ligament.

The differences in the AP translation likely were associated with the interplay between the posterior cruciate ligament or its substitute and active muscle contraction during the swing phase (nonweightbearing) portion of the stair climbing cycle. It seems that the motion of the femur during the nonweightbearing phase of the cycle determines the position of the femur during the weightbearing phase. The posterior-stabilized design had the largest anterior displacement of the femur during swing phase, because the cam did not engage until approximately 70° flexion, which likely is too late in flexion to replicate normal posterior cruciate ligament function. The cruciate-retaining design also showed increased anterior displacement of the femur during the swing phase, suggesting tensioning of the posterior cruciate ligament near 45° might be an important consideration. As noted previously, the swing phase motion of the femur determines the posterior position of the femur at the beginning of stance (approximately 60° flexion). The position of the femur at the beginning of stance determines the lever arm of the quadriceps when there is maximum demand on the quadriceps muscle. These findings support the observation that patients with a posterior-stabilized design adapt a reduced quadriceps moment during stair climbing to compensate for a reduced quadriceps lever arm. 4

Kinematics and Wear

The kinematics of the knee is a critical factor influencing wear at the joint. 9 Subtle variations in rolling, tractive rolling and sliding motion, and the direction of the pathway of motion can have substantial affects on the production of wear debris or cyclic fatigue of the ultrahigh molecular weight polyethylene. 9,44,46 The degree of rolling and sliding can be quantified by the slip velocity. The magnitude of the interfacial slip velocity provides quantification of the rolling versus sliding behavior of the tibiofemoral joint when relative motion occurs. For pure rolling, the interfacial slip velocity will approach 0. 23,24 The purpose of the current study was to analyze the influence of the tibiofemoral interfacial slip velocity during walking on wear rates and wear patterns using a displacement controlled knee wear simulator.

Ten patients with a posterior cruciate-retaining knee design were tested while walking in the gait laboratory. All patients were selected on the basis of a good or excellent clinical result (> 85 Hospital for Special Surgery rating). 37 Institutional Review Board approval was obtained for all patients and all patients gave informed consent. The previously described point cluster method was used to determine the six-degrees-of-freedom motion of the femur with respect to the tibia. 3 A computed tomography (CT) scan of the knee was used to locate a solid computer-aided design model of the specific implant (size and orientation) tested in vivo. This computer-aided model was located precisely by deriving a transformation between a subcluster of markers common to the CT image and the marker cluster used during the gait test. The in vivo contact locations and interfacial slip velocity profiles were derived using a previously described proximity detection and approach algorithm, which maintained continuous physical tibiofemoral contact by slight iterative perturbation of at most two displacements and the abduction and adduction rotation. 24 The in vivo patient-derived kinematics were implemented on a displacement controlled knee wear simulator (Model KS-2–6-1000, Advanced Mechanical Technology, Inc, Watertown, MA) through the appropriate application of coordinate transformations between the patient data and the machined-based coordinate systems. 24–26

In Vivo Interface Slip Velocity Produces Increased Wear

The kinematics of the knee during walking showed several unique kinematic features. At heelstrike the knee is near full extension and the femoral component is located posteriorly and internally rotated relative to the tibia. During the period from midstance, the femur displaces anteriorly and externally rotates while flexing and extending to terminal extension during stance phase (Fig 4). This complex set of motions produces a local maximum during stance phase in the slip velocity on both condyles immediately after heelstrike. A previous study described this local maximum as a heelstrike transient. 25 The absolute maximum slip velocities occur during swing phase just before heelstrike. A previous knee simulator study 26 showed that the maximum wear rate was significantly higher (27.9 +/−2.9 mg/106 cycles) when these slip velocities were incorporated as input to the simulator relative to studies where the slip velocities were not applied (approximately 15–20 mg/106 cycles). Therefore, the high slip velocities during heelstrike and during swing phase indicate the potential for sliding motion that can produce a greater volume of abrasive wear debris.

Fig 4.:
This graph shows the average knee motion and slip velocity at the contact surface during walking. The greatest stance phase slip velocity occurs just after heel strike, and the largest slip velocity occurs during swing phase just before heel strike.

Knee Kinematics in Deep Flexion

Deep flexion is essential for activities of daily living for Indian, Middle Eastern, and Japanese cultures. 16 Their activities of daily living include kneeling for praying or tea ceremonies, squatting, and sitting cross-legged. These activities require flexion angles of as much as 160°. 17,18 In these cultures, deep flexion is fundamental to maintaining a normal lifestyle. However, even in western cultures, there is a wide range of activities (recreational and occupational) that require deep flexion. Any limitation in the range of possible knee flexion can limit the overall quality of life and employment. 39 The purpose of the current study was to examine the kinematics of the knee in deep flexion.


Twenty (10 males, 10 females) native Japanese subjects (35 +/− 13 years, 1.6 m +/− 0.1, 588 +/− 166 N) were tested while moving from standing into a deep squat resting position (both legs). All subjects were selected on the basis of history of no previous musculoskeletal injury or disease that would influence doing a deep squat and a history of doing deep squatting during normal activities of daily living. The previously described point cluster technique was used to obtain the six-degrees-of-freedom motion of the knee.

Internal External Rotation in Deep Flexion

The squat activity began in a standing position and ended with the subject having both knees flexed to approximately 150° in a resting squat. As the knee initially flexed in the range between 0° and 120°, the femur externally rotated at a uniform rate. The total external rotation between 0° and 120° was approximately 10° (Fig 5). After 120° flexion, the rate of external rotation of the femur with flexion increased substantially. Between 120° and 150° flexion, the femur externally rotated approximately 20°. Therefore, beyond 120° flexion, the knee requires substantial external rotation to achieve deep flexion. Currently, most designs of total knee arthroplasty can achieve 120° flexion. However, patients requiring deeper flexion need the capacity for substantial rotation beyond 120° flexion.

Fig 5.:
A graph shows femoral rotation as a function of knee flexion while going from a standing position to a squat into deep flexion. The rate of external rotation with flexion increases substantially after 120° flexion (Point A).

The precise characterization of the kinematics of the knee during ambulatory activities is important for future enhancement and evaluation of total knee replacement. Numerous factors can influence the motion of the joint during ambulation. The results described in the current study for walking, stair climbing, and deep squatting indicate that the kinematics of the knee are activity-dependent. In addition, there can be important variations in the kinematics within one activity such as walking, because muscle activity will influence joint kinematics. Also, patients can adapt different patterns of locomotion that are dependent on the design of the implant. The ability of patients to adapt different patterns of locomotion places additional burdens on in vivo testing protocols. Testing should be done with a minimal encumbrance to the natural movement of the patients, because the testing environment could cause a functional adaptation that does not reflect conditions during normal activities of daily living. Care also should be taken in the definition of the description of motion as shown in Figure 1. The approach described permits a physically meaningful interpretation even with the knee in deep flexion.

An analysis of functional in vivo six-degrees-of-freedom motion has helped to identify the functional role of the posterior cruciate ligament during stair climbing. The functional importance of the posterior cruciate ligament can be shown during the swing phase of the stair climbing cycle where the forward movement of the femur is restrained to move posteriorly after approximately 45° flexion for the normal knee. This swing phase restraint provided by the posterior cruciate ligament produces the posterior contact of the femur and increased lever of the quadriceps in the early stance phase when maximum demand is placed on the quadriceps. Therefore, posterior cruciate ligament tensioning at approximately 45° flexion seems to be important for stair climbing function.

The current authors also presented results that show that the kinematics of the knee is a critical factor influencing wear at the joint. Subtle variations in rolling, tractive rolling, and sliding motion and the direction of the pathway of motion can have substantial effects on the production of wear debris or cyclic fatigue of the ultrahigh molecular weight polyethylene. Therefore, a rigorous analysis of in vivo kinematics is crucial to establishing appropriate wear criteria for bearing surfaces at the joint. Finally, an analysis of the knee in deep flexion showed the importance of providing substantial rotational capacity beyond 120° flexion.


The authors thank Melanie Cole for assistance in the preparation of this manuscript.


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Section Description

William J. Maloney, MD; and John C. Clohisy, MD—Guest Editors

© 2003 Lippincott Williams & Wilkins, Inc.