Assessment of Anteroposterior Instability of the Knee During Gait

Abstract

A noninvasive kinematic recording technique involving geometric modeling of the knee joint was employed to determine anteroposterior displacements of the knee during walking. The model estimated how much the femoral condyles slid and rolled on the tibial plateau. Movement not due to sliding or rolling was attributed to horizontal translation of the tibia with respect to the femur. Thirty normal adults participated in this study. A three-dimensional analysis system with noninvasive skin markers was employed to collect kinematic data of the femur and tibia during walking. Within-session and between-session reliabilities were high in the tested subjects. Normal subjects had an average of 5.5 mm of maximum anterior displacement of the tibia during stance phase of walking. These results differed neither between left and right knees, nor between men and women. Dynamic instability of the knee during walking can be reasonably measured by the proposed method in normal subjects.

The anterior cruciate ligament (ACL) is the most important structure in the knee joint to maintain joint integrity against anterior force¹⁾. A rupture of the ACL significantly increases anterior instability when passive anterior force is applied to the proximal end of the tibia^2–6). This anterior instability of the human knee has been tested by various forms of instrumentation, positioning, and forces^7–13). Patients with isolated ruptures of the ACL exhibit over 3.0 mm of difference between injured and uninjured knees^7)8)10)13).

In clinical settings, this anterior displacement from passive traction has been used as an index of functional instability in the knee joint^{7–10)12–14)}. Recent research, however, suggests that the amount of anterior displacement in the passive test does not correlate with functional ability of the knee joint in patients with injury to the ACL^15–18), because of compensatory mechanisms operating under dynamic conditions^19–25). Epidemiological studies found that eleven percent of patients with complete rupture of the ACL do not complain of instability or discomfort during functional activities, even though they exhibit some instability in the passive test¹⁵⁾²⁶⁾. Although these patients form a minority, their presence implies the existence of compensatory mechanisms for the injured ACL¹⁵⁾.

This suggests a need to systematically examine how a knee operates under various functional dynamic circumstances. Henning et al.²⁷⁾ inserted a strain gage into the ACL in vivo and measured elongation of the anterior cruciate ligament during various functional activities. Lafortune et al.²⁸⁾ measured anteroposterior displacement from Steinmann pins inserted into the tibia and femur during walking. Although these invasive methods are well designed to provide precise information, they are not amenable to use in everyday clinical examination. This study reports on an effort to design a viable and reliable clinical method, based on geometric modeling of the knee joint, for determining anteroposterior displacements of the knee during walking by a noninvasive kinematic recording technique. The purpose of the present study was to examine the applicability of this kinematic technique, using an optoelectric motion analysis system, for analyzing anteroposterior displacement of the tibia during walking in persons with healthy knees.

Table 1. Glossary of terms used in the model.

α:	Angular change attributable to sliding (in radians).
β:	Angular change attributable to rolling (in radians).
θ:	Angular change from full extension of the knee in the sagittal plane (in radians).
Dfte:	Estimated distance between PF and PT as a function only of knee flexion.
Dftm:	Measured distance between PF and PT.
HT:	Horizontal translation along the tibial plateau.
K:	Value of Dfte at θ=0, based on measurement of θ when the subject is standing still.
PF (femoral point):	Point of intersection between the long axis of the femur and the tibial plateau line.
PT (tibial point):	Point of intersection between the tibial plateau line and the long axis of the tibia.
R:	Radius of curvature of the femoral condyles.
Rolling:	Component of Dfte due to rotation with displacement of the center of rotation, dependent on the radius of the femur.
Sliding:	Component of Dfte due to rotation without displacement of the center of rotation.
TP (tibial plateau line):	Perpendicular line to the long axis of the tibia at the fibular head.

The scope of this study involved developing a novel and clinically feasible approach, with descriptive data for subjects with healthy knees included as well as a report on reliability of the method. This study did not extend to examining the usefulness of the method for patients with dysfunctions of the knee, which would best be undertaken subsequently as a separate and independent clinical study.

Methods

Subjects

Thirty adults, 15 men and 15 women who had no orthopedic injuries in their legs, volunteered to participate in this study. Characteristics of the subjects are summarized in Table 2. Of those thirty subjects, four subjects were randomly selected for examining between-session correlation. Written consent forms, approved by the Human Subjects Committee at Georgia State University, were gathered prior to the experiment from all subjects.

Table 2. Physical characteristics of subjects.

	Male (n=15)		Female (n=15)
	Mean	SD	Mean	SD
	Age (yrs)	32.1	10.8	26.9	5.2
Weight (kg)	73.5	13.9	55.3	6.4
Height (cm)	174.9	8.1	162.5	5.7

Instrumentation

The Waterloo Spatial Motion Analysis and Recording Technique (WATSMART: Northern Digital Inc., Ontario, Canada), a system of both hardware and software for recording and analyzing the movements of infrared emitting diodes (IREDs) that can be affixed to parts of the body, was used to record movement at the knee. The accuracy of this system under static and dynamic conditions has been well documented by Scholz²⁹⁾. Two cameras were used to obtain three-dimensional spatial coordinates through direct linear transformation. For the present study, two cameras were set 2 m apart parallel to the walkway with their focal axes forming an angle of 44 degrees (Fig. 1). The perpendicular bisector of the distance between the two cameras extended 2.5 m to the walkway. Each camera was 1.1 m above the floor. A segment of space, one meter long, 0.53 m wide, and 0.53 m high, was calibrated on the walkway using a 0.53 m cube with 24 IREDs through a multiple calibration technique designed for WATSMART. The variability (standard deviation) at this setting was 0.1 degrees for angular measurements, and 0.2 mm, 0.5 mm, and 0.2 mm for anteroposterior, mediolateral, and vertical axes, respectively, over 1000 frames of measurement of an IRED attached to a stationary board.

Fig. 1.

Arrangement of cameras for collecting data.

For the models, the tibia was hypothetically fixed, so that movement of the knee was represented as displacement of the femur on the tibial plateau. Total horizontal translation of the femoral condyle on the tibial plateau (Dftm) was derived from a relationship between the femoral and tibial axes (Fig. 2). The femoral axis linked the marker on the greater trochanter (marker 1) with that on the lateral epicondyle (marker 2). The tibial axis similarly joined a marker 1 cm anterior to the fibular head (marker 3) and another 3 cm superior to the lateral malleolus (marker 4). A line perpendicular to the tibial axis at the fibular head served as the tibial plateau axis. The point of intersection between the femoral axis and the tibial plateau axis is designated as PF. The distance between PF and one centimeter superior to the fibular head (PT) is designated as Dftm.

Fig. 2.

Definition of motion at the knee. Motion in the model is characterized as horizontal displacement of the femur with respect to the tibia. See Table 1 for explanation of the abbreviations.

Models of the knee

Movement at the knee consists of displacements due partly to angular motion between the tibia and femur and partly to linear motion between the two bones. Because horizontal displacement due to linear motion is the subject of this study, any horizontal displacement that can be attributed to angular motion at the knee needs to be accounted for and removed.

Theoretical model: Horizontal displacement due to angular motion can be derived via arthrokinematic representation. In general, rotation of the femur in the sagittal plane is explained by two arthrokinematic movements: sliding and rolling (Fig. 3). Sliding is rotation without displacement of the center of rotation of the curvature of the femoral condyles. Rolling is rotation with concomitant displacement of the center of rotation dependent on the radius of curvature of the femoral condyles. The sliding and rolling components of Dfte are mathematically expressed as follows:

Fig. 3.

Movement of the femur on the tibial plateau. See Table 1 for explanation of the abbreviations.

Because the theoretical model allows only for sliding and rolling, α and β have the following relationship in composing a given amount (θ) of flexion:

One technical limitation in implementing this model is that, because the sliding and rolling occur simultaneously during movement, their respective magnitudes cannot be precisely partitioned. If, for the sake of argument, the relative magnitude of each component could be estimated from data taken during a gait cycle with the aid of multiple regression analysis,

where C₁ and C₂ would be coefficients of each component derived from the regression analysis.

Practical model: Notice that if θ, which can be measured, were substituted for both α and β in the theoretical model (Fig. 4),

Fig. 4.

Flowchart of regression analysis for the models.

where C₃, C₄, C₅, and C₆ would be coefficients of each component derived from the regression analysis.

Can the practical model serve as a reasonable surrogate for the more sensible but unfortunately impractical theoretical model? This was investigated by assigning hypothetical values to R, α, and β of the theoretical model, such that α + β = θ, to produce paragon data, and then examining how closely use of the practical model, based on θ alone, generates data to fit the paragon. Data were constructed by using θ ranging from 0 to 55 degrees. The relationship between the data and models utilizing nine different sets of α and β was examined through regression analysis. The relative contributions of α and β in the nine combinations ranged from predominantly rolling to predominantly sliding. The adjusted squared multiple regression coefficient of the estimation was 1.00 in every case, so the combined model appears to implicitly contain information determined by α and β (Table 3).

Table 3. Difference in correlation of coefficients due to determination of alpha and beta.

α	β	R	Adj R2	SD
0.1	0.9	1.000	1.000	0.002
0.2	0.8	1.000	1.000	0.002
0.3	0.7	1.000	1.000	0.002
0.4	0.6	1.000	1.000	0.002
0.5	0.5	1.000	1.000	0.002
0.6	0.4	1.000	1.000	0.002
0.7	0.3	1.000	1.000	0.002
0.8	0.2	1.000	1.000	0.002
0.9	0.1	1.000	1.000	0.002

Adj R²: Adjusted R square. Dependent variable: tan (θ) + [tan (θ)−θ]. Independent variable: tan (α)−[tan (β)−β] where θ = α + β, 0<θ<55.

Estimating anterior displacement

Because the practical model was designed to account for rolling and sliding but not for horizontal translation, a discrepancy between motion predicted by the model and actually measured motion can be attributed in great part to horizontal translation. Anterior displacement of the femur on the tibial plateau can thus be estimated by subtracting Dfte, the estimated distance between PF and PT, from Dftm, the corresponding measured distance.

The description thus far refers to movement of the femoral condyles relative to the tibial plateau. Clinical convention, however, dictates that the action be described as anterior displacement of the tibial plateau relative to the femoral condyles, so the anterior displacement of interest must be calculated instead by subtracting Dftm from Dfte.

Procedure

Four IREDs were first affixed to the lateral aspect of each subject's left lower limb. One IRED was placed over the greater trochanter, another over the lateral femoral condyle, a third 10 mm anterior to the head of the fibula, and the fourth 30 mm superior to the lateral malleolus. The subject practiced walking along the five meter walkway, right to left from the perspectives of the two cameras, in such a way that the left foot would land in a 530 mm by 530 mm square drawn in the middle of the walkway. The subject's arms were folded in front of the chest during the trial, so that the IRED over the greater trochanter would be visible to both cameras throughout the left stance phase in which the foot had entered the square. After practicing sufficiently to feel comfortable performing the task correctly, the subject walked three times along the walkway with their self-selected pace for data collection. The cameras recorded the positions of the four IREDs at 200 samples per second as the subject entered and traversed the one meter stretch of space in the middle of the walkway that had been calibrated. Heel strike was registered by a foot switch on the subject's left shoe and synchronized with the kinematic data via an analog-to-digital converter.

The procedure was then repeated for the other leg with the subject walking left to right.

Data analysis

The two-dimensional data from the two cameras were processed by direct linear transformation, via software provided with the WATSMART instrumentation (Northern Digital Inc., Ontario, Canada), into three-dimensional data in a cartesian coordinate system oriented by the calibration frame during the calibration procedure. In this system, referred to hereinafter as the initial coordinate system, the x'-axis was a horizontal axis parallel to the walkway, the y'-axis a horizontal axis perpendicular to the walkway, and the z'-axis vertical.

The displacement data of the four IREDs on the subject's lower limb were filtered by a second-order Butterworth digital filter with a low pass at 20 Hz. From the filtered data, the flexion angle of the knee in the sagittal plane was calculated, i.e., the angle θ of the knee projected in the x'-z' plane of the initial coordinate system. Because close correspondence of the two models was established over a range of 0 to 55 degrees of flexion at the knee, data beyond 55 degrees of flexion of the knee were truncated from both the beginning and end of the original data files. Using the truncated displacement data, the direction of the vertical plane was rotated to most closely approximate, in a least square sense, the plane of trajectories of the four IREDs. That is, if the subject in a given trial did not walk exactly in the direction of the walkway, the x' and y' axes were rotated from the initial coordinate system into an adjusted coordinate system in which the x-axis was parallel with the actual direction of gait, the y-axis was perpendicular to that actual direction, and the z-axis was the same as the z'-axis of the initial coordinate system. This rotation of axes minimized errors due to deviation of the sagittal angle of knee flexion from the x-z plane of motion.

The angle θ was then recalculated, this time only for the extracted data of interest and in the adjusted coordinate system. The practical model was then constructed from the data for θ. The displacement data in the adjusted coordinate system were also used to calculate Dftm. Anterior displacement of the tibia was subsequently estimated by subtracting Dftm from Dfte.

A Pearson product moment correlation was employed to examine within-session reliability of the maximum anterior displacement during stance phase of gait in all participants, and between-session reliability of the anteroposterior displacement through the gait cycle studied in four randomly selected subjects. Intraclass correlation of coefficients [ICCs(2,1)] of measurements were also calculated on right and left knees to confirm within-session reliability of the measurement. Sample mean and standard deviation of the maximum anterior displacement of the tibia during stance phase were calculated. A three way analysis of variance was used to examine the effects on maximum anterior displacement of men versus women, right knee versus left, and first trial versus second versus third.

Results

Figure 5 shows typical anteroposterior displacement of the tibia of one extracted gait cycle (angular translation of the knee ranges between 0 to 55 degrees of flexion). Anterior displacement immediately followed posterior displacement as shown in the figure. Anteroposterior displacements of the tibia were most prominent early in stance phase and least prominent from late stance phase through early swing phase. Anteroposterior displacements during mid-stance varied from subject to subject. Overall, a small amount of anterior displacement was observed in the mid-stance portion of gait. Individual characteristics of anteroposterior displacement of the tibia during stance phase of walking are presented in Table 4. The average maximum anterior displacements during stance phase were 5.7 mm for the right knee and 5.4 mm for left. The average difference in maximum anterior displacement between knees was 1.9 mm (Table 5). Maximum anterior displacement of the tibia during stance phase was neither different between left and right knees, nor different between men and women (p>0.05, Table 6).

Fig. 5.

Typical record of anteroposterior displacement of the tibia with respect to the femur. Positive values indicate anterior displacement.

Table 4. Mean, minimum, maximum, and standard deviation of anterior displacement during stance phase.

	Right				Left
Subj	MIN	MAX	MEAN	SD	MIN	MAX	MEAN	SD
1	−3.3	4.8	0.1	1.9	−3.5	7.9	1.6	3.2
2	−2.3	3.3	0.4	1.5	−1.1	4.5	1.4	1.5
3	−4.1	9.7	3.3	3.9	−1.4	7.9	3.6	2.8
4	−2.1	5.9	1.1	2.3	−2.7	6.3	2.2	2.4
5	−4.4	8.4	1.5	3.4	−0.6	6.2	3.0	1.6
6	−0.6	4.9	2.5	1.4	−1.4	3.9	1.3	1.4
7	−3.0	2.4	−0.0	1.5	−3.4	3.0	0.1	1.7
8	−0.5	1.7	0.6	0.7	−0.9	2.8	0.9	1.1
9	−3.7	10.1	1.0	3.4	−2.9	9.4	1.9	3.1
10	−0.0	5.6	2.2	1.5	−0.6	3.7	1.4	1.2
11	−1.9	4.0	1.7	1.5	−1.8	4.4	1.5	1.6
12	−3.7	3.8	0.4	2.1	−3.4	5.6	1.0	2.6
13	−2.8	2.9	0.6	1.6	−3.0	5.4	1.2	2.1
14	1.0	6.8	4.0	1.6	−0.4	5.4	3.0	1.6
15	−3.0	2.9	−0.1	1.6	−2.0	4.3	1.6	1.8
16	−2.6	10.7	3.4	3.7	−2.6	6.6	1.5	2.6
17	−6.8	9.6	1.4	4.3	−3.1	2.7	−0.7	1.5
18	−1.9	4.1	0.9	1.5	−1.9	10.4	3.7	3.2
19	−1.6	4.9	1.4	1.9	1.8	7.2	4.6	1.5
20	−3.6	3.7	−0.8	1.9	−2.3	3.2	0.3	1.2
21	−6.3	7.2	−0.3	3.7	−1.7	4.3	1.0	2.0
22	−3.2	6.1	0.7	2.8	−3.2	6.1	1.1	2.5
23	−3.0	4.1	0.2	1.9	−3.7	5.8	1.2	2.5
24	−1.2	5.0	1.5	1.8	−2.3	4.8	1.3	2.0
25	−4.9	5.1	−0.7	2.6	−1.3	3.4	0.7	1.1
26	−2.3	9.8	2.0	3.2	−3.2	6.0	0.8	2.3
27	−3.8	12.1	2.9	4.4	−5.1	7.4	0.3	3.3
28	−3.8	2.4	−1.5	1.3	−3.4	3.7	−0.2	2.1
29	−0.7	5.7	2.9	2.2	−6.1	5.7	0.1	2.7
30	−1.7	3.8	1.2	1.4	−1.4	3.8	0.7	1.2
MEAN	−2.72	5.72	1.15	2.28	−2.29	5.39	1.40	2.05
SD	1.70	2.74	1.31	0.98	1.49	1.91	1.18	0.67

MIN: Maximum posterior displacement (mm). MAX: Maximum anterior displacement (mm). MEAN: Average anterior displacement. (+: anterior, −: posterior). SD: Standard deviation of anterior displacement.

Table 5. Differences of anteroposterior displacement between left and right knees (n=90).

	Max post dis.	Max ant dis.	Mean dis.	SD dis.
Mean	1.37	1.94	1.21	0.71
SD	1.52	1.76	0.83	0.67

Max post dis.: Maximum posterior displacement (mm). Max ant dis.: Maximum anterior displacement (mm). Mean dis.: Mean anteroposterior displacement (mm). SD dis.: Standard deviation of anteroposterior displacement (mm). (+: anterior; −: posterior).

Table 6. Analysis of variance of subjects' data.

	Sum-of-Squares	DF	Mean-Square	F-Ratio	p
Gender	12.301	1	12.301	1.924	0.167
Side	3.468	1	3.468	0.542	0.462
Trial	2.089	2	1.044	0.163	0.850
Error	1119.167	175	6.395

Within-session correlation of maximum anterior displacement during stance phase was in the range of 0.81 to 0.87. Data were highly correlated within sessions (Table 7). ICCs(2,1) of the measurements were 0.85 for the right knee and 0.79 for the left. Between-session correlation between first and second sessions ranged from 0.62 to 0.97 (Table 8) through the portion of extracted gait cycle.

Table 7. Within-Session reliability of maximum anterior displacement (Pearson Product Moment Correlation Coefficients).

	Trial 1	Trial 2	Trial 3
Trial 1	—
Trial 2	0.834	—
Trial 3	0.809	0.868	—

Table 8. Correlation of anterior displacement between two sessions.

Subject No.	Side	Correlation
1	Right	0.617
	Left	0.826
2	Right	0.901
	Left	0.831
3	Right	0.952
	Left	0.822
4	Right	0.969
	Left	0.904

Discussion

Recording kinematics of the knee during walking

To assess functional instability of the knee in the clinic, noninvasive methods such as photogrammetry of markers on the skin and electrogoniometry can readily be adapted to study motion at the knee.

Shiavi et al.³⁰⁾ used electrogoniometry to ascertain in eight normal subjects and seven patients with injury of the ACL that the tibia moves backward from its resting position during the stance phase of gait, but not forward from that position. This conflicts with subsequent observations by Lafortune et al.²⁸⁾, based on photogrammetry of Steinmann pins attached directly to the tibia and femur, that the tibia can indeed move anterior to its resting position during part of stance phase. A direct comparison between electrogoniometry and radiographic measurement of anterior displacement of the tibia during an anterior drawer test revealed that the electrogoniometric measurements were twice as great as the radiographic measurements⁴⁾. These findings indicate that, although some goniometric systems may be more precise than others, such systems generally suffer from problems of mechanical linkage, giving rise to high variability.

Although photogrammetry of markers attached to the skin of the subject avoids the problem of poor precision due to play in mechanical linkage of the system for measurement, two lesser problems arise: 1) movement of the skin to which the markers are attached over the bone whose displacement is to be measured and 2) difficulty in adequately representing the center of rotation for the movement under study.

Skin movement: Insofar as soft tissues covering bone slide over the bony surface, true movement of the bone cannot be measured from the overlying skin. When a bone does move, however, concomitant movement of the overlying skin does tend to be proportional³¹⁾³²⁾. If the distal end of a tibia is struck by a hammer, the overlying soft tissue decreases the actual amplitude of the resulting vibration at the proximal end of the tibia, but the measurement represents proportional changes in the bone that depend on the thickness of the overlying soft tissue³³⁾. If an object is attached to the skin, the discrepancy between movement of the object and movement of the underlying structure diminishes as the mass of the object decreases³⁴⁾. These findings suggest that light objects attached to skin at loci with little intervening tissue between skin and bone can be expected to be in relatively favorable positions to mimic the movements of bones underneath. Infrared light emitting diodes (IREDs) utilized in this study are thus useful for this purpose.

Defining the center of rotation: Another difficulty of photogrammetry is determining the center of rotation about the knee. In a traditional three-dimensional analysis of movement at a joint, the center of rotation of the joint must be accurately located for this method to work properly, but finding such a location is technically difficult. Ideally, roentgenography should be used to reduce discrepancies between anatomical and calculated points of reference, but liberal use of roentgenography for clinical analysis of movement is both hazardous and impractical. As an alternative, one pragmatic approach to this problem is to select the point of reference after gathering kinematic data of the movement by retrospectively determining a center of rotation whose data would most closely approximate the actually obtained values. This can effectively be done by the method of least squares³⁵⁾.

The practical model in this study employs a least squares method to determine two coefficients that implicitly contain information about the center of rotation. Although the center of rotation, deducible only from the radius of curvature R of the femoral condyles, cannot be explicitly determined in the practical model, the problem of error that could arise from poor choice of a representative center of rotation is nonetheless minimized by retrospectively using the method of least squares.

Reproducibility of measurement

To test reproducibility of this measurement, the maximum anterior displacement during stance phase was compared across three consecutive trials. The correlation among the three trials ranged from 0.81 to 0.87 (Table 7). The result confirmed high reliability of the measurement within one session. Another question concerning the measurement was whether the same pattern of anteroposterior displacement would appear on separate days. Eight knees in four randomly selected subjects were examined for reproducibility of the measurement. With one exception, the correlation between first and second sessions ranged from 0.82 to 0.97 (Table 8) for the portion of gait cycle studied. Data obtained from a given subject over two different sessions could thus be considered reproducible.

Summary and Conclusion

Not only passive instability but also dynamic instability of the knee should be examined to predict functional ability in patients. In this study, a clinically applicable procedure has been proposed for measuring anteroposterior displacement by utilizing a three dimensional optoelectric measurement system with noninvasive skin markers. The reliability of the optoelectric measurement system was high for three consecutive measurements in one session of data collection, as well as between two separate sessions for the same subject. In subjects with healthy knees, peak anterior displacement of the tibia followed a distinctive posterior displacement after heel strike. Displacement during the mid-stance phase of gait varied from subject to subject. Posterior displacement was noticed during late stance phase to early swing phase. An average of 5.5 mm maximum anterior displacement and of 1.9 mm difference between knees was observed in normal subjects.

This method may merit investigation for applicability to functional assessment of patients with rupture of the anterior cruciate ligament or other conditions of instability at the knee.