Identifying the Functional Flexion-extension Axis of the Knee: An In-Vivo Kinematics Study

Abstract

Purpose: This study aimed to calculate the flexion-extension axis (FEA) of the knee through in-vivo knee kinematics data, and then compare it with two major anatomical axes of the femoral condyles: the transepicondylar axis (TEA) defined by connecting the medial sulcus and lateral prominence, and the cylinder axis (CA) defined by connecting the centers of posterior condyles.

Methods: The knee kinematics data of 20 healthy subjects were acquired under weight-bearing condition using bi-planar x-ray imaging and 3D-2D registration techniques. By tracking the vertical coordinate change of all points on the surface of femur during knee flexion, the FEA was determined as the line connecting the points with the least vertical shift in the medial and lateral condyles respectively. Angular deviation and distance among the TEA, CA and FEA were measured.

Results: The TEA-FEA angular deviation was significantly larger than that of the CA-FEA in 3D and transverse plane (3.45° vs. 1.98°, p < 0.001; 2.72° vs. 1.19°, p = 0.002), but not in the coronal plane (1.61° vs. 0.83°, p = 0.076). The TEA-FEA distance was significantly greater than that of the CA-FEA in the medial side (6.7 mm vs. 1.9 mm, p < 0.001), but not in the lateral side (3.2 mm vs. 2.0 mm, p = 0.16).

Conclusion: The CA is closer to the FEA compared with the TEA; it can better serve as an anatomical surrogate for the functional knee axis.

Fig 1. The algorithm to calculate the center of rotation of the femoral condyle.

A. The center of rotation in a rolling object with circular contact profile keeps a constant vertical distance to the supporting ground; points away from the center of rotation undergo vertical shifts of different magnitudes, depended on their respective distance to the center of rotation. B. When the rolling occurs on an oblique ground, the center of rotation declines naturally; the amount of downward shift of the center of rotation (ΔZ_p0) approximates that of the contact points (ΔZ_pc).

Fig 2. The positions and orientations of the transepicondylar axis (TEA), cylinder axis (CA) and the computed flexion-extension axis (FEA).

The TEA (marked blue) is defined by connecting the most prominent point on the lateral epicondyle and the sulcus point (or, when absent, the prominence) on the medial epicondyle; The CA (marked red) is defined by connecting the two centers of the best fitted spheres to the medial and lateral posterior condyles. The FEA is marked green. The absolute angles of the three axes in the coronal and transverse plane are measured by their in-plane projections in relation to the X axis. The dashed line represents the orientation of the X axis. A. Coronal view. B. Sagittal view. C. Transverse view.

Fig 3. The mapping of the cumulative vertical shift value (cVSV).

The graph shows the distribution of the cVSV from 0° to 120° of knee flexion in the left femur of one subject. The points with the lowest cVSV concentrate at the center of posterior condyles. A. Medial view. B. Lateral view.

Fig 4. The positional relationship between the flexion-extension axis (FEA) and two anatomical axes.

The FEA is marked green, the transepicondylar axis (TEA) is marked blue, and the cylinder axis (CA) is marked red. The presented positions of the CA and TEA were identified by averaging the locations of their end points related to those of the FEA throughout the 20 subjects. The red and blue circles represent the 95% confidence interval of the positions of the CA and TEA end points, respectively. A. Posteromeidal view. B. Posterolateral view.