0
Research Papers

Virtual Axis Finder: A New Method to Determine the Two Kinematic Axes of Rotation for the Tibio-Femoral Joint

[+] Author and Article Information
Michelle Roland

Biomedical Engineering Program, One Shields Ave., University of California, Davis, CA 95616

M. L. Hull1

Biomedical Engineering Program and Department of Mechanical Engineering, One Shields Ave., University of California, Davis, CA 95616mlhull@ucdavis.edu

S. M. Howell

Department of Mechanical Engineering, One Shields Ave., University of California, Davis, CA 95616

1

Corresponding author.

J Biomech Eng 132(1), 011009 (Dec 18, 2009) (9 pages) doi:10.1115/1.4000163 History: Received March 03, 2009; Revised June 30, 2009; Posted September 04, 2009; Published December 18, 2009; Online December 18, 2009

The tibio-femoral joint has been mechanically approximated with two fixed kinematic axes of rotation, the longitudinal rotational (LR) axis in the tibia and the flexion-extension (FE) axis in the femur. The mechanical axis finder developed by Hollister (1993, “The Axes of Rotation of the Knee,” Clin. Orthop. Relat. Res., 290, pp. 259–268) identified the two fixed axes but the visual-based alignment introduced errors in the method. Therefore, the objectives were to develop and validate a new axis finding method to identify the LR and FE axes which improves on the error of the mechanical axis finder. The virtual axis finder retained the concepts of the mechanical axis finder but utilized a mathematical optimization to identify the axes. Thus, the axes are identified in a two-step process: First, the LR axis is identified from pure internal-external rotation of the tibia and the FE axis is identified after the LR axis is known. The validation used virtual simulations of 3D video-based motion analysis to create relative motion between the femur and tibia during pure internal-external rotation, and flexion-extension with coupled internal-external rotation. The simulations modeled tibio-femoral joint kinematics and incorporated 1 mm of random measurement error. The root mean squared errors (RMSEs) in identifying the position and orientation of the LR and FE axes with the virtual axis finder were 0.45 mm and 0.20 deg, and 0.11 mm and 0.20 deg, respectively. These errors are at least two times better in position and seven times better in orientation than those of the mechanical axis finder. Variables, which were considered a potential source of variation between joints and/or measurement systems, were tested for their sensitivity to the RMSE of identifying the axes. Changes in either the position or orientation of a rotational axis resulted in high sensitivity to translational RMSE (6.8 mm of RMSE per mm of translation) and rotational RMSE (1.38 deg of RMSE per degree of rotation), respectively. Notwithstanding these high sensitivities, corresponding errors can be reduced by segmenting the range of motion into regions where changes in either position or orientation are small. The virtual axis finder successfully increased the accuracy of the mechanical axis finder when the axes of motion are fixed with respect to the bones, but must be used judiciously in applications which do not have fixed axes of rotation.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Topics: Rotation , Motion , Errors , Knee
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Flow chart representing the sequence of steps for the virtual axis finder

Grahic Jump Location
Figure 2

A schematic shows the coordinate systems used to determine the LR axis of rotation (line from LR1 to LR2). From the motion that resulted from an applied internal-external rotational moment on the tibia, two points (LR1,LR2) were identified in the tibia that did not move with respect to the femur: LR1 is constrained to a plane in the tibia which was adjacent to the tibial plateau, and LR2 is constrained to a plane in the tibia distal to the tibial plateau. Fo is the origin of the femoral anatomic coordinate system which is fixed in the femur. To is the origin of the tibial anatomic coordinate system fixed in the tibia.

Grahic Jump Location
Figure 3

A schematic represents the coordinate systems used to determine the FE axis of rotation (line from FE1 to FE2). With an applied flexion-extension rotation of the femur, the tibia will naturally internally and externally rotate. Therefore, the search for two position vectors whose magnitudes do not change during the rotation was initialized from a point on the LR axis (LR1). The search for the first point, FE1, is constrained to a plane fixed in the femur which contains the medial epicondylar eminence. The search for the second point, FE2, is constrained to a plane fixed in the femur which contains the lateral epicondylar eminence. Fo is the origin of the femoral anatomic coordinate system which is fixed in the femur. To is the origin of the tibial anatomic coordinate system fixed in the tibia.

Grahic Jump Location
Figure 4

The RMSE, precision, and bias in determining the LR axis as the random measurement error increases. (A) The pooled rotational errors and (B) the pooled translational errors. The rotational and translational RMSE for the LR axis at the baseline condition of σ=1 mm was 0.21 deg and 0.45 mm, respectively.

Grahic Jump Location
Figure 5

The RMSE, precision, and bias in identifying the LR axis which results from varying levels of internal-external tibial rotation. (A) The pooled rotational errors and (B) the pooled translational errors. The rotational and translational RMSE for the LR axis at the baseline condition of 20 deg was 0.21 deg and 0.45 mm, respectively.

Grahic Jump Location
Figure 6

The RMSE, precision, and bias which results from determining the position of the LR axis when its position (A) and (B), or orientation (C) and (D) does not stay fixed. (A) and (C) The pooled rotational error, and (B) and (D) the pooled translation errors. Note that the RMSE in (A) and (D) are nearly equivalent to the baseline RMSE for the LR axis. Thus, the error is due to the random error term in the data rather than the translation and/or rotation of the LR axis.

Grahic Jump Location
Figure 7

The RMSE, precision, and bias for determining the FE axis after an error in the position of LR1 was incorporated into the optimization. (A) The pooled rotational errors and (B) the pooled translational errors. Note that the nonzero rotational and translational RMSE reported for 0 mm of input error in the position of LR1 equates to the baseline error for determining the FE axis given 90 deg of flexion with 15 deg of internal rotation and a random error term (σ=1 mm, μ=0).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In