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Research Papers

# Validation of a New Method for Finding the Rotational Axes of the Knee Using Both Marker-Based Roentgen Stereophotogrammetric Analysis and 3D Video-Based Motion Analysis for Kinematic Measurements

[+] Author and Article Information
Michelle Roland

Department of Biomedical Engineering, University of California, One Shields Avenue, Davis, CA 95616

M. L. Hull1

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

S. M. Howell

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

1

Corresponding author.

J Biomech Eng 133(5), 051003 (Apr 11, 2011) (7 pages) doi:10.1115/1.4003437 History: Received June 11, 2010; Revised December 20, 2010; Posted January 14, 2011; Published April 11, 2011; Online April 11, 2011

## Abstract

In a previous paper, we reported the virtual axis finder, which is a new method for finding the rotational axes of the knee. The virtual axis finder was validated through simulations that were subject to limitations. Hence, the objective of the present study was to perform a mechanical validation with two measurement modalities: 3D video-based motion analysis and marker-based roentgen stereophotogrammetric analysis (RSA). A two rotational axis mechanism was developed, which simulated internal-external (or longitudinal) and flexion-extension (FE) rotations. The actual axes of rotation were known with respect to motion analysis and RSA markers within $±0.0006 deg$ and $±0.036 mm$ and $±0.0001 deg$ and $±0.016 mm$, respectively. The orientation and position root mean squared errors for identifying the longitudinal rotation (LR) and FE axes with video-based motion analysis (0.26 deg, 0.28 m, 0.36 deg, and 0.25 mm, respectively) were smaller than with RSA (1.04 deg, 0.84 mm, 0.82 deg, and 0.32 mm, respectively). The random error or precision in the orientation and position was significantly better ($p=0.01$ and $p=0.02$, respectively) in identifying the LR axis with video-based motion analysis (0.23 deg and 0.24 mm) than with RSA (0.95 deg and 0.76 mm). There was no significant difference in the bias errors between measurement modalities. In comparing the mechanical validations to virtual validations, the virtual validations produced comparable errors to those of the mechanical validation. The only significant difference between the errors of the mechanical and virtual validations was the precision in the position of the LR axis while simulating video-based motion analysis (0.24 mm and 0.78 mm, $p=0.019$). These results indicate that video-based motion analysis with the equipment used in this study is the superior measurement modality for use with the virtual axis finder but both measurement modalities produce satisfactory results. The lack of significant differences between validation techniques suggests that the virtual sensitivity analysis previously performed was appropriately modeled. Thus, the virtual axis finder can be applied with a thorough understanding of its errors in a variety of test conditions.

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## Figures

Figure 6

Bar chart comparing marker-based RSA and 3D video-based motion analysis as the measurement modality for the (a) orientation and (b) position RMSE, bias, and precision (error bars) for identifying the FE axis of rotation. There was no significant difference.

Figure 5

Bar chart comparing marker-based RSA and 3D video-based motion analysis as the measurement modality for the (a) orientation and (b) position RMSE, bias, and precision (error bars) for identifying the LR axis of rotation. There was a significant difference between precisions for the orientation (p∗=0.008) and the position (p∗∗=0.024) errors and a significant difference between RMSE for the orientation (+p=0.01) and position (++p=0.03) errors.

Figure 4

Diagram of the transformations used to perform the error analysis with the FE axis shaft and RSA markers. The marker coordinate system (Fm), which was defined by three markers fixed to the shaft, is transformed into an axial coordinate system (Fa) such that one axis is aligned with the actual axis of rotation (TFa/Fm). The position error was defined by the 2D position vector from the FE axis to the measured axis in a plane that was perpendicular to the actual axis and contained the minimum distance between the actual and measured axes. The orientation error was defined by two projection angles (ϕ and α) between the measured and actual axes onto the two perpendicular planes that were parallel to the FE axis and contained the origin of the axial coordinate system (ZFa-YFa and YFa-XFa planes).

Figure 3

Photograph of the video-based motion analysis set-up. The calibration volume was 0.6×0.9×0.6 m3 and the four Raptor 4 cameras (Motion Analysis Corp., Santa Rosa, CA) were positioned 1–1.3 m above the bottom of the calibrated volume in a 1.5 m arc around the center of the calibrated volume.

Figure 2

Photographs of the two orientation axis mechanism with (a) RSA markers and (b) motion analysis markers. The shafts were rotated in 5 deg steps by rigidly pinning the large end disks to the pillow block by means of precision-machined holes placed in 5 deg steps along a 90 deg arc. The pillow blocks were mounted to a base plate to fix the orientation axes with respect to one another. The shafts rotated in ball bearings that were press fit into each pillow block. Axial compression along the inner race minimized off-axis motion.

Figure 1

Diagram of the two orientation axis mechanism. The horizontal shaft simulated the FE axis of rotation and the vertical axis simulated the LR axis of rotation. The axes of rotation were fixed with respect to one another so that they were perpendicular and intersecting. Six 0.8 mm diameter tantalum RSA markers were fixed to both shafts and two 0.8 mm diameter tantalum RSA axial markers were fixed along the geometric axes to identify the axes of rotation with respect to the RSA markers. An array of four reflective motion analysis markers was fixed to each shaft. A coordinate measurement machine was used to measure centroids of the reflective markers and the geometric axes of the shafts to identify the axes of rotation with respect to the motion analysis markers.

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