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Research Papers

Design, Calibration and Validation of a Novel 3D Printed Instrumented Spatial Linkage that Measures Changes in the Rotational Axes of the Tibiofemoral Joint

[+] Author and Article Information
Daniel P. Bonny

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

M. L. Hull

Biomedical Engineering Graduate Group,
University of California, Davis,
One Shields Avenue,
Davis, CA 95616
Department of Mechanical Engineering,
University of California,
Davis One Shields Avenue,
Davis, CA 95616
Department of Biomedical Engineering,
University of California, Davis,
One Shields Avenue,
Davis, CA 95616
e-mail: mlhull@ucdavis.edu

S. M. Howell

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

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received March 28, 2013; final manuscript received September 4, 2013; accepted manuscript posted September 26, 2013; published online November 26, 2013. Assoc. Editor: Sean S. Kohles.

J Biomech Eng 136(1), 011003 (Nov 26, 2013) (8 pages) Paper No: BIO-13-1163; doi: 10.1115/1.4025528 History: Received March 28, 2013; Revised September 04, 2013; Accepted September 26, 2013

An accurate axis-finding technique is required to measure any changes from normal caused by total knee arthroplasty in the flexion–extension (F–E) and longitudinal rotation (LR) axes of the tibiofemoral joint. In a previous paper, we computationally determined how best to design and use an instrumented spatial linkage (ISL) to locate the F–E and LR axes such that rotational and translational errors were minimized. However, the ISL was not built and consequently was not calibrated; thus the errors in locating these axes were not quantified on an actual ISL. Moreover, previous methods to calibrate an ISL used calibration devices with accuracies that were either undocumented or insufficient for the device to serve as a gold-standard. Accordingly, the objectives were to (1) construct an ISL using the previously established guidelines,(2) calibrate the ISL using an improved method, and (3) quantify the error in measuring changes in the F–E and LR axes. A 3D printed ISL was constructed and calibrated using a coordinate measuring machine, which served as a gold standard. Validation was performed using a fixture that represented the tibiofemoral joint with an adjustable F–E axis and the errors in measuring changes to the positions and orientations of the F–E and LR axes were quantified. The resulting root mean squared errors (RMSEs) of the calibration residuals using the new calibration method were 0.24, 0.33, and 0.15 mm for the anterior–posterior, medial–lateral, and proximal–distal positions, respectively, and 0.11, 0.10, and 0.09 deg for varus–valgus, flexion–extension, and internal–external orientations, respectively. All RMSEs were below 0.29% of the respective full-scale range. When measuring changes to the F–E or LR axes, each orientation error was below 0.5 deg; when measuring changes in the F–E axis, each position error was below 1.0 mm. The largest position RMSE was when measuring a medial–lateral change in the LR axis (1.2 mm). Despite the large size of the ISL, these calibration residuals were better than those for previously published ISLs, particularly when measuring orientations, indicating that using a more accurate gold standard was beneficial in limiting the calibration residuals. The validation method demonstrated that this ISL is capable of accurately measuring clinically important changes (i.e. 1 mm and 1 deg) in the F–E and LR axes.

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Figures

Grahic Jump Location
Fig. 1

An illustration of the ISL attached to a tibiofemoral joint. The six revolute joints are indicated by the black lines and are labeled R1 through R6. Each link is labeled and shaded for clarity.

Grahic Jump Location
Fig. 2

A rendering of link 1 of the ISL showing the “base” coordinate system B and the coordinate system of link 1. The origin of B was the intersection of the axis of the pin and the end of the pin. The coordinate system was oriented such that the j∧B axis was perpendicular to the face of the pin and the i∧B axis was parallel to the side of the link and oriented toward the revolute joint. The coordinate system E was defined identically on link 7 (not shown).

Grahic Jump Location
Fig. 3

A rendering of the calibration fixture (grey) with the ISL (black) attached. The ISL was calibrated on the fixture using the CMM. The calibration fixture consisted of two shafts, pressed into precision bearings, which represented the F–E and LR axes of the tibiofemoral joint.

Grahic Jump Location
Fig. 4

A rendering of link 1 of the ISL showing the approximate locations of the eleven surface points measured using the CMM to define the coordinate system B at each calibration position. Four points on the end of the pin formed a plane defining three degrees of freedom necessary to establish a coordinate system. Four points about the pin formed a circle when projected on the end of the pin; thus defining two more degrees of freedom. The three points on the side of the ISL defined the orientation of the coordinate system about the axis of the pin. The coordinate system E was defined using the same procedure; thus 22 points were located for each ISL position.

Grahic Jump Location
Fig. 5

A photograph of the validation fixture (grey), shown at approximately 60 deg flexion, with the ISL (black) attached. The validation fixture adjusted the relative positions and orientations of the ISL and the F–E axis in the A–P, P–D, V–V, and I–E degrees of freedom. The validation fixture was similar to the calibration fixture and consisted of two fixed axes that represented the F–E and LR axes and allowed for a flexion range of approximately 0 to 110 deg.

Grahic Jump Location
Fig. 6

A diagram of the anatomic coordinate systems that were defined using the location of the F–E and LR axes of the validation fixture in its reference configuration at 0 deg flexion. The origin of the femoral coordinate system Fa was on the intersection of the F–E axis and the shortest line connecting the F–E and LR axes at 0 deg flexion. The j∧Fa axis was coincident with the F–E axis and oriented medially, treating the validation fixture as a right limb. The i∧Fa axis was oriented anteriorly, coincident with the shortest line connecting the F–E and LR axes. The tibial coordinate system was 20 mm distal to the femoral coordinate system along the k∧Fa axis.

Grahic Jump Location
Fig. 7

The bias, precision, and RMSE in measuring changes to the (a) F–E axis and (b) LR axis. For each position and orientation variable, the errors shown were for the starting flexion angle where the maximum RMSE of each variable occurred.

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