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Research Papers

Errors in Calculating Anterior–Posterior Tibial Contact Locations in Total Knee Arthroplasty Using Three-Dimensional Model to Two-Dimensional Image Registration in Radiographs: An In Vitro Study of Two Methods

[+] Author and Article Information
Derrick S. Ross

Biomedical Engineering Graduate Group,
University of California, Davis, Davis,
CA 95616

Stephen M. Howell

Department of Biomedical Engineering,
University of California, Davis,
Davis, CA 95616

Maury L. Hull

Department of Mechanical and Aerospace Engineering,
University of California, Davis,
Davis, CA 95616;
Department of Biomedical Engineering,
University of California, Davis,
Davis, CA 95616;
Department of Orthopaedic Surgery,
University of California, Davis,
1 Shields Avenue,
Davis, CA, 95616
e-mail: mlhull@ucdavis.edu

1Corresponding author.

Manuscript received January 10, 2017; final manuscript received August 10, 2017; published online September 28, 2017. Assoc. Editor: Paul Rullkoetter.

J Biomech Eng 139(12), 121003 (Sep 28, 2017) (10 pages) Paper No: BIO-17-1015; doi: 10.1115/1.4037632 History: Received January 10, 2017; Revised August 10, 2017

Knowledge of anterior–posterior (A-P) tibial contact locations provides an objective assessment of the relative motion of the tibia on the femur following total knee arthroplasty (TKA), which can be used to compare the effects of different components, surgical techniques, and alignment goals on knee function in vivo. Both the lowest point method and the penetration method have been used to calculate A-P tibial contact locations using three-dimensional (3D) model to two-dimensional (2D) image registration. The primary objective of this study was to quantify errors in calculating the A-P tibial contact location using the lowest point and penetration methods because the errors in calculating the A-P tibial contact locations using these two methods are unknown. The A-P tibial contact locations were calculated with the two methods and simultaneously measured with a tibial force sensor in ten fresh-frozen cadaveric knee specimens with a TKA. Single-plane radiographs of the knee specimens were acquired at 0 deg, 30 deg, 60 deg, and 90 deg of flexion in neutrally, internally, and externally rotated orientations. While the radiographs were exposed, reference A-P tibial contact locations were simultaneously collected using the tibial force sensor to be compared to the calculated A-P tibial contact locations. The overall root-mean-squared-errors (RMSEs) in the A-P tibial contact location calculated with the lowest point method, the penetration method with penetration, and penetration method without penetration were 5.5 mm, 3.6 mm, and 8.9 mm, respectively. The overall RMSE was lowest for the penetration method with penetration, making it the superior method for calculating A-P tibial contact locations.

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Figures

Grahic Jump Location
Fig. 1

Flowchart of steps to compute A-P tibial contact locations. The flowchart depicts the inputs and outputs for each of the four steps necessary to calculate the A-P tibial contact locations.

Grahic Jump Location
Fig. 2

Schematic showing the testing fixture and aluminum square tubes used to position the cadaveric specimens. The femur was rigidly fixed in all degrees-of-freedom, except F-E, by clamping the femoral aluminum square tube to the fixture. The tibia rested on top of the femur and only F-E was constrained. The F-E of the tibia was constrained by placing a plexiglass cylindrical tube around the tibial aluminum square tube and placing the plexiglass cylindrical tube between two metal rods. These two metal rods together with the plexiglass cylindrical tube prevented the tibia from flexing or extending without restricting any of the other degrees-of-freedom. An 89 N compressive load was applied to the distal end of the inverted tibia to ensure contact between the femoral component and tibial force sensor.

Grahic Jump Location
Fig. 3

Diagram of the laboratory coordinate system used to determine the absolute 3D position and orientation of the tibial and femoral components relative to the X-ray source. The origin of the laboratory coordinate system was located at the X-ray source. The XLab and YLab axes were located within the imaging plane, and the ZLab axis was oriented normal to the imaging plane.

Grahic Jump Location
Fig. 4

Rendering of a proximal view of the tibial force sensor showing the tibial coordinate system. The origin of the coordinate system is defined by the center of the black bounding box drawn around the tibial force sensor in the axial view. The x-axis is parallel to the M-L axis of the component (+ lateral), the y-axis is parallel to the A-P direction of the component (+ posterior), and the z-axis is perpendicular to the plateau of the tibial baseplate (+ proximal). Although the coordinate system of the tibial component was based solely on the geometry of the tibial component, the alignment goal for the tibial component in kinematically aligned TKA is to align the A-P axis of the tibial component perpendicular to the F-E axis of the knee [32,33]. Accordingly, the A-P tibial contact locations have clinical relevance.

Grahic Jump Location
Fig. 5

Diagram of a sagittal cross section of the femoral and tibial components to visually demonstrate the cause of the greater bias for the lowest point method. The black, white, and gray points represent the reference A-P tibial contact location, the A-P tibial contact location computed with the lowest point method, and the A-P tibial contact location computed with the penetration method with penetration, respectively. The error for the penetration method with penetration (ePM) is less than the error for the lowest point method (eLPM). The lowest point method will always underestimate the translation of the A-P tibial contact locations.

Grahic Jump Location
Fig. 6

Diagram of a sagittal cross section of the femoral and tibial components to depict the cause of the greater error for the penetration method without penetration compared to the lowest point method. The gray silhouettes represent relative 3D position and orientation of the components while the dotted outline of the femoral component represents a small error in the relative 3D position and orientation of the femoral component. The black and white points represent the A-P tibial contact location computed for the relative 3D position and orientation and for the relative 3D position and orientation with the small error present, respectively. The figure depicts how a small error in the relative 3D position and orientation can substantially affect the A-P tibial contact location computed for the penetration method without penetration while the small error will only slightly affect the A-P tibial contact location computed for the lowest point method.

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