Research Papers

Characterization and Correction of Errors in Computing Contact Location Between Curved Articular Surfaces: Application to Total Knee Arthroplasty

[+] Author and Article Information
Joshua D. Roth

Biomedical Engineering Graduate Group,
UC Davis,
4635 2nd Avenue (Building 97),
Sacramento, CA 95817
e-mail: jdroth@ucdavis.edu

Stephen M. Howell

Department of Biomedical Engineering,
UC Davis,
451 E. Health Sciences Drive,
Davis, CA 95616
e-mail: sebhowell@mac.com

Maury L. Hull

Department of Orthopaedic Surgery,
UC Davis,
4635 2nd Avenue (Building 97),
Sacramento, CA 95817;
Department of Biomedical Engineering,
UC Davis,
451 E. Health Sciences Drive,
Davis, CA 95616;
Department of Mechanical Engineering,
UC Davis,
One Shields Avenue,
Davis, CA 95616
e-mail: mlhull@ucdavis.edu

1Corresponding author.

Manuscript received November 6, 2016; final manuscript received February 23, 2017; published online April 26, 2017. Assoc. Editor: Guy M. Genin.

J Biomech Eng 139(6), 061006 (Apr 26, 2017) (10 pages) Paper No: BIO-16-1441; doi: 10.1115/1.4036147 History: Received November 06, 2016; Revised February 23, 2017

In total knee arthroplasty (TKA), one common metric used to evaluate innovations in component designs, methods of component alignment, and surgical techniques aimed at decreasing the high rate of patient-reported dissatisfaction is tibiofemoral contact kinematics. Tibiofemoral contact kinematics are determined based on the movement of the contact locations in the medial and lateral compartments of the tibia during knee flexion. A tibial force sensor is a useful instrument to determine the contact locations, because it can simultaneously determine contact forces and contact locations. Previous reports of tibial force sensors have neither characterized nor corrected errors in the computed contact location (i.e., center of pressure) between the femoral and tibial components in TKA that, based on a static analysis, are caused by the curved articular surface of the tibial component. The objectives were to experimentally characterize these errors and to develop and validate an error correction algorithm. The errors were characterized by calculating the difference between the errors in the computed contact locations when forces were applied normal to the tibial articular surface and those when forces were applied normal to the tibial baseplate. The algorithm generated error correction functions to minimize these errors and was validated by determining how much the error correction functions reduced the errors in the computed contact location caused by the curved articular surface. The curved articular surface primarily caused bias (i.e., average or systematic error) which ranged from 1.0 to 2.7 mm in regions of high curvature. The error correction functions reduced the bias in these regions to negligible levels ranging from 0.0 to 0.6 mm (p < 0.001). Bias in the computed contact locations caused by the curved articular surface of the tibial component as small as 1 mm needs to be accounted for, because it might inflate the computed internal–external rotation and anterior–posterior translation of femur on the tibia leading to false identifications of clinically undesirable contact kinematics (e.g., internal rotation and anterior translation during flexion). Our novel error correction algorithm is an effective method to account for this bias to more accurately compute contact kinematics.

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Grahic Jump Location
Fig. 1

Image showing an isometric view of the custom tibial force sensor [10] with the medial compartment exploded to show the five layers. The first layer, which is the most distal, is a modified tibial baseplate (Persona CR size D, Zimmer Biomet, Warsaw, IN) that has been hollowed out from the proximal surface. The second layer consists of printed circuit boards that are used to complete the Wheatstone bridge circuit of each of the six transducers. The third layer consists of two triangular arrays of three custom transducers each; one array is in the medial compartment, and the other is in the lateral compartment. The fourth layer consists of the medial and lateral trays. The interface trays provide a rigid connection between the transducers and the tibial articular surface inserts, which make up the fifth layer. Conversion trays can be attached to the interface trays to accommodate larger articular surface inserts. The fifth and most proximal layer consists of independent medial and lateral tibial articular surface inserts that have the same articular surface shape and thickness as a standard tibial articular surface. Different configurations of this sensor, which allow this sensor to be used in different size knees, are possible by using different size and thickness tibial articular surface inserts with the corresponding conversion trays.

Grahic Jump Location
Fig. 2

Free body diagram of the medial compartment of the tibial force sensor. F1, F2, and F3 are the forces measured by the transducers, which are proportional to the voltage output of each transducer (V1, V2, and V3, respectively), and Fcomputed,medial is the computed contact force in the medial compartment. The coordinates (ML1, AP1), (ML2, AP2), and (ML3, AP3) are the medial–lateral and anterior–posterior locations, respectively, of the three transducers, and (MLcomputed,medial, APcomputed,medial) is the contact location of the computed contact force in the medial compartment.

Grahic Jump Location
Fig. 3

Diagram showing proximal view (top) and sagittal view (bottom) of characterization and validation inserts. These inserts represent the most-common configuration. The inserts for the worst-case configuration (not shown) were larger and thicker but had the same overall design. Each stainless steel sphere (dark gray) rests in a hemispherical detent and defines a contact location. At each contact location, forces were applied both normal to the tibial baseplate and normal to the articular surface.

Grahic Jump Location
Fig. 4

Photograph showing custom dead-weight fixture and two-axis articulating fixture used to characterize the errors in the computed contact location caused by the curved articular surface and validate the error correction algorithm. The cross member slides vertically on the vertical posts using linear ball bearings. Weight plates are stacked on top of the cross member to apply force to the sensor. To eliminate inaccuracies in the applied force due to uncertainty of the actual weight of each weight plate and friction in the bearings, the applied force was measured using a commercially available load cell with a reported maximum error of 0.3 N. Using a digital level with 0.1 deg resolution, the coronal and sagittal orientations of the two-axis articulating fixture were adjusted to set the fixed vertical orientation of the dead-weight fixture either normal to the articular surface at the selected contact location (Fig.3) or oblique to the articular surface of insert (Fig. 6).

Grahic Jump Location
Fig. 5

Flow chart summarizing the three-step error correction algorithm. In step 1, error prediction functions were determined to predict the error in the coordinates of computed contact location as a function of the height above the mounting plane of the transducers (h), the in-plane orientation of the surface normal (i.e., coronal orientation (φ) for medial–lateral (ML) and sagittal orientation (θ) for anterior–posterior (AP)), and the applied force (F). In step 2, virtually computed contact locations were generated by adding virtually generated errors computed using the error prediction functions to points on the articular surface inserts of all configurations of the tibial force sensor where each point was considered an actual contact location. In step 3, error correction functions for the computed contact location were determined that minimized the error between the corrected contact locations and the actual contact locations.

Grahic Jump Location
Fig. 6

Diagram showing proximal (left) and sagittal (right) views of lateral insert used to set levels of the height factor in the first step of the three-step error correction algorithm. The height above the mounting plane of the transducers was set using inserts of three different thicknesses: one representing the minimum height (10 mm), one representing the average height (14.5 mm), and one representing the maximum height (19 mm). Forces were applied at the centroid of the triangle formed by connecting the three transducers (orange), and this location was defined by a stainless steel ball (dark gray) resting in a hemispherical detent. The centroid was selected so that the forces measured by the transducers were equal when the applied force was normal to the tibial baseplate.

Grahic Jump Location
Fig. 7

Regions for the analysis of the errors in (a) the AP coordinate of the computed contact location and (b) ML coordinate of the computed contact location caused by the curved articular surface of the tibial component. Note that only two regions are included in (b) because the coronal curvature is not symmetric; hence, no locations had φ > 5 deg, which would be considered the outer (i.e., peripheral) region. The 5 deg-threshold was selected because it divided the articular surface into nearly equal sections.

Grahic Jump Location
Fig. 8

Errors caused by the curved articular surface precorrection (error set 3) and postcorrection with the error correction functions (error set 5) for the most-common configuration in (a) the ML coordinate in the medial compartment, (b) ML coordinate in the lateral compartment, (c) AP coordinate in the medial compartment, and (d) AP coordinate in the lateral compartment. Each asterisk (*) indicates that the errors precorrection are significantly different than those postcorrection (p < 0.001) based on a post hoc Tukey test. Each number indicates the bias.




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