Research Papers

An Improved Tibial Force Sensor to Compute Contact Forces and Contact Locations In Vitro After Total Knee Arthroplasty

[+] Author and Article Information
Joshua D. Roth

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

Stephen M. Howell

Department of Biomedical Engineering,
University of California, Davis,
4635 2nd Avenue (Building 97),
Sacramento, CA 95817
e-mail: sebhowell@mac.com

Maury L. Hull

Department of Mechanical Engineering,
Department of Biomedical Engineering,
Department of Orthopaedic Surgery,
University of California, Davis,
4635 2nd Avenue (Building 97),
Sacramento, CA 95817
e-mail: mlhull@ucdavis.edu

1Corresponding author.

Manuscript received July 11, 2016; final manuscript received November 22, 2016; published online February 14, 2017. Assoc. Editor: Kenneth Fischer.

J Biomech Eng 139(4), 041001 (Feb 14, 2017) (8 pages) Paper No: BIO-16-1290; doi: 10.1115/1.4035471 History: Received July 11, 2016; Revised November 22, 2016

Contact force imbalance and contact kinematics (i.e., motion of the contact location in each compartment during flexion) of the tibiofemoral joint are both important predictors of a patient's outcome following total knee arthroplasty (TKA). Previous tibial force sensors have limitations in that they either did not determine contact forces and contact locations independently in the medial and lateral compartments or only did so within restricted areas of the tibial insert, which prevented them from thoroughly evaluating contact force imbalance and contact kinematics in vitro. Accordingly, the primary objective of this study was to present the design and verification of an improved tibial force sensor which overcomes these limitations. The improved tibial force sensor consists of a modified tibial baseplate which houses independent medial and lateral arrays of three custom tension–compression transducers each. This sensor is interchangeable with a standard tibial component because it accommodates tibial articular surface inserts with a range of sizes and thicknesses. This sensor was verified by applying known loads at known locations over the entire surface of the tibial insert to determine the errors in the computed contact force and contact location in each compartment. The root-mean-square errors (RMSEs) in contact force are ≤ 6.1 N which is 1.4% of the 450 N full-scale output. The RMSEs in contact location are ≤ 1.6 mm. This improved tibial force sensor overcomes the limitations of the previous sensors and therefore should be useful for in vitro evaluation of new alignment goals, new surgical techniques, and new component designs in TKA.

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Grahic Jump Location
Fig. 7

Composite showing computed contact forces (a) and contact locations (b)–(d) during knee flexion from 0 deg to 120 deg in an example knee specimen after TKA using the improved tibial force sensor. No clinically undesirable imbalances were observed because the medial and lateral contact force imbalance was ≤ 54 N throughout flexion. Anterior translation of the contact location was observed in both compartments from 30 deg to 90 deg of flexion.

Grahic Jump Location
Fig. 6

Schematic of a model knee specimen mounted in the six degree-of-freedom load application system [29] used to flex and extend the knee specimen. An image of a knee specimen is included to show the location of the knee relative to the load application system (i.e., patella is located toward the base). The knee specimen is located to align the flexion-extension (F–E) and longitudinal rotation axes of the tibiofemoral joint with the F–E and internal-external (I–E) axes of the load application system, respectively. The degrees of freedom follow the coordinate system of Grood and Suntay [34] so that the flexion–extension axis is fixed to the femoral assembly and the longitudinal rotation axis is fixed to the tibial assembly. Accordingly, the femoral assembly provides two degrees of freedom, F–E rotation and medial–lateral (M–L) translation. The tibial assembly provides the remaining four degrees of freedom including I–E and varus–valgus (V–V) rotations and anterior–posterior (A–P) and compression–distraction (C–D) translations. Stepper motor actuators (omitted for clarity) are used to apply loads in all degrees of freedom except M–L. An air spring mounted parallel to the A–P actuator (omitted for clarity) counteracts any A–P forces across the joint caused by gravity. Unconstrained motions in all degrees of freedom are enabled through the use of low-friction bearings.

Grahic Jump Location
Fig. 5

Images showing (a) the deadweight fixture used for calibration/verification of the tibial force sensor with all five layers in place and (b) the proximal surface of the medial (right) and lateral (left) calibration/verification inserts. A stainless steel ball (not shown), which served as an applied contact location, was fit in each of the 114 total detents in the lateral compartment and 119 total detents in the medial compartment. The detents in black served as the applied contact locations for calibration (i.e., calibration points), and those in light gray served as the applied contact locations for verification (i.e., verification points).

Grahic Jump Location
Fig. 4

Diagrams show posterior (left) and proximal (right) views of the tibial force sensor with the coordinate system for each compartment. In both compartments, the compression–distraction (C–D) direction is defined as normal to the transverse surface of the tibial baseplate. The anterior–posterior (A–P) direction is perpendicular to the C–D direction and parallel to the central printed circuit board housing, which is parallel to the central mating features of the tibial articular surface and is designed to be the A–P direction by the manufacturer. The medial–lateral (M–L) direction is the cross-product of the C–D and A–P unit vectors. The origin in the lateral compartment is located one-quarter of the M–L width of the entire articular surface from the lateral edge of the articular surface in the M–L direction and one-half the depth of the lateral compartment of the articular surface in the A–P direction. The origin in the medial compartment is located one-quarter of the M–L width of the entire articular surface from the medial edge of the articular surface in the M–L direction and at the same A–P location as in the lateral compartment in the anterior–posterior direction.

Grahic Jump Location
Fig. 3

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 thecomputed contact force in the medial compartment. The coordinates (M–L1, A–P1), (M–L2, A–P2), and (M–L3, A–P3) are the locations of the three transducers, and (M–Lcomputed,medial, A–Pcomputed,medial) are the coordinates of the contact location of the computed contact force in the medial compartment.

Grahic Jump Location
Fig. 2

Rendering showing how each of the six transducers measures force in either tension or compression. Four electrical resistance strain gauges are mounted to the arms of the transducer. Gauges 1 and 3 are mounted to the proximal surfaces of the arms of the transducer, and gauges 2 and 4 are mounted directly below gauges 1 and 3, respectively, on the distal surfaces of the arms of the transducer. The two sides of the transducer are rigidly mounted to the baseplate. When the transducer is loaded in compression, the arms of the transducer are loaded in bending putting gauges 1 and 3 into compression and gauges 2 and 4 into tension. The opposite occurs when the transducer is loaded in tension (not shown).

Grahic Jump Location
Fig. 1

Images showing (a) an isometric view of the improved tibial force sensor with the medial compartment exploded to show the five layers, and (b) the improved tibial force sensor implanted in a human cadaveric knee. 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 tibial force sensor is connected to external electronics throughout testing via a cable attached to the connector in the central printed circuit board (PCB) housing which passes through the patellar tendon. 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. These inserts have the same articular shape as the standard tibial articular surfaces and come in different sizes and thicknesses so that the overall size and thickness of the tibial force sensor match those of the standard tibial component with the proper thickness articular surface. Once assembled, the internal cavity between the hollowed out baseplate and interface trays was filled with a low stiffness dielectric gel (SYLGARD 527 Silicone, Dow Corning, Midland, MS) to seal the electrical components but not interfere with the load transfer. The sensor can be used in different size knees by using different size and thickness tibial articular surface inserts with the correct conversion trays.



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