EVALUATING MEASUREMENT UNCERTAINTY IN PREDICTED TIBIOFEMORAL CONTACT POSITIONS USING FLUOROSCOPY-DRIVEN FEA

*Pal, S; *Mitra, S; *Laz, P J; **Petrella, A J; +*Rullkoetter, P J +*University of Denver, Denver, CO

prullkoe@du.edu

Introduction Fluoroscopy-based kinematic evaluation has been an invaluable tool for quantifying knee replacement mechanics in vivo [1,2]. In addition to relative tibiofemoral kinematics, implant contact locations during different activities have been estimated [3]. However, uncertainty in spatial position exists in the process, due in part to image clarity, operator experience and differences in geometry between the implant CAD models and the as-manufactured parts. Especially with conforming implants, small measurement uncertainty in the model-fitting process to determine relative implant position can lead to substantial differences in estimated center-of-pressure contact location [4]. In addition, when evaluating cam-post contact in posterior stabilized implants, relative positional uncertainty could create erroneous conclusions regarding whether or not post contact actually occurred. Hence, the objective of the present study was to develop an efficient method to account for measurement uncertainty in the model-fitting process, and to evaluate the potential bounds of implant center-of-pressure contact estimates. Methods A probabilistic finite element model of TKA contact was developed based on single plane fluoroscopy data for a patient with a fixed-bearing, semi-constrained, posterior stabilized (PS) implant [4]. The patient’s TKA was clinically successful, with no ligamentous laxity or pain. Fluoroscopic images from 0° to 90° flexion at 10° intervals were digitized for the implant in the sagittal plane. Three-dimensional (3D) models of the implants were overlaid on the images using an interactive model-fitting technique [5], with reported errors less than 0.5 mm and 0.5° for in-plane translations and rotations, respectively [6]. For each image, the positions and orientations, or pose, of the femoral and tibial components with respect to the fluoroscopy machine were extracted. The probabilistic finite element model was used to evaluate the impact of uncertainty in component spatial position from the fluoroscopy model-fitting technique on contact position. The femoral component was modeled using 3D rigid surface elements and the tibial insert was represented by rigid 8-noded hexahedral elements, with a previously-verified nonlinear pressure-overclosure relationship [7]. The probabilistic analysis parameters were the 6 degrees of freedom (DOF) describing the pose of each component at each flexion angle. The DOFs were represented as Gaussian distributions with parameter mean values from the model-fitting process. Standard deviations for in-plane DOFs (AP, IS and FE) were set to 0.17 mm and 0.17° so that ±3σ captured the reported 0.5 mm and 0.5° errors [5], while out-of-plane DOFs (ML, VV and IE) standard deviations were assumed to be 0.34 mm and 0.34°. To allow both medial and lateral condyles to contact throughout flexion and estimate AP contact position, the applied loading conditions were a combination of joint loading and kinematic parameters derived from fluoroscopic analysis. The distal surface of the tibial insert was fixed and all boundary conditions were applied to the femoral component. A compressive load of 750N was applied in the inferior-superior (IS) direction to maintain contact. The applied fluoroscopic kinematic data included anterior-posterior (AP) displacement and internal-external (IE) and flexion-extension (FE) rotations of the femoral component. Medial-lateral (ML) and varus-valgus (VV) DOFs were unconstrained. Based on the distributions of implant positions, the distribution of condylar contact position was determined from the center of contact pressure on the tibial insert. Results The predicted envelopes (1 to 99 percentiles) of AP contact position showed substantial variability for both condyles, with greater variability observed within the first 30° of flexion (Figure 1). Based on the small input parameter variability levels, the average ranges (1 to 99%) of AP contact position were 10.9 mm (0°-30°) and 5.4 mm (30°-90°) for the medial condyle, and 9.3 mm (0°-30°) and 6.3 mm (30°-90°) for the lateral condyle. Maximum AP ranges for the medial and lateral condyles were 12.2 mm (at 0°) and 10.7 mm (at 20°), respectively. While the input distributions were Gaussian distributed, the contact positions were skewed anteriorly with a majority of the posterior data closer to the mean (Figure 1). In general, contact locations for the AP

envelopes were posterior to the mid-coronal plane (Figure 1 inset) beyond 30°, with the exception of the 99% bound for the medial condyle at 90° when the femoral cam came in contact with the insert post (Figure 2b). Uncertainty in the relative positions of the implants affected cam post interaction; no contact was observed at the 1% and 50% probability levels, while contact was seen at the 99% level (Figure 2). Discussion Incorporating measurement uncertainty in the fluoroscopy-driven contact analysis resulted in significant bounds for both medial and lateral AP contact position, and is likely a factor in the large variability in kinematic studies in vivo [1,2,3]. As expected, variability was greater at smaller flexion angles due to greater conformity. In addition, it was shown that the extremal positions resulted in both contact and no contact conclusions for the cam-post interaction. Contact location distributions will likely be smaller for flat, less conforming implant designs and larger for highly conforming devices, such as many mobile bearing implants. Incorporating additional DOFs, such as measured ML and VV displacements, will also induce further variability. The variability observed highlights the need for careful, consistent procedures when performing fluoroscopy contact evaluation. Using the probabilistic method as developed here is preferable to simple perturbation analyses, as variable interaction effects are included; a priori knowledge of the combination of measurement uncertainty values resulting in extremal positions is not always possible. The efficiency of the optimization-based probabilistic approach utilized makes it feasible to include in all patient kinematic studies, and results in a more holistic evaluation of tibiofemoral contact during weight bearing activities.

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Figure 1. Mean and bounds (1 and 99%) of predicted tibiofemoral contact position for (a) medial and (b) lateral condyles; inset: typical contact pressure patches.

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Figure 2. Tibiofemoral contact patches for the (a) 1% and (b) 99% bounds at 90° flexion. Note cam-post contact in (b). References [1] Dennis, D.A., et al., 2003, CORR 416, 37-57. [2] Banks, S.A., et al., 2003, CORR 410, 131-138. [3] Li, G., et al., 2006, JBJS Am 88, 395-402. [4] Pal, S., et al., 2004, Trans 5th Comb ORS, 0242. [5] Dennis, D.A., et al., 1998, CORR 356, 47-57. [6] Dennis, D.A., et al., 2003, CORR 410, 114-130. [7] Halloran, J.P., et al., 2005, J. Biomech Eng 127, 813-818. Acknowledgement This research was supported in part by DePuy, a Johnson & Johnson Company. **DePuy, a Johnson & Johnson Company, Warsaw, IN

53rd Annual Meeting of the Orthopaedic Research Society

Poster No: 0770