Development of a Computational Tool to Predict Wear in UHMWPE Tibial Bearings
Matthew A. Hamilton
STLE Scholarship Award Winner 2001
Department of Mechanical Engineering
University of Florida
Gainesville, Fl. 32611

Introduction

Wear and the results of wear are widely reported to be the most significant problems limiting the life of orthopedic joint replacements. While computational tools such as Finite Element Analysis (FEA) have reached a level of sophistication that enables them to be used during the design phase of new implants for stress analysis, the current "gold standard" for tribological evaluation remains tedious laboratory testing on one of the newer joint simulators. Such testing is both expensive and time consuming. There appears to be an opportunity for a computational tool that predicts wear for these components to be a useful adjunct to laboratory testing, if such predictions can be validated.

In a proof of concept study, M.C. Sucec (2001) used Archard's wear law and a creep penetration model by Lee and Pienkowski (1998) to make predictions on a tibial bearing in a Total Knee Replacement (TKR). These predictions were made for the Ultra High Molecular Weight Polyethylene (UHMWPE) tibial bearings from three different implanted TKRs. The results from this preliminary study were encouraging.

Software Development Outline

A project to develop an easily distributable software package that could make predictions of wear and creep for components of widely different geometry was undertaken. Further, these predictions would be made from the patient specific data compiled by Sucec (2001). The software was written entirely in Java, which is an object oriented programming language that compiles the code in such a way that it can be run via the Internet on a wide variety of computer operating systems.

Figure 1 A generic tibial bearing component comprised of 1600 quadrilateral surface elements used in this candidate study of three knee replacements.

The fundamental approach was to use a mesh of discretized polygons to represent the functional surface of the tibial bearing. The polygons can be either triangles (to support Stereo Lithography surface meshing) or quadrilaterals (to support many finite element meshes). A generic tibial bearing component is shown in figure 1. The surface elements contain contact and slip data for a series of discrete time steps (subscript i). Currently elements have contact pressure (), slip velocity vector (), the time period between intervals (), and the slip distance for each interval (). Values for such things as the modulus of elasticity (), wear-rate (), and average component thickness () are model variables.

The software currently makes a prediction for per cycle depth-of-wear () for each element using Archard's wear law (), a contour is shown in figure 2. Creep was predicted using a model developed by Lee and Pienkowski (1998), where the creep depth () is calculated as shown by Eqn. 1 -- the summations are over the entire activity period (), and the model estimates a terminal stress relaxation depth.

equation 1

Because the patient specific data is imported for only one activity cycle (i.e. one stair rise), any prediction for the cumulative damage over a patient's lifetime must be extrapolated from this calculation.

Figure 2 A contour map of per-cycle wear predictions using Archard's wear equation and contact data compiled by Sucec (2001) for HM (right).

The pressure distribution is based on a Hertzian contact analysis where the femoral condyle contacts the tibial bearing. The contact load is estimated by combining a measurement of ground reaction force with estimates of the muscle co-contraction forces. The load is partitioned 60/40 between the medial and lateral compartments respectively. The wear factor for UHMWPE used for this study is and the number of cycles per year was estimated to be 1million, both of these are taken from Maxian (1996), who made predictions in wear depth for total hip replacements using finite elements.

Candidate Study Results and Discussion

The Orthopaedic Research Laboratory in West Palm Beach Florida, using both ground mounted force plates and a shuttered fluoroscopy unit, collected data for three patient knees performing a stair rise activity exercise. Table 1 gives the general patient statistics. In Sucec's thesis, the fluoroscopy data was compiled into a format that projected a calculated Hertzian contact pressure over the functional surface mesh of the tibial bearing. This data is used to make predictions for values of wear-depth and creep penetration for each compartment. The location and values for the maximum wear-depth and creep predictions are shown in figure 3 and given in table 2.

Table 1 Patient and implant statistics.

In this candidate study the post mortem retrievals for the three knees investigated were available for coordinate metrology analysis. The measured values of maximum penetration, which is a combination of both wear and creep, is given in table 2 next to the predictions, and is shown graphically in figure 3 along with the predictions.

Figure 3 A schematic of predicted locations of maximum penetration and measured locations of maximum penetration from 3 post-mortem retrievals.

The predictions of maximum penetration location as compared to the measurements appeared good, however, the difference between the predicted values of penetration and the measurements is poor. Two possible explanations for this are offered: (1) is that stair-climbing activities were used to extrapolate wear over what was certainly a broad spectrum of less rigorous activities, and (2) is that predictions of slip were not made using differences in the positions of elements in contact between the time intervals, rather the rigid body velocities were projected onto the contact area and assumed to act uniformly through the contact. These issues will hopefully be addressed over the next few years as the software is further developed.

Table 2 Comparison between predicted and measured penetration depths.

Acknowledgments

The STLE Scholarship awarded at the 2001 Annual Meeting in Orlando Florida supported the research of M.A. Hamilton during the summer of 2001. The author is extremely grateful to the Society of Tribologists and Lubrication Engineers and its members for this award.

This work was also supported by the ongoing efforts of the entire group at the Orthopaedic Research Laboratory and the Biomotion Foundation in West Palm Beach Florida. Particularly Scott Banks for providing the video fluoroscopy data, and Melinda Harman for collecting the retrieved components, subject data, and performing the coordinate measuring of these components.

The author is also very grateful for the help of Torkel Svanes, who frequently provided sage counsel and advice during much of the difficult software coding.

References

Lee, K., Pienkowski, D. (1998). Compressive creep characteristics of extruded ultrahigh-molecular-weight polyethylene. Journal of Biomedical Materials Research, 39(2), 261-265.

Maxian, T., Brown, T., Pederson, D., Callaghan, J. (1996B). Adaptive finite element modeling of long-term polyethylene wear in total hip arthroplasty. Journal of Orthopaedic Research, 14, 668-675.

Sucec, M. (2001). Computational Wear Prediction of total knee replacements using patient specific kinematics. Masters Thesis, University of Florida.