Predictive Bio-Computational Wear Modeling for Joint Replacements

Abstract

Polyethylene wear has long been a topic of concern for the longevity of joint replacement systems as bearing failure is the leading cause for the need of revision surgery. Experimental simulations are costly and time consuming; therefore, a more efficient solution for predicting wear is computer simulation. Predictive computational modeling of the adhesive/abrasive wear mechanism has been in use for over a decade, but the accuracy of such models is still under debate [1-7]. Recent studies have shown that cross-path motion, as seen in joint replacements, results in elevated wear and shortens the life of the polyethylene bearing surface [8-10]. Modern computer simulations have attempted to address the effects of cross-path motion and range from simple to complex formulations [9, 11-13]. Current models are limited by their complexity, computational efficiency, joint-specificity, or motion-cycle path dependence. In this study, an adaptive finite element (FE) model was used to implement a modified form of Archard's Wear law [1] that accounts for the effects of cross-path motion and polymer chain realignment. The proposed model was validated to three separate experimental wear systems, each with three loading scenarios. As seen in Equation 1, the proposed Modified Archard's law sums the effects of unidirectional and cross-path motion and also accounts for polymer chain realignment, referred to as 'memory'. This Modified Archard's law is simple and generally applicable to any wear system: [Eqn 1.] where 'k0' and 'k*' are experimentally derived wear coefficients for uni-directional and cross-path sliding, respectively. The variable 'p' refers to contact pressure and the variable s is the magnitude of incremental sliding distance. The variable 'm' incorporates memory and sliding trajectory effects; its full definition can be found in [14]. Validation of the proposed wear model was completed through comparisons to published experimental data for three wear systems. The first system was a pin-on-disk wear experiment by Dressler et al. [15]. They concluded that wear was elevated by changes in direction but that the elevated wear diminished with sliding in a consistent direction up to 5 millimeters. Application of previous models to this experimental system resulted in incorrect wear predictions. Application of the proposed Modified Archard's law was able to predict the experimental wear volume results exactly. Further validation was confirmed when the Modified Archard's law was applied to FE models of a cervical disk replacement and a total knee replacement, as seen in Figure 1. The cervical disk model was made in accordance with the experimental setup by Bushelow et al. [16]. The total knee replacement model was made in accordance to the setup by McEwen et al. [10]. Experimental wear depth and volume results were compared to predictions from both the classical and Modified forms of Archard's Wear law for each of the two experiments three distinct loading scenarios. Wear coefficients were scaled to a standard loading scenario for each system. In each of the two predicted scenarios of both experiments, the Modified Archard's Wear law showed a better fit to the experimental data than the classical Archard's Wear formulation. Bibliography: [1] Archard 1953; [2] Maxian et al. 1995; [3] Kang et al 2009; [4] Knight et al 2007; [5] Pal et al 2008; [6] Ghiglieri et al 2008; [7] Goreham-Voss 2009; [8] Bragdon et al 1996; [9] Turrel et al 2003; [10] McEwen et al 2005; [11] Wang 2001; [12] Hamilton et al 2005; [13] Knight et al 2006; [14] Petrella et al 2009; [15] Dressler et al 2009; [16] Bushelow et al 2009.