Modelling protein aggregation lubrication in prosthetic joints

Abstract

Protein aggregation lubrication is the term given to the experimentally observed accumulation of protein matter at the inlet region of protein-rich, fluid-lubricated contacts. This lubrication mechanism causes larger than predicted fluid film thickness when compared to classical elasto-hydrodynamic lubrication theory and also exhibits the behaviour of decreasing film thickness with increasing sliding speed between the contact surfaces, again in contrast to theory. In the last decade, experiments have been carried out to capture the transient development of inlet aggregates in pin-on-flat tribometers. Understanding the lubrication mechanisms present in such lubricated contacts is vital for the continued development of prosthetic joint implant design and success.

In this study, a computational protein aggregation lubrication model has been created by using classical elasto-hydrodynamic lubrication theory coupled with a protein-dependent constitutive equation for fluid viscosity. The transport of protein matter in the thin film lubricated contact has been subject to an advection-diffusion model using geometry-based attenuation of flow rates, resulting in protein concentration aggregation at the inlet of the contact zone. The model parameters have been calibrated and the resulting transient protein aggregation lubrication simulation agrees well with previous experimentally observed transient film thickness behaviour when a cobalt–chromium–molybdenum alloy femoral head implant is tested in a pin-on-flat tribometer using diluted bovine calf serum as a synovial fluid analogue.

The model developed in this study requires the calibration of two separate parameters that relate to the shape of an approximate protein particle size distribution and to the nature of the exponential dependency of viscosity on protein concentration. Prior knowledge of the particle size distribution and rheological testing of experimental fluid would allow for these parameters to be fixed without calibration, however a parameter search method has been proposed for situations where these values are unknown. The calibration overhead is significant even at the current level of model complexity and further refinement of computational efficiency is needed before it can be viably applied to a wide range of test cases.

Modelling prosthesis lubrication in this way provides a simple method to incorporate the effect of protein aggregation into simulations that can be used to provide greater insight into the conditions in the contact zone of joint prostheses including pressure, film height, and protein concentration which can in turn be used to derive friction coefficients and aid the study of surface wear.