Comparison of two methods for calculating the frictional properties of articular cartilage using a simple pendulum and intact mouse knee joints

Abstract

In attempts to better understand the etiology of osteoarthritis, a debilitating joint disease that results in the degeneration of articular cartilage (AC) in synovial joints, researchers have focused on joint tribology, the study of joint friction, lubrication, and wear. Several different approaches have been used to investigate the frictional properties of articular cartilage. In this study, we examined two analysis methods for calculating the coefficient of friction ( μ) using a simple pendulum system and BL6 murine knee joints ( n=10) as the fulcrum. A Stanton linear decay model (Lin μ) and an exponential model that accounts for viscous damping (Exp μ) were fit to the decaying pendulum oscillations. Root mean square error (RMSE), asymptotic standard error (ASE), and coefficient of variation (CV) were calculated to evaluate the fit and measurement precision of each model. This investigation demonstrated that while Lin μ was more repeatable, based on CV (5.0% for Lin μ; 18% for Exp μ), Exp μ provided a better fitting model, based on RMSE (0.165° for Exp μ; 0.391° for Lin μ) and ASE (0.033 for Exp μ; 0.185 for Lin μ), and had a significantly lower coefficient of friction value (0.022±0.007 for Exp μ; 0.042±0.016 for Lin μ) ( p=0.001). This study details the use of a simple pendulum for examining cartilage properties in situ that will have applications investigating cartilage mechanics in a variety of species. The Exp μ model provided a more accurate fit to the experimental data for predicting the frictional properties of intact joints in pendulum systems.