The Role of Synovial Fluid Properties in a Dynamic Hip Joint Simulation

Accurate mathematical modelling of joints is directly related to the need to obtain a better fundamental understanding of the role that elements of the system have on the dynamic tribological behaviour of the component it represents. Simulation models also make a contribution towards reduction of the cost of in-situ experimentation in biotribological systems, as well as overcoming difficulties with ethical and practical problems related to in-situ testing. The aim of the current work is to report on the results obtained from a dynamic model of a human hip joint. The model is used to investigate the tribological performance of the synovial fluid over a varying range of operating conditions – specifically pressure, temperature and varying load conditions. The model is based on a minimum of empirical relationships, preferring relationships grounded in solid fundamental theory. This reduces the number of parameters that can be modified in the model and ensures that predictions made are not based on external manipulations. INTRODUCTION Several investigators have attempted to simulate the in-situ conditions of the human hip joint. It is often assumed in work of this nature that the synovial fluid is Newtonian. This is very useful in minimizing the complexity of numeric solution of the problem, but does not correlate with the actual characteristics of the fluid found in human joints. In fact, synovial fluid exhibits a whole range of non-Newtonian characteristics under different conditions, like pseudoplasticity, elasticity and thixotropy [1]. In synovial fluid, hyaluronic acid is responsible for the lubrication and viscoelastic properties [2]. This investigation aims at understanding the rheological behavior of non-Newtonian synovial fluid in a dynamic hip joint simulation. The properties of the fluid are simulated under normal joint in-situ conditions, obtained by calculating the pressure and temperature profiles that occur due to the load induced during a typical walking cycle [3]. The effect of the fluid properties on the lubricating ability of the joint is also investigated. The model can be used to predict the lubricity behavior of the synovial fluid of patients with varying arthritic conditions. The predictions obtained by assuming Newtonian behavior will be compared to the non-Newtonian case. NOMENCLATURE ρ Synovial fluid density t Time ψ θ , Spherical coordinate v Fluid speed r Ball diameter P Pressure τ Shear stress g Gravitational acceleration μ Viscosity γ Shear rate NUMERICAL MODEL The hip joint is modeled as a simple ball-in-cup system. The geometry was chosen in accordance with that of Mabuchi et al [3] and is shown in Figure 1. It is important to note that the system was chosen to be axysymmetrical. This assumption implies that the model variables are only dependent on the angular coordinate θ and are independent of ψ . [3] The aim of the model is to develop a mathematical environment for simulating a hip joint from first principle fluid dynamics. The control volume of the system was chosen to be the fluid in the gap between the articulating surfaces. The system models hydrodynamic lubrication where there is a sufficient fluid film to prevent contact between surfaces. The system was geometrically characterized in spherical coordinates. Formulating the model from first principles promotes fundamental understanding of the hip joint system. 1 Copyright © 2005 by ASME