Biomechanical Insights into Synovial Fluid Flow: A Modelling Study of Pressure and Shear Stress in the Knee

Abstract

Synovial fluid (SF) and cartilage play a crucial role in ensuring smooth and efficient motion in diarthrodial joints. At low shear rates, SF exhibits high viscosity to cushion cartilage surfaces during slow movements. As shear rates increase, viscosity declines in a characteristic shear-thinning manner, enabling smooth joint articulation under dynamic load. This study presents a computational and rheological analysis of shear-dependent viscosity at varying concentrations, alongside the influence of cartilage thickness on joint mechanics. In this study, the problem is formulated as a fluid flow analysis within the joint cavity, bounded by articular cartilage layers of variable thickness. In the present proposed problem, the flow of synovial fluid in the human knee joint due to a pressure gradient was considered. The flow of the synovial fluid in the joint cavity and articular cartilage is governed by the Navier-Stokes Equation and the Brinkman equation. The viscosity–shear rate curves demonstrated a distinct shear-thinning behaviour, with higher concentrations exhibiting greater viscosities across all regimes. Power-law fits confirmed pseudoplasticity, showing that shear-thinning intensified with increasing concentration. Shear stress–shear rate relationships further highlighted non-linear stress responses, consistent with non-Newtonian fluid dynamics. Normalisation of viscosity by concentration revealed partial data collapse, suggesting concentration-independent scaling in the mid-shear regime. Overall, the findings underscore the balance between synovial fluid viscosity and cartilage thickness in maintaining healthy joint lubrication. High viscosity enhances load support but increases resistance to flow, whereas reduced cartilage thickness elevates stress concentration, potentially contributing to joint degeneration. These insights not only improve our understanding of natural joint mechanics but also provide a framework for designing biomimetic lubricants and therapeutic interventions for osteoarthritis and related joint disorders.