Mathematical Model to Study the Squeeze Film Characteristics of Diseased Human Synovial Knee Joint

Abstract

Synovial fluid functions as a biological lubricant and lubricates articular cartilage to reduce friction and wear. Lubricin and hyaluronic acid are the primary components of synovial fluid responsible for its lubricating properties. The loss of properties in synovial fluid and articular cartilage due to aging and activities can restrict mobility in synovial joints, resulting in the degradation of articular cartilage and ultimately leading to pathological synovial joints, which is a major cause of disability. Thus, research on synovial joints remains crucial, and despite previous investigations on synovial joint lubrication, there are several issues related to squeeze film lubrication that require further attention. The Newtonian model of squeeze film lubrication in synovial joints needs to be extensively studied. In this study, lubrication and other related properties of synovial fluid are studied theoretically. In this paper, we have studied the flow of synovial fluid in the diseased synovial joint. Further, we have studied the effect of the viscosity of the synovial fluid, the permeability of articular cartilage, thickness of articular cartilage, and fluid film thickness on the characteristic of the squeeze film formed between the articular cartilages of the diseased human knee joint. The flow of synovial fluid is modeled by considering it as a viscous, incompressible and Newtonian fluid. We have derived the modified Reynolds equation using the principle of hydrodynamic lubrication and continuum mechanics theory and solved it by applying the suitable boundary conditions according to the physical considerations. Subsequently, we obtained the expression for pressure distribution in fluid film, load-bearing capacity, and squeeze time and have done the theoretical analysis on these properties for different parameters. Pressure increases with squeeze velocity and viscosity of the synovial fluid and decreases with permeability and fluid film thickness. Human knee joint becomes diseased due to excessive pressure, and the mobility of the knee joint decreases. The load capacity increases with viscosity and squeeze velocity and decreases with permeability resulting in the reduction of the load-carrying capacity of the knee joint in diseased conditions. Moreover, the squeeze time also increased in the diseased state of the joint.