Study of inertial flow of synovial fluid through a knee joint in normal condition

This research aims to analyze the flow of synovial fluid through a joint capsule during activities with constant re-absorption rate of water and nutrients at the synovium. The mathematical modeling of synovial fluid is made by the couple-stress fluid model in the presence of inertial forces because inertial flow of synovial fluid through the knee joint has significance for reducing the drag and enhancing the lubrication. The mathematical model of nonlinear system is transformed into a set of linear partial differential equations by a recursive approach, and inverse method is employed to convert the linear partial differential equations into a system of ordinary differential equations that are solved by the software MATHEMATICA. The mathematical results reveal that the flow of synovial fluid through joint capsule produces high pressure and shear stress at the synovium due to inertial forces, constant re-absorption rate and microrotation of couple-stress fluid. The axial flow of synovial fluid rises at the center of the joint capsule due to the activities, re-absorption of water and internal rotation of molecules, whereas the transverse flow becomes high near the synovium due to its permeable structure. This study will provide valuable insights for biomedical engineers to quantify re-absorption rates and stresses on the synovial fluid under normal physiological conditions.