Analytical Investigation of Synovial Fluid Motion Across Cartilage Layers in the Knee Joint

Abstract

Understanding the flow behaviour of synovial fluid is essential for analysing lubrication, nutrient transport, and mechanical functionality within the knee joint. This study presents a mathematical model describing axial and transverse velocity components under pressure driven flow with variable viscosity and porous-like resistance parameters. The governing equations were solved to obtain velocity profiles and volumetric flow rate, enabling a detailed assessment of fluid transport under physiological conditions. The results show that axial velocity follows a smooth parabolic pattern typical of laminar lubrication flow, while transverse velocity is highly sensitive to viscosity ratios and structural resistance, reflecting the influence of synovial membrane permeability. The computed flow rates demonstrate that elevated viscosity and decreased permeability conditions associated with osteoarthritis—significantly reduce fluid transport capacity. The study provides mechanistic insight into synovial fluid dynamics and offers a theoretical basis for improving visco supplementation strategies, developing biomimetic joint lubricants, and informing therapeutic approaches for degenerative knee disorders.