A Model for Intra-Articular Heat Exchange in a Knee Joint

A mathematical model has been developed for the understanding of temperature distribution in knee joint. Temperature rises in knee joint as a result of frictional energy. This heated synovial fluid enters into the articular cartilage by the process of filtration and supplies heat to cartilage and bone. This cooled fluid again mixes well with the lubricant in the joint cavity. The problem is formulated as a two-region flow and diffusion model: flow and thermal diffusion within the intra-articular gap; and within the porous matrix covering the approaching bones at the joint. The solution of the coupled mixed boundary value problem is solved by using perturbation method. It has been observed that, in certain diseased and or old synovial joints, the movement of the fluid into or out of the cartilage resisted, and therefore, the temperature does rise. The temperature does rise in old and diseased joints as observed by varying the values of parameters from its normal values. These values refer to old age and/or diseases affecting degeneration of synovial fluid and or cartilage.