Rheumatoid arthritis - a mathematical model. (14th January 2019) - Moise, Nicolae; Friedman, Avner
Highlights: This is the first mathematical model of RA which quantitatively describes the progression of the disease. The model explains the roles of macrophages, inflammatory fibroblasts, and T cells in the degradation of cartilage in a joint. Example is given how to achieve the same efficacy in stabilization of the cartilage while decreasing negative side-effects. Abstract: Rheumatoid arthritis (RA) is a common autoimmune disease that mainly affects the joints. It is characterized by synovial inflammation, which may result in cartilage and bone destruction. The present paper develops a mathematical model of chronic RA. The model is represented by a system of partial differential equations (PDEs) in the synovial fluid, the synovial membrane, and the cartilage. The model characterizes the progression of the disease in terms of the degradation of the cartilage. More precisely, we assume a simplified geometry in which the synovial membrane and the cartilage are planar layers adjacent to each other. We then quantify the state of the disease by how much the cartilage layer has decreased, or, equivalently, how much the synovial layer has increased. The model is used to evaluate treatments of RA by currently used drugs, as well as by experimental drugs.