Mathematical Model of Cartilage Regeneration via Hydrogel

Because of the large number of individuals with cartilage problems, whether due to sports injuries or diseases such as arthritis, there is a medical need for effective cartilage regeneration. To assist with the development of a procedure for regeneration, a mathematical model is desirable. A mathematical model is useful because it can allow regeneration times to be calculated for various initial conditions, without having to biologically test those certain conditions in lab. In this project, we present and discuss a mathematical model for cartilage regeneration via hydrogel, a biocompatible scaffolding material. The novel model presented in this work was designed to be more biological in nature than previous models. Cartilage is a connective tissue that contains special cells (chondrocytes) and is found in joints as well as other places. In a healthy environment, chondrocytes are able to repair minor damage, but more extensive damage can render the cartilage irreparable by natural means. Consequently, researchers are seeking techniques to encourage cartilage regeneration. One possibility for cartilage repair involves injecting the damaged site with hydrogel, a gelatinous substance containing chondrocytes. Our model uses a system of ordinary differential equations (ODE) that illustrates the build-up of extracellular matrix (ECM), the structural material of cartilage, using hydrogel to stimulate repair. Introduction The focus of this work is on articular cartilage, which is found only in joints (hips, knees, etc), preventing bone on bone contact (Erggelet et al., 2008). Excluding water, cartilage is comprised of two main elements: specialized cells called chondrocytes and an extracellular matrix (ECM) composed of a framework of proteins and proteoglycans (Lodish et al., 2008, Erggelet et al., 2008). The majority of the tissue is not comprised of