A continuous model studying T cell differentiation and lymphomagenesis and its distinction with discrete models.

The development of T-lymphocytes (T cells) constitute one of the basic and most vital processes in immunology. Conventional mathematical models, being based on the systems theory, fail to sufficiently distinguish the constituents of thymocytes and are thus of limited significance. On the basis of some well thought-out definitions and concepts, a continuous model was designed to describe T cell maturation in the thymus. A partial differential equation was first derived through the analysis of an infinitesimal element of the flow of thymocytes. A computation scheme was designed to determine the growth field in the thymus based upon available experimental data. The corresponding algorithm proved quite simple. A numerical example is given that focuses on the DN stage of the T cell development. The model opens a window for investigating the thymic microenvironment. The potential of the model in studying lymphomagenesis is discussed.