Estimation of the proliferation and maturation functions in a physiologically structured model of thymocyte development
The thymus provides a stable microenvironment for post-natal thymocyte development that is finely regulated by a complicated network of cytokines, chemokines, cell-cell contacts, etc., the dysregulations of which contribute to many immunologic diseases including malignant lymphomas. A physiologically structured model in the form of first order partial differential equation (PDE) was developed to simulate the whole process. The combined effects of the thymic microenvironment were conceptualized into two (proliferation and differentiation) fields to serve as kernels of the PDE. In this paper, a novel method is developed to estimate the maturity-time structures of the two fields based solely on cell population data that are experimentally viable. Numerical examples demonstrate the effectiveness of the present method in revealing the two-dimensional (maturity and time) landscapes of the thymic microenvironment.