Mathematical models and parameter estimation for heterogeneous cell population dynamics

The functioning of the immune system involves tightly regulated proliferation, differentiation and death processes of heterogeneous cell populations, including T lymphocytes, B lymphocytes, antigen presenting cells, etc. To quantify the turnover kinetics of specific subsets of immune cells under normal conditions and during infections, labeling techniques (e.g., with fluorescent markers CFSE or BrdU) in conjunction with flow cytometry analysis (FACS) are used in experimental and clinical immunology. To obtain information about the kinetic structure of the cellular responses of heterogenous cell populations from data that in addition to experimental fluctuations (noise) exhibit considerable variation between different study animals, careful computational analysis is needed. The primary objectives of this chapter are: (i) to introduce mathematical models in the form of hyperbolic partial differential equations (PDEs) which allow direct reference to single or double label histograms of cell distributions, (ii) to illustrate the potential of our modeling and parameter identification technology by representative examples from CFSE and BrdU labeled T cell proliferation studies, and (iii) to compare the proposed PDE models with alternative modeling approaches which are based upon the use of ordinary differential equations.status: publishe