Anna Marciniak-Czochra

Dynamics of stem cell systems is dictated by a number of key parameters, including stem cell renewal rate, progenitor proliferation and flux of cells into various differentiation pathways. The multifactorial nature of stem cell control severely limits the intuitive interpretation of experimental and clinical data. There, as in case of cancer, predictions regarding the quantitative effects of system perturbations are almost impossible without mathematical modeling.
The lectures will focus on mathematical modeling, analysis, and simulation of cell dynamics that are critically linked to the processes of stem cell self-renewal, differentiation, and clonal evolution. We will apply rigorous mathematical methods to formulate and analyze models using partial and integro-differential equations. The need for such models follows from the multiscale modeling approach. We will show model derivation from stochastic description of cell differentiation dynamics, anlyze structured population models with discrete and continuous structures and finally present a nonlocal multi-stage structured population model exhibiting mass concentration effect, i.e. convergence of solutions to a sum of Dirac measures. All mathematical results will be discussed in the context of biological and medical applications. In particular, we focus on modeling of blood production system, its regeneration and stem cell malignancies. We show how to quantitatively approach clinically relevant questions of efficient dynamics of blood regeneration after bone marrow transplantation, mechanisms of leukemogenesis and resistance to therapies by integrating mathematical and biological/clinical approaches.
The lectures will be based on state-of-art available in literature and new models and techniques developed by the group of Marciniak-Czochra in long-term collaboration with experimentalists and clinicians from Department of Medicine V, Heidelberg University and German Cancer Research Center.