Acute leukemias are cancerous diseases of the blood forming (hematopoietic) system resulting in rapid expansion of aberrant cells. Similar as the hematopoietic system, leukemias are maintained by a stem cell population (leukemic stem cells, LSCs) that gives rise to the leukemic cell bulk. Since successful treatment requires eradication of the LSC population, it is crucial to better understand their dynamic behavior. Recent genetic studies suggest that the leukemic cell population consists of multiple clones which change their sizes over time.

We propose a class of mathematical models describing proliferation and self-renewal of multiple leukemic clones. The models consist of systems of ordinary differential equations describing nonlinear interactions of different cell types and environmental signals. We address the following questions using a combination of systematic mathematical analysis and clinical data:

(i) How do stem cell properties, such as proliferation and self-renewal, influence clonal dynamics? Which clones are selected during evolution of the disease?

(ii) What might be the impact of chemotherapy on the selected cell properties? How could cells present at relapse differ from those present at primary manifestation?

(iii) How could stem cell properties influence clinical dynamics of the disease and patient prognosis? Is it possible to estimate LSC properties based on clinical parameters?

The presented results are based on a joint work with Anna Marciniak-Czochra (Institute of Applied Mathematics, University of Heidelberg), Anthony Ho and Natalia Baran (Department of Inner Medicine, University Hospital of Heidelberg).