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Mathematical Modeling of Blood Cell Formation and Stem Cell Transplantation

Blood cell formation (hematopoiesis) is maintained by hematopoietic stem cells (HSC) that reside in the bone marrow and give rise to all types of mature blood cells. Mathematical models help to understand how blood cell formation is regulated and how this can be used to optimize clinical interventions such as bone marrow transplantation.

Cooperation partners: A. D. Ho (Department of Hematology and Oncology, Heidelberg University Hospital), W. Wagner (Helmholtz Institute for Biomedical Engineering), A. Marciniak-Czochra (Institute for Applied Mathematics, Heidelberg University)

Blood cell formation is a complex and tightly regulated process. Stem cells are non-spezialized cells that give rise to more specialized so-called progenitor and precursor cells. Precursor cells finally produce fully specialized mature cells. Hormonal signals (cytokines) regulate cell properties to adapt their activity to the need for mature blood cells. Mathematical models can help to understand details of these regulations and to apply this knowledge in a clinical setting.

Stem cell transplantation (bone marrow transplantation) is a treatment option for several cancers. It includes eradication of a host's bone marrow by high dose chemotherapy and irradiation. To restore the blood cell production hematopoietic stem and progenitor cells from a donor are infused.

Stem cell transplantation is a strong perturbation of the blood forming system. For this reason it is well suited to study how blood cell production is regulated far away from the equilibrium state. Before recovery of peripheral blood cell counts (so-called reconstitution) a patient is prone to infections and other complications. For this reason it is clinically relevant to understand which processes determine the time to reconstitution and how it can be shortened.

Relevant processes that could change after transplantation are the cell proliferation rate (number of cell divisions per unit of time), the mature cell life-span or the self-renewal probability. Self-renewal describes a process during which cells give rise to progeny that are identical to the parent cell, e.g., progeny of stem cells are again stem cells (and not progenitor cells). In the opposite case, referred to as differentiation, progeny cells are more specialized than their parent cells.

The combination of mathematical model analysis, computer simulations and patient data suggest that up-regulation of stem and progenitor cell self-renewal is crucial for fast reconstitution. A carefully calibrated model of human white blood cell formation implies that short-term recovery after transplantation is driven by progenitor and not by stem cells. It can take several months before equilibrium stem cell counts are restored. The model suggests that patients prone to delayed reconstitution could benefit from larger transplant doses than recommended in clinical guidelines. Model simulations help to understand the reasons for unsuccessful transplantation (so-called graft failure) and provide hypotheses in which cases it can be avoided by increasing the number of transplanted cells (mega-dose transplant).

White blood cell production model
Simple model of white blood cell formation.

Key publications

  1. F. Knauer, T. Stiehl, A. Marciniak-Czochra, "Oscillations in a white blood cell production model with multiple differentiation stages". J Math Biol 80(3):575-600, 2020.
  2. T. Stiehl, A. D. Ho, A. Marciniak-Czochra, "The impact of CD34+ cell dose on engraftment after Stem Cell Transplantations: personalized estimates based on mathematical modeling", Bone Marrow Transplantation 49: 30-37, 2014.
  3. T. Stiehl, A. D. Ho, A. Marciniak-Czochra, "Assessing hematopoietic (stem-) cell behavior during regenerative pressure", Adv Exp Med Biol 844: 347-67, 2014.
  4. T. Stiehl, A. Marciniak-Czochra, "Characterization of stem cells using mathematical models of multistage cell lineages", Math. Comput. Model 53: 1505-1517, 2011.
  5. A. Marciniak-Czochra, T. Stiehl, W. Wagner, "Modeling of replicative senescence in hematopoietic development", Aging 1: 723-732, 2009.
  6. A. Marciniak-Czochra, T. Stiehl, A. D. Ho, W. J├Ąger, W. Wagner, "Modeling asymmetric cell division in hematopietic stem cells regulation of self-renewal is essential for efficient repopulation", Stem Cells Dev. 18: 377-385, 2009.