Mathematical modeling of cell dynamics after allogeneic bone marrow transplantation


In this paper a basic mathematical model is introduced to describe the dynamics of three cell lines after allogeneic stem cell transplantation: normal host cells, leukemic host cells and donor cells. Their evolution is one of competitive type and depends upon kinetic and cell–cell interaction parameters. Numerical simulations prove that the evolution can ultimately lead either to the normal hematopoietic state achieved by the expansion of the donor cells and the elimination of the host cells, or to the leukemic hematopoietic state characterized by the proliferation of the cancer line and the suppression of the other cell lines. One state or the other is reached depending on cell–cell interactions (anti-host, anti-leukemia and anti-graft effects) and initial cell concentrations at transplantation. The model also provides a theoretical basis for the control of post-transplant evolution aimed at the achievement of normal hematopoiesis.


Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Smaranda Arghirescu
Department of Hematology, “Victor Babeş” University of Medicine and Pharmacy, Timişoara 300041, Romania

Andrei Cucuianu
Department of Hematology, “Iuliu Haţieganu” University of Medicine and Pharmacy, Cluj 400012, Romania

Margit Şerban
Department of Hematology, “Victor Babeş” University of Medicine and Pharmacy, Timişoara 300041, Romania


Mathematical modeling; dynamical system; numerical simulation; stem cell transplantation; acute myeloid leukemia

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R. Precup, S. Arghirescu, A. Cucuianu, M. Serban, Mathematical modeling of cell dynamics after allogeneic bone marrow transplantation, Int. J. Biomath. 5 (2012) no. 2, 1250026 (18 pages),



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International Journal of Biomathematics

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