This review article presents some mathematical models of hematopoietic cell dynamics related to bone marrow transplantation. Both allogeneic and autologous stem cell transplantations are considered. The models are expressed by three-dimensional systems of ordinary differential equations whose variables stand for the abundances of healthy, leukemic and infused cells. Model parameters quantify the cellular processes of growth, cell death and sensibility to microenvironment, and cell-cell interactions such as anti-host, anti-cancer and anti-graft effects. Numerical simulations and stability analysis of system equilibria are performed in order to conclude about effectiveness of transplantation procedures. In the case of allogeneic transplantation, the role of initial cell concentrations is highlighted and several therapeutic scenarios for correction of bad posttransplant evolution are suggested. The exposition is mainly based on authors’ papers.

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

Delia Dima
Institutul Oncologic Prof. Dr.I. Chiricuta

Ciprian Ionut Tomuleasa
Iuliu Haţieganu University of Medicine and Pharmacy

Marcel-Adrian Serban
Babeş-Bolyai University

Lorand Gabriel Parajdi
West Virginia University

Dynamic system; Hematopoiesis stem cells; Mathemacial model; Myeloid leukemia;  Numerical simulation; Stability; Stem cell transplantation.

R. Precup, D. Dima, C. Tomuleasa, M-A Serban, L-G Parajdi, Theoretical models of hematopoietic cell dynamics related to bone marrow transplantation, in Frontiers in Stem Cell and Regenerative Medicine Research, vol. 8, Eds.: Atta-ur-Rahman, Shazia Anjum, Bentham Science, Sharjah, UAE, 2018, pp 202-241, https://doi.org/10.2174/97816810858901180801

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