A Mathematical Model of Clonal Hematopoiesis Explaining Phase Transitions in Chronic Myeloid LeukemiaResearch Paper, May 07, 2025 / Lorand Gabriel Parajdi
Published in Mathematical Medicine and Biology, Oxford University Press, a journal of the IMA (MMB) DOI: 10.1093/imammb/dqaf004, 2025.
The full paper is available on the Mathematical Medicine and Biology, a journal of the IMA (MMB) website: https://academic.oup.com/imammb/advance-article/doi/10.1093/imammb/dqaf004/8126123
Authors: Lorand Gabriel Parajdi1,2,3, Xue Bai1, David Kegyes3,4,5 and Ciprian Tomuleasa3,4,5
1 Department of Mathematics, West Virginia University, Morgantown, WV, USA 2 Department of Mathematics, “Babeş–Bolyai” University, Cluj-Napoca, Romania 3 Academy of Romanian Scientists, Ilfov 3, Bucharest, Romania 4 Department of Hematology, “Ion Chiricuță” Clinical Cancer Center, Cluj-Napoca, Romania5 Research Center for Advanced Medicine, “Iuliu Hațieganu” University of Medicine and Pharmacy, Cluj-Napoca, Romania
Abstract: This study presents a mathematical model describing cloned hematopoiesis in chronic myeloid leukemia (CML) through a nonlinear system of differential equations. The primary objective is to understand the progression from healthy hematopoiesis to the chronic and accelerated-acute phases in myeloid leukemia. The model incorporates intrinsic cellular division events in hematopoiesis and delineates the evolution of chronic myeloid leukemia into five compartments: cycling stem cells, quiescent stem cells, progenitor cells, differentiated cells and terminally differentiated cells. Our analysis reveals the existence of three distinct non-zero steady states within the dynamical system, representing healthy hematopoiesis, the chronic phase and the accelerated-acute stage of the disease. We investigate the local and global stability of these steady states and provide a characterization of the hematopoietic states based on this analysis. Additionally, numerical simulations are included to illustrate the theoretical results.
Keywords: mathematical modeling; dynamical system; steady state; stability; clonal hematopoiesis; chronic myeloid leukemia; cycling stem cells; quiescent stem cells; progenitor cells; differentiated cells; terminally differentiated cells; pseudo-chemical reactions.
Cite As: Parajdi LG, Bai X, Kegyes D, Tomuleasa C. A mathematical model of clonal hematopoiesis explaining phase transitions in chronic myeloid leukemia. Mathematical Medicine and Biology, a journal of the IMA. 2025;
This work of the first author was supported by the project “The Development of Advanced and Applicative Research Competencies in the Logic of STEAM + Health” (POCU/993/6/13/153310), a project co-financed by the European Social Fund through the Romanian Operational Programme ‘Human Capital’, 2014-2020. For more details about the project, please visit the project website: https://sites.euro.ubbcluj.ro/steam/ . The authors of this paper, L.G. Parajdi, D. Kegyes and C. Tomuleasa, received funding through a grant from the Academy of Romanian Scientists for the years 2023–2024. D. Kegyes and C. Tomuleasa are funded by a national grant of the Romanian Research Ministry — PNRR 2024–2026 (PNRR/2022/C9/MCID/18, Contract No. 760278/26.03.2024).
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