Mathematical models of the leukemic hematopoiesis


Starting from a classification of acute myeloid leukemias which takes into account the vital characteristics of the leukemic clones, we present several mathematical models for the understanding of the origin and the dynamic of these diseases and for providing a theoretical basis of more adapted therapeutic approaches.


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

Andrei Cucuianu
Andrei Cucuianu, “Ion Chiricuta” Cancer Institute, Department of Hematology,  Cluj, Romania,


Hematopoiesis; Acute myeloid leukemia; Dynamic system; Numerical simulation

Paper coordinates

R. Precup, A. Cucuianu, Mathematical models of the leukemic hematopoiesis, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 7 (2009), 169-181.


About this paper


Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity

Publisher Name
Print ISSN


Online ISSN

google scholar link

[1] M. Adimy, F. Crauste and A. El Abdllaoui. Discrete-maturity structured model of cell differentiation with applications to acute myelogenous leukemia, J. Biol. Systems 16 (2008), 395–424.
[2] L.K. Andersen and M.C. Mackey. Resonance in periodic chemotherapy: A case study of acute myelogenous leukemia, J. Theor. Biol. 209 (2001), 113–130.
[3] F. Brauer and C. Castillo-Chavez. Mathematical Models in Population Biology and Epidemiology. Springer, Berlin, 2001.
[4] A. Cucuianu. Dominant and opportunistic leukemic clones: Proposal for a pathogenesis oriented classification in acute myeloid leukemia, Medical Hypotheses 65 (2005), 107–113.
[5] A. Cucuianu and R. Precup. A hypothetical-mathematical model of acute myeloid leukemia, Computational and Mathematical Methods in Medicine, to appear.
[6] D.R. Head. Revised classification of acute leukemias, Leukemia 10  (1996), 1826–1831.
[7] V. Kolmanovskii and A. Myshkis. Applied Theory of Functional Differential Equations. Kluwer, Dordrecht, 1992.
[8] B. Lowenberg. Acute myeloid leukemia: The challenge of capturing disease variety, Hematology 2008, 1–11.
[9] M.C. Mackey and L. Glass. Oscillation and chaos in physiological control systems, Science 197 (1977), 287–289.
[10] I.B. Resnick, M.Y. Shapira and S. Slavin. Nonmyeloablative stem cell transplantation and cell therapy for malignant and nonmalignant diseases. Transpl. Immunol. 14 (2005), 207–219.
[11] R.F. Schlenk, K. Dohner, J. Krauter, S. Frohling, A. Corbacioglu, L. Bullinger, M. Habdank, D. Spath, M. Morgan, A. Benner, B. Schlegelberger, G. Heil, A. Ganser, H. Dohner and German-Austrian Acute Myeloid Leukemia Study Group. Mutations and treatment outcomes in cytogenetically normal acute myeloid leukemia, N. Engl. J. Med. 358 (2008), 1909–1918.
[12] J.W. Vardiman, N.L. Harris, R.D. Bruning et al. The World Health Organization classification of the myeloid neoplasms, Blood 100 (2002), 2292–2303.


Related Posts