Mathematical modeling of cell dynamics after allogeneic bone marrow transplantation

2 years ago

Abstract

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.

Authors

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

Keywords

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

Paper coordinates

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), https://doi.org/10.1142/S1793524511001684

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About this paper

Journal

International Journal of Biomathematics

Publisher Name

World Scientific
Connecting great Minds

DOI

https://doi.org/10.1142/S1793524511001684

Print ISSN

17935245

Online ISSN

17937159

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[1] M. Adimy, F. Crauste and A. El Abdllaoui, J. Biol. Syst. 16, 395 (2008). Link, ISI, Google Scholar
[2] L. K. Andersen and M. C. Mackey, J. Theor. Biol. 209, 113 (2001). Crossref, ISI, Google Scholar
[3] F. Aversaet al., J. Clin. Oncol. 23, 3447 (2005), DOI: 10.1200/JCO.2005.09.117. Crossref, ISI, Google Scholar
[4] F. Brauer and C. Castillo-Chávez , Mathematical Models in Population Biology and Epidemiology ( Springer , Berlin , 2001 ) . Crossref, Google Scholar
[5] A. M. Carella, S. Giralt and S. Slavin, Haematologica 85, 304 (2000). ISI, Google Scholar
[6] F. Castiglione and B. Piccoli, Bull. Math. Biol. 68, 255 (2006), DOI: 10.1007/s11538-005-9014-3. Crossref, ISI, Google Scholar
[7] C. Colijn and M. C. Mackey, J. Theor. Biol. 237, 117 (2005), DOI: 10.1016/j.jtbi.2005.03.033. Crossref, ISI, Google Scholar
[8] J. J. Cornelissen and B. Löwenberg, Hematology 2005, 151 (2005), DOI: 10.1182/asheducation-2005.1.151. Crossref, Google Scholar
[9] A. Cucuianu and R. Precup, Comput. Math. Methods Med. 11, 49 (2010), DOI: 10.1080/17486700902973751. Crossref, ISI, Google Scholar
[10] R. De Condeet al., J. Theor. Biol. 236, 39 (2005). Crossref, ISI, Google Scholar
[11] B. R. Dey and T. R. Spitzer, Brit. J. Haematol. 135, 423 (2006), DOI: 10.1111/j.1365-2141.2006.06300.x. Crossref, ISI, Google Scholar
[12] D. Dingli and F. Michor, Stem Cells 24, 2603 (2006), DOI: 10.1634/stemcells.2006-0136. Crossref, ISI, Google Scholar
[13] D. Dingli and J. M. Pacheco, Wiley Interdiscip. Rev. Syst. Biol. Med. 2, 235 (2010). Crossref, ISI, Google Scholar
[14] B. Djulbegovic and S. Svetina, Cell Proliferat. 18, 307 (1985). Crossref, Google Scholar
[15] M. Eapen and V. Rocha, Lifetime Data Anal. 14, 379 (2008), DOI: 10.1007/s10985-008-9090-4. Crossref, ISI, Google Scholar
[16] A. S. Fokas, J. B. Keller and B. D. Clarkson, Cancer Res. 51, 2084 (1991). ISI, Google Scholar
[17] C. Foley and M. C. Mackey, J. Math. Biol. 58, 285 (2009), DOI: 10.1007/s00285-008-0165-3. Crossref, ISI, Google Scholar
[18] L. Fouillardet al., Haematologica 93, 834 (2008), DOI: 10.3324/haematol.11277. Crossref, ISI, Google Scholar
[19] P. S. Kim, P. P. Lee and D. Levy, J. Theor. Biol. 246, 33 (2007), DOI: 10.1016/j.jtbi.2006.12.012. Crossref, ISI, Google Scholar
[20] P. S. Kim, P. P. Lee and D. Levy, Biology and Control Theory: Current Challenges, Lecture Notes in Control and Information Sciences 357 (Springer, Berlin, 2007) pp. 3–20. Crossref, Google Scholar
[21] P. S. Kim, P. P. Lee and D. Levy, Plos Comput. Biol. 4, 1 (2008). ISI, Google Scholar
[22] M. C. Mackey, Blood 51, 941 (1978). Crossref, ISI, Google Scholar
[23] R. Martinoet al., Blood 108, 836 (2006), DOI: 10.1182/blood-2005-11-4503. Crossref, ISI, Google Scholar
[24] J. Mehtaet al., Blood 90, 3808 (1997). Google Scholar
[25] H. Moore and N. K. Li, J. Theor. Biol. 227, 513 (2004), DOI: 10.1016/j.jtbi.2003.11.024. Crossref, ISI, Google Scholar
[26] J. D. Murray , Mathematical Biology II: Spatial Models and Biomedical Applications ( Springer , New York , 2003 ) . Crossref, Google ScholarM. N. Obeyesekere, P. P. Spicer and M. Korbling, A Mathematical Model for the Progression of an Abnormality in the Hematopoietic System, Lecture Notes in Control and Information Sciences 321 (Springer, New York, 2005) pp. 257–268. Crossref, Google Scholar
[27] V. Rocha, G. Sanz and E. Gluckman, Curr. Opin. Hematol. 11, 375 (2004), DOI: 10.1097/01.moh.0000145933.36985.eb. Crossref, ISI, Google Scholar
[28] S. I. Rubinow and J. L. Lebowitz, Biophys. J. 16, 897 (1976). Crossref, ISI, Google Scholar
[29] S. I. Rubinow and J. L. Lebowitz, Biophys. J. 16, 1257 (1976). Crossref, ISI, Google Scholar
[30] S. Slavinet al., Blood 91, 756 (1998). ISI, Google Scholar
[31] R. Storb, Curr. Opin. Hematol. 21(), S3 (2009). Google Scholar
[32] J. F. Tisdale and C. E. Dunbar, Clinical Hematology (Mosby-Elsevier, 2006) pp. 2–15. Google Scholar