Mathematical understanding of the autologous stem cell transplantation

Abstract

A simple mathematical model is provided for understanding the cell dynamics after autologous stem cell transplantation, concluding about the effectiveness of this therapeutic procedure for acute myeloid leukemia and suggesting some biological and clinical directions of further possible investigation.

Authors

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

Keywords

mathematical model; medical application; dynamic system; numerical simulation; stem cell transplantation; acute myeloid leukemia.

Paper coordinates

R. Precup, Mathematical understanding of the autologous stem cell transplantation, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 10 (2012), 155-167.

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Journal

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

Publisher Name
DOI
Print ISSN

1584-4536

Online ISSN

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[1] X. Cao et al. Irradiation induces bone injury by damaging bone marrow microenvironment for stem cells. Proc. Natl. Acad. Sci. USA, 108(4) (2011), 1609-1614, doi: 10.1073\pnas.1015350108.
[2]A.D. Chantry et al. Autologous stem cell tgransplantation for acute myeloid leukemia, Biol. Blood Marrow Transplant., 12 (2006), 1310-1317.
[3] A. Cucuianu and R. Precup, A hypothetical-matehamtical model of acute myeloid leukemia pathogenesis, Comput. Math. Mathods Med., 11 (2020), 40-65.
[4] D. Dingli and F. Michor. Successful therapy must eradicate cancer stem cells, Stem Cells, 24 (2006), 2603-2610.
[5] D. Kaplan and L. Gass, Understanding Nonlinear Dynamics. Springer, New Yprk, 1995.
[6] C.A. Linker, Autologous stem cell transplantation for acute myeloid leukemia, Bone Marrow Transplant., 31 (2003), 731-738.
[7] M.C. Mackey and L. Glass. Oscillation and chaos in physiological control systems, Science, 197 (1977), 287-289.
[8] P.C. Nathan, L. Sung, M. Crump and J. Beyene. Consolidation therapy with autologous b one marrow transplantation in adults with acute myeloid leukemia: a meta-analysis, J. Natl. Cancer Inst., 96 (2004), no.1, 38-45.
[9] R. Precup, S. Arghirescu, A. Cucuianu and M. Serban. Mathematical modelin g of cell dynamics after allogeneic bone marrow transplantation, Inst. J. Biomath., 5 (2012), no.2 1250026 (18 pages), doi: 10.1142/S1793524511001684.
[10] R. Precup, M.A. Serban and D. Trif, Asymptotic stability for a model of cellular dynamics after allogeneic bone marrow transplantation, submitted.
[11] R. Precup, D. Trif, M.A. Serban and A. Cucuianu, A planning algorithm for correction therapies after allogeneic stem cell transplantation, J. Math. Model. Algor., 11 (2012), no.3, 309-323, doi: 10.1007/s10852-012-9187-3.
[12] A. Shimoni and M. Korbling. Tumor cell contamination in re-infused stem cell autografts: does it have clinical significance?, Crit. Rev. Oncol. Hemat., 41 (2002), 241-250.

2012

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