Modeling the treatment of tumor cells in a solid tumor

Volume 7, Issue 3, pp 188--195 http://dx.doi.org/10.22436/jnsa.007.03.05

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Authors

Lorand Parajdi - Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania.

Abstract

It is well known that the theory of differential equations and some software packages are important tools for solving several actual problems from different real world domains. The novelty of this paper is the fact that the mathematical model of evolution of leukemic cells is adapted to the case of tumor cells, from a solid tumor, together with the treatment of the solid homogeneous tumor. Using the paper Dingli and Michor [D. Dingli, F. Michor, STEM-CELLS, 24 (2006), 2603-2610], we consider the model of evolution of a leukemic population for the case of solid tumors.

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Keywords

• Cauchy problem
• mathematical model
• solid tumor
• tumor cells
• system of differential equations.

MSC

•  92B05
•  34C60
•  34A12

References

• [1] S. Arghirescu, A. Cucuianu, R. Precup, M. Şerban, Mathematical Modeling of Cell Dynamics after Allogeneic Bone Marrow Transplantation in Acute Myeloid Leukemia , Int. J. Biomath., 5 (2012), 18 Pages.


• [2] A. Cucuianu, R. Precup, , A Hypothetical-Mathematical Model of Acute Myeloid Leukaemia Pathogenesis , Comput. Math. Methods Med., 11 (2010), 49-65.


• [3] D. Dingli, F. Michor , Successful Therapy Must Eradicate Cancer Stem Cells, STEM-CELLS, 24 (2006), 2603- 2610.


• [4] J. Guckenheimer, P. Holmes, Nonlineat Oscillations, Dynamical Systems, and Bifurcation of Vector Fields , Springer-Verlag, (1983)


• [5] C. Iancu, I. A. Rus, Mathematical Modeling, Transilvania Press, Cluj-Napoca (1996)


• [6] S. Lynch, Dynamical Systems with Applications using Maple, second edition, Birkhäuser , Boston (2009)


• [7] L. Preziosi , Cancer modelling and simulation, Ed. Chapman & Hall/CRC, (2003)


• [8] R. Precup, M. A. Şerban, D. Trif , Asymptotic stability for cell dynamics after bone marrow transplantation, The 8th Joint Conference on Mathematics and Computer Science, Komarno, Slovakia, , (2010), 1-11.


• [9] R. W. Shonkwiler, J. Herod, Mathematical Biology, Ed. Springer, (2009)


• [10] Z. Zeng , Scientific Computing with Maple Programming, , (2001)