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This article is cited in 1 scientific paper (total in 1 paper)
Mathematical Modeling, Numerical Methods and Software Complexes
Tumor growth and mathematical modeling of system processes
Sh. Gantseva, R. N. Bakhtizinb, M. V. Frantsc, K. Gantseva a Bashkir State Medical University,
Ufa, 450000, Russian Federation
b Ufa State Petroleum Technological University,
Ufa, 450062, Russian Federation
c Ufa State Aviation Technical University, Ufa, 450008, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
The paper deals with applying mathematical modeling to study tumor growth process and optimizing cancer treatment. A structured review of the studies devoted to this problem is given. The role of the cell life cycle in understanding the tumor growth and the mechanisms of cancer treatment is discussed. It is important that modern cancer treatment methods, in particular, chemotherapy and radiation therapy, affect both normal and tumor cells in certain stages of the life cycle and do not influence on cells in other stages. Cell life cycle description is given as well as the mechanisms that maintain and restore normal density of the cell population. A graph of cell life cycle stages and transitions is demonstrated. Dynamic mathematical model of proliferative homeostasis in the cell population is proposed, which takes into account the heterogeneity of cell populations by life cycle stages. The model is a system of differential equations with delays. The stationary state of the model is investigated, which allows to determine the parameters values for the normal cell population. The results of a numeric experiment is obtained, which is focused on the process of cell population density recovery after mass death of cells. As the experiment shows, after cell death, the densities of cells in different life cycle stages are restored to normal values, which corresponds to the concepts of proliferative homeostasis in cell populations.
Keywords:
tumor growth, proliferative homeostasis, cell life cycle, cell kinetics.
Received: November 18, 2018 Revised: January 22, 2019 Accepted: January 27, 2019 First online: March 11, 2019
Citation:
Sh. Gantsev, R. N. Bakhtizin, M. V. Frants, K. Gantsev, “Tumor growth and mathematical modeling of system processes”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:1 (2019), 131–151
Linking options:
https://www.mathnet.ru/eng/vsgtu1661 https://www.mathnet.ru/eng/vsgtu/v223/i1/p131
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Abstract page: | 604 | Full-text PDF : | 476 | References: | 62 |
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