Tumor growth and mathematical modeling of system processes
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 discusse...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2019-12-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/34684/23033 |
| _version_ | 1818059849822371840 |
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| author | Shamil Khanafievich Gantsev Ramil N Bakhtizin Marina Valerievna Frants Kamil Shamilevich Gantsev |
| author_facet | Shamil Khanafievich Gantsev Ramil N Bakhtizin Marina Valerievna Frants Kamil Shamilevich Gantsev |
| author_sort | Shamil Khanafievich Gantsev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T13:23:04Z |
| format | Article |
| id | doaj.art-33f3ea37b35649549f95d77abaec1336 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T13:23:04Z |
| publishDate | 2019-12-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-33f3ea37b35649549f95d77abaec13362022-12-22T01:47:17ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812019-12-0123113115110.14498/vsgtu166131197Tumor growth and mathematical modeling of system processesShamil Khanafievich Gantsev0Ramil N Bakhtizin1Marina Valerievna Frants2Kamil Shamilevich Gantsev3Bashkir State Medical UniversityUfa State Petroleum Technological UniversityUfa State Aviation Technical UniversityBashkir State Medical UniversityThe 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.https://journals.eco-vector.com/1991-8615/article/viewFile/34684/23033tumor growthproliferative homeostasiscell life cyclecell kinetics |
| spellingShingle | Shamil Khanafievich Gantsev Ramil N Bakhtizin Marina Valerievna Frants Kamil Shamilevich Gantsev Tumor growth and mathematical modeling of system processes Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki tumor growth proliferative homeostasis cell life cycle cell kinetics |
| title | Tumor growth and mathematical modeling of system processes |
| title_full | Tumor growth and mathematical modeling of system processes |
| title_fullStr | Tumor growth and mathematical modeling of system processes |
| title_full_unstemmed | Tumor growth and mathematical modeling of system processes |
| title_short | Tumor growth and mathematical modeling of system processes |
| title_sort | tumor growth and mathematical modeling of system processes |
| topic | tumor growth proliferative homeostasis cell life cycle cell kinetics |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/34684/23033 |
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