Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cells
This paper presents a mathematical analysis on our proposed physiologically structured PDE model that incorporates multiscale and nonlinear features. The model accounts for both mutated and healthy populations of quiescent and proliferating cells at the macroscale, as well as the microscale dynamics...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023621?viewType=HTML |
| _version_ | 1797850972416901120 |
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| author | Iqra Batool Naim Bajcinca |
| author_facet | Iqra Batool Naim Bajcinca |
| author_sort | Iqra Batool |
| collection | DOAJ |
| description | This paper presents a mathematical analysis on our proposed physiologically structured PDE model that incorporates multiscale and nonlinear features. The model accounts for both mutated and healthy populations of quiescent and proliferating cells at the macroscale, as well as the microscale dynamics of cell cycle proteins. A reversible transition between quiescent and proliferating cell populations is assumed. The growth factors generated from the total cell population of proliferating and quiescent cells influence cell cycle dynamics. As feedback from the microscale, Cyclin D/CDK 4-6 protein concentration determines the transition rates between quiescent and proliferating cell populations. Using semigroup and spectral theory, we investigate the well-posedness of the model, derive steady-state solutions, and find sufficient conditions of stability for derived solutions. In the end, we executed numerical simulations to observe the impact of the parameters on the model's nonlinear dynamics. |
| first_indexed | 2024-04-09T19:10:13Z |
| format | Article |
| id | doaj.art-617a301d40fc404598437698b5bfdc8b |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T19:10:13Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-617a301d40fc404598437698b5bfdc8b2023-04-07T01:29:54ZengAIMS PressAIMS Mathematics2473-69882023-03-0185123421237210.3934/math.2023621Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cellsIqra Batool0Naim Bajcinca1Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau, Mechanical and Process Engineering, 67663 Kaiserslautern, GermanyRheinland-Pfälzische Technische Universität Kaiserslautern-Landau, Mechanical and Process Engineering, 67663 Kaiserslautern, GermanyThis paper presents a mathematical analysis on our proposed physiologically structured PDE model that incorporates multiscale and nonlinear features. The model accounts for both mutated and healthy populations of quiescent and proliferating cells at the macroscale, as well as the microscale dynamics of cell cycle proteins. A reversible transition between quiescent and proliferating cell populations is assumed. The growth factors generated from the total cell population of proliferating and quiescent cells influence cell cycle dynamics. As feedback from the microscale, Cyclin D/CDK 4-6 protein concentration determines the transition rates between quiescent and proliferating cell populations. Using semigroup and spectral theory, we investigate the well-posedness of the model, derive steady-state solutions, and find sufficient conditions of stability for derived solutions. In the end, we executed numerical simulations to observe the impact of the parameters on the model's nonlinear dynamics.https://www.aimspress.com/article/doi/10.3934/math.2023621?viewType=HTMLmultiscale modelproliferationquiescencecell cycle dynamicssteady-statescancer |
| spellingShingle | Iqra Batool Naim Bajcinca Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cells AIMS Mathematics multiscale model proliferation quiescence cell cycle dynamics steady-states cancer |
| title | Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cells |
| title_full | Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cells |
| title_fullStr | Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cells |
| title_full_unstemmed | Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cells |
| title_short | Stability analysis of a multiscale model including cell-cycle dynamics and populations of quiescent and proliferating cells |
| title_sort | stability analysis of a multiscale model including cell cycle dynamics and populations of quiescent and proliferating cells |
| topic | multiscale model proliferation quiescence cell cycle dynamics steady-states cancer |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023621?viewType=HTML |
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