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The Role Of Time Delays, Slow Processes And Chaos In Modulating The Cell-Cycle Clock
A Single-Cell Approach in Modeling the Dynamics of Tumor Microregions
1. | Mathematical Biosciences Institute, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, United States |
[1] |
Didier Bresch, Thierry Colin, Emmanuel Grenier, Benjamin Ribba, Olivier Saut. A viscoelastic model for avascular tumor growth. Conference Publications, 2009, 2009 (Special) : 101-108. doi: 10.3934/proc.2009.2009.101 |
[2] |
Shihe Xu, Yinhui Chen, Meng Bai. Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 997-1008. doi: 10.3934/dcdsb.2016.21.997 |
[3] |
Zejia Wang, Suzhen Xu, Huijuan Song. Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2593-2605. doi: 10.3934/dcdsb.2018129 |
[4] |
Andrea Tosin. Multiphase modeling and qualitative analysis of the growth of tumor cords. Networks and Heterogeneous Media, 2008, 3 (1) : 43-83. doi: 10.3934/nhm.2008.3.43 |
[5] |
Fujun Zhou, Shangbin Cui. Well-posedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 929-943. doi: 10.3934/dcds.2008.21.929 |
[6] |
Junde Wu, Shangbin Cui. Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 737-765. doi: 10.3934/dcds.2010.26.737 |
[7] |
Shihe Xu. Analysis of a delayed free boundary problem for tumor growth. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 293-308. doi: 10.3934/dcdsb.2011.15.293 |
[8] |
Elena Izquierdo-Kulich, José Manuel Nieto-Villar. Mesoscopic model for tumor growth. Mathematical Biosciences & Engineering, 2007, 4 (4) : 687-698. doi: 10.3934/mbe.2007.4.687 |
[9] |
Hyun Geun Lee, Yangjin Kim, Junseok Kim. Mathematical model and its fast numerical method for the tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1173-1187. doi: 10.3934/mbe.2015.12.1173 |
[10] |
Rudolf Olach, Vincent Lučanský, Božena Dorociaková. The model of nutrients influence on the tumor growth. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2607-2619. doi: 10.3934/dcdsb.2021150 |
[11] |
Harald Garcke, Kei Fong Lam. Analysis of a Cahn--Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4277-4308. doi: 10.3934/dcds.2017183 |
[12] |
Andrea Signori. Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme. Mathematical Control and Related Fields, 2020, 10 (2) : 305-331. doi: 10.3934/mcrf.2019040 |
[13] |
Jian-Guo Liu, Min Tang, Li Wang, Zhennan Zhou. Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3011-3035. doi: 10.3934/dcdsb.2018297 |
[14] |
Shihe Xu, Meng Bai, Fangwei Zhang. Analysis of a free boundary problem for tumor growth with Gibbs-Thomson relation and time delays. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 3535-3551. doi: 10.3934/dcdsb.2017213 |
[15] |
Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, Magda Lopes Texeira, José Manuel Nieto-Villar. The dynamics of tumor growth and cells pattern morphology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 547-559. doi: 10.3934/mbe.2009.6.547 |
[16] |
Ebraheem O. Alzahrani, Yang Kuang. Nutrient limitations as an explanation of Gompertzian tumor growth. Discrete and Continuous Dynamical Systems - B, 2016, 21 (2) : 357-372. doi: 10.3934/dcdsb.2016.21.357 |
[17] |
Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1141-1156. doi: 10.3934/mbe.2015.12.1141 |
[18] |
Dongxi Li, Ni Zhang, Ming Yan, Yanya Xing. Survival analysis for tumor growth model with stochastic perturbation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5707-5722. doi: 10.3934/dcdsb.2021041 |
[19] |
Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2729-2749. doi: 10.3934/dcdss.2020457 |
[20] |
Cornel M. Murea, H. G. E. Hentschel. A finite element method for growth in biological development. Mathematical Biosciences & Engineering, 2007, 4 (2) : 339-353. doi: 10.3934/mbe.2007.4.339 |
2018 Impact Factor: 1.313
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