2009, 6(3): 521-546. doi: 10.3934/mbe.2009.6.521

A spatial model of tumor-host interaction: Application of chemotherapy


Institute for Mathematics and its Applications, University of Minnesota, 114 Lind Hall, Minneapolis, MN 55455, United States


Niels Bohr Institute, Center for Models of Life, Blegdamsvej 17, 2100 Copenhagen, Denmark


Department of Cancer Biology, Vanderbilt University, Nashville, TN 37232, United States, United States


Department of Chemistry, Vanderbilt University, Nashville, TN 37235, United States


Department of Surgical Research, Beckman Research Institute of City of Hope, Duarte, CA 91010, United States


Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States, United States


Department of Applied Mathematics and Department of Pathology, University of Washington, Seattle, WA 98195, United States, United States


Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, United States


H. Lee Moffitt Cancer Center & Research Institute, Integrated Mathematical Oncology, 12902 Magnolia Drive, Tampa, FL 33612, United States

Received  October 2008 Revised  February 2009 Published  June 2009

In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. When no treatment is applied the model reproduces the typical dynamics of early tumor growth. The initially avascular tumor reaches a diffusion limited size of the order of millimeters and initiates angiogenesis through the release of vascular endothelial growth factor (VEGF) secreted by hypoxic cells in the core of the tumor. This stimulates endothelial cells to migrate towards the tumor and establishes a nutrient supply sufficient for sustained invasion. To this model we apply cytostatic treatment in the form of a VEGF-inhibitor, which reduces the proliferation and chemotaxis of endothelial cells. This treatment has the capability to reduce tumor mass, but more importantly, we were able to determine that inhibition of endothelial cell proliferation is the more important of the two cellular functions targeted by the drug. Further, we considered the application of a cytotoxic drug that targets proliferating tumor cells. The drug was treated as a diffusible substance entering the tissue from the blood vessels. Our results show that depending on the characteristics of the drug it can either reduce the tumor mass significantly or in fact accelerate the growth rate of the tumor. This result seems to be due to complicated interplay between the stromal and tumor cell types and highlights the importance of considering chemotherapy in a spatial context.
Citation: Peter Hinow, Philip Gerlee, Lisa J. McCawley, Vito Quaranta, Madalina Ciobanu, Shizhen Wang, Jason M. Graham, Bruce P. Ayati, Jonathan Claridge, Kristin R. Swanson, Mary Loveless, Alexander R. A. Anderson. A spatial model of tumor-host interaction: Application of chemotherapy. Mathematical Biosciences & Engineering, 2009, 6 (3) : 521-546. doi: 10.3934/mbe.2009.6.521

Adam Glick, Antonio Mastroberardino. Combined therapy for treating solid tumors with chemotherapy and angiogenic inhibitors. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020343


Min Chen, Olivier Goubet, Shenghao Li. Mathematical analysis of bump to bucket problem. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5567-5580. doi: 10.3934/cpaa.2020251


Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020457


Xin Guo, Lexin Li, Qiang Wu. Modeling interactive components by coordinate kernel polynomial models. Mathematical Foundations of Computing, 2020, 3 (4) : 263-277. doi: 10.3934/mfc.2020010


Jianquan Li, Xin Xie, Dian Zhang, Jia Li, Xiaolin Lin. Qualitative analysis of a simple tumor-immune system with time delay of tumor action. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020341


Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020446


Yining Cao, Chuck Jia, Roger Temam, Joseph Tribbia. Mathematical analysis of a cloud resolving model including the ice microphysics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 131-167. doi: 10.3934/dcds.2020219


Jun Zhou. Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5581-5590. doi: 10.3934/cpaa.2020252

[Back to Top]