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Mathematical Biosciences and Engineering (MBE)
 

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

Pages: 521 - 546, Volume 6, Issue 3, July 2009

doi:10.3934/mbe.2009.6.521       Abstract        Full Text (830.1K)       Related Articles

Peter Hinow - Institute for Mathematics and its Applications, University of Minnesota, 114 Lind Hall, Minneapolis, MN 55455, United States (email)
Philip Gerlee - Niels Bohr Institute, Center for Models of Life, Blegdamsvej 17, 2100 Copenhagen, Denmark (email)
Lisa J. McCawley - Department of Cancer Biology, Vanderbilt University, Nashville, TN 37232, United States (email)
Vito Quaranta - Department of Cancer Biology, Vanderbilt University, Nashville, TN 37232, United States (email)
Madalina Ciobanu - Department of Chemistry, Vanderbilt University, Nashville, TN 37235, United States (email)
Shizhen Wang - Department of Surgical Research, Beckman Research Institute of City of Hope, Duarte, CA 91010, United States (email)
Jason M. Graham - Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States (email)
Bruce P. Ayati - Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States (email)
Jonathan Claridge - Department of Applied Mathematics and Department of Pathology, University of Washington, Seattle, WA 98195, United States (email)
Kristin R. Swanson - Department of Applied Mathematics and Department of Pathology, University of Washington, Seattle, WA 98195, United States (email)
Mary Loveless - Department of Biomedical Engineering, Vanderbilt University, Nashville, TN 37232, United States (email)
Alexander R. A. Anderson - H. Lee Moffitt Cancer Center & Research Institute, Integrated Mathematical Oncology, 12902 Magnolia Drive, Tampa, FL 33612, United States (email)

Abstract: 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.

Keywords:  tumor invasion, hypoxia, chemotherapy, anti-angiogenic therapy, mathematical modeling.
Mathematics Subject Classification:  92C17.

Received: October 2008;      Accepted: February 2009;      Published: June 2009.