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

Peter Hinow, Philip Gerlee, Lisa J. McCawley, Vito Quaranta, Madalina Clobanu, Shizhen Wang, Jason M. Graham, Bruce P. Ayati, Jonathan Claridge, Kristin R. Swanson, Mary Loveless, Alexander R.A. Anderson

Research output: Contribution to journalArticle

51 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)521-546
Number of pages26
JournalMathematical Biosciences and Engineering
Volume6
Issue number3
DOIs
StatePublished - Jul 2009

Keywords

  • Anti-angiogenic therapy
  • Chemotherapy
  • Hypoxia
  • Mathematical modeling
  • Tumor invasion

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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  • Cite this

    Hinow, P., Gerlee, P., McCawley, L. J., Quaranta, V., Clobanu, M., Wang, S., Graham, J. M., Ayati, B. P., Claridge, J., Swanson, K. R., Loveless, M., & Anderson, A. R. A. (2009). A spatial model of tumor-host interaction: Application of chemotherapy. Mathematical Biosciences and Engineering, 6(3), 521-546. https://doi.org/10.3934/mbe.2009.6.521