  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.
