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

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.

Rapid optimization of drug combinations for the optimal angiostatic treatment of cancer

“…S3B). This may suggest that proliferation is more dominant in the process of angiogenesis than cell migration, which has also been proposed by others [53]. The same may also be reflected by clinical trials, where proliferation inhibitors (such as sunitinib and BEZ-235) were more successful than migration inhibitors (the α v β 3 inhibitor cilengitide [54] and the α 5 β 1 antibody volociximab [55]).…”

Exploring the Competition between Proliferative and Invasive Cancer Phenotypes in a Continuous Spatial Model

“…The tumor microenvironment and its genetic composition are modeled based on [17], [21]. The microenvironment consists of the extracellular matrix (ECM), f and the vasculature, V , which provides oxygen to tumor cells.…”

“…In addition to their random movement, tumor cells can haptotactically migrate to denser areas of ECM [21], [31]. The structure and composition of the ECM affect cell adhesion and motility thus, play a critical role in tumor invasion, morphology and metastasis [32].…”

“…In this work, we extend a previously developed continuous spatial model of monoclonal tumor growth [17], [21] to account for two cancer subpopulations of distinct phenotypic characteristics that play an important role in tumor growth, invasion and metastasis. In particular, we assume a vascularized solid tumor that consists of one more proliferative and another more motile/invasive phenotype, which are in a constant competition for space and resources within the tumor microenvironment.…”

Hierarchical Models of Tumor Growth

“…The reasoning behind OP algorithm led us to pursue a simpler strategy to develop a hierarchical family of tumor growth models from the basic model derived from [4]. We use a simple sensitivity analysis method to investigate the influence of the input parameters on the tumor volume evolution.…”