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 endotheli
al 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.
In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph re
present particles of drug, excipient and polymer, respectively. The graph itself is the contact graph of a multidisperse random sphere packing. The second model describes the dissolution and the subsequent diffusion of the active drug out of a porous matrix using a system of partial differential equations. The predictions of both models show good qualitative agreement with experimental release curves. The models will provide tools for designing better controlled release devices.
Transforming growth factor (TGF) $beta$ is known to have properties of both a tumor suppressor and a tumor promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cell--cell adhesion. Coupling mathematical modeli
ng and experiments, we investigate the growth and motility of oncogene--expressing human mammary epithelial cells under exposure to TGF--$beta$. We use a version of the well--known Fisher--Kolmogorov equation, and prescribe a procedure for its parametrization. We quantify the simultaneous effects of TGF--$beta$ to increase the tendency of individual cells and cell clusters to move randomly and to decrease overall population growth. We demonstrate that in experiments with TGF--$beta$ treated cells textit{in vitro}, TGF--$beta$ increases cell motility by a factor of 2 and decreases cell proliferation by a factor of 1/2 in comparison with untreated cells.
