Modeling Vascular Diffusion of Oxygen in Breast Cancer

Oxygen is a vital nutrient necessary for tumor cells to survive and proliferate. Oxygen is diffused from our blood vessels into the tissue, where it is consumed by our cells. This process can be modeled by partial differential equations with sinks and sources. This project focuses on adding an oxygen diffusion module to an existing 3D agent-based model of breast cancer developed in Dr. Norton’s lab. The mathematical diffusion module added to an existing agent-based model (ABM) includes deriving the 1-dimensional and multi-dimensional diffusion equations, implementing 2D and 3D oxygen diffusion models into the ABM, and numerically evaluating those equations using the Finite Difference Method. I started by diffusing a point source in a 2D grid, then diffusing a line in a 2D grid, then a cubic patch in a 3D grid, and finally, diffusing oxygen from blood vessels into the tissue. Then, I programmed the supply function to represent the continuous oxygen supply from vasculature, and the uptake function to represent the oxygen uptake by cancer cells