A Mathematical Model to Predict Tumor Responses to Cancer Drugs Based on Dose Response Curves in the Continuous Case
Keywords: mathematical models, drug effectiveness, cancer treatment, dose response curves,
AbstractThis project is associated with the PIC Math Program of the Mathematical Association of America (MAA). This project investigates how to mathematically model the drug concentration that kills 50 percent of the 3-D tumor cells and generate a dose response curve. These curves allow us to more accurately predict effective drug dosages, such as, the ideal balance between the drug toxicity and drug effectiveness. The PDEs developed in this paper allow us to vary multiple variables (like tumor density and drug concentration) at once within a set of coupled equations, which can reduce the amount of time spent planning experiments and allow for greater accuracy in drug dosages. In future applications, we can develop a discrete model to further analyze independent parameters.