Mathematical Modeling of Drug Response
This chapter provides evidence for improving cancer treatment plan efficacy through the inclusion of mathematical modeling techniques, based on our capability to consider the multiple scales of the human body when predicting patient-specific treatment outcomes. It develops a mathematical model that is capable of predicting the response of cancer cells to any drug concentration in vitro based on the uptake rate of drug by the cells. The chapter considers a mathematical model to predict breast cancer growth inhibition in vitro and in vivo, in order to demonstrate the inhibitory effects of tissue-scale diffusion barriers on drug delivery. It also develops a more general model that includes a spatial variable at the tissue scale to predict tumor response, leading to the discovery of how the effectiveness of chemotherapy is dependent on the vasculature of the tumor microenvironment. The chapter investigates how anticancer drugs are successful in monolayer experiments, but often fail to have the same effectiveness in cancer patients.