A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy

A mathematical model is developed that describes the reduction in volume of a vascular tumor in response to specific chemotherapeutic administration strategies. The model consists of a system of partial differential equations governing intratumoral drug concentration and cancer cell density. In the model the tumor is treated as a continuum of two types of cells which differ in their proliferation rates and their responses to the chemotherapeutic agent. The balance between cell proliferation and death within the tumor generates a velocity field which drives expansion or regression of the spheroid. Insight into the tumorʹs response to therapy is gained by applying a combination of analytical and numerical techniques to the model equations.