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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 tumor's response to therapy is gained by applying a combination of analytical and numerical techniques to the model equations.

Original publication




Journal article


Math Biosci

Publication Date





17 - 38


Animals, Antineoplastic Agents, Cell Death, Cell Division, Computer Simulation, Drug Resistance, Neoplasm, Humans, Mice, Mice, Nude, Models, Biological, Vascular Neoplasms