Quantitative models in cancer chemotherapy

Several experimental and clinical studies have documented that the order in which chemotherapy drugs are administered affects the outcome of cancer treatment. Two notable examples are Bonadonna's treatment of breast cancer and Schwartz's treatment of gastric cancer and breast cancer. Mathematical models can be used to explain this drug sequencing phenomenon. Several models were formulated as systems of ordinary differential equations, dNdt = AN, accounting for cell cycle specificity and cellular resistance. A numerical parameter estimation tool was developed to determine the rate constants within these ODE systems. This tool is capable of simulating instantaneous kill by drug impulse, resistance development, and changes to the transition rates. Parametric studies verify the preferred regimens for the experimental and clinical findings of Schwartz and Bonadonna, and the results indicate possible mechanisms responsible for the preferred ordering.