Mathematical Modeling of Tumor Growth, Drug-Resistance, Toxicity, and Optimal Therapy Design

The combination of mathematical modeling and optimal control techniques holds great potential for quantitatively describing tumor progression and optimal treatment planning. Hereby, we use a Gompertz-type growth law and a pharmacokinetic-pharmacodynamic approach for modeling the effects of drugs on tumor progression in tumor bearing mice, and we combine these in order to design optimal therapeutic patterns. Specifically, we describe colon cancer progression in both untreated mice as well as mice treated with widely used anticancer agents. We also present a pharmacokinetic model to describe the kinetics of drugs in the body as well as detailed toxicity models to describe the severity of side effects. Finally, we propose a promising methodology by which cancer progression in mice with drug resistance can be controlled. By using optimal control, we demonstrate that the optimal planning of the frequency and magnitude of treatment interruptions is key to the control of cancer progression in subjects with resistance and should be further investigated in an experimental setting, which is currently underway.