Model-based control of tumor progression

Abstract

This paper presents our work on the application of mathematical modeling and optimal control techniques in the modeling of tumor progression and optimal treatment planning. We present a pharmacokinetic-pharmacodynamic approach to the modeling of tumor progression in mice. Specifically, we describe colon cancer progression in both untreated mice as well as mice treated with anti-cancer agents. We also a present pharmacokinetic model to describe the drug kinetics in the body as well as toxicity models to describe the severity of side-effects. Lastly, 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 breaks is key to cancer control in subjects with resistance and should be further investigated in an experimental setting, which is currently underway.