Towards tumor growth control subject to reduced toxicity

This study examines the application of mathematical modeling and optimal control in the investigation of optimal cancer therapy. We present models to predict cancer dynamics in mice with colon cancer as well as pharmacokinetic and drug-related toxicity models to study the effect of anti-cancer agents irinotecan and 5-fluorouracil. We present two methodologies which can be used to design optimal therapies subject to reduced toxicity. The first methodology employs a toxicity model based on body weight loss as is usually the case in an experimental setting whilst the other utilises a well-documented side-effect chart to quantify overall toxicity. These drug-specific formulations are proved to be especially useful when formulating multidrug therapies. Our models replicate both tumor and toxicity data successfully and can be used in treatment planning. The optimal control results suggest that optimal therapy is a balance between minimum toxicity and minimum tumor growth. Whilst in the original experimental studies from which the data was extracted, treatment was not succesful in controlling tumor growth, our schedules successfully control growth while at the same time preventing undesirable toxicity beyond the tolerated limits set by experimental guidelines. The control study on the combination 5-FU/CPT-11 favours 5-FU administration, the main reason being that this drug has been shown experimentally to be less toxic. Lastly, we show that combination therapy is more effective than monotherapy.