AN ADAPTIVE PHARMACOKINETIC OPTIMAL CONTROL APPROACH IN CHEMOTHERAPY FOR HETEROGENEOUS TUMOR

Abstract

The mathematical study of cancer received great attention in recent years. The theoretical and numerical investigations of models employed for studying the growth of cancer cells and treatment of cancer can help the clinical practitioners in adapting new strategies to face the challenges posed by the deadly disease. Chemotherapy is the most common method of treatment for cancer. The resistance of tumor cells toward the administered drug and the toxic effect of anti-cancer agents on healthy cells are major hurdles to the success of therapy. In this paper, we study this as an optimal control problem in which the amount of drug injected is taken as control. The evolution of different types of cells — sensitive tumor cells, resistant tumor cells and normal cells — under treatment are analyzed. The pharmacokinetics of the drug is also incorporated into the mathematical model. We propose a treatment protocol that assures the death of a maximum number of tumor cells but also manages to keep the normal cells at a sufficient level. We also validated our theoretical results numerically.