A Multi-Drug Pharmacokinectic Optimal Control Approach in Cancer Chemotherapy

The mathematical study of the growth and treatment of cancer has been of great interest to researchers in the recent past as that can help clinical practitioners in adopting new treatment strategies to fight effectively against cancer. Although chemotherapy is the most common method of cancer treatment, the drug-resistant nature of tumor cells and the toxic effect of chemotherapeutic drugs on normal cells are major threats to the success of chemotherapy. In this paper, we propose a multi-drug chemotherapy model combined with an optimal control approach in which the amount of drugs is taken as control functions. The underlying mathematical model discusses the evolution of a heterogeneous tumor population and the dynamics of normal cells under chemotherapy. The model incorporates the pharmacokinetics of the anticancer agents as well. The proposed optimal control approach ensures maximum decay of the tumor cells while preserving a sufficient level of normal cells that would help faster recovery.