3 – Compartment Model for Chemotherapy of Heterogenous Tumors Incorporating Pharmacokinetics of the Drug
Chemotherapy, being a systemic treatment, has its effect on tumor cells as well as normal cells of the patient’s
body. The chemotherapy regimen for a single chemotherapeutic agent acting on a heterogeneous tumor population is studied
mathematically as an optimal control problem. A treatment protocol is proposed which seeks to strike a balance between
maximizing its toxicity on tumor cells while minimizing the side – effects on normal cells. Three different tumor sub
populations are considered based on the difference in their drug sensitivity – sensitive cells, partially sensitive cells and
resistant cells. Pharmacokinetics of the drug is also taken into account. In this paper, chemotherapy is studied as an optimal
control problem and viable singular controls are studied, which correspond to an intermediate drug dose administered
without long rest periods in between.
Keywords - Mathematical model of chemotherapy, pharmacokinetics, drug resistance, tumor heterogeneity.