Analysis and optimization of tumor inhibitor treatments in a free boundary tumor growth model

Abstract

This paper investigates a free boundary model describing the growth of a spherical tumor in the presence of inhibitors. Specifically, we analyze the optimal inhibitor concentration to minimize both tumor size and side effects of the inhibitor. We establish the existence and uniqueness of the optimal control, and provide a characterization of the optimal control. Numerical simulations illustrate how the optimal control strategy varies with different emphases on controlling tumor size throughout the treatment period and at its terminal time. The findings indicate that when the focus is on controlling tumor size throughout the treatment, a higher dose is administered initially; conversely, when the objective is to minimize tumor size at the treatment’s end, a higher dose is applied towards the end of the treatment period. Additionally, we explore the impact of varying parameters on the optimal control strategy. The optimal treatment dosages might be adjusted based on factors such as maximum tolerated concentrations, the severity of side effects, and the rates at which side effects decay.