Optimal Chemotherapy for Brain Tumor Growth in a Reaction-Diffusion Model
Mohsen Yousefnezhad, Chiu‐Yen Kao, Seyyed Abbas Mohammadi
Abstract
In this paper we address the question of determining optimal chemotherapy strategies to prevent the growth of brain tumor population. To do so, we consider a reaction-diffusion model which describes the diffusion and proliferation of tumor cells and a minimization problem corresponding to it. We shall establish that the optimization problem admits a solution and obtain a necessary condition for the minimizer. In a specific case, the optimizer is calculated explicitly, and we prove that it is unique. Then, a gradient-based efficient numerical algorithm is developed in order to determine the optimizer. Our results suggest a bang-bang chemotherapy strategy in a cycle which starts at the maximum dose and terminates with a rest period. Numerical simulations based upon our algorithm on a real brain image show that this is in line with the maximum tolerated dose (MTD), a standard chemotherapy protocol.