Optimal Chemotherapy for Brain Tumor Growth in a Reaction-Diffusion Model

TY - JOUR

T1 - Optimal Chemotherapy for Brain Tumor Growth in a Reaction-Diffusion Model

AU - Yousefnezhad, Mohsen

AU - Kao, Chiu-Yen

AU - Mohammadi, Seyyed Abbas

N1 - Copyright: © by SIAM. Unauthorized reproduction of this article is prohibited.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - reaction-diffusion equation

KW - brain tumor

KW - optimal chemotherapy strategy

UR - https://www.scopus.com/pages/publications/85107560666

U2 - 10.1137/20M135995X

DO - 10.1137/20M135995X

M3 - Article

SN - 0036-1399

VL - 81

SP - 1077

EP - 1097

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 3

ER -