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

Mohsen Yousefnezhad (Lead / Corresponding author), Chiu-Yen Kao (Lead / Corresponding author), Seyyed Abbas Mohammadi (Lead / Corresponding author)

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1077 - 1097
Number of pages21
JournalSIAM Journal on Applied Mathematics
Issue number3
Early online date3 Jun 2021
Publication statusPublished - 2021


  • reaction-diffusion equation
  • brain tumor
  • optimal chemotherapy strategy


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