Is maximum tolerated dose (MTD) chemotherapy scheduling optimal for glioblastoma multiforme?

In this study, we investigate a control problem involving a reaction–diffusion partial differential equation (PDE). Specifically, the focus is on optimizing the chemotherapy scheduling for brain tumor treatment to minimize the remaining tumor cells post-chemotherapy. Our findings establish that a ba...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2024-12, Vol.139, p.108292, Article 108292
Main Authors: Kao, Chiu-Yen, Mohammadi, Seyyed Abbas, Yousefnezhad, Mohsen
Format: Article
Language:English
Subjects:
Analytical solution
Bang-bang solution
Chemotherapy scheduling
Glioblastoma multiforme
Optimal control of PDEs
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Summary:In this study, we investigate a control problem involving a reaction–diffusion partial differential equation (PDE). Specifically, the focus is on optimizing the chemotherapy scheduling for brain tumor treatment to minimize the remaining tumor cells post-chemotherapy. Our findings establish that a bang-bang increasing function is the unique solution, affirming the MTD scheduling as the optimal chemotherapy profile. Several numerical experiments on a real brain image with parameters from clinics are conducted for tumors located in the frontal lobe, temporal lobe, or occipital lobe. They confirm our theoretical results and suggest a correlation between the proliferation rate of the tumor and the effectiveness of the optimal treatment.
ISSN:1007-5704
DOI:10.1016/j.cnsns.2024.108292