Abstract
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.
| Original language | English |
|---|---|
| Article number | 108292 |
| Number of pages | 21 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 139 |
| Early online date | 28 Aug 2024 |
| DOIs | |
| Publication status | Published - Dec 2024 |
Keywords
- Analytical solution
- Bang-bang solution
- Chemotherapy scheduling
- Glioblastoma multiforme
- Optimal control of PDEs
ASJC Scopus subject areas
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics