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 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.