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.

中文翻译：

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最大耐受剂量 (MTD) 化疗方案对于多形性胶质母细胞瘤来说是最佳选择吗？


在本研究中，我们研究涉及反应扩散偏微分方程（PDE）的控制问题。具体来说，重点是优化脑肿瘤治疗的化疗方案，以尽量减少化疗后剩余的肿瘤细胞。我们的研究结果表明，爆炸式增加函数是唯一的解决方案，证实 MTD 调度是最佳化疗方案。针对位于额叶、颞叶或枕叶的肿瘤，使用来自诊所的参数对真实脑图像进行了多次数值实验。他们证实了我们的理论结果，并表明肿瘤的增殖率与最佳治疗的有效性之间存在相关性。