SIAM Journal on Applied Mathematics, Volume 81, Issue 3, Page 1077-1097, January 2021.
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.

中文翻译：

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反应扩散模型中脑肿瘤生长的最佳化疗

SIAM Journal on Applied Mathematics，第 81 卷，第 3 期，第 1077-1097 页，2021 年 1 月。
在本文中，我们解决了确定最佳化疗策略以防止脑肿瘤种群增长的问题。为此，我们考虑了一个反应扩散模型，该模型描述了肿瘤细胞的扩散和增殖以及与之对应的最小化问题。我们将确定优化问题有一个解并获得最小化器的必要条件。在特定情况下，优化器是显式计算的，我们证明它是唯一的。然后，开发了一种基于梯度的高效数值算法以确定优化器。我们的研究结果表明，在一个循环中采用 bang-bang 化疗策略，从最大剂量开始，以休息期结束。