The goal in external beam radiotherapy (EBRT) for cancer is to maximize damage to the tumour while limiting toxic effects on the organs-at-risk. EBRT can be delivered via different modalities such as photons, protons and neutrons. The choice of an optimal modality depends on the anatomy of the irradiated area and the relative physical and biological properties of the modalities under consideration. There is no single universally dominant modality. We present the first-ever mathematical formulation of the optimal modality selection problem. We show that this problem can be tackled by solving the Karush-Kuhn-Tucker conditions of optimality, which reduce to an analytically tractable quartic equation. We perform numerical experiments to gain insights into the effect of biological and physical properties on the choice of an optimal modality or combination of modalities.

中文翻译：

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外照射治疗中的最佳模式选择。

癌症体外放射线疗法（EBRT）的目标是最大程度地破坏肿瘤，同时限制对处于危险中的器官的毒性作用。EBRT可以通过不同的方式（例如光子，质子和中子）进行传递。最佳模态的选择取决于照射区域的解剖结构以及所考虑模态的相对物理和生物学特性。没有单一的普遍主导的方式。我们提出了最佳模态选择问题的第一个数学公式。我们表明，可以通过解决最优的Karush-Kuhn-Tucker条件来解决该问题，该条件可以简化为解析可处理的四次方程。