标题： 原理证明：多模态放疗优化 显示英文标题

标题： A Proof of Principle: Multi-Modality Radiotherapy Optimization

摘要： 放射治疗通过电离辐射损伤肿瘤细胞的DNA来治疗癌症患者。 光子是治疗中最广泛使用的辐射类型，自1895年首次发现X射线后不久就被投入使用。 然而，由于质子和碳离子等其他辐射模式独特的生物和物理特性，使其与光子有所不同，因此对这些模式的兴趣和开发正在增加。 目前确定最佳辐射模式或多种模式的最佳组合的尝试是经验性的，并处于发展的早期阶段。 在本文中，我们提出一个数学框架，以优化多种辐射模式的完整辐射剂量分布和分割方案，旨在最大程度地破坏肿瘤，同时将正常组织的损伤限制在相应的耐受水平。 该公式产生了一个非凸的混合整数规划问题，我们提出了一种双层优化算法，以高效求解。 上层问题是使用下层优化得到的剂量分布来优化分割方案。 我们在一个简单的二维幻影中展示了我们新框架和算法的可行性，该幻影使用了两种不同的辐射模式，临床直觉可以轻松得出。 我们数值模拟的结果与临床直觉一致，验证了我们的方法，并展示了该框架在进一步临床研究中的前景。 显示英文摘要

摘要： Radiotherapy is used to treat cancer patients by damaging DNA of tumor cells using ionizing radiation. Photons are the most widely used radiation type for therapy, having been put into use soon after the first discovery of X-rays in 1895. However, there are emerging interests and developments of other radiation modalities such as protons and carbon ions, owing to their unique biological and physical characteristics that distinguish these modalities from photons. Current attempts to determine an optimal radiation modality or an optimal combination of multiple modalities are empirical and in the early stage of development. In this paper, we propose a mathematical framework to optimize full radiation dose distributions and fractionation schedules of multiple radiation modalities, aiming to maximize the damage to the tumor while limiting the damage to the normal tissue to the corresponding tolerance level. This formulation gives rise to a non-convex, mixed integer program and we propose a bilevel optimization algorithm, to efficiently solve it. The upper level problem is to optimize the fractionation schedule using the dose distribution optimized in the lower level. We demonstrate the feasibility of our novel framework and algorithms in a simple 2-dimensional phantom with two different radiation modalities, where clinical intuition can be easily drawn. The results of our numerical simulations agree with the clinical intuition, validating our approach and showing the promise of the framework for further clinical investigation.