A class of optimization problems in radiotherapy dosimetry planning
A class of optimization problems in radiotherapy dosimetry planning
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放疗剂量规划中的一类优化问题
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
L. Núñez
中科院分区：
文献类型：
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作者：
J. Alfonso;G. Buttazzo;B. García;M. Herrero;L. Núñez
放射治疗是抗击恶性肿瘤的重要临床手段。要做到这一点，关键在于选择合适的辐射剂量，在不对周围健康组织造成重大损害的情况下实现肿瘤控制。尽管最近取得了重大进展，但任何正在使用的放射治疗计划主要依赖于临床医生在几种可能的选择中做出的基于经验的决定。
在这项工作中，我们考虑了一个与决策过程相关的数学问题。更准确地说，我们假设给出了一个定义明确的目标区域，称为规划目标体积(PTV)。然后我们考虑确定哪种辐射分布能够实现对肿瘤细胞的最大影响和对健康细胞的最小影响的问题。这种剂量分布被定义为PTV和健康组织上多参数最小化问题的解决方案，受临床和技术要求的一些限制。对于任意的参数选择，得到了该问题存在唯一解的充分条件。然后通过适当的数值算法来逼近这样的解。最后给出了一些实例，在此基础上讨论了不同临床效率指标对模型参数的依赖性。
Radiotherapy is an important clinical tool to fight malignancies. To do so, a key point consists in selecting a suitable radiation dose that could achieve tumour control without inducing significant damage to surrounding healthy tissues. In spite of recent significant advances, any radiotherapy planning in use relies principally on experience-based decisions made by clinicians among several possible choices.
In this work we consider a mathematical problem related to that decision-making process. More precisely, we assume that a well-defined target region, called planning target volume (PTV), is given. We then consider the question of determining which radiation distribution is able to achieve a maximum impact on tumour cells and a minimum one in healthy ones. Such dose distribution is defined as the solution of a multi-parameter minimization problem over the PTV and healthy tissues, subject to a number of constraints arising from clinical and technical requirements. For any choice of parameters, sufficient conditions for the existence of a unique solution of that problem are derived. Such solution is then approximated by means of a suitable numerical algorithm. Finally, some examples are considered, on which the dependence on model parameters of different clinical efficiency indexes is discussed.