Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects
Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects
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DOI：
10.1088/0031-9155/53/22/006
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发表时间：
2008-11-21
影响因子：
3.5
通讯作者：
Huizenga, Henk
中科院分区：
文献类型：
--
作者：
Hoffmann, Aswin L.;den Hertog, Dick;Huizenga, Henk
调强放射治疗（IMRT）的能量密度图的寻找可以用公式表示为一个多准则优化问题，其中存在帕累托最优治疗计划。为了解释分次调强放射治疗的剂量效应，需要利用基于线性二次（LQ）细胞存活模型的放射生物学治疗计划评价标准作为平衡生物反应方面的辐射获益和风险的手段。然而，基于线性Q模型的放射生物学准则是非凸函数，这使得优化问题难以求解。我们应用Romeijn等人（2004 Phys. Med. Biol. 49 1991-2013）提出的框架来寻找基于LQ模型的放射生物学函数的变换，并建立条件，在该条件下，变换后的函数产生不改变帕累托最优治疗计划集的等效凸准则。所分析的功能是：根据莱曼、Kutcher和Burman，肿瘤控制概率（TCP）的基于LQ-Poisson的模型（有和无患者间放射敏感性异质性）、正常组织并发症概率（NTCP）的基于LQ-Poisson的相对序列性s-模型、LQ-Poisson模型下的等效均匀剂量（EUD）和NTCP的基于分数校正的Probit模型。这些函数不同于之前分析的那些函数，因为它们不能被分解为初等EUD或广义EUD函数。此外，我们表明，应用增加和凹变换的凸函数是有益的Pareto有效前沿的分段逼近。
Finding fluence maps for intensity-modulated radiation therapy (IMRT) can be formulated as a multi-criteria optimization problem for which Pareto optimal treatment plans exist. To account for the dose-per-fraction effect of fractionated IMRT, it is desirable to exploit radiobiological treatment plan evaluation criteria based on the linear-quadratic (LQ) cell survival model as a means to balance the radiation benefits and risks in terms of biologic response. Unfortunately, the LQ-model-based radiobiological criteria are nonconvex functions, which make the optimization problem hard to solve. We apply the framework proposed by Romeijn et al (2004 Phys. Med. Biol. 49 1991-2013) to find transformations of LQ-model-based radiobiological functions and establish conditions under which transformed functions result in equivalent convex criteria that do not change the set of Pareto optimal treatment plans. The functions analysed are: the LQ-Poisson-based model for tumour control probability (TCP) with and without inter-patient heterogeneity in radiation sensitivity, the LQ-Poisson-based relative seriality s-model for normal tissue complication probability (NTCP), the equivalent uniform dose (EUD) under the LQ-Poisson model and the fractionation-corrected Probit-based model for NTCP according to Lyman, Kutcher and Burman. These functions differ from those analysed before in that they cannot be decomposed into elementary EUD or generalized-EUD functions. In addition, we show that applying increasing and concave transformations to the convexified functions is beneficial for the piecewise approximation of the Pareto efficient frontier.