等效均匀剂量的数理基础及在调强放疗应用价值的研究

Value of the physical basis of equivalent uniform dose as applied to intensity modulated radiation therapy

目的 对等效均匀剂量（EUD）的数理特征在调强放疗（IMRT）临床应用中的意义进行研究。方法 用数学方法和MATLAB数值分析软件对d值趋向＋∞、-∞、0、1情况下EUD的特征进行分析。在随机选取的两组IMRT病例计划中，分别用基于DVH和EUD的优化方法对靶区和危及器官剂量进行逆向设计，对两者在计划剂量分布、优化效率、约束条件、复杂性等指标进行比较，同时利用数学分析结果考察基于EUD优化中α不同取值对计划结果的影响。结果 分析结果表明α取值与EUD表达有直接关系，两种分析结果一致。用EUD方法优化时，当靶区和危及器官α值分别设置在-∞α〈0、α=1、0〈α〈＋∞（α≠1）时，该器官EUD分别表现为接近最小剂量、平均剂量和最大剂量。当α：0时，EUD收敛于吸收剂量的几何平均值，其临床意义和用途需要进一步分析研究。两组病例IMRT计划研究表明，在f用EUD优化过程中调整权重W和α值可使优化系统用较少次数迭代计算得到满意剂量分布，靶区和危及器官的EUD在不同α值下表达不同。结论 EUD数理特征的研究使EUD优化IMRT计划对不同组织设置α值提供了数理依据，α的赋值能较大影响靶区和危及器官中EUD的表达，对计划结果、优化重点、优化效率都有明显影响，具有一定的临床应用价值。

Objeαive To study the mathematic and physical basis of the equivalent uniform dose （EUD） and its optimization mechanism in the control of dose distribution in the organs at risk （OAR） and targets in IMRT optimization process, as well as its significance in clinical application. Methods The mathematic limit analysis method and MATLAB mathematic analysis software were applied to observe the consistence with two different methods. The results of all formulae introduced by Niemierko were compared with the numerical value direαly computed. The optimization mechanism of the dose distribution in the target/OAR in IMRT optimization process on the base of 2 units most simplified EUD optimization analysis model was studied. Results When parameter α tends to ＋ ∞ , - ∞ , 0 and 1, the result of EUD direαly computed on the MATLAB mathematic analysis software was similar to that relied on the limit analysis on condition, which provided evidence for experience that we should apply a positive value to OAR and a negative value to targets. By giving a suitable parameter ＂α＂ and ＂n＂, we may get a better target coverage and improve the sparing of critical struαures through small number of iterations while using multiple dose-volume constrains for each anatomic struαure and with considering great trial-and-error to adjust a larger number of objeαive funαion parameters, all of which were helpful to improve the target control probability and reduce the normal tissue complication probability. Conclusions The use of parameter ＂ α＂ does significantly influence the optimization results on EUD based optimization method for patients with head and neck cancer and prostate cancer. Meanwhile, the EUD based optimization method has significant advantages in aspeαs of optimization results and optimization efficiency when compared with DVH based optimization, which does have greater significance in clinical application.