Relativistic Optimization Force Concept for gEUD Biological Optimization and Novel a-value Selection Viewpoint
Relativistic Optimization Force Concept for gEUD Biological Optimization and Novel a-value Selection Viewpoint
复制标题
DOI：
10.21203/rs.3.rs-154650/v1
复制
发表时间：
2021-02
期刊：
影响因子：
--
通讯作者：
Y. Anetai;H. Takegawa;Y. Koike;Satoaki Nakamura;N. Tanigawa
中科院分区：
文献类型：
--
作者：
Y. Anetai;H. Takegawa;Y. Koike;Satoaki Nakamura;N. Tanigawa
广义等效均匀剂量（gEUD）优化是一种用于调强放射治疗（IMRT）的生物优化方法。尽管参数分析已被广泛报道，但参数 a 值在优化方法中的使用仍然难以捉摸。本研究旨在阐明 gEUD 的数学特性并提供有效的 a 值选择。 gEUD 通常使用微分剂量体积直方图 (DVH) 获得。这可以使用累积 DVH (cDVH) 重写并应用于变分分析。然后获得 gEUD 和剂量之间的等效值；低或高 a 值分别对应于宽或窄的优化剂量范围。接下来，我们重点关注 gEUD 曲线针对 a 值变化的行为，尽管进行了优化，但它仍保留了其曲线特征。使用微分几何，可以将这种曲线移动视为相对论优化力优化前和优化后之间的测地线偏差。力产生的总作用包括 gEUD 曲线的曲率。这个想法提供了一个新颖的观点，即gEUD曲线的曲率受到优化效果的影响。 gEUD 曲线的曲率驻点（顶点，a = a_k）预计是导致有效 a 值选择的特殊点。使用11个头颈部患者病例来验证曲率效果。我们使用Eclipse的光子优化器（PO）进行优化，并集中上部gEUD来简化需要平衡重叠计划目标体积（PTV）的危及器官（OAR）的剂量约束。采用静态七视野IMRT进行优化，改变腮腺患侧a值，在不同a值优化时保留PTV D95%=70Gy。最后，评估cDVH偏移(ΔDVH)、gEUD偏移(ΔgEUD)、它们的平均值和a_k。 a = a_k 优化显示较低和较高 a 值对 ΔDVH、ΔgEUD 及其平均值的中间影响。使用a=a_k作为基点定义“较低”（a=0.5/1.0/2.0/3.0）、“中”（a=4.0/5.0/6.0/8.0/10/a_k）和“较高”（a=12/15/20/40）。较低的 a 值优化对于低剂量区域有效，并且对 cDVH 权重的整个范围影响较弱。相反，较高的 a 值优化解决了高剂量区域的问题，并强烈影响了 cDVH 权重的高剂量范围，正如理论预测的那样。此外，a值优化的中间范围导致临床重要的中高剂量范围的减少，从而保留了PTV的高剂量。有趣的是，平均 ΔDVH 和 ΔgEUD 与 gEUD 曲线的曲率和梯度呈指数关系。使用我们的相对论优化力概念，gEUD 优化被表示为 gEUD 曲线平移，强调 gEUD 曲线的曲率是 gEUD 优化的本质。曲率驻点(a = a_k)，即gEUD曲线的顶点，在a值由低到高的条件下起到中间作用。在临床复杂的优化情况下，我们可以从a=a_k的基点有效地选择较低/中/较高的a值。
Generalized equivalent uniform dose (gEUD) optimization is a biological optimization method used for intensity modulated radiation therapy (IMRT). Although parametric analyses have been widely reported, the use of parameter a-value in the optimization method remains elusive. This study aims to clarify the mathematical characteristics of the gEUD and to provide effective a-value selection. The gEUD is typically obtained using a differential dose volume histogram (DVH). This can be rewritten using a cumulative DVH (cDVH) and applied to variational analysis. The equivalence between the gEUD and the dose is then obtained; a low or high a-value corresponds to a wide or narrow dose range of optimization, respectively. Next, we focused on the gEUD curve behavior against a-value shifts and it retained its curve characteristics despite optimization. Using differential geometry, this curve shift can be considered as a geodesic deviation between pre- and post-optimization by a relativistic optimization force. The total action enacted by the force includes the curvature of the gEUD curve. This idea provides a novel viewpoint that the curvature of the gEUD curve is influenced by the optimization effect. The curvature stationary point of the gEUD curve (the vertex point, a = a_k) is expected to be a special point that leads to effective a-value selection. Eleven head and neck patient cases were used to verify the curvature effect. We used the Photon Optimizer (PO) of Eclipse for optimization and focused the upper gEUD to simplify the dose constraint for the organ at risk (OAR) that requires balancing of the overlapped planning target volume(PTV). Static seven-field IMRT was used for optimization, changing the a-value of the affected side of the parotid and retaining PTV D95% = 70Gy at the different a-value optimization. Finally, cDVH shift (ΔDVH), gEUD shift (ΔgEUD), their average values, and a_k were evaluated. The a = a_k optimization showed an intermediate effect of lower and higher a-values on ΔDVH, ΔgEUD, and their averages. “Lower” (a=0.5/1.0/2.0/3.0), “middle” (a=4.0/5.0/6.0/8.0/10/a_k), and “higher” (a=12/15/20/40) were defined using a=a_k as a base point. Lower a-value optimization was effective for the low-dose region and weakly affected the whole range of cDVH weight. In contrast, higher a-value optimization addressed the high-dose region and strongly affected the high-dose range of the cDVH weight as theoretically predicted. In addition, the middle range of the a-value optimization induced a decrease in the clinically important middle-to-high dose range, which retained the high dose of the PTV. Interestingly, the average ΔDVH and ΔgEUD corresponded exponentially to the curvature and the gradient of the gEUD curve. Using our relativistic optimization force concept, gEUD optimization is represented as a gEUD curve shift, highlighting that the curvature of the gEUD curve is the essence of gEUD optimization. The curvature stationary point (a = a_k), namely the vertex point of the gEUD curve, played an intermediate role in the low-to-high a-value condition. We can effectively select a lower/middle/higher a-value from a base point of a = a_k under clinically complex optimization situation.