Cao Tingting, Yuan Qingqing, Dai Zhitao
Tongji Hospital Tongji Medical College of Huazhong University of Science and Technology Wuhan China.
Cancer Hospital Chinese Academy of Medical Sciences Shenzhen Center Shenzhen China.
Precis Radiat Oncol. 2024 Sep 19;8(3):126-131. doi: 10.1002/pro6.1240. eCollection 2024 Sep.
To facilitate the use of quantitative modeling of biological effects in treatment planning by introducing a simpler function equivalent to the Lyman formula for calculating normal tissue complication probability (NTCP).
We first provide an approximation of the Lyman-Kutcher-Burman (LKB) formula using three parameters (, , TD) as a function of equivalent uniform dose (EUD). The parameters for the new formula are defined in terms of the Lyman model's m and TD. Conversely, and TD are expressed in terms of the parameters of the new equation. The role of the Lyman volume-effect parameter remains unchanged from its role in the Lyman model.
The new formula, which exhibits a sigmoidal shape, demonstrates symmetry about TD, akin to the LKB model. The difference in NTCP between the two formulas is less than 0.1%. The parameters (, , TD) are preserved through rigorous mathematical deduction and have been recalibrated to the tolerance data of Emani using the proposed formula. This new model provides a better fit to these data than the model by Burman , which was fitted "by eye" rather than using statistical methods.
We have developed a formula that represents NTCP as a function of EUD, which proves to be potentially useful. The parameters derived in this study are mathematically robust and offer a superior fit to the data compared to previous efforts. Additionally, the new model fits brain data as well as, if not better than, the LKB model.
通过引入一个与莱曼公式等效的更简单函数来计算正常组织并发症概率（NTCP），以促进在治疗计划中使用生物效应的定量建模。
我们首先使用三个参数（、、TD）作为等效均匀剂量（EUD）的函数，给出莱曼 - 库彻 - 伯曼（LKB）公式的近似值。新公式的参数根据莱曼模型的m和TD来定义。相反，和TD则根据新方程的参数来表示。莱曼体积效应参数的作用与其在莱曼模型中的作用保持不变。
新公式呈现出S形，与LKB模型类似，关于TD对称。两个公式之间NTCP的差异小于0.1%。通过严格的数学推导保留了参数（、、TD），并使用所提出的公式将其重新校准到埃马尼的耐受数据。与伯曼通过“目测”而非使用统计方法拟合的模型相比，这个新模型对这些数据的拟合更好。
我们开发了一个将NTCP表示为EUD函数的公式，事实证明该公式具有潜在用途。本研究中推导的参数在数学上是稳健的，与之前的研究相比，对数据的拟合更好。此外，新模型对脑部数据的拟合效果与LKB模型相当，甚至可能更好。
