A new formula for calculating normal tissue complication probability
Tingting Cao, Qingqing Yuan, Zhitao Dai
Abstract
Abstract Purpose 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). Methods We first provide an approximation of the Lyman‐Kutcher‐Burman (LKB) formula using three parameters ( n , m , TD 50 ) 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 50 . Conversely, m and TD 50 are expressed in terms of the parameters of the new equation. The role of the Lyman volume‐effect parameter n remains unchanged from its role in the Lyman model. Results The new formula, which exhibits a sigmoidal shape, demonstrates symmetry about TD 50 , akin to the LKB model. The difference in NTCP between the two formulas is less than 0.1%. The parameters ( n , m , TD 50 ) are preserved through rigorous mathematical deduction and have been recalibrated to the tolerance data of Emani et al. using the proposed formula. This new model provides a better fit to these data than the model by Burman et al. , which was fitted “by eye” rather than using statistical methods. Conclusion 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.